Purpose
This document, along with accompanying analysis, outlines the current design status of the Advanced LIGO Input Optics It provides a detailed preliminary design that supersedes the previous IOO Conceptual Design, ensuring compliance with the Advanced LIGO Input Optics Design Requirements (LIGO-T020020-00-D) This information is specifically tailored for the LIGO Detector Team.
Scope
The Input Optics (IO) design effort focuses on conditioning laser light from the PSL before it enters the IFO, while also managing the reflected light directed to the ISC subsystems Key components of this design include power control for the interferometer, RF phase modulation to create sidebands for length and alignment control, and a mode cleaner cavity that filters the PSL beam in terms of spatial, amplitude, and frequency characteristics Additionally, the IO ensures proper mode matching of the light to the IFO, facilitates beam steering into the IFO, and incorporates diagnostic beam pick-offs for ISC subsystems.
Figure 1.1 Block Diagram of the Input Optics
• Outside vacuum o RF modulation o Power control into the IFO o Steering and mode matching optics for the input mode cleaner o Required IO diagnostics
• In vacuum o Input mode cleaner cavity o IFO mode matching and beam steering o Faraday isolation and signal extraction for ISC o Signal extraction for PSL intensity control
Definitions
The modulation index (m) plays a crucial role in the application of RF sidebands through an Electro-Optic Modulator (EOM) This process yields a modulated output field represented by the equation E mod = E in exp[ – iωt – i m cos Ωt], where ω denotes the carrier frequency, Ω signifies the modulation frequency, and E in indicates the amplitude of the input field.
Acronyms
AOS Auxiliary Optics Support (detector subsystem)
CDS Control and Data System (detector subsystem)
CMRR Common Mode Rejection Ratio
COC Core Optics Components (detector subsystem)
DC Direct Current (steady state - low frequency)
EOM Electro-Optic Modulator (optical hardware)
ETM End Test Mass (optical component)
FI Faraday Isolator (optical component)
GPM Gallons Per Minute (flow rate)
HWP Half-Wave Plate (optical hardware)
IMC Input Mode Cleaner (formerly, just the ‘MC’)
IO Input Optics (detector subsystem)
ISC Interferometer Sensing / Control (detector subsystem)
ITM Input Test Mass (optical component)
LVEA Laser and Vacuum Equipment Area
MMT IFO Mode Matching Telescope
Nd:YAG Neodymium doped Yttrium Aluminum Garnet
PSL Pre-Stabilized Laser (detector subsystem)
PZT Piezo-electric Transducer (mechanical hardware)
RC Radius of Curvature of a Reflective Mirror
RM Recycling Mirror (detector subsystem)
SEI Seismic Isolation (detector subsystem)
SPRC Stable Power Recycling Cavity
TCS Core Optics Thermal Compensation System
TGG Terbium-Gallium-Garnet (optical material used in Faraday Isolators)
TFP Thin Film Polarizer (optical hardware)
Applicable Documents
Advanced LIGO Input Optics Preliminary Design Document, LIGO T-020020-00-D
Advanced LIGO Input Optics Conceptual Design Document, LIGO T-020027-00-D
Advanced LIGO Input Optics Subsystem: Design Requirements Review Panel Report, LIGO- T020065-02-R
Upgrading the Input Optics for High Power Operation, LIGO-T060267-00-D
Response to EOM-FI Preliminary Design Action Items, LIGO T060081-00-D
Modulators and Isolators for Advanced LIGO, LIGO-G060361-00-D
Effect of sideband of sideband on 40m and Advanced LIGO, LIGO-G040081-00-R
Analysis of Stray Magnetic Fields from the Advanced LIGO Faraday Isolator, LIGO T060025-00- Z
E Khazanov, N Andreev, A Mal’shakov, O Palashov, A Poteomkin, A M Sergeev, A Shaykin,
V Zelenogorsky, Igor Ivanov, Rupal Amin, Guido Mueller, D B Tanner, and D H Reitze,
“Compensation of thermally induced modal distortions in Faraday isolators”, IEEE J Quant. Electron 40, 1500-1510 (2004).
In their 2006 study, Quetschke et al explored adaptive control of laser modal properties, published in Optics Letters The research highlights the testing of input-output (IO) components in Enhanced LIGO, specifically focusing on electro-optic modulators and Faraday isolators.
Summary of the design changes from the Conceptual Design
Since the completion of the IO Conceptual Design in April 2002, there have been the following changes to the IO design:
Recent modifications to the in-vacuum layout have occurred, including the relocation of HAM3 to HAM1 and the repositioning of the ISC sensing table into HAM1 Consequently, the beam injection path from the PSL table has been altered, with the current injection route still under evaluation It is anticipated that the beam will predominantly enter through HAM1.
The ISC group is exploring the transition from unstable to stable power and signal recycling cavities, which would impact the input-output (IO) configuration due to the integration of the mode matching telescope within the power recycling cavity (PRC) Although the marginally stable design remains the baseline, a preliminary layout for the stable recycling cavity has been developed.
The double demodulation length sensing scheme introduced by ISC was found to be affected by serial modulation, known as the 'sidebands-on-sidebands' issue, during research conducted at the 40 m In response, we have created new modulation schemes that effectively eliminate the generation of sideband cross products.
The preliminary design efforts have primarily concentrated on establishing requirements and prototyping a Mach-Zehnder (MZ) modulation scheme, while also exploring advanced modulation techniques that integrate both amplitude and phase modulation.
We adopt the MZ modulation as the baseline for the preliminary design
2.1.3 Reduction in the IMC finesse
The proposed finesse of approximately 2000 for the IMC was considered conservative, taking into account the expected performance of PSL pointing and the necessary jitter suppression This high finesse, combined with elevated input powers, results in significant intracavity powers around 100 kW and peak intensities of about 700 kW/cm² on the mirror surfaces Consequently, this leads to an estimated 100 mW absorption with a 1 ppm loss, which can degrade the IMC's performance at maximum operating power To mitigate thermal loading on the IMC and ease the tolerances on mirror coatings, adjustments are necessary.
We adopt a finesse of 500 for the Advanced LIGO input mode cleaner
1 O Miyakawa, “Effect of sideband of sideband on 40m and Advanced LIGO”, LIGO-G040081-00-R
If the jitter specification of ε1 ~ (3 x 10 -5 /f) /Hz 1/2 for the PSL is satisfied, the IMC will easily comply with the requirement Recent findings from the LZH and MPG groups suggest that meeting this specification is highly feasible.
Areas that need more work
Since the introduction of MZ modulation as the baseline for AdvLIGO, we have focused on establishing requirements and prototyping this system Additionally, an alternative modulation system utilizing a single amplitude modulator and phase modulator is feasible We have conducted experiments and modeling on complex modulation that aligns with a conceptual design, though it has not yet reached the full maturity of a preliminary design.
2.2.2 Faraday Isolator Performance in Vacuum
A recent test showed a notable decline in the isolation ratio, dropping from 47 dB to 30 dB when vacuum pressure was reduced to 10^-4 Torr at 100W power levels Preliminary findings suggest that inadequate thermal contact between the optical components, such as TGG and polarizers, and their casings and mounts may be responsible for this performance degradation Further investigations are needed to confirm this hypothesis.
This is a high priority which we are actively investigating since the effect also impacts Enhanced LIGO somewhat
The mode matching telescope design is well-established, encompassing critical aspects such as distances, mirror specifications, and tolerances Recently, the adaptive mode matching approach has evolved from the initial concept of CO2 heating for the MMT mirrors to a new design featuring a four-segment ring heater on the FI DKDP While preliminary modeling has been conducted, experimental testing of this innovative idea is still pending.
AOS and IO have recently updated the interface to incorporate the beam dump, suspension protection, and scattered light baffling within the IO subsystem As this change is recent, progress on its implementation is still in the early stages.
Areas that have been de-emphasized
The IO CD has introduced high bandwidth active jitter suppression through the use of electro-optic actuators, specifically RTP-prisms, to enhance the passive suppression capabilities of the IMC Additionally, we have decreased the IMC finesse to address thermal effects, and we believe that further measures are unnecessary.
3 LIGO G070137-00-Z “Status of the Advanced LIGO PSL Development”, Benno Willke
4 V Quetschke, “Complex Optical Modulation”, LIGO G060452-00-Z
This section contains the IO interfaces with other subsystems, including:
PSL
The PSL output beam will be directed to the IOO at coordinates (X,Y,Z) = (144”, 50”, 3”) in the optical table's local coordinate system, as illustrated in Figure X The spot size at the beam waist of the PSL output beam is yet to be determined (TBD) in millimeters Additionally, the location of the PSL output beam waist must be within 5.0 cm of the designated PSL output beam location.
The polarization of the beam shall be ‘p’
The intensity stabilization beam for the PSL will be delivered to the PSL photodiode located (TBD
The ISC seismic platform in HAM 1(7) will utilize the PSL/ISC interface At the IOO/PSL interface, the size of the IOO output beam sample for power stabilization will be determined (TBD) Additionally, the power of the beam will also be specified (TBD) for the PSL/ISC configuration.
The IOO shares an optical table with the PSL (PSL/IOO table) Components of the IO that are located on the PSL table include
• mode matching optics for the IMC,
• periscope and beam injection optics
Figure 3.1 illustrates the distribution of table space for each subsystem, highlighting that the PSL subsystem is responsible for both the optical table and its physical enclosure, which is designed to mitigate acoustic noise, air currents, dust, and thermal fluctuations.
Figure 3.2 Defined IO and PSL areas on the PSL table,
The IFO power control beam dump needs to effectively dissipate 180W of power, necessitating the use of water-cooled beam dumps To achieve this, we require inlets and outlets that facilitate a flow rate of 0.5 GPM through a ¾” outer diameter tube connected to the IO power control beam dump.
COC
The IO delivers the main beam to the power recycling mirror (PRM) at (X,Y,Z) = (-3930.48mm,222.355mm, -156.562mm) in LIGO Global Coordinates and direction cosines (θx, θy, θz) = (1,-0.0000951851, -2.5693 x 10 -14 ).
ISC/CDS
3.3.1.1 Interferometer Length and Alignment Sensing Beams
The IOO provides diagnostic beams for interferometer length and alignment control to the ISC subsystem via the REFL port, utilizing Faraday Isolators situated in HAMs 2 and 8 These beams are directed to the ISC sensing tables located in HAM1 and 7, featuring a spot size of 2 mm and nominal powers that are yet to be determined (TBD) during the lock acquisition phase of the IFO.
3.3.1.2 IMC length and alignment sensing beams
The IO provides diagnostic beams for controlling the length and alignment of the IMC to the ISC subsystems via the IMC_REFL port These beams utilize the reflected output from IMC1 and are directed to the ISC sensing tables located in HAM1 and HAM7 With a spot size of 2 mm, these beams operate at nominal powers of 300 mW, reaching up to 6 W during the lock acquisition phase of the IFO.
IO mode matching sensors for measuring laser-induced thermal distortions in the IO optical components will be located on sensing tables in HAMS 1,7.
The RF modulation signals for the interferometer control sidebands and the IMC sideband are provided to the IO EOMs by ISC/CDS The IOO utilizes in-house resonant RTP electro-optic phase modulators, which feature specific characteristics tailored for optimal performance.
• Maximum Optical Power: 7 kW/cm 2
• Modulation Depth : 0.071 rad/V (depends on frequency; assumes matching circuit with Q , 20 mm long, 4 mm thick RTP crystal)
At the time of this review, the choice of modulation frequencies is still under discussion by the ISC group The signal characteristics are given in Table 1.
Table 1 Required RF inputs to IO EOMs.
Upper IFO control sideband 9 (TBR ISC) 0.8 (TBR ISC) 10 V (TBR ISC) 2 W (TBR ISC) Lower IFO control sideband
45 (TBR ISC) 0.8 (TBR ISC) 10 V (TBR ISC) 2 W (TBR ISC)
The IO manages the power control of the PSL within the interferometer, facilitating both commissioning and various operational modes Control signals for rotating a 1/2 wave plate are provided by the CDS (refer to section 5.2.1.3) The Newport URS-100 CC motorized stage is operated through an ESP 300 controller equipped with a GPIB/RS232 interface Users can either execute a script with the necessary commands to drive the ESP 300 or connect directly to the URS-100 CC for operation.
5 IO HIGH POWER UPGRADE DOCUMENT
All in-vacuum IO components are located on seismic isolation platforms in HAMs 2,3 and HAMs 8,9
AOS features eleven optical lever beams that connect with the IO subsystem, with one lever assigned to each suspended optic, including IMC1, IMC2, IMC3, SM1, SM2, MMT1, MMT2, MMT3, and PRM Additionally, there is one optical lever for each of the HAM tables, specifically HAM 2 and HAM 3.
SUS provides IMC triple suspensions and MMT3 LOS-type suspension to the IO, while all small optics suspensions, including those for SMs and small MMT mirrors, will utilize LIGO 1 small optics suspensions (SOS) produced by UF.
This section includes the status of the physical layout of the IO components for Advanced LIGO.
We assume that the LIGO facilities meet the specifications for vibrational and acoustic noise given in the Civil Construction Facilities Design Configuration Control Document, LIGO C960703-0
The configuration of the IO optical components on the PSL table is illustrated in Figures 4.3 and 4.4 To reduce environmental impact, all beam paths are contained within beam tubes or plexiglass enclosures In this setup, the main beam is indicated in red, while green signifies beams designated for dumping or diagnostic purposes.
Figure 4.3 Diagram of the PSL Table showing IO components
Figure 4.4 Blow up of the main area of the IO components on the PSL table showing functional blocks of IO components.
All transmissive optical components (excepting modulators and wave plates) will use fused silica for minimal thermal distortions.
Newport Ultima®/Suprema® kinematic mounts or Linos Lee’s mounts will be used for all in-air mirror mounts in the IO subsystem
Table 2 gives the physical dimensions and clear apertures for the optical components on the IO table.
Table 2 Summary of PSL table optical component sizes component Physical Diameter (MM) clear aperture (MM) Comments
Thin Film Polarizer 50 27.5 Brewster angle
MZ active mirror 10 8 Low mass for
High Loop Gains for MZ LSC servo
Currently, the method of injecting the laser beam into the vacuum system is being debated, with options including injection beneath HAM1,7, above the HAMs, or directly through HAM1,7 The IO group strongly favors direct injection through HAM1,7, which would utilize a periscope similar to the one employed in the existing LIGO setup.
The in-vacuum layout of the IO components was driven by several considerations:
• MC length - the requirements on mode cleaner lengthdetermine the positions of the SOS in the HAMS
6 PERISCOPE DESIGN DOCUMENT OR DRAWING REF D010231-A
• Minimization of coupling of stray magnetic field (B) to the suspended IMC mirror actuators
To minimize displacement noise from B-field fluctuations affecting the suspended mirror, a minimum separation distance of 30 cm between the FI and the suspension is essential This distance helps ensure that the induced noise remains below the ambient displacement noise caused by seismic activity.
To reduce scattered light coupling between the Input Optics (IO) and the Central Optical Component (COC), a large baffle plate will be installed on HAM 3,9 It is essential that the IO components do not obstruct these baffles, ensuring optimal performance and functionality.
The current state of the layouts is shown in the figures below Lines representing beams are drawn at the 25 ppm intensity contour
The layouts presented here are based on laser beam injection from HAM 1 Alternative methods, such as injection from the floor via the bottom of HAM 2 or through side viewports, have been considered; however, these options would introduce additional complexities to the layout design.
The overall layout and close-ups of HAM2,3 are shown below
Figure 4.5 Layout drawing of HAM2,3 for the stable power recycling cavity configuration.
7 LIGO T060025-00-Z, “Analysis of Stray Magnetic Fields from the Advanced LIGO Faraday Isolator”, G Mueller
Figure 4.6 Another view of the SPRC layout looking from HAM2 to HAM3.
Figure 4.7 Close up views of HAM2 and HAM3 for the SPRC configuration.
Figure 4.8 Layout drawing of HAM2,3 for the marginally stable power recycling cavity configuration Red indicates the path of the main laser; optical lever beams are shown in blue.
Figure 4.9 Another view of the MSPRC layout looking from HAM2 to HAM3 Red indicates the path of the main laser; optical lever beams are shown in blue.
Figure 4.10 Close up views of HAM2 and HAM3 for the MSPRC configuration.
MC suspensions feature baffles that serve dual functions: safeguarding the suspension from stray beams and reinforcing the MC support structure Crafted from single pieces of aluminum, these baffles are typically milled to a thickness of 050”, with 500” thickness in sections requiring diagonal bracing Importantly, baffles are strategically positioned only on the sides of the suspensions that require protection from errant beams.
Figure 4.13 MC1 and MC3 with baffles.
SOS baffles serve to shield suspensions from stray beams and are constructed from either bent sheet metal (SM1, SM2, MMT2) or flat sheet metal (MMT1) The MMT1 baffle features a flat design due to the beam's large angle of incidence While the specific type of metal is still to be identified, it is essential that it possesses high thermal conductivity to mitigate overheating.
Figure 4.14 SOS baffle for SM1, SM2, and MMT2.
Figure 4.15 SOS baffle for MMT1.
The modified LOS baffle is used to protect the MMT3 suspension from errant beams It is similar in design to the bent SOS baffles, just on a larger scale.
The MC cleaning baffle is an aperture used to clean light circulating off path in the MC The material is TBD.
The HAM 2 baffle serves to safeguard the wires and electronics from stray beams coming from HAM 3 Once the positions and dimensions of the wires are identified, the baffle can be substituted with smaller, individual baffles tailored to those spots Additionally, the baffle features a second hole to permit a heating beam to pass through if the MMT2 requires heating The material for the baffle is yet to be determined.
The IO baffle is essential for distinguishing the IO section from the COC section As illustrated in Figure 4.19, the IO baffle's fundamental design must be segmented into multiple pieces to accommodate the positioning of MMT2 and to ensure complete coverage of the beam tube aperture while avoiding contact with the ceiling of the HAM chamber.
AOS
AOS features eleven optical lever beams that connect with the IO subsystem, with one optical lever assigned to each suspended optic, including IMC1, IMC2, IMC3, SM1, SM2, MMT1, MMT2, MMT3, and PRM Additionally, there is one optical lever for each HAM table, specifically HAM 2 and HAM 3.
SUS
SUS provides the IMC triple suspensions and MMT3 LOS-type suspension to the IO, while all small optics suspensions for SMs and small MMT mirrors will utilize LIGO 1 small optics suspensions (SOS) produced by UF.
This section includes the status of the physical layout of the IO components for Advanced LIGO.
Assumptions
We assume that the LIGO facilities meet the specifications for vibrational and acoustic noise given in the Civil Construction Facilities Design Configuration Control Document, LIGO C960703-0.
PSL Table Layout
The arrangement of IO optical components on the PSL table is illustrated in Figures 4.3 and 4.4 To reduce environmental interference, all beam paths will be contained within beam tubes or plexiglass enclosures In this setup, the main beam is indicated in red, while green signifies beams designated for dumping or diagnostic purposes.
Figure 4.3 Diagram of the PSL Table showing IO components
Figure 4.4 Blow up of the main area of the IO components on the PSL table showing functional blocks of IO components.
All transmissive optical components (excepting modulators and wave plates) will use fused silica for minimal thermal distortions.
Newport Ultima®/Suprema® kinematic mounts or Linos Lee’s mounts will be used for all in-air mirror mounts in the IO subsystem
Table 2 gives the physical dimensions and clear apertures for the optical components on the IO table.
Table 2 Summary of PSL table optical component sizes component Physical Diameter (MM) clear aperture (MM) Comments
Thin Film Polarizer 50 27.5 Brewster angle
MZ active mirror 10 8 Low mass for
High Loop Gains for MZ LSC servo
Currently, the method for injecting the laser beam into the vacuum system is being debated, with options including injection beneath HAM1,7, above the HAMs, or directly through HAM1,7 The IO group strongly favors direct injection through HAM1,7, which would utilize a periscope similar to the one employed in the current LIGO setup.
In-vacuum optical layout
The in-vacuum layout of the IO components was driven by several considerations:
• MC length - the requirements on mode cleaner lengthdetermine the positions of the SOS in the HAMS
6 PERISCOPE DESIGN DOCUMENT OR DRAWING REF D010231-A
• Minimization of coupling of stray magnetic field (B) to the suspended IMC mirror actuators
To minimize displacement noise on the suspended mirror caused by B-field fluctuations, it is essential to maintain a minimum separation distance of 30 cm between the FI and the suspension This distance ensures that the induced noise remains below the ambient displacement noise generated by seismic fluctuations.
To minimize scattered light coupling between the Input Optics (IO) and the Central Optical Component (COC), a large baffle plate will be installed on HAM 3,9 It is crucial that the IO components do not interfere with these baffles to ensure optimal performance.
The current state of the layouts is shown in the figures below Lines representing beams are drawn at the 25 ppm intensity contour
The layouts presented here are based on laser beam injection from HAM 1 Alternative injection methods, such as from the floor via the bottom of HAM 2 or through side viewports, have been considered; however, these options would introduce additional complexities to the layout.
The overall layout and close-ups of HAM2,3 are shown below
Figure 4.5 Layout drawing of HAM2,3 for the stable power recycling cavity configuration.
7 LIGO T060025-00-Z, “Analysis of Stray Magnetic Fields from the Advanced LIGO Faraday Isolator”, G Mueller
Figure 4.6 Another view of the SPRC layout looking from HAM2 to HAM3.
Figure 4.7 Close up views of HAM2 and HAM3 for the SPRC configuration.
Figure 4.8 Layout drawing of HAM2,3 for the marginally stable power recycling cavity configuration Red indicates the path of the main laser; optical lever beams are shown in blue.
Figure 4.9 Another view of the MSPRC layout looking from HAM2 to HAM3 Red indicates the path of the main laser; optical lever beams are shown in blue.
Figure 4.10 Close up views of HAM2 and HAM3 for the MSPRC configuration.
Baffles
MC suspensions feature baffles that fulfill dual functions: safeguarding the suspension from stray beams and reinforcing the MC support structure Crafted from single pieces of aluminum, these baffles are typically milled to a thickness of 050”, with 500” thickness in regions requiring diagonal bracing Importantly, baffles are strategically positioned only on the sides of the suspensions that require protection from errant beams.
Figure 4.13 MC1 and MC3 with baffles.
SOS baffles are designed to shield suspensions from stray beams and are constructed from either bent (SM1, SM2, MMT2) or flat (MMT1) sheet metal The MMT1 baffle is flat due to the significant angle of incidence of the beam Although the specific type of metal has not been identified, it is essential that it possesses high thermal conductivity to effectively prevent overheating.
Figure 4.14 SOS baffle for SM1, SM2, and MMT2.
Figure 4.15 SOS baffle for MMT1.
The modified LOS baffle is used to protect the MMT3 suspension from errant beams It is similar in design to the bent SOS baffles, just on a larger scale.
The MC cleaning baffle is an aperture used to clean light circulating off path in the MC The material is TBD.
The HAM 2 baffle serves to safeguard the wires and electronics within HAM 2 from stray beams emitted by HAM 3 Once the specific locations and dimensions of the wires are identified, the baffle can be substituted with smaller, individual baffles tailored to those locations Additionally, the baffle features a second hole to permit the passage of a heating beam, should the MMT2 require heating The material for the baffle is yet to be determined.
The IO baffle serves to distinguish the IO section from the COC section, as illustrated in Figure 4.19 To accommodate the positioning of MMT2 and ensure full coverage of the beam tube aperture without interfering with the HAM chamber ceiling, the baffle must be constructed in multiple segments.
The IO baffle, as shown in Figure 4.19, allows for continuously adjustable variable power input into the interferometer while ensuring uninterrupted operation However, it's important to note that the power control system is not intended to serve as an intensity stabilization servo loop system.
Requirements
The power control system should:
The system delivers continuous power adjustments to the IMC, ranging from approximately 0 W to the maximum available power It is crucial that the minimum incremental power step is carefully calibrated to ensure that the resulting radiation pressure kick does not disrupt the IMC's locked state.
• provide an interface to CDS
• be able to dump the excess light according to the stray light requirements of AdLIGO The power control system should not:
• introduce fluctuations in the output power
• unlock the interferometer or IMC undergoing adjustment
Design
We will use a design similar to that used in initial LIGO based on a polarizer and rotating half wave plate as shown in Figure 5 20.
Figure 5.20 Conceptual Design of Power Control System.
A p-polarized IFO optical beam with intensity I1 traverses a HP plate oriented at an angle θ to the vertical axis, followed by a TFP aligned vertically The transmitted s-polarized light exhibits an intensity of I2, while the horizontally polarized rejected beam is classified as 'p' polarized This relationship is described by Malus’s Law.
The full power range is achieved as the HP plate rotates from 0 to 45 degrees LIGO 1 employs New Focus Picomotors to adjust the 1/2 waveplate in 1 dB increments, controlled by CDS software In Advanced LIGO, a Newport URS-100 CC motorized rotational stepper stage enables nearly continuous rotation at 0.0005 degrees per step, with the resulting incremental power changes illustrated in Figure 5.21.
T ra n s m it te d I n c re m e n ta l P o w e r
Figure 5.21 illustrates the relationship between incremental transmitted power and the motor drive count required to send control signals to the rotational motorized stage controller, with the x-axis represented in units of 10^4 counts.
5.2.1 Radiation pressure and IMC displacement
The IMC and IFO mirrors experience varying radiation pressure as input power fluctuates Due to the IMC mirrors being 20 times lighter than the TMs, along with the IFO's significantly lower cavity pole compared to the IMC, and the IMC storing approximately one-fourth of the power of the FP arm cavities, the IMC is particularly vulnerable to radiation pressure kicks.
To ensure optimal performance, power adjustments must be made carefully to prevent the incremental movement of the mirrors from causing longitudinal or angular displacements that exceed the bandwidth limitations of the servos responsible for controlling length and alignment.
The force exerted on a mirror by light pressure, which causes displacement, can be expressed as the light incident on the mirror When the cavity is in resonance and the excitation frequency is significantly higher than the pendulum's resonance frequency, the resulting longitudinal displacement of the mirror relative to the cavity axis can be represented by the equation φ ω cos.
In the context of IMC, the displacement kicks can be expressed by considering the mirror mass (M), angular frequency (ω), and the cosφ term, which represents the difference between displacement and cavity length Notably, in this scenario, the cosφ terms in both the radiation force and the displacement offset each other, leading to a simplified representation of the displacement kicks.
∆ (5.4) where P in is the input power andℑis the finesse of the IMC cavity
Table 3 Parameter Values for Triple Pendulum IMC Mirror.
To ensure stable lock, the radiation pressure kick must be balanced by the IMC LSC, which necessitates a specific slew rate for the servo In the case of the LSC, we evaluate the most challenging scenario, which is 82.5.
The incremental input power change in the IMC is set at 2.1 mW per step, with the maximum power increment occurring at the half power point (HWP set to 22.5°) This power change results in an additive total displacement experienced by all three IMC mirrors due to the radiation pressure kick.
∆x total = ∆x IMC1 + ∆x IMC2 + ∆x IMC3 From Eqs 5.4, this produces a radiation pressure cavity length displacement ∆x total of 131.4 pm/step
The power build-up time is constrained by the cavity pole filter, f p,IMC, or the stepper stage's speed In our design, the maximum speed of the motorized rotational stage serves as the limiting factor for dP/dt.
The Newport URS-100 CC achieves a maximum IMC mirror velocity of 0.233 pm/às, calculated by multiplying the displacement per step (1778 steps/s) by the steps per second This velocity is influenced by radiation pressure as power adjustments are made via the motorized rotational stage Consequently, this establishes a lower limit on the actuator's slew rate, which should exceed 0.08 pm/às To ensure reliability, the MC servo is recommended to maintain a slew rate better than 1 pm/às, incorporating a safety margin of 10.
Improper alignment of beams on the MC mirrors can lead to an angular displacement, or 'kick,' due to radiation pressure torque This torque is generated when an input power, P, impacts a mirror at a distance, d, from the center, countered by a restoring torque.
T P in (5.5) where α is the angle, Θ is the angular moment and ω is the angular frequency in yaw Simplifying Eqs ( 5 4) and ( 5 5) for α:
, (5.6) where Θ along the orthogonal directions to the beam propagation various directions is given by
The equation 1MR Mh yy xx =Θ = + Θ describes the relationship between mass (M), radius (R), and thickness (h) of the mirror, as detailed in Table 3 With a maximum decentering of 1 mm on the MC mirror, the resulting angular 'kick' is calculated to be 0.077 nrad/step at the half power point When this value is multiplied by the rotational stage's transfer function of 1778 step/s, it yields a rate of 0.137 prad/ás Given that there are three mirrors and a safety margin of 10, the IMC ASC servo loop should provide a minimum slew rate of 4.2 prad/ás.
5.2.1.3 CDS Control of the Input Power
If commissioning reveals that the incremental radiation pressure from the power control system leads to unexpected issues in the interferometer, it is advisable to limit the power's slew rate through software adjustments.
Beam Dump
Proper disposal of the rejected beam in the power control system is essential, even in the absence of formal requirements It is recommended that the rejected beam, which can reach up to 180 W, be managed to minimize backscatter For effective beam dumping, commercially available water-cooled beam dumps, such as the Kentek ABD-2C, are suggested, as they feature a specular reflectance of less than 0.1%.
The preliminary design document for the Advanced LIGO input optics, identified as LIGO T-020020-00-D, presents a fitted 4th degree polynomial using the least squares method, illustrated in Figure 5.22 This analysis integrates the results over a 2π steradian (half hemisphere), revealing that the total power radiated into the half hemisphere is approximately 10 mW.
The graph in Figure 5.22 illustrates the power in watts recorded at a 1 cm² detector positioned 18.5 cm from the beam dump, plotted against the angle relative to the beam dump's normal The blue squares represent the power measurements obtained from the Kentek beam dump, while the red circles indicate the power values measured from a custom-built beam dump detailed in the article.
Figure 5.23 UF-made beam dump for ultra-low scattering/reflection high power laser power absorption.
Water Out Water In Water-Ink Solution
5.3.1 Alternative Low Backscatter Beam Dump
An innovative ultralow backscatter beam dump has been developed and tested, utilizing a commercially available infrared spectrometer gas cell where light absorption occurs in circulating water mixed with India ink The design features a glass cylinder sealed with fused silica windows, equipped with antireflective coatings on both surfaces This cylinder includes two inlets: one for water intake and another for water discharge An experiment conducted with a 42 W laser power yielded significant results, as illustrated in Figure 5.24.
A 0.8 ml/L India Ink solution in water, contained within a 10 cm path, effectively dissipates 100 W of laser power, as illustrated in Figure 5.24 To minimize non-specular back-reflectance, AR-coated fused silica windows are utilized, as shown in Figure 5.23 This method serves as an alternative when commercially available beam dumps fail to meet desired standards for back-reflectance and scattering.
Figure 5.24 Experimental results showing the transmission (1 pass attenuation) of the low scatter beam dump.
RF modulation is essential for sensing and controlling the length and alignment degrees of freedom (DOFs) in an interferometer To achieve this, three modulation frequencies are required: one for locking the mode cleaner and two additional frequencies to extract control signals from the main interferometer, which includes the Michelson, power recycling cavity, signal recycling cavity, and arm cavities The input-output (IO) system must generate and monitor these sidebands effectively.
RF signals from the ISC.
• the design, fabrication, and assembly of all RF electro-optic modulators for the production of sidebands for controlling the interferometer and mode cleaner length and alignment sensing systems;
• a ‘clean’ sideband spectrum The modulation must avoid the sidebands on sidebands problem 9 for the interferometer’s central part control signals (either by using a Mach-
Zehnder setup or a complex modulation scheme);
• ancillary optical and mechanical components.
AdvLIGO utilizes the same vacuum chambers as the existing LIGO interferometer, which limits the cavity lengths The internal mode cavity (IMC) free spectral range (FSR) is approximately 9 MHz, and for signals to successfully pass through the IMC, the interferometer (IFO) control modulation frequencies must meet the condition: mc mc L n c f = 2.
The modulation frequencies for the core interferometer are TBD but the current modulation schemes [6] favor either 9 MHz/108 MHz allowing still the resonant readout scheme 10 or
When selecting modulation frequencies of 27 MHz or 45 MHz, it is crucial to ensure that these frequencies do not coincide with the harmonics of the 4 km arm cavity's free spectral range, which is 37.5 kHz.
The modulation frequency for locking the mode cleaner is not transmitted due to heavy attenuation by the IMC, making it non-critical as long as it does not overlap with the core interferometer's modulation frequencies We have selected a value of 31.457 MHz for IMC locking, which is approximately 100 kHz away from the fourth antiresonance (n = 3.5).
9 LIGO–T040119–00–R, “Mach-Zehnder interferometer forAdvanced-LIGO optical configurations to eliminate sidebands of sidebands, O Miyakawa, et al.
10 The upper modulation frequency is constrained by the space in the vacuum chambers that limits the maximum
The constraints on the modulation frequencies are mainly given by the vacuum system The mode cleaner and recycling cavities span vacuum chambers whose separations determine the various cavity lengths.
The optical modulation requirements for Advanced LIGO, detailing modulation depths and the relative stability of modulation frequency and amplitude, are outlined in the IO DRD (LIGO-T020020) and the EO-Modulators for Advanced LIGO, Part I (LIGO-T020025-00-D).
A recent study outlined in the LIGO-T060267-00-D document, titled “Upgrading the Input Optics for High Power Operation,” provides technical details about the modulator This document also discusses the design and performance enhancements of the AdvLIGO modulators compared to the earlier ELIGO modulators.
The final values for the modulation frequencies are TBD ISC; nominal values are given Table 4 below Section 7.2.3 lists possible combinations for the modulation frequencies for the IFO.
Table 4 Performance of the Advanced LIGO FI
Modulation depths are set by GW shot noise considerations at the asymmetric port In addition, the
IO must provide for a range of modulations about the specified depths to accommodate diagnostic functions and potential degradation.
• The IO must provide for modulation depths in the range m = 0-0.8.
We have developed prototype RTP-based phase modulators utilizing crystals measuring 1.5 cm in length, 0.4 cm in width, and 0.4 cm in thickness For further details, please refer to the preliminary design outlined in the LIGO-T060267-00-D document, titled “Upgrading the Input Optics for High Power Operation.”
The modulator is housed in an industry-standard enclosure designed to ensure that the high power laser beam interacts solely with the crystal, protecting the electrodes from potential damage This housing will be produced by UF and is specifically designed without the resonant circuit and impedance matching network It operates at an impedance of 50 Ω, enhancing the RF voltage at the crystal by utilizing the Q factor, which represents the quality of the resonator.
Figure 6.25 Equivalent circuit of the resonant circuit / impedance matching network.
We developed and tested matching networks for frequencies of 19.7 MHz and 180 MHz, adhering to previous ISC requirements The crystal utilized has a capacitance of 6 pF, with an electrode and wiring impedance of approximately 2 Ω, and a shunt capacitance around 20 pF The 19.7 MHz circuit demonstrated a quality factor (Q) of 20, while the 180 MHz circuit exhibited a lower Q of 3.
To ensure optimal performance, a temperature control circuit will be implemented to actively stabilize the modulator crystal temperature Standard low voltage temperature sensors, such as the TMP35/36/37, will be utilized for accurate temperature measurement, boasting a sensitivity of 10mV/K The stabilization process will involve using the error signal to regulate Peltier elements, which will effectively manage the temperature of the modulator housing.
6.5.4 Damage testing and thermal lensing
Results of damage testing and thermal lensing are given in “Upgrading the Input Optics for HighPower Operation”, LIGO-T060267-00-D, and “Modulators and Isolators for Advanced LIGO”,LIGO-G060361-00-D
Baseline Design
AdvLIGO utilizes the existing vacuum chambers from the current LIGO interferometer, which limits the cavity lengths The input mode cleaner (IMC) has a free spectral range (FSR) of approximately 9 MHz due to its length To effectively pass through the IMC, the interferometer control modulation frequencies must adhere to the equation mc mc L n c f = 2.
The modulation frequencies for the core interferometer are TBD but the current modulation schemes [6] favor either 9 MHz/108 MHz allowing still the resonant readout scheme 10 or
When selecting modulation frequencies of 27 MHz and 45 MHz, it is crucial to ensure that these values do not coincide with the harmonics of the 4 km arm cavity's free spectral range, which is 37.5 kHz.
To effectively lock the mode cleaner, a modulation frequency that is heavily attenuated by the IMC is selected, which is deemed non-critical as long as it does not overlap with the core interferometer's modulation frequencies We have chosen a modulation frequency of 31.457 MHz (TBR IO) for IMC locking, positioning it approximately 100 kHz away from the fourth antiresonance (n = 3.5).
9 LIGO–T040119–00–R, “Mach-Zehnder interferometer forAdvanced-LIGO optical configurations to eliminate sidebands of sidebands, O Miyakawa, et al.
10 The upper modulation frequency is constrained by the space in the vacuum chambers that limits the maximum
Constraints
The constraints on the modulation frequencies are mainly given by the vacuum system The mode cleaner and recycling cavities span vacuum chambers whose separations determine the various cavity lengths.
RF modulation requirements
Advanced LIGO's optical modulation requirements, which encompass modulation depths and the stability of both modulation frequency and amplitude, are detailed in the IO DRD (LIGO-T020020) and the document EO-Modulators for Advanced LIGO, Part I (LIGO-T020025-00-D).
The LIGO-T060267-00-D document titled “Upgrading the Input Optics for High Power Operation” presents a recent investigation into the advancements in AdvLIGO modulators compared to their ELIGO counterparts For detailed technical information on the modulator, refer to this document, which outlines the design and performance enhancements made in the latest modulators.
The final values for the modulation frequencies are TBD ISC; nominal values are given Table 4 below Section 7.2.3 lists possible combinations for the modulation frequencies for the IFO.
Table 4 Performance of the Advanced LIGO FI
Modulation depths are set by GW shot noise considerations at the asymmetric port In addition, the
IO must provide for a range of modulations about the specified depths to accommodate diagnostic functions and potential degradation.
• The IO must provide for modulation depths in the range m = 0-0.8.
We developed prototype RTP-based phase modulators utilizing crystals measuring 1.5 cm in length, 0.4 cm in width, and 0.4 cm in thickness For further details, refer to the preliminary design outlined in the LIGO-T060267-00-D document, titled “Upgrading the Input Optics for High Power Operation.”
The modulator features an industry-standard housing designed to ensure that the high power laser beam interacts solely with the crystal, safeguarding the electrodes from potential damage Manufactured by UF, this housing excludes the resonant circuit and impedance matching network, maintaining a 50 Ω impedance to enhance the RF voltage at the crystal through the quality factor (Q) of the resonator.
Figure 6.25 Equivalent circuit of the resonant circuit / impedance matching network.
We developed and tested matching networks for frequencies of 19.7 MHz and 180 MHz, adhering to previous ISC requirements The crystal utilized has a capacitance of 6 pF, with an associated impedance of approximately 2 Ω from the electrodes and wiring Additionally, the shunt capacitance is around 20 pF The circuit operating at 19.7 MHz achieved a quality factor (Q) of 20, whereas the circuit at 180 MHz had a Q of 3.
To ensure effective stabilization of the modulator crystal temperature, a temperature control circuit will be implemented Standard low-voltage temperature sensors, such as the TMP35/36/37, which offer a sensitivity of 10mV/K, will be used for accurate temperature measurement The stabilization process will involve using the error signal to regulate Peltier elements, which will control the temperature of the modulator housing.
6.5.4 Damage testing and thermal lensing
Results of damage testing and thermal lensing are given in “Upgrading the Input Optics for HighPower Operation”, LIGO-T060267-00-D, and “Modulators and Isolators for Advanced LIGO”,LIGO-G060361-00-D
Three techniques are currently recognized to address the issue of sidebands on sidebands that occurs when phase modulators are used in series The primary approach involves utilizing a Mach-Zehnder interferometer to split the beam and apply modulations in separate arms, which will be the focus of the first part of the next section Additionally, our group is exploring the use of complex modulation to create arbitrary modulation configurations as an alternative solution Another option is the use of two phase-locked lasers to generate a frequency-shifted sub-carrier, although this method is not a current focus of our research due to its divergence from the scope of IO.
The parallel phase modulation technique was initially evaluated using a Mach-Zehnder (MZ) interferometer at Caltech's 40 m prototype This method involves dividing laser light with a beam splitter, applying distinct modulation frequencies to the transmitted and reflected beams, and then recombining them with a second beam splitter, as illustrated in Figure 6.26.
Although the MZ method avoids the generation of sidebands on sidebands, it creates some other complications:
• An additional servo loop to control MZ differential arm length
• Overdriving the EOMs to achieve the required modulation index
• Possible introduction of excess intensity, frequency and sideband noises
• Additional intensity modulation (noise) at modulation and mixing (sum/difference) frequencies
To ensure optimal beam overlap and visibility in an interferometric method, it is essential to control the differential length of the arms, maintaining equal lengths on a macroscopic scale This precision allows for the effective recombination of beams at the output port, promoting constructive interference for the carrier signal.
11 LIGO–T040119–00–R, “Mach-Zehnder interferometer forAdvanced-LIGO optical configurations to eliminate sidebands of sidebands, O Miyakawa, et al
12 LIGO–T040161–00–R, “Effect of Mach Zehnder Residual Displacement Noise on the 40m Detuned RSEInterferometer, S Kawamura and O Miyakawa.
Figure 6.26 Parallel modulation using a Mach-Zehnder interferometer.
Using 50/50 beamsplitters at both the input and output ports results in only half of the light being modulated at each modulation frequency, with an additional 50% loss at the combining beamsplitter, effectively reducing the modulation index by a factor of four The recombined light travels through two distinct optical paths, making it susceptible to environmental noise that can introduce unwanted intensity, phase, or pointing variations Moreover, if the interferometer is maintained on the bright fringe, phase modulation can directly affect intensity modulation at the second harmonic and may even influence the fundamental frequency if the length is not precisely controlled.
The recombined light from the Mach-Zehnder (MZ) interferometer can display amplitude, phase, or pointing noise, which varies across different frequency components, unlike the noise seen in serial modulation This noise originates from mirror movements or changes in the index of refraction, which can be common or differential between the two arms of the interferometer or even among mirrors within a single arm Additionally, these mirror movements can occur in both angular and longitudinal directions, and non-normal angles of incidence or misaligned beams can further complicate the noise effects.
The laser field exiting the MZ is given by:
E i t ik L ik L im t ik L im t
Where Ω 1 and Ω 2 are the modulator frequencies, and m 1 and m 2 are the modulation depths of the two EOMs We also define the common and differential MZ lengths to:
13 In the event that one modulation frequency dominates, the BS ratios can be adjusted to allow for increased power in
Advanced LIGO LIGO-T060269-01-D with the L i denoting the length of the two MZ arms.
Longitudinal common motion generates phase noise that affects both the carrier and radio-frequency sidebands, similar to noise from vibrating serial modulation components Given its familiarity, we can address this type of noise using established techniques Effective mitigation is achieved through laser frequency monitoring and feedback via the mode-cleaner, which is synchronized with the common mode of the long arm cavities.
When the lengths of the MZ arms change differentially, denoted as ∆L→∆L(t), two significant noise effects arise Firstly, the amplitude of the recombined carrier fluctuates, and secondly, relative phase noise emerges between the recombined carrier and the sidebands.
6.6.2.2.1 Sideband-carrier relative phase noise
The Advanced LIGO design faces challenges with noise in the relative phase between carrier and sideband light, which can translate into laser frequency noise The laser's frequency is stabilized to the mode cleaner, which is also locked to the common-mode of the arm cavities The common-mode error signal S is likely measured through the beat between the carrier and one of the sidebands In this setup, relative phase noise appears indistinguishable from laser frequency noise, leading to a corrective signal that inadvertently adds noise to the laser The established limit on laser frequency noise for Advanced LIGO is illustrated in Figure 6.27.
To establish a limit on the differential motion of the Mach-Zehnder arms, we analyze the transfer functions related to the sideband-carrier relative phase in conjunction with the arm cavity common-mode error signal and the frequency noise transfer function With a defined frequency noise limit ∆f(f), we can derive the corresponding relative phase noise limit ∆Φ(f).
Here S is the arm cavities' common-mode error signal.
Optical Configuration and Definitions
The input mode cleaner is designed as a Fabry-Perot cavity with a high finesse, featuring a narrow isosceles triangle shape that enhances optical isolation The cavity consists of a flat-flat-curved configuration, with two flat mirrors (MC1 and MC3) serving as the input and output couplers, positioned in HAM2, while the curved mirror (MC2) is located in HAM3 All three mirrors are suspended to maintain stability and performance.
Figure 7.37 Diagram of the input mode cleaner, defining the names of the mirrors.
A Fabry-Perot cavity has transmission
In the context of optical systems, the parameters t1 and r1 represent the amplitude transmissivity and reflectivity of the input mirror, while t2 and r2 denote the amplitude transmissivity and reflectivity of the output mirror Additionally, the optical phase δ is related to the cavity length L This analysis applies specifically to plane waves interacting with plane-parallel mirrors.
The input mode cleaner, situated within the vacuum, plays a crucial role in determining the range of lengths and the free spectral range due to the separation between its chambers Its mirrors are supported by Mode Cleaner Triple Suspensions, ensuring optimal performance and stability.
The specific functions of the input mode cleaner are discussed in the following paragraphs.
Input Mode Cleaner Optical Parameters
The interrelation between the input mode cleaner (MC), power recycling cavity (PRC), signal recycling cavity (SRC), and arm cavity lengths is crucial for optimal performance The arm cavity length dictates the dimensions of the PRC, SRC, and MC, with arm cavities allowing only a ±30 mm adjustment It is essential for both the input mode cleaner and power-recycling cavity to resonate the carrier along with the locking sidebands, while the arm cavities should resonate solely the carrier Additionally, the sideband frequency must be positioned 5-6 Hz away from achieving maximum antiresonance in the arm cavities.
The sideband frequencies must comply with the equation f prc = (k + 1/2)c/2L prc, where k represents non-negative integers (0, 1, 2, ), and L prc denotes the length of the power recycling cavity, measured from the Power Recycling Mirror (PRM) to the average of the two Input Test Masses (ITMs) The inclusion of the 1/2 factor is due to the carrier being resonant in the arm cavities, while the sidebands are not, resulting in an additional 180-degree phase shift in the arms' reflectivity.
For effective RF modulation, both sidebands must align with one of the input mode cleaner's resonances, as this modulation occurs prior to the input mode cleaner The resonant frequencies of the input mode cleaner are determined by the formula f imc = nc / 2L imc, where n represents an integer (1, 2, 3, ) and L imc denotes the length of the input mode cleaner.
The signal recyling cavity length is also tied to these frequencies; its length is 15
L scc = (p + δφ /2 π )c/2f src (7.20) where p is an integer (1,2,3 ), δφ is the signal recycling detuning (0.1 rad), and f src is the frequency used to sense the position of the SRM.
The adjustments for L prc and L imc are limited, influenced by the dimensions of the LIGO vacuum envelope, the size of the optical tables, and the specifications of other components.
The Advanced LIGO system, specifically LIGO-T060269-01-D, must be positioned on designated tables, which in turn establishes a specific range of frequencies for both f prc and f imc The combination of these frequencies is essential for the control mechanisms of the interferometer A summary of the lengths is provided in Table 5, with all dimensions measured in meters.
Table 5 Allowed range of lengths for LIGO cavities
The maximum length is actually 0.6 meters longer, allocated for input injection optics Utilizing this additional space for an extended mode cleaner will not impact the length-related issues, including the absence of a 9 MHz frequency for the folded Power Recycling Cavity (PRC), as outlined in the following discussion.
To fix the modulation frequencies, we first establish the arm cavity lengths, with the straight interferometer recommended at 3994.750 m and the folded interferometer at 3994.450 m These specified lengths allow for the determination of a discrete set of frequencies, spaced by 37.5 kHz, that fulfill the conditions outlined in equations (7.3) and (7.4) while also meeting the nearly antiresonant condition for the sidebands relative to the arm cavities Subsequently, the length of the Signal Recycling Cavity (SRC) can be determined using equation (7.5).
The power recycling cavity length is of course quite different depending on whether marginal or stable configurations are chosen, and also differs between the straight (H1/L1) and folded (H2) interferometers
The current positioning of the HAM chambers limits the folded interferometer's minimum frequency to 27.3 MHz with a marginal Power Recycling Cavity (PRC) and 17.6 MHz for a stable PRC By increasing the separation between HAM2 and HAM3 by 1.8 meters, these minimum frequencies could potentially be lowered to 16.4 MHz (marginal) and 8.4 MHz (stable).
The cases are discussed in the following sections.
16 “Constraints of Advanced LIGO Cavity Lengths, Version 2” by Luke Williams, LIGO T-### frequencies) that meet the requirements is:
Table 6 Straight IFO, Marginal PRC
SRC length for high frequency m 8.999
*This length is 229 mm longer than allowed by physical constraints in the SRC HAM
One could use MC and PRC lengths of 16.406 m and 8.203 m respectively also; this is the only other possibility if the low modulation frequency is to be near 9 MHz
The length ranges for the MC are 15.910-16.461 m The length ranges for the PRC are 55.685- 57.614 m A set of lengths (and corresponding frequencies) that meet the requirements are”
Table 7 Straight IFO, Stable PRC
SRC length for high frequency m 9.246
The length ranges for the MC are 15.980-16.461 m The length ranges for the PRC are 13.317- 13.718 m A set of lengths (and corresponding frequencies) that meet the requirements are:
Table 8 Folded IFO, Marginal PRC
SRC length for high frequency m 13.731
* 46.4386 MHz leads to a SRC length of 12.936 m, 255 mm too short.
The folded interferometer in the PRC exhibits a longer configuration, with its initial resonance occurring between 5.2-5.6 MHz and a subsequent resonance near 15.7-16.9 MHz These frequencies do not align with the 9.26 MHz median input mode cleaner FSR, as the first resonance is identified for n = 3 and k = 2 in the relevant equations.
Increasing the length of the tube connecting HAM2 and HAM3 by 1.8 meters results in a decrease of the input mode cleaner's free spectral range (FSR) to 8.33 MHz, allowing for the utilization of a frequency of 16.65 MHz This tube is also slated for replacement in the Advanced LIGO project.
The length ranges for the MC are 16.160-17.061 m The length ranges for the PRC are 60.602- 63.979 m A set of lengths (and corresponding frequencies) that meet the requirements are:
Table 9 Folded IFO, Stable PRC
SRC length for high frequency m 8.551
This article outlines the selected optical parameters for the input mode cleaner, focusing specifically on the straight interferometer and marginal PRC case to conserve space It is noted that the Gaussian parameters exhibit only slight variations of a few percent in other scenarios.
Table 10 Optical parameters for the straight interferometer, marginal PRC
IMC free spectral range Hz 9,174,449
MC2 radius of curvature (cold) m 26.769
Mirror absorption/scatter loss (each) ppm 30
Intensity at Flat mirrors kW/cm 2 167
MC1,3 HR center-center distance cm 43.18
MC1,3 intracavity angle of incidence, θ deg 44.625
Static radiation pressure (MC1/MC3) Pa 7.9
Static radiation pressure (MC2) Pa 4.3
Static force from radiation pressure (MC2) àN 155
7.2.9 Input Mode Cleaner Locking Frequency
The modulation frequency for locking the mode cleaner is heavily attenuated and non-critical, provided it does not overlap with the core interferometer's modulation frequencies We have selected a frequency of 32.011 MHz for the IMC locking, which is approximately 100 kHz away from the fourth antiresonance (n = 3.5).
Input Mode Cleaner Expected Performance
Figure 7 38 shows the calculated mode cleaner transmission as a function of frequency for one FSR above the carrier.
Figure 7.38 illustrates the calculated transmission of the input mode cleaner as a function of frequency, specifically one FSR above the carrier The left panel presents a broad frequency spectrum alongside a logarithmic scale for transmission, while the right panel provides a detailed view of the data.
For Advanced LIGO, the input beam jitter at the core optics necessitates a relative amplitude of the TEM10 mode of 4 x 10⁹ /Hz¹/² at frequencies of 230 Hz and higher, with an increase of 1/f² below this threshold The pointing stability from the PSL is projected to be 1 x 10⁶ /Hz¹/², which means the input mode cleaner must achieve a filtering factor of 250 to ensure optimal performance.
Beam wiggle, characterized by angular and lateral deviations, can be understood as the combination of higher-order Gaussian modes over the fundamental TEM00 mode The input mode cleaner effectively suppresses these higher-order modes, leading to a reduction in beam wiggle The degree of this suppression is proportional to the finesse (F) of the cavity Given that the selected quantity is not an integer multiple of π, the sinusoidal value remains non-zero Assuming a typical value of 1 rad, and considering that F is significantly greater than 1, the suppression effect is pronounced.
A finesse of 500 will meet the jitter requirements.
In TEM lm Gaussian modes, the input mode cleaner Fabry-Perot resonances are defined by the condition g = 1 - L/R, where R represents the radius of curvature of the curved mirror The resonator is specifically tuned for resonance with the TEM00 mode, resulting in a value of n around 30 million The selection of cavity length and mirror radius of curvature is crucial to ensure that the resonance condition is met exclusively for n and l=m=0, while other combinations of {n,l,m} are not satisfied This unique resonance condition is achieved when ε indicates the degree to which higher-order modes avoid resonance, with the assumption that the fundamental and higher-order mode frequencies from the laser remain identical.
The transmittance of the mode cleaner, depicted in Figure 7.39, illustrates the relationship between transmittance (in ppm) and the mirror radius of curvature The mode cleaner is illuminated with light containing fundamental and higher modes, constrained by 0 < l + m < 65, with amplitudes approximating 1/sqrt(l + m) The fundamental mode achieves a transmittance of unity, while varying the radius of curvature allows for the transmission of specific higher order modes Notably, a significant peak of 14% occurs at a radius of curvature of 26.73 m, corresponding to modes where l + m = 7, followed by a gradual decline at larger radii and several narrow peaks for higher l + m values Given the radius of curvature shifts by 0.13 m between cold and hot conditions, the cold radius of curvature is selected at 26.769 m, with an expected increase to 26.9 m when the system heats up.
Figure 7.39 Transmission of MC Cavity
The input mode cleaner functions as a length standard for the laser, playing a crucial intermediary role in the length control system, while the arms serve as more effective standards.
The input mode cleaner functions as a low-pass filter, characterized by a corner frequency of f c = 1/τ, where τ represents the light storage time in the cavity, defined as 2FL/c This design effectively suppresses amplitude and frequency noise at frequencies exceeding the corner frequency, achieving a noise reduction of 1/f (20 dB/decade).
The input mode cleaner transmission exhibits polarization characteristics, as the light experiences an odd number of reflections during a complete round-trip circuit This results in a phase reversal for s-polarized light, which is oriented normal to the cavity plane Consequently, the resonance condition is altered from the standard ν = cn/2L, allowing for the transmission of other polarizations.
The input mode cleaner uses s-polarized light.
The static radiation pressure force in the IMC at resonance is 155 àN, and altering the IMC length decreases this force, resembling a spring behavior The unique spring constant, k opt, is linearly dependent on the distance from the cavity resonance, calculated as k opt = dF RP (x)/dx, where F RP (x) follows the Fabry-Perot resonance model This resonance occurs over a range of 1.2 nm (FWHM), yielding a maximum optical spring constant of approximately +/- 130,000 N/m, significantly surpassing the 170 N/m restoring force of the pendulum suspension The mode cleaner servo maintains the mirror position within +/- 1 pm of resonance, resulting in an optical spring constant below 160 N/m, which is comparable to the gravitational spring and could lead to a 40% alteration in pendulum resonances.
Angular misalignment of the beam within the cavity, known as decentering, creates a torque on the suspended mirrors When the fluctuations in this radiation-induced torque exceed the restoring torque of the torsion pendulum, the resonator becomes unstable.
17 V B Braginsky, M L Gorodetsky, and F Ya Khalili, Phys Lett A 232, 340 (1997);
Benjamin S Sheard, Malcolm B Gray, Conor M Mow-Lowry, David E McClelland and Stanley
E Whitcomb, “Observation and characterization of an optical spring,” Phys Rev A 69, 051801(R) (2004); A Di Virgilio, et al “Experimental evidence for an optical spring.” Phys Rev A 74,
John A Sidles and Daniel Sigg explored the concept of optical torques in suspended Fabry-Perot interferometers in their 2006 paper published in Physics Letters A Sigg further investigated angular instabilities in high-power Fabry-Perot cavities and the angular stability in triangular Fabry-Perot cavities, contributing to the understanding of these optical systems within the LIGO project.
The analysis of Advanced LIGO's instability in document LIGO-T060269-01-D reveals a critical power (P crit) of 2.0 MW for the Input Mode Cleaner (IMC), calculated using parameters such as suspension angular moment (Θ), pitch angular frequency (ω), and a g-dependent eigenvalue (k 2 = 0.39) This value significantly exceeds the 23 kW circulating power specified in the advanced LIGO IMC design, indicating that the mode cleaner will remain unaffected by this instability.
The IMC is also free of these instabilities, on account of the small spot sizes and large free spectral ranges.
7.3.8 Input Mode Cleaner Thermal effects
The stored power in the input mode cleaner is larger than the incident power by 1/T, with T the (power) transmittance of the input and output couplers
Absorption in the coatings and substrates of input mode cleaner mirrors affects their effective radii of curvature, leading to distortions in the spatial eigenmode Additionally, heating in the coating alters the sagitta (δs) across the beam profile This phenomenon can be approximated using the Hello-Vinet theory, with further details available in the supporting document LIGO T070090-00-D.
The absorption coefficient for coatings is 0.5 ppm, while the substrate absorption is 10 ppm/cm, leading to a sagitta change of δs = 0.523 nm for the MC1 and MC3 fused silica mirrors with a beam waist of 2.1028 mm This results in the flat mirror's radius of curvature altering to -4 km Additionally, the radius of curvature for the curved mirror shifts from 26.769 m to 26.840 m, corresponding to a sagitta of 0.62 nm for a beam size of 3.4 mm Notably, the effective radius of curvature at MC2 accounts for the -4 km change observed at MC1.
The hot radius of curvature (ROC) of the curved mirror in MC3, along with the 10 km change at MC2, can be effectively modeled with a value of 26.9116 m This measurement is essential for calculating the hot beam waist and determining the g-factor of the cavity.
Faraday Isolator Design
The Faraday Isolator consists of a birefringence-compensated Faraday Rotator (consisting of two TGG crystals and a quartz rotator), polarizers, a λ/2 waveplate, and a negative dn/dT material for thermal lens compensation 21
The Advanced LIGO facility is expected to implement a configuration of three polarizers for improved performance This setup will include two calcite wedge polarizers (CWP) known for their high extinction ratios, ensuring optimal isolation Additionally, a thin film polarizer (TFP) will be placed between the CWPs to reduce power-dependent beam steering in the REFL port.
Optical Characterization
Here, we separately investigated the isolation and the beam steering at optical powers as high as
103 W using a mode size of 3.9 mm, nearly identical to that expected in Advanced LIGO Two different configurations 22 were tested:
• A hybrid configuration, consisting of a fused silica thin film polarizer and a 2.5 mm thick calcite wedge, with a 4.3 o wedge angle (TFP + CWP).
• A pair of identical calcite wedge polarizers (CWP + CWP) – same as in the (TFP + CWP) setup.
The performances of the FI are summarized in Error: Reference source not found below.
Although the complete characterization of the 3-polarizer setup is still pending, the preliminary tests conducted have instilled confidence in its functionality A comprehensive evaluation is scheduled to occur at LLO in the coming months.
19 LIGO-T060267-00-D, "Upgrading the Input Optics for High Power Operation", UF LIGO Group, IAP Group; LIGO- G060361-00-D, Modulators and Isolators for Advanced LIGO, UF IO Group
20 LIGO-T070021-00-D “Status of High Power Measurements in Faraday Isolators”, R Martin for IO Group, University of Florida.
21 E Khaznov, N F Andreev, a Mal'shakov, O Palashov, A K Poteomkin, A Sergeev, A A Shaykin,V Zelenogorsky,
I A Ivanov, R Amin, G Mueller, D B Tanner, and D H Reitze, "Compensation of thermally Induced Modal Distortions in Faraday Isolators" IEEE J Quantum Electron., 40, 1500-1510 (2004).
The high power performance of the FI has been successfully tested in a third configuration, which includes two thin film polarizers, yielding very satisfactory results.
Table 12 Performance of the Advanced LIGO FI
Performance TFP + CWP CWP + CWP Comments
For TFP + CWP, 39 dB is limited by the extinction of the TFP.
For CWP + CWP, isolation is maximum at maximum input power and decreases at lower powers
12.9 mW 1.3 mW Better suppression for the CWP +
% Transmitted Power: 94 % 95 % The FI was optimized for max. isolation (min back reflection)
103W input): 6 W 5 W Of which ~ 3 W are lost in the second polarization of the second CWP.
Larger drift for CWP + CWP setup
Drift in reflection is ~twice as in transmission (FR and first CWP are double passed).
The optical isolation was quantified as the decibel (dB) ratio between the incoming and reflected light The graph below illustrates the isolation ratio in relation to incident optical power for both configurations Each setup was fine-tuned to achieve optimal isolation at the peak power of 103 W and remained unchanged thereafter.
Figure 8.41 Power-dependent optical isolation for FI using one TFP and CWP (blue diamonds) and a pair of CWPs (red triangles)
The TFP + CWP configuration achieves a lower isolation ratio of 39 dB, constrained by the TFP extinction ratios of 40 dB In contrast, the CWP + CWP setup yields a higher isolation ratio of 49 dB at 103 W, remaining stable across power variations from 80 to 103 W, but decreasing to 44 dB when power is lowered.
Thermal beam steering was assessed during forward transmission and back reflection at an incident power of 103 W, using a Quadrant Photodetector (QPD) positioned approximately 2.5 meters from the fiber reflector (FR) Initially, the beam was obstructed for 45 minutes, followed by a 30-minute period where beam displacement was recorded post-illumination.
As optical elements heat up when illuminated, it becomes challenging to distinguish the thermal drift caused by the optical system from environmental temperature fluctuations In experiments using a double calcite wedge setup, a maximum thermal drift of 80 µrad was recorded at 103 W in reflection, corresponding to 0.40 µrad/W, while a lower drift of 50 µrad was observed under the same conditions, equating to 0.25 µrad/W.
A previous study examined the effects of a double calcite polarizer setup, specifically by positioning a DKDP crystal after the second polarizer of the isolator The investigation revealed a total thermal lensing of 40 m at an incident power of 70 W Upcoming tests will be conducted in a vacuum at LLO in the coming months.
Vacuum compatibility
In December 2006, a modified housing design for the Faraday rotator underwent vacuum baking at 60°C and was tested at Caltech Dennis Coyne's analysis of the outgassing rate revealed it was sufficient for Enhanced LIGO and potentially Advanced LIGO, although it exhibited significant "broad carbon peaks" occurring every 14 AMU, specifically around the values of 41, 55, 69, and 83, with a strong signal detected.
This unit was then rebaked at 80 C showing improved outgassing and no degradation in magnetic field strength
For details, see http://www.ligo.caltech.edu/~rtaylor/your%20folder/Luke_Williams.htm
The modified design is being tested for cavity contamination at Caltech Additionally, three new units for Enhanced LIGO have been ordered and are scheduled for vacuum baking in June or July 2007, which will provide us with more data.
The Faraday isolator, tested in a two-calcite polarizer configuration under vacuum conditions as low as 40 mTorr, was optimized at 1 atm Throughput light measurements were conducted at various pressures while pumping, with incident powers of 104 W, 50 W, and 30 W Preliminary findings indicate significant degradation of isolation below 0.1 Torr, particularly at the highest power level of 104 W, where isolation fell below 30 dB at 40 mTorr Although the data reflects pressure variations, the rapid pump-down time relative to the thermal time constant at low pressures suggests that increased rotator temperature primarily contributes to the loss of isolation, with lower pressures leading to longer response times.
Figure 8.42 Isolation degradation with pressure, at 104 W, 50 W and 30 W.
The observed decrease in isolation from 40 dB to just below 36 dB over 90 minutes can be attributed to less efficient convection cooling of the Faraday isolator's optical elements at higher vacuum levels This pressure increase is linked to the outgassing of the isolator as its temperature rises Recovery of the initial isolation was achieved through a fractional adjustment of the waveplate.
Fig 8.43 Isolation recovery with waveplate adjustment The measurement was made at 30
Ongoing experiments at LLO are focused on studying the time dependence of thermally induced depolarization in both the Faraday rotator and calcite polarizers, while maintaining a constant, minimum achievable pressure Furthermore, efforts are being made to design more efficient conduction cooling channels.
Excess Phase Noise
The Faraday Isolator's transmissive optics are not suspended, resulting in greater motion compared to suspended optics, which may introduce additional phase and frequency noise in the light post-mode cleaner This article will explore the effects of moving focusing elements and wedges on optical performance.
To analyze phase changes resulting from the transverse movement of perfect lenses or curved mirrors, we focus solely on ideal lenses, including those generated thermally The optimal configuration of a focusing element, characterized by a focal length f and devoid of aberrations, can be expressed as a modification of the optical path for a specified distance r from the optical axis.
To calculate the optical path change that a light beam undergoes when moving from the center of an optical element (r = 0) to a position r, we utilize a specific formula This calculation is essential for understanding the corresponding phase change for light with a wavelength of λ.
From we can use the motion at 10 Hz (
3⋅ − 11 ) to estimate the introduced phase noise For a focal length of f = 50 m this leads to a phase noise of
2 ⋅ − 17 This corresponds to a frequency noise of
1 ⋅ − 15 and is well below the frequency noise requirement in LIGO-T010075-00-D at
The following picture illustrates the effect of a prism moving “perpendicular” to the beam.
Figure 8.44 Prism moving perpendicular to the beam.
The previous graph, while based on the assumption of plane waves, can effectively approximate the phase change experienced by a moving prism In this scenario, the primary effect observed is a phase change without any accompanying beam shift The change in path length is represented as: y l ∆.
The angle θ represents the bending of the beam in relation to the incident beam This bending results in a corresponding phase change Despite common ground motion, a residual angle persists due to the alignment of each wedge, leading to a slight deviation For an assumed residual angle of 0.005 degrees and motion occurring at a frequency of 10 Hz, the impact of these factors must be considered.
3⋅ − 11 ) this leads to a phase noise of:
2 ⋅ − 6 This is still within the specification but great care has to be used when setting up the two anti-parallel wedges
To ensure optimal performance of TFP polarizers, it is essential that their surfaces remain parallel to each other within a tolerance of 0.005 degrees (1/3 minute) This precision is approximately ten times better than that of standard commercial flats, highlighting the need for meticulous effort in the production of high-quality TFPs.
Note that the motion of the prism along the beam introduces a parallel beam shift of x r ∆
, (8.25) but has no effect on the phase.
The IO Mode Matching Telescope (MMT) efficiently transmits light from the mode cleaner to the interferometer (IFO) while ensuring optimal mode content To meet the requirements of the IO Differential Readout Detector (DRD), the light coupling efficiency into the main interferometer must be 0.95 or higher in the TEM00 mode Additionally, the IO MMT aligns with the average characteristics of the two interferometer arm cavities, referred to as the 'common mode.'
The MMT is designed to:
• compensate for static variations from design values in IO as well as thermally-induced variations in the IO components
• provide for diagnostic measurement of the mode-matching in the IFO
• Meet constraints imposed by the physical dimensions of the HAM stacks and vacuum system
• Correct for differential mode changes between the X and Y arms due to static errors in the COC ROC This falls in the scope of AOS (TCS).
• Correct for thermally induced variations in the COC components This also falls in the scope of AOS (TCS).
Overview of Mode Matching Telescope Design
The configuration of the MMT depends upon the choice of specific recycling cavity design, i.e., Stable Power Recycling Cavity (SPRC) or Marginally Stable Power Recycling Cavity (MSPRC).
Currently, the MSPRC serves as the baseline, while SYS is exploring the potential for a SPRC Notably, the MMT is incorporated within the SPRC, contrasting with its separation in the MSPRC Consequently, initial designs for the MMT related to both the MSPRC and SPRC are outlined.
The MMT design philosophy is governed by the following criteria:
• Minimizing the number of optics after the mode cleaner.
• Adjustment of the mode parameters in the IFO sufficient to meet the requirements through either (re)positioning of the MMT mirrors or adaptive heating of DKDP
• Provide for diagnostic measurement of the mode-matching.
• Minimize astigmatism and other aberrations introduced into the main beam.
To achieve effective steering of the beam into the mode IFO with minimal higher order modal contamination, we propose a design where MMT1 is a flat mirror This design is supported by the physical layout of the input optics in vacuum, the adjustable mode matching through MMT1's motion, and the ability for adaptive in situ tuning For the Advanced LIGO FP arm cavities, mode matching remains largely unaffected by MMT1's position within its operational range on HAM2 Notably, the HAM2 configuration requires an incidence angle of 6.675° for MMT1, and employing a flat mirror will prevent any aberrations in the system In contrast, MMT2 and MMT3 have much smaller incidence angles (approximately 0.5°), resulting in a negligible reduction of less than 0.1% in TEM00 power coupling into the arm cavity.
9.1.1.2 Stable Power Recycling Cavity MMT
In the SPRC setup, MMT1, MMT2, and MMT3 are strategically positioned to ensure effective ROC matching with the recycling cavity mode The beam from the Input Mode Cleaner (IMC) strikes MMT1, also known as the Power Recycling Mirror (PRM), at a normal incidence It is essential that the suspensions for MMT2 and MMT3 are designed to be similar to those of the IMC mirrors for optimal performance.
In designing the MMT, the following assumptions are used:
• Values for COC ROC and their tolerances as given in LIGO-E060268, “Advanced LIGO Pathfinder Polish”
• Values for the IMC mirror ROC and their tolerances are as given in Section 9.2
• TCS will hold the COC ROC to their nominal values, ensuring that IO will mode match to the same arm cavity mode at all power levels
• Static or fixed errors will be corrected by changing the distance between MMT2 and MMT3. Adaptive heating will be used to correct dynamic (power-dependent) errors in the IO
Aberration and wavefront modeling for the initial LIGO MMT indicated that surface figure errors from polishing and coating did not adversely affect wavefront quality Additionally, small angles of incidence on the curved MMT mirrors introduced astigmatism, but this did not significantly impact the theoretical TEM00 mode matching in the FP arms A minor 0.1% reduction in TEM00 power coupling is accounted for due to astigmatism when incidence angles are kept below 0.6 degrees on the curved mirrors, with further details provided in Section 9.2.5.2.
MSPRC MMT
23 LIGO-T970143-00, Design Considerations for LIGO Mode-Matching Telescopes, T Delker, et al.
Figure 9.45 illustrates the conceptual layout and defines key parameters, while Table 13 details the design parameters for the MSPRC The distance values presented in Table 13 are derived from the IO optical layout Additionally, the MMT radii of curvature were calculated using an ABCD Gaussian propagation code in conjunction with an optimization routine.
Figure 9.45 Marginally Stable Recycling Cavity Optical Layout MMT 1,3 are located on HAM 2 ; MMT 2 is located on HAM 3 Ring Heater (RH) of DKDP is used for adaptive adjustment.
W mc = Waist Size in IMC mm 2.1028 d mf = Distance b/w IMC waist and FI m 3.1925 d fs = Distance from FI to MMT 1 m 0.5539
25 POINTER TO YOUR MATLAB CODE
To Sensing and Control System for
Adaptive Mode matching d 23 = Distance b/w MMT 3 and MMT 3 m 15.54088
R 3 = MMT 3 ROC m 28.7936 d pr = Distance b/w MMT 3 and PR m 15.40822
R pr = PR ROC m 1436.1 d pb = Distance b/w PR and BS m 3.50880 d bs = BS Effective thickness mm 68.783 d bt =Distance b/w BS and ITM m 4.5
The required beam waist size at the ITM is 11.53 mm, with a spot size of 6.0 cm and a beam waist location 2000 m from the ITM At MMT 1, the incident angle is 44.88 degrees, resulting in a spot size of 2.2 mm For MMT 2, the incident angle is 0.62 degrees, with a spot size of 3.9 mm At MMT 3, the incident angle is 0.74 degrees, yielding a spot size of 6.13 cm Finally, the spot size at PR measures 6.03 cm.
General optical component specifications for the MSPRC are represented in Table 13
Definition Unit MMT1 MMT2 MMT3 Notes
Marginally Stable Power Recycling Cavity
Substrate material Fused Silica BK7 1 BK7 1 1 See 9.2.3.1
HR Surface ROC m >10000 1.813, ±0.05 2 28.82,±0.025 2 2 Similar to LIGO1
The tolerances for the ROC are comparable to those established in Initial LIGO, ensuring that any errors can be effectively mitigated By repositioning MMT2, it is possible to maintain a power coupling of TEM00 into the arm cavity with less than a 0.5% decrease.
To address unforeseen challenges in TCS during commissioning and to enhance flexibility in IFO thermal compensation methods, we utilize BK7 as the material for MMT mirrors This choice leverages BK7's thermal expansion coefficient, which is ten times greater than that of FS, ensuring effective adaptive control for the mirrors if necessary.
The IO layout is designed to facilitate the injection of CO2 heating beams on MMT2 and MMT3 as necessary, while also incorporating provisions for anticipated relative humidity (RH) at MMT3 to support effective Thermal Control System (TCS) operations.
9.2.3.2 Thermal Effects in MMT Mirrors
Thermal effects in MMT mirrors can be completely neglected The power incident on MMT2,3 is
125 W and at 1 ppm coating absorption, the amount of heat absorbed is 100 àW Therefore no correction is required for thermal effects in MMT mirrors
Adaptive mode matching is essential to address thermal effects in frequency interferometry (FI) While passive thermal compensation is achieved using DKDP crystals, residual thermal lensing may persist Additionally, thermal lensing from MC mirrors can further exacerbate mode mismatch within the interferometer To mitigate these issues, an adaptive system is proposed that incorporates DKDP for improved performance.
RH around its barrel for adaptive mode matching
9.2.5 MSPRC Mode Matching Operation and Performance
To address static errors in the IOO ROC, adjustments will be made to the distance between MMT2 and MMT3 By optimizing the ROC tolerances for MMT mirrors, mode matching can be enhanced to 99.9% even in the worst-case scenario of ROC errors, achieved through the strategic repositioning of MMT2 in the MSPRC setup.
The innovative dynamic adaptive heating system on DKDP effectively manages thermal effects in MC and mitigates residual thermal lensing in FI By utilizing the proposed RH, it achieves an impressive 99.5% mode matching at full power.
The proposed MMT is engineered to achieve over 99% mode matching by addressing simultaneous errors, including static errors from MMT2, MMT3, IMC mirrors, and tolerances at their worst-case values This is accomplished by adjusting the distance between MMT2 and MMT3 Additionally, both passive and adaptive DKDP compensations through RH on DKDP effectively mitigate residual thermal lensing in the FI, ensuring that mode matching loss remains below 0.5% For further details, refer to LIGO-E060268.
• Arm cavity ITM-ETM ROC mismatch tolerance = ± 3 m
The analysis of absolute ROC values reveals potential beam waist locations and sizes, as illustrated in Figure 9.46 Implementing a fixed MMT design may lead to static mode-mismatch within the arm cavity, potentially resulting in a maximum coupling efficiency decrease of 3.0%, particularly under worst-case tolerances for the ROC of both the COC and IO, along with necessary adjustments to the MMT mirrors Despite this, the mismatch remains acceptable, as it adheres to the IOO standards of maintaining over 95% coupling efficiency In the future, an adaptive mode-matching system, incorporating CO2 heating at MMT2 and a RH at MMT3, could be integrated if required.
Figure 9.46 illustrates the modal space, highlighting the beam waist location and size within the arm cavity as the radii of curvature (ROC) of the input test mass (ITM) and end test mass (ETM) are varied between 2076 m and 2137 m This exploration encompasses all possible combinations of the two cavity mirrors, with solid lines representing contours of constant ITM ROC.
9.2.5.2 Assignment of ROC Tolerances for MMT 2 , MMT 3
The ROC tolerances for MMT2 and MMT3 are designed to allow for independent mitigation of mode mismatch by adjusting the MMT optics, achieving a remarkable 99.9% mode-matching recovery These tolerances, akin to the specifications used in the initial LIGO project, are detailed in the accompanying table.
The designed value of MMT2 ROC is 1.8130 m and the tolerance is ± 0.05 m while designed value
The Advanced LIGO specifications indicate that the MMT2 radius of curvature (ROC) tolerance is ±3.0% (0.03 Normalized) of its designed value, while the MMT3 ROC tolerance corresponds to 17 km, with a precision of ±12.0 × 10^-5 Diopter This translates to a normalized tolerance of ±0.15% (0.0015 Normalized) for the designed MMT3 ROC.
9.2.5.3 Mode Matching Adjustments for the MSPRC
Static errors in the Input Optics (IOO) can arise from several factors, including the radius of curvature (ROC) tolerance of the MC curved mirror, which may lead to a mismatch in the MC waist from the Interferometer (IFO) mode Additionally, incorrect positioning of optics, particularly the MC flat mirrors and the MMT1, as well as misalignment of MMT2 and MMT3, can contribute to these errors It is assumed that the TCS maintains the ETM/ITM curvatures at their nominal value of 2076 m The impact of these static errors on mode matching performance is detailed in Table 15.
Table 15 Static Errors Sources and Mode Miss-Match
Static Error Source Nominal Value Tolerance Mode Mismatch
Distance from MC-MMT 1 3.7464 m ±24 cm ±6.5 0.01
Note A: This is for controlling purposes Otherwise, the expected tolerance on positioning is ±1.0 mm
Table 15 indicates that a budget of 0.5% mode mismatch is generally sufficient, with the exception of the ROC tolerance for MMT2 and MMT3 Notably, repositioning MMT2 and MMT3 can significantly impact mode mismatch This adjustment can be utilized to correct ROC tolerance errors in MMT mirrors Since relocating MMT2 is more feasible due to its smaller size, it is recommended as the primary method for mitigating static error corrections in ROC tolerances Additionally, it is advisable to fabricate MMT3 first, measure its ROC, and then assign the appropriate ROC to MMT2 based on these measurements.
SPRC Mode Matching Telescope
The Stable Power Recycling cavity is an alternative design that incorporates the MMT, resulting in a G-factor of 0.4 The choice between this design and another will depend on factors such as parametric instabilities, alignment control, and layout considerations Consequently, both designs are under consideration for inclusion in the IOO design document.
9.3.1 Optical Layout of Mode Matching Telescope
The Stable Power Recycling Cavity (SPRC) features an optical layout where the Power Recycling Mirror (PRM) and MMT3 are positioned on HAM2, while MMT2 is located on HAM3 A key distinction between the SPRC and the Modified Stable Power Recycling Cavity (MSPRC) is the placement of the PRM, which in the SPRC configuration replaces MMT1.
Same procedure was used as outlined in Section 9.2.1 for determining the ROC of MMT mirrors. The distance values in Table 16 come from the IO optical layout
To Sensing and Control System for
Definition Unit Value) w mc = Waist Size in MC mm 2.1028 d mf = Distance b/w MC waist and FI m 3.1925 d fp = Distance from FI to PR m 0.5539
PR radius of curvature m -70.3 d 12 = Distance b/w PR and MMT 2 m 16.585
R 2 = MMT 2 ROC m 1.8560 d 23 = Distance b/w MMT 2 and MMT 3 m 16.655
R 3 = MMT 3 ROC m 31.059 d mb = Distance b/w MMT 3 and BS m 20.655 d bs = BS Effective thickness mm 68.783 d bt =Distance b/w BS and ITM m 4.5
The required beam waist size in the arm is 11.53 mm, with a spot size at the ITM measuring 6.0 cm The beam waist location from the ITM is 2000 m At the PR, the incident angle is 0.0 degrees, resulting in a spot size of 2.2 mm For MMT 2, the incident angle is 0.745 degrees, with a corresponding spot size of 3.7 mm Finally, at MMT 3, the incident angle is 1.265 degrees, leading to a spot size of 6.11 cm.
Substrate material Fused Silica BK7 1 BK7 1 1 See 9.3.3.1
(Intensity) 0.9985 0.9999 0.9999 MMT 1 transmission specified by required PRC gain
9.3.3.2 Thermal Effects in MMT Mirrors
The power incident on MMT2 and MMT3 is 2.1 kW, leading to a heat absorption of 2.1 mW at a 1 ppm coating absorption rate This generates a thermal lens effect of 2 km at MMT2 and 6000 km at MMT3, with corresponding sagitta changes of 3 nm and 0.3 nm, respectively Therefore, the thermal distortion caused by coating absorption can be considered negligible.
The adaptive mode matching using DKDP is independent of the geometry of the recycling cavity and therefore it will remain same for the SPRC
9.3.5 MSPRC Mode Matching Operation and Performance
This section mirrors Section 9.2.5, with the key distinction that the PRM must be adjusted by double the change in the distance between MMT2 and MMT3 to maintain a constant recycling cavity length.
9.3.5.1 Assignment of ROC Tolerances for MMT 2 , MMT 3
The ROC tolerances for MMT2 and MMT3 are designed to allow independent mitigation of mode mismatch through the repositioning of MMT optics, achieving a recovery of 99.5% mode-matching, alongside adaptive heating techniques These tolerances, which are comparable to the initial specifications for LIGO MMT, are detailed in Table 17.
The MMT2 radius of curvature (ROC) is designed at 1.8560 m with a tolerance of ± 0.05 m, while the MMT3 ROC is set at 31.059 m with a tolerance of ± 0.025 m The tolerance for MMT2 relates to a lens with an ROC of -33 m, equivalent to -0.06 Diopter, and in normalized terms, this corresponds to ±3.0.
The designed MMT2 ROC has a tolerance of 0.03 normalized, while MMT3 corresponds to a ROC of 17 km with a tolerance of ±12.0 ×10 -5 Diopter This translates to a normalized value of ±1.5% (0.0015 normalized) for the designed MMT3 ROC, indicating the distance by which MMT2 is repositioned.
9.3.5.2.2 Static Error Corrections using Adaptive Heating
Adaptive heating of MMT2 and MMT3 has the potential to correct static errors, although this approach is not currently in development However, maintaining the option to heat these mirrors could enhance mode matching in the future if necessary.
9.3.5.2.3 Dynamic Error Correction using Adaptive Heating
9.3.6 Preliminary Adaptive Mode Matching Specifications
Angular Noise
Document T060075-00-D by P Fritschel verifies that the new AdvLIGO OSEMs used small optics suspensions meet the angular noise requirements For the modematching/steering mirrors the following can be estimated.
For the new OSEMs a position sensitivity of
1⋅ − 10 at 1 Hz is targeted, see T050111-01-K
“OSEM Preliminary Design Document & Test Report” The current LIGO OSEMs reach a sensitivity of
1⋅ − 10 at 100 Hz, see figure 22 in LIGO-T960103-00-D “ASC: Environmental Input to Alignment noise”.
The requirement for the angular stability ∆φ of the beam after the mode cleaner for a beam waist of w(z) on the mirror at a given frequency is
Hz z πw φ λ assuming a misalignment of 10 − 9 rad for the ITM (from: Beam jitter coupling in advanced LIGO, G Mueller).
At 7 Hz for 2 mm beam radius this leads to
∆φ ≤ This is nearly exactly the angular noise of small optics suspensions with the (new) OSEMs spaced ca 5 cm apart and a unity gain frequency slightly lower than that.
Optical throughput
Table 18 presents the overall throughput derived from the IO layout, with estimation bases provided for each subsystem or component It is assumed that the PSL will achieve its specification of 165 W TEM00 at the PSL IO handoff.
IO Subsystem or Component Transmission Cumulative
From PSL 1.0 1.0 Input beam from PSL
CCD pickoff wedge 0.995 0.9950 Fused silica substrate; 300 ppm
AR coatings, scatter due to dust from ambient environment
Lens 1 0.995 0.9900 Fused silica substrate; 300 ppm
AR coatings, scatter due to dust from ambient environment
M1 0.998 0.9880 HR, scatter due to dust from ambient environment
M2 0.998 0.9861 HR, scatter due to dust from ambient environment
Lens 2 0.998 0.9841 Fused silica substrate; 300 ppm
AR coatings, scatter due to dust from ambient environment
1/2 wave plate 0.99 0.9743 Quartz components, commercial
Thin film polarizer 0.98 0.9548 Measured transmission in P-pol
MZ EOM 0.9 0.8593 Assumes 50/50 BS, ~100% visibility, m=0.6 in each arm
M3 0.998 0.8576 HR, scatter due to dust from ambient environment
EMMT1 0.998 0.8559 HR, scatter due to dust from ambient environment
EMMT2 0.998 0.8541 HR, scatter due to dust from ambient environment
EMMT3 0.998 0.8524 HR, scatter due to dust from from ambient environment
1/2 wave plate 0.98 0.8312 Quartz components, commercial
Thin film polarizer 0.99 0.8229 Measured transmission in P-pol
Lower periscope mirror 0.995 0.8188 HR, scatter due to dust from ambient environment; vertically oriented surface
Upper periscope mirror 0.998 0.8171 HR, scatter due to dust from ambient environment
Feedthrough 0.995 0.8131 Fused silica, 300 ppm AR coatings, some scatter
Feedthrough 0.999 0.8130 Fused silica, 300 ppm AR coatings, clean environment
IMC 0.9 0.7315 Historical data with some optimism thrown in…
MMT1 0.995 0.6913 5000 ppm transmission, clean environment
MMT3 0.9999 0.6912 HR, includes worst case beam clip losses, clean environment
The IO is expected to transmit about 69.1% of its light output, equating to approximately 114 W, to the PRM While this amount falls short of the required value, it is based on conservative estimates regarding scatter loss from the PSL table optics.
The primary challenges in our system are the MZ modulation, the IMC, and the Faraday isolator While options for addressing the MZ and Faraday isolator are limited, enhancing the IMC transmission to 96% could potentially improve overall performance to approximately 74%.
The IOO will have an optical spectrum analyzer (Tropel) on the PSL/IOO table for analyzing RF sidebands on the PSL table.
A fast photodiode with a frequency of 2 GHz from Thorlabs will be utilized to monitor the amplitude sidebands of light following the Mach-Zehnder interferometer Additionally, a radio frequency spectrum analyzer is required, capable of detecting frequencies at least three times higher than the maximum modulation frequency employed in the measurement.
A photodiode capable of measuring intensity fluctuations at the 10 -8 RIN noise level will be present to monitor the intensity noise in the DC to 10 MHz range.
Since we are not actively controlling the sideband frequency relative to the mode cleaner length, an
RF photodiode will be used to monitor the amount of sideband power that gets rejected RF frequency and/or MC length adjustments can be made manually when necessary.
The IOO will have the capability to monitor MC cavity ring down times using a fast photodiode on located on the ISC table.
Cameras behind the MC mirrors can be used to monitor the MC alignment and also to guide the initial alignment or restore the alignment back to a known value.
The intensity of the second (unwanted) polarization at the second polarizer will be monitored to identify an increase or decrease in the polarization losses.
The polarization observed from the second polarizer can be utilized to assess thermal lensing effects, including those caused by a ring heater surrounding the DKDP This assessment is achieved by measuring the beam diameter with a CCD camera Additionally, the captured image provides insights into depolarization by analyzing the mode picture.
11.1.4.1Measurement of Mode-Matched Power
To measure mode matched power, two Bull's Eye position sensors will be employed to assess the mismatch in cavity waist size and position based on the back-reflected light from the interferometer (IFO).
11.1.4.2Sensing and Control of Adaptive Heating
The adaptive mode matching needs a quadrant camera and a CCD camera (Spiricon L230) to monitor the effects of the adaptive heating, see Section 9.2.6.3 for more details.
All components designated for vacuum use must adhere to the vacuum preparation procedures detailed in LIGO Vacuum Compatibility, Cleaning Methods and Procedures (LIGO-E960022-B-D) Following the specified wrapping of vacuum parts, it is essential to include an extra layer of protective outer wrapping along with appropriate lifting provisions.
• Electronic components shall be wrapped according to standard procedures for such parts.
Vendor-supplied transport packaging will be utilized for small optical components with a diameter of less than 7.5 cm, similar to the initial LIGO setup At the installation sites, we will employ clean trays (D9890509-00) to securely hold the clean optics.
12.2.2 Mode Cleaner Mirrors and Large MMT mirror
The MC and Large MMT mirrors will be housed in custom-designed containers currently under development by the COC group Although a final design is still pending, it will feature essential elements such as o-ring seals to protect the optics from atmospheric exposure, along with Teflon or silicon o-rings for enhanced sealing and cushioning of the optic surface The IO group plans to modify the finalized design to accommodate the dimensions of the MC and Large MMT mirrors.
Proper product identification is essential on packaging and shipping containers, including all necessary markings for delivery and storage Compliance with regulations, statutes, and common carrier requirements is crucial, as well as ensuring all safety markings are clearly displayed for secure handling and delivery.
For catalog products, vendor-supplied model numbers are adequate for identification In the case of optical components like lenses and mirrors, while no markings will be applied directly to the optics, each item will be identifiable through its packaging.
For non-catalog products, vendors will be requested to provide markings In the event that is not possible, we will identify parts by labeled packaging until installation.
12.3.3 UF manufactured mechanical and opto-mechanical components
At UF, parts are produced with DCC and serial numbers precision-machined onto their surfaces using CNC technology For smaller components that cannot accommodate this machining, identification is ensured through labeled packaging.
All materials must be consistently identified throughout the manufacturing process, ensuring each component has a unique identifier This identification allows for a comprehensive history of each component to be tracked alongside its associated documentation Records for each component should detail any weld repairs and fabrication irregularities Additionally, serial numbers will be assigned to the suspended mirrors as specified in the manufacturing guidelines.
The IO alignment process involves utilizing fixtures for the assembly and installation of optical components, followed by precise optical alignment using a low-power beam from the PSL or another co-aligned low-power laser Essential tooling and fixtures will be necessary for this procedure.
• Other standard optical lab facilities
• TBD awaiting choice of injection location
The mode cleaner triple suspensions will be provided by SUS Vacuum preparation, cleaning, assembly, mirror insertion, and mirror balancing will follow SUS procedures, TBD.
After assembly/balancing the following will be needed: (Definition of who is responsible is TBD.)
• Mechanism to transport towers from assembly area to LVEA
• Apparatus to lift towers over beam tube to access the folded interferometer
• Apparatus to lift, position, and place towers on HAM table
• IO will provide fixtures to define position on HAM table (see below)
LASTI experience could be very helpful here.
The IO group will manufacture the suspensions and supply essential hardware components such as silver-plated stainless screws, ordinary stainless screws, and dowel pins ISC will provide the OSEMS, while IO will outline the necessary items for assembly The definition of responsibilities is yet to be determined.
• Vacuum bake ovens for cleaning parts
• Air-bake oven for curing epoxy
• Low power laser and quad photodiode for balancing optic
• SOS EPICS controller for testing OSEMS, balance (from ISC?)
• IO will manufacture the glue fixtures for attaching magnets (including fixtures for attaching magnets to standoffs)
IO will design and provide fixtures to define the SOS locations.
These suspensions will be manufactured by SUS, including assembly and hardware ISC provides the OSEMS After arrival at the site, IO will require:
• Vacuum bake ovens for cleaning parts
• Glue fixtures for attaching magnets (including fixtures for attaching magnets to standoffs)
• Air-bake oven for curing epoxy
• Low power laser and quad photodiode for balancing optic
• SOS EPICS controller for testing OSEMS, balance (from ISC?)
• IO will provide fixtures to define position on HAM table (see below)
Packaging
Vendor-supplied transport packaging will be utilized for small optical components with a diameter of less than 7.5 cm, similar to the initial LIGO setup Clean trays (D9890509-00) will be employed at the sites to securely hold the clean optics.
12.2.2 Mode Cleaner Mirrors and Large MMT mirror
The MC and Large MMT mirrors will be securely housed in custom-designed containers, currently under development by the COC group While the final design is yet to be finalized, it will feature essential components such as o-ring seals to protect the optics from atmospheric exposure, along with Teflon or silicone o-rings for enhanced sealing and cushioning of the optic surface The IO group plans to modify this design to accommodate the specific dimensions of the MC and Large MMT mirrors.
Marking
Proper product identification on packaging and shipping containers is essential This includes all necessary markings for delivery and storage, compliance with regulations and statutes, and requirements from common carriers Additionally, safety markings must be clearly provided to ensure safe delivery.
For catalog products, identification can be achieved using vendor-provided model numbers In the case of optical components like lenses and mirrors, there will be no markings on the optics themselves; instead, these items will be identified through their packaging.
For non-catalog products, vendors will be requested to provide markings In the event that is not possible, we will identify parts by labeled packaging until installation.
12.3.3 UF manufactured mechanical and opto-mechanical components
At UF, parts are produced with DCC and serial numbers precision-machined onto their surfaces using CNC technology For smaller components that cannot accommodate surface numbering, identification will be ensured through labeled packaging.
All manufacturing processes must ensure the consistent identification of materials, with each component assigned a unique identifier This identification system allows for the complete tracking of each component's history, linked to documentation "travelers." Records for each component will detail any weld repairs and fabrication irregularities Additionally, serial numbers will be assigned to the suspended mirrors as specified in the individual manufacturing guidelines.
The IO alignment process involves using specialized fixtures for the assembly and installation of optical components, followed by precise optical alignment utilizing a low-power beam from the PSL or a similarly co-aligned low-power laser Essential tooling and fixtures will be necessary for this procedure.
• Other standard optical lab facilities
• TBD awaiting choice of injection location
The mode cleaner triple suspensions will be provided by SUS Vacuum preparation, cleaning, assembly, mirror insertion, and mirror balancing will follow SUS procedures, TBD.
After assembly/balancing the following will be needed: (Definition of who is responsible is TBD.)
• Mechanism to transport towers from assembly area to LVEA
• Apparatus to lift towers over beam tube to access the folded interferometer
• Apparatus to lift, position, and place towers on HAM table
• IO will provide fixtures to define position on HAM table (see below)
LASTI experience could be very helpful here.
The IO group will manufacture the suspensions and supply essential hardware components, including silver-plated stainless screws, ordinary stainless screws, and dowel pins ISC is tasked with providing the OSEMS, while IO will need specific items for assembly The definition of responsibilities is yet to be determined.
• Vacuum bake ovens for cleaning parts
• Air-bake oven for curing epoxy
• Low power laser and quad photodiode for balancing optic
• SOS EPICS controller for testing OSEMS, balance (from ISC?)
• IO will manufacture the glue fixtures for attaching magnets (including fixtures for attaching magnets to standoffs)
IO will design and provide fixtures to define the SOS locations.
These suspensions will be manufactured by SUS, including assembly and hardware ISC provides the OSEMS After arrival at the site, IO will require:
• Vacuum bake ovens for cleaning parts
• Glue fixtures for attaching magnets (including fixtures for attaching magnets to standoffs)
• Air-bake oven for curing epoxy
• Low power laser and quad photodiode for balancing optic
• SOS EPICS controller for testing OSEMS, balance (from ISC?)
• IO will provide fixtures to define position on HAM table (see below)
IO oversees the Faraday isolator, ensuring that all components of the Faraday rotator—including the case, magnets, TGG and quartz crystals, polarizers, waveplate, mounts, breadboard, and other small parts—are cleaned and baked individually at a designated location Additionally, IO will supply the necessary apparatus for assembling the completed rotator on-site.
• Air bake oven for cleaning class B assembly apparatus
• Low power laser and quad photodiode for aligning Faraday
• SOS EPICS controller for testing OSEMS, balance (from ISC?)
• IO will provide fixtures to define positions of parts on the breadboard and of the breadboard on HAM table (see below).
IO will provide any fixtures necessary to define position of auxiliary beam steering mirrors.
Other units (steering mirrors, mode matching optics for the IMC and for the core optics) will be placed in position individually.
The fixtures will accurately align the part to the table holes, targeting a precision of ±50 µm (0.002 inch) with proper shop practices A comprehensive Solidworks model of the IO will aid in establishing the part's position on the table Additionally, the chamber separation is estimated to be ±1 mm, based on the characteristics of the initial LIGO mode cleaner.
The fixtures for advanced LIGO will consist of L-shaped brackets that contact the part at three specific points, ensuring precise translational and angular positioning While initial LIGO utilized a universal fixture with adjustable micrometers, this method was cumbersome and prone to systematic errors due to potential installation issues To improve efficiency and accuracy, advanced LIGO will feature custom-designed fixtures for each component, which can be easily manufactured in-house in Florida, keeping costs manageable.
Fixtures for use in the vacuum chambers will be cleaned and bake to class B standards
Optical alignment will employ a low power PSL beam
In the PSL/IO table setup, fixed apertures are utilized to establish both the beam height and lateral position with the aid of a fixture This method ensures that components are aligned to the beam, rather than the other way around, thereby optimizing the alignment process This approach significantly reduces the pointing and displacement of the beam in relation to the fiduciary points Additionally, the beam's polarization is configured to be perpendicular to the table surface, specifically in s-polarization.
In the vacuum chamber, targets mounted on suspension frames will be utilized for beam alignment To enhance transmittance through IMC1 and IMC3, the input polarization of the light will be adjusted to horizontal using a half wave plate located at the base of the telescope.
Beam height targets are essential for ensuring the beam is properly aligned horizontally and positioned at the correct height above the table in the HAM Adjustments can be made using either the periscope mirrors or the mirrors located on the PSL/IO table.
Table height and level will need to be monitored and adjusted during this process
To align the beam through the IMC, we will utilize targets while ensuring that the beam closes on itself with the help of suspension controls If the initial pointing is significantly off, small rotations of the towers can be employed for adjustments It is important to note that we will not attempt to resonate the IMC in air.
The IMC reflected beams and transmitted beams (the latter taken through SM1) will be aligned intoHAM1 and onto the detectors.