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REVIEW OF SCIENTIFIC INSTRUMENTS 83.033109(2012) Thermal effects in the Input Optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers Katherine L.Dooley,1.a)Muzammil A.Arain,1.b)David Feldbaum,1 Valery V.Frolov,2 Matthew Heintze,1 Daniel Hoak,2.c)Efim A.Khazanov,3 Antonio Lucianetti,1.d) Rodica M.Martin,1 Guido Mueller,1 Oleg Palashov,3 Volker Quetschke,1.) David H.Reitze,1.R.L.Savage,4 D.B.Tanner,1 Luke F.Williams,1 and Wan Wu1.9) University of Florida,Gainesville,Florida 32611.USA 2LIGO,Livingston Observatory,Livingston,Louisiana 70754.USA 3Institute of Applied Physics,Nizhny Novgorod 603950.Russia ALIGO.Hanford Observatory,Richland,Washington 99352.USA (Received 9 December 2011;accepted 23 January 2012;published online 23 March 2012) We present the design and performance of the LIGO Input Optics subsystem as implemented for the sixth science run of the LIGO interferometers.The Initial LIGO Input Optics experienced thermal side effects when operating with 7 W input power.We designed,built,and implemented improved versions of the Input Optics for Enhanced LIGO,an incremental upgrade to the Initial LIGO inter- ferometers,designed to run with 30 W input power.At four times the power of Initial LIGO,the Enhanced LIGO Input Optics demonstrated improved performance including better optical isolation, less thermal drift,minimal thermal lensing,and higher optical efficiency.The success of the Input Optics design fosters confidence for its ability to perform well in Advanced LIGO.2012 American Institute of Physics.[http://dx.doi.org/10.1063/1.3695405] I.INTRODUCTION the arm lengths,producing signal at the AS port proportional The field of ground-based gravitational-wave (GW) to the GW strain and the input power.The Fabry-Perot cavi- physics is rapidly approaching a state with a high likelihood ties in the Michelson arms and a power recycling mirror(RM) of detecting GWs for the first time in the latter half of this at the symmetric port are two modifications to the Michelson interferometer that increase the laser power in the arms and decade.Such a detection will not only validate part of Ein- stein's general theory of relativity,but also initiate an era therefore improve the detector's sensitivity to GWs. of astrophysical observation of the universe through GWs. A network of first generation kilometer scale laser in- Gravitational waves are dynamical strains in space-time,h terferometer gravitational-wave detectors completed an in- =AL/L,that travel at the speed of light and are gener- tegrated 2-year data collection run in 2007,called Science Run 5(S5).The instruments were:the American Laser Inter- ated by non-axisymmetric acceleration of mass.A first de- ferometer Gravitational-Wave Observatory (LIGO).one in tection is expected to witness an event such as a binary black hole/neutron star merger. Livingston,LA with 4 km long arms and two in Hanford, WA with 4 km and 2 km long arms;the 3 km French-Italian The typical detector configuration used by current gen- eration gravitational-wave observatories is a power-recycled detector VIRGO (Ref.3)in Cascina,Italy;and the 600 m Fabry-Perot Michelson laser interferometer featuring sus- German-British detector GEO(Ref.4)located near Hannover, pended test masses in vacuum as depicted in Figure 1.A Germany.Multiple separated detectors increase detection confidence through signal coincidence and improve source lo- diode-pumped,power amplified,and intensity and frequency stabilized Nd:YAG laser emits light at =1064 nm.The calization via waveform reconstruction. The first generation of LIGO,now known as Initial laser is directed to a Michelson interferometer whose two arm LIGO,achieved its design goal of sensitivity to GWs in the lengths are set to maintain destructive interference of the re- combined light at the anti-symmetric(AS)port.An appropri- 40-7000 Hz band,including a record strain sensitivity of ately polarized gravitational wave will differentially change 2 x 10-23/Hz at 155 Hz.However,only nearby sources produce enough GW strain to appear above the noise level of Initial LIGO and no gravitational wave has yet been found aAuthor to whom correspondence should be addressed.Electronic mail: in the S5 data.A second generation of LIGO detectors,Ad- kate.dooley@aei.mpg.de.Present address:Albert-Einstein-Institut,Max- Planck-Institut fur Gravitationsphysik,D-30167 Hannover,Germany. vanced LIGO,has been designed to be at least an order of b)Present address:KLA-Tencor,Milpitas.California95035,USA. magnitude more sensitive at several hundred Hz and above c)Present address:University of Massachusetts-Amherst,Amherst, Massachusetts 01003.USA. and to give an impressive increase in bandwidth down to d)Present address:Ecole Polytechnique,91128 Palaiseau Cedex,France. 10 Hz.Advanced LIGO is expected to open the field of GW e)Present address:The University of Texas at Brownsville,Brownsville, astronomy through the detection of many events per year.To Texas 78520.USA. test some of Advanced LIGO's new technologies and to in- DPresent address:LIGO Laboratory,Califoria Institute of Technology. Pasadena,California 91125,USA. crease the chances of detection through a more sensitive data g)Present address:NASA Langley Research Center,Hampton,Virginia taking run,an incremental upgrade to the detectors was car- 23666.USA. ried out after S5.5 This project,Enhanced LIGO,culminated 0034-6748/2012/83(3)/033109/12/S30.00 83,033109-1 2012 American Institute of Physics Reuse of AlP Publishing content is subject to the terms at:https://publishing.aip.org/authors/nghts-and-permi D0wmlo8 d to IP:183.195251.60Fi.22Apr2016 00:54:10

REVIEW OF SCIENTIFIC INSTRUMENTS 83, 033109 (2012) Thermal effects in the Input Optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers Katherine L. Dooley,1,a) Muzammil A. Arain,1,b) David Feldbaum,1 Valery V. Frolov,2 Matthew Heintze,1 Daniel Hoak,2,c) Efim A. Khazanov,3 Antonio Lucianetti,1,d) Rodica M. Martin,1 Guido Mueller,1 Oleg Palashov,3 Volker Quetschke,1,e) David H. Reitze,1,f) R. L. Savage,4 D. B. Tanner,1 Luke F. Williams,1 and Wan Wu1,g) 1University of Florida, Gainesville, Florida 32611, USA 2LIGO, Livingston Observatory, Livingston, Louisiana 70754, USA 3Institute of Applied Physics, Nizhny Novgorod 603950, Russia 4LIGO, Hanford Observatory, Richland, Washington 99352, USA (Received 9 December 2011; accepted 23 January 2012; published online 23 March 2012) We present the design and performance of the LIGO Input Optics subsystem as implemented for the sixth science run of the LIGO interferometers. The Initial LIGO Input Optics experienced thermal side effects when operating with 7 W input power. We designed, built, and implemented improved versions of the Input Optics for Enhanced LIGO, an incremental upgrade to the Initial LIGO interferometers, designed to run with 30 W input power. At four times the power of Initial LIGO, the Enhanced LIGO Input Optics demonstrated improved performance including better optical isolation, less thermal drift, minimal thermal lensing, and higher optical efficiency. The success of the Input Optics design fosters confidence for its ability to perform well in Advanced LIGO. © 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3695405] I. INTRODUCTION The field of ground-based gravitational-wave (GW) physics is rapidly approaching a state with a high likelihood of detecting GWs for the first time in the latter half of this decade. Such a detection will not only validate part of Einstein’s general theory of relativity, but also initiate an era of astrophysical observation of the universe through GWs. Gravitational waves are dynamical strains in space-time, h = L/L, that travel at the speed of light and are generated by non-axisymmetric acceleration of mass. A first detection is expected to witness an event such as a binary black hole/neutron star merger.1 The typical detector configuration used by current generation gravitational-wave observatories is a power-recycled Fabry-Perot Michelson laser interferometer featuring suspended test masses in vacuum as depicted in Figure 1. A diode-pumped, power amplified, and intensity and frequency stabilized Nd:YAG laser emits light at λ = 1064 nm. The laser is directed to a Michelson interferometer whose two arm lengths are set to maintain destructive interference of the recombined light at the anti-symmetric (AS) port. An appropriately polarized gravitational wave will differentially change a)Author to whom correspondence should be addressed. Electronic mail: kate.dooley@aei.mpg.de. Present address: Albert-Einstein-Institut, MaxPlanck-Institut für Gravitationsphysik, D-30167 Hannover, Germany. b)Present address: KLA-Tencor, Milpitas, California 95035, USA. c)Present address: University of Massachusetts–Amherst, Amherst, Massachusetts 01003, USA. d)Present address: École Polytechnique, 91128 Palaiseau Cedex, France. e)Present address: The University of Texas at Brownsville, Brownsville, Texas 78520, USA. f)Present address: LIGO Laboratory, California Institute of Technology, Pasadena, California 91125, USA. g)Present address: NASA Langley Research Center, Hampton, Virginia 23666, USA. the arm lengths, producing signal at the AS port proportional to the GW strain and the input power. The Fabry-Perot cavities in the Michelson arms and a power recycling mirror (RM) at the symmetric port are two modifications to the Michelson interferometer that increase the laser power in the arms and therefore improve the detector’s sensitivity to GWs. A network of first generation kilometer scale laser interferometer gravitational-wave detectors completed an integrated 2-year data collection run in 2007, called Science Run 5 (S5). The instruments were: the American Laser Interferometer Gravitational-Wave Observatory (LIGO),2 one in Livingston, LA with 4 km long arms and two in Hanford, WA with 4 km and 2 km long arms; the 3 km French-Italian detector VIRGO (Ref. 3) in Cascina, Italy; and the 600 m German-British detector GEO (Ref. 4) located near Hannover, Germany. Multiple separated detectors increase detection confidence through signal coincidence and improve source localization via waveform reconstruction. The first generation of LIGO, now known as Initial LIGO, achieved its design goal of sensitivity to GWs in the 40–7000 Hz band, including a record strain sensitivity of 2 × 10−23/ √Hz at 155 Hz. However, only nearby sources produce enough GW strain to appear above the noise level of Initial LIGO and no gravitational wave has yet been found in the S5 data. A second generation of LIGO detectors, Advanced LIGO, has been designed to be at least an order of magnitude more sensitive at several hundred Hz and above and to give an impressive increase in bandwidth down to 10 Hz. Advanced LIGO is expected to open the field of GW astronomy through the detection of many events per year.1 To test some of Advanced LIGO’s new technologies and to increase the chances of detection through a more sensitive data taking run, an incremental upgrade to the detectors was carried out after S5 .5 This project, Enhanced LIGO, culminated 0034-6748/2012/83(3)/033109/12/$30.00 © 2012 American Institute of Physics 83, 033109-1 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 183.195.251.6 On: Fri, 22 Apr 2016 00:54:10

033109-2 Dooley et al Rev.Sci.Instrum.83,033109(2012) End tion System,13 the Alignment Sensing and Control,14 and the Input Optics (IO)were modified. Mirror This paper reports on the design and performance of the LIGO Input Optics subsystem in Enhanced LIGO,focusing specifically on its operational capabilities as the laser power is increased to 30 W.Substantial improvements in the IO power handling capabilities with respect to Initial LIGO per- Input formance are seen.The paper is organized as follows.First, Test in Sec.II.we define the role of the IO subsystem and detail Mass the function of each of the major IO subcomponents.Then,in LASER Sec.III we describe thermal effects which impact the opera- Beam Input Test End Test tion of the IO and summarize the problems experienced with Power Splitter Mass Mirror Mass Mirror Recycling the IO in Initial LIGO.In Sec.IV we present the IO design for Mirror Advanced LIGO in detail and describe how it addresses these ④ detection photodiode problems.Sect.V presents the performance of the prototype Advanced LIGO IO design as tested during Enhanced LIGO. FIG.1.Optical layout of a Fabry-Perot Michelson laser interferometer, Finally,we extrapolate from these experiences in Sec.VI to showing primary components.The four test masses,beam splitter,and power recycling mirror are physically located in an ultrahigh vacuum system and discuss the expected IO performance in Advanced LIGO.The are seismically isolated.A photodiode at the anti-symmetric port detects dif- paper concludes with a summary in Sec.VII. ferential arm length changes. II.FUNCTION OF THE INPUT OPTICS The Input Optics is one of the primary subsystems of the with the S6 science run from July 2009 to October 2010.Cur- LIGO interferometers.Its purpose is to deliver an aligned, rently,construction of Advanced LIGO is underway.Simul- spatially pure,mode-matched beam with phase-modulation taneously,VIRGO and GEO are both undergoing their own upgrades.3.6 sidebands to the power-recycled Fabry-Perot Michelson in- terferometer.The IO also prevents reflected or backscattered The baseline Advanced LIGO design?improves upon light from reaching the laser and distributes the reflected field Initial LIGO by incorporating improved seismic isolation,8 from the interferometer(designated the reflected port)to pho- the addition of a signal recycling mirror at the output port, todiodes for sensing and controlling the length and alignment homodyne readout,and an increase in available laser power of the interferometer.In addition,the IO provides an interme- from 8 W to 180 W.The substantial increase in laser power diate level of frequency stabilization and must have high over- improves the shot-noise-limited sensitivity,but introduces a all optical efficiency.It must perform these functions without multitude of thermally induced side effects that must be ad- limiting the strain sensitivity of the LIGO interferometer.Fi- dressed for proper operation. nally,it must operate robustly and continuously over years of Enhanced LIGO tested portions of the Advanced LIGO operation.The conceptual design is found in Ref.15. designs so that unforeseen difficulties could be addressed and As shown in Fig.2,the IO subsystem consists of four so that a more sensitive data taking run could take place.An principle components located between the pre-stabilized laser output mode cleaner was designed,built and installed,and dc readout of the GW signal was implemented.10 An Advanced and the power recycling mirror: LIGO active seismic isolation table was also built,installed. electro-optic modulator(EOM) and tested(Chapter 5 of Ref.11).In addition,the 10 W Initial mode cleaner cavity (MC) LIGO laser was replaced with a 35 W laser.12 Accompanying 。Faraday isolator(F) the increase in laser power,the test mass Thermal Compensa- mode-matching telescope (MMT) Input Optics Electro-optic Faraday modulator Mode cleaner Isolator Pre-stabilized laser Mode-matching telescope FIG.2.Block diagram of the Input Optics subsystem.The IO is located between the pre-stabilized laser and the recycling mirror and consists of four principle components:electro-optic modulator,mode cleaner,Farday isolator,and mode-matching telescope.The electro-optic modulator is the only IO component outside of the vacuum system.Diagram is not to scale. Reuse of AlP Publishing content is subject to the terms at:https://publishing.aip.org/authors/rights-and-permissions.Download to IP:183.195.251.6 On:Fri.22 Apr 2016 00:54:10

033109-2 Dooley et al. Rev. Sci. Instrum. 83, 033109 (2012) FIG. 1. Optical layout of a Fabry-Perot Michelson laser interferometer, showing primary components. The four test masses, beam splitter, and power recycling mirror are physically located in an ultrahigh vacuum system and are seismically isolated. A photodiode at the anti-symmetric port detects differential arm length changes. with the S6 science run from July 2009 to October 2010. Currently, construction of Advanced LIGO is underway. Simultaneously, VIRGO and GEO are both undergoing their own upgrades.3, 6 The baseline Advanced LIGO design7 improves upon Initial LIGO by incorporating improved seismic isolation,8 the addition of a signal recycling mirror at the output port,9 homodyne readout, and an increase in available laser power from 8 W to 180 W. The substantial increase in laser power improves the shot-noise-limited sensitivity, but introduces a multitude of thermally induced side effects that must be addressed for proper operation. Enhanced LIGO tested portions of the Advanced LIGO designs so that unforeseen difficulties could be addressed and so that a more sensitive data taking run could take place. An output mode cleaner was designed, built and installed, and dc readout of the GW signal was implemented.10 An Advanced LIGO active seismic isolation table was also built, installed, and tested (Chapter 5 of Ref. 11). In addition, the 10 W Initial LIGO laser was replaced with a 35 W laser.12 Accompanying the increase in laser power, the test mass Thermal Compensation System,13 the Alignment Sensing and Control ,14 and the Input Optics (IO) were modified. This paper reports on the design and performance of the LIGO Input Optics subsystem in Enhanced LIGO, focusing specifically on its operational capabilities as the laser power is increased to 30 W. Substantial improvements in the IO power handling capabilities with respect to Initial LIGO performance are seen. The paper is organized as follows. First, in Sec. II, we define the role of the IO subsystem and detail the function of each of the major IO subcomponents. Then, in Sec. III we describe thermal effects which impact the operation of the IO and summarize the problems experienced with the IO in Initial LIGO. In Sec. IV we present the IO design for Advanced LIGO in detail and describe how it addresses these problems. Sect. V presents the performance of the prototype Advanced LIGO IO design as tested during Enhanced LIGO. Finally, we extrapolate from these experiences in Sec. VI to discuss the expected IO performance in Advanced LIGO. The paper concludes with a summary in Sec. VII. II. FUNCTION OF THE INPUT OPTICS The Input Optics is one of the primary subsystems of the LIGO interferometers. Its purpose is to deliver an aligned, spatially pure, mode-matched beam with phase-modulation sidebands to the power-recycled Fabry-Perot Michelson interferometer. The IO also prevents reflected or backscattered light from reaching the laser and distributes the reflected field from the interferometer (designated the reflected port) to photodiodes for sensing and controlling the length and alignment of the interferometer. In addition, the IO provides an intermediate level of frequency stabilization and must have high overall optical efficiency. It must perform these functions without limiting the strain sensitivity of the LIGO interferometer. Finally, it must operate robustly and continuously over years of operation. The conceptual design is found in Ref. 15. As shown in Fig. 2, the IO subsystem consists of four principle components located between the pre-stabilized laser and the power recycling mirror: electro-optic modulator (EOM) mode cleaner cavity (MC) Faraday isolator (FI) mode-matching telescope (MMT) FIG. 2. Block diagram of the Input Optics subsystem. The IO is located between the pre-stabilized laser and the recycling mirror and consists of four principle components: electro-optic modulator, mode cleaner, Farday isolator, and mode-matching telescope. The electro-optic modulator is the only IO component outside of the vacuum system. Diagram is not to scale. Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 183.195.251.6 On: Fri, 22 Apr 2016 00:54:10

033109-3 Dooley et al Rev.Sci.Instrum.83,033109(2012) Each element is a common building block of many opti- ferometer.The mode-matching telescope is a set of three sus- cal experiments and not unique to LIGO.However,their pended concave mirrors between the MC and interferometer roles specific to the successful operation of interferometry for that expand the beam from a radius of 1.6 mm at the MC gravitational-wave detection are of interest and demand fur- waist to a radius of 33 mm at the arm cavity waist.The MMT ther attention.Here,we briefly review the purpose of each of should play a passive role by delivering properly shaped light the IO components;further details about the design require- to the interferometer without introducing beam jitter or any ments are in Ref.16 significant aberration that can reduce mode coupling. A.Electro-optic modulator III.THERMAL PROBLEMS IN INITIAL LIGO The Length Sensing and Control (LSC)and Angular The Initial LIGO interferometers were equipped with a Sensing and Control(ASC)subsystems require phase modu- 10 W laser,yet operated with only 7 W input power due lation of the laser light at RF frequencies.This modulation is produced by an EOM,generating sidebands of the laser light to power-related problems with other subsystems.The EOM was located in the 10 W beam and the other components expe- which act as references against which interferometer length and angle changes are measured.17 The sideband light must rienced anywhere up to 7 W power.The 7 W operational limit was not due to the failure of the IO;however,many aspects of be either resonant only in the recycling cavity or not resonant the IO performance did degrade with power. in the interferometer at all.The sidebands must be offset from One of the primary problems of the Initial LIGO IO the carrier by integer multiples of the MC free spectral range (Ref.18)was thermal deflection of the back propagating beam to pass through the MC due to thermally induced refractive index gradients in the FI. A significant beam drift between the interferometer's locked B.Mode cleaner and unlocked states led to clipping of the reflected beam on Stably aligned cavities,limited non-mode-matched the photodiodes used for length and alignment control (see (junk)light,and a frequency and amplitude stabilized laser Fig.3.Our measurements determined a deflection of approx- are key features of any ultra sensitive laser interferometer.The imately 100 urad/W in the FI.This problem was mitigated at MC,at the heart of the IO,plays a major role the time by the design and implementation of an active beam A three-mirror triangular ring cavity,the MC suppresses steering servo on the beam coming from the isolator. laser output not in the fundamental TEMoo mode,serving two There were also known limits to the power the IO could major purposes.It enables the robustness of the ASC because sustain.Thermal lensing in the FI optics began to alter signif- higher order modes would otherwise contaminate the angu- icantly the beam mode at powers greater than 10 W,leading lar sensing signals of the interferometer.Also,all non-TEMoo to a several percent reduction in mode matching to the in- light on the length sensing photodiodes,including those used terferometer.19 Additionally,absorptive FI elements would for the GW readout,contributes shot noise but not signal and create thermal birefringence,degrading the optical efficiency therefore diminishes the signal to noise ratio.The MC is thus and isolation ratio with power.20 The Initial LIGO New Focus largely responsible for achieving an aligned,minimally shot- EOMs had an operational power limit of around 10 W.There noise-limited interferometer. was a high risk of damage to the crystals under the stress of The MC also plays an active role in laser frequency the 0.4 mm radius beam.Also,anisotropic thermal lensing stabilization,17 which is necessary for ensuring that the signal with focal lengths as severe as 3.3 m at 10 W made the EOMs at the anti-symmetric port is due to arm length fluctuations unsuitable for much higher power.Finally,the MC mirrors rather than laser frequency fluctuations.In addition,the MC exhibited high absorption(as much as 24 ppm per mirror) passively suppresses beam jitter at frequencies above 10 Hz. enough that thermal lensing of the MC optics at enhanced LIGO powers would induce higher order modal frequency C.Faraday isolator degeneracy and result in a power-dependent mode mismatch into the interferometer.21.22 In fact,as input power increased Faraday isolators are four-port optical devices which uti- from 1 W to 7 W the mode matching decreased from 90% lize the Faraday effect to allow for non-reciprocal polarization to83%. switching of laser beams.Any backscatter or reflected light In addition to the thermal limitations of the Initial LIGO from the interferometer (due to impedance mismatch,mode IO,optical efficiency in delivering light from the laser into mismatch,non-resonant sidebands,or signal)needs to be di- the interferometer was not optimal.Of the light entering the verted to protect the laser from back propagating light,which IO chain,only 60%remained by the time it reached the power can introduce amplitude and phase noise.This diversion of recycling mirror.Moreover,because at best only 90%of the the reflected light is also necessary for extracting length and light at the recycling mirror was coupled into the arm cavity angular information about the interferometer's cavities.The mode,room was left for improvement in the implementation FI fulfills both needs of the MMT. D.Mode-matching telescope IV.ENHANCED LIGO INPUT OPTICS DESIGN The lowest order MC and arm cavity spatial eigenmodes The Enhanced LIGO IO design addressed the thermal ef- need to be matched for maximal power buildup in the inter- fects that compromised the performance of the Initial LIGO Reuse of AlP Publishing content is subject to the terms at:https://publishing.aip.org/authors/rights-and-per D0wmlo8doP:183.195251.60:Fi.22Apr2016 00:54:10

033109-3 Dooley et al. Rev. Sci. Instrum. 83, 033109 (2012) Each element is a common building block of many optical experiments and not unique to LIGO. However, their roles specific to the successful operation of interferometry for gravitational-wave detection are of interest and demand further attention. Here, we briefly review the purpose of each of the IO components; further details about the design requirements are in Ref. 16. A. Electro-optic modulator The Length Sensing and Control (LSC) and Angular Sensing and Control (ASC) subsystems require phase modulation of the laser light at RF frequencies. This modulation is produced by an EOM, generating sidebands of the laser light which act as references against which interferometer length and angle changes are measured. 17 The sideband light must be either resonant only in the recycling cavity or not resonant in the interferometer at all. The sidebands must be offset from the carrier by integer multiples of the MC free spectral range to pass through the MC. B. Mode cleaner Stably aligned cavities, limited non-mode-matched (junk) light, and a frequency and amplitude stabilized laser are key features of any ultra sensitive laser interferometer. The MC, at the heart of the IO, plays a major role. A three-mirror triangular ring cavity, the MC suppresses laser output not in the fundamental TEM00 mode, serving two major purposes. It enables the robustness of the ASC because higher order modes would otherwise contaminate the angular sensing signals of the interferometer. Also, all non-TEM00 light on the length sensing photodiodes, including those used for the GW readout, contributes shot noise but not signal and therefore diminishes the signal to noise ratio. The MC is thus largely responsible for achieving an aligned, minimally shotnoise-limited interferometer. The MC also plays an active role in laser frequency stabilization,17 which is necessary for ensuring that the signal at the anti-symmetric port is due to arm length fluctuations rather than laser frequency fluctuations. In addition, the MC passively suppresses beam jitter at frequencies above 10 Hz. C. Faraday isolator Faraday isolators are four-port optical devices which utilize the Faraday effect to allow for non-reciprocal polarization switching of laser beams. Any backscatter or reflected light from the interferometer (due to impedance mismatch, mode mismatch, non-resonant sidebands, or signal) needs to be diverted to protect the laser from back propagating light, which can introduce amplitude and phase noise. This diversion of the reflected light is also necessary for extracting length and angular information about the interferometer’s cavities. The FI fulfills both needs. D. Mode-matching telescope The lowest order MC and arm cavity spatial eigenmodes need to be matched for maximal power buildup in the interferometer. The mode-matching telescope is a set of three suspended concave mirrors between the MC and interferometer that expand the beam from a radius of 1.6 mm at the MC waist to a radius of 33 mm at the arm cavity waist. The MMT should play a passive role by delivering properly shaped light to the interferometer without introducing beam jitter or any significant aberration that can reduce mode coupling. III. THERMAL PROBLEMS IN INITIAL LIGO The Initial LIGO interferometers were equipped with a 10 W laser, yet operated with only 7 W input power due to power-related problems with other subsystems. The EOM was located in the 10 W beam and the other components experienced anywhere up to 7 W power. The 7 W operational limit was not due to the failure of the IO; however, many aspects of the IO performance did degrade with power. One of the primary problems of the Initial LIGO IO (Ref. 18) was thermal deflection of the back propagating beam due to thermally induced refractive index gradients in the FI. A significant beam drift between the interferometer’s locked and unlocked states led to clipping of the reflected beam on the photodiodes used for length and alignment control (see Fig. 3. Our measurements determined a deflection of approximately 100 μrad/W in the FI. This problem was mitigated at the time by the design and implementation of an active beam steering servo on the beam coming from the isolator. There were also known limits to the power the IO could sustain. Thermal lensing in the FI optics began to alter significantly the beam mode at powers greater than 10 W, leading to a several percent reduction in mode matching to the interferometer. 19 Additionally, absorptive FI elements would create thermal birefringence, degrading the optical efficiency and isolation ratio with power.20 The Initial LIGO New Focus EOMs had an operational power limit of around 10 W. There was a high risk of damage to the crystals under the stress of the 0.4 mm radius beam. Also, anisotropic thermal lensing with focal lengths as severe as 3.3 m at 10 W made the EOMs unsuitable for much higher power. Finally, the MC mirrors exhibited high absorption (as much as 24 ppm per mirror)— enough that thermal lensing of the MC optics at enhanced LIGO powers would induce higher order modal frequency degeneracy and result in a power-dependent mode mismatch into the interferometer.21, 22 In fact, as input power increased from 1 W to 7 W the mode matching decreased from 90% to 83%. In addition to the thermal limitations of the Initial LIGO IO, optical efficiency in delivering light from the laser into the interferometer was not optimal. Of the light entering the IO chain, only 60% remained by the time it reached the power recycling mirror. Moreover, because at best only 90% of the light at the recycling mirror was coupled into the arm cavity mode, room was left for improvement in the implementation of the MMT. IV. ENHANCED LIGO INPUT OPTICS DESIGN The Enhanced LIGO IO design addressed the thermal effects that compromised the performance of the Initial LIGO Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 183.195.251.6 On: Fri, 22 Apr 2016 00:54:10

033109-4 Dooley et al. Rev.Sci.Instrum.83,033109(2012) Interferometer Sensing and Control table ④ Photodiode ⊕ Quadrant photodiode Interferometer RF length detector feck beam reflected beam RF alignment detector Pre-stabilized laser table 12.2m LASER Electro-optic Mode Mode cleaner Mode cleahe modulator matching reflected beam lenses Input Optics table 卤卤 FIG.3.Enhanced LIGO Input Optics optical and sensing configuration.The HAMI(horizontal access module)vacuum chamber is featured in the center,with locations of all major optics superimposed.HAM2 is shown on the right,with its components.These tables are separated by 12 m.The primary beam path, beginning at the pre-stabilized laser and going to the power recycling mirror,is shown in red as a solid line,and auxiliary beams are different colors and dotted. The MMTs,MCs,and steering mirror(SM)are suspended;all other optics are fixed to the seismically isolated table.The laser and sensing and diagnostic photodiodes are on in-air tables. IO,and accommodated up to four times the power of Ini- crystal dimensions are 4 x 4 x 40 mm and their faces are tial LIGO.Also,the design was a prototype for handling the wedged by 2.85 and anti-reflection (AR)coated.The wedge 180 W laser planned for Advanced LIGO.Because the ad- serves to separate the polarizations and prevents an etalon ef- verse thermal properties of the Initial LIGO IO(beam drift, fect,resulting in a suppression of amplitude modulation.Only birefringence,and lensing)are all attributable primarily to ab- one crystal is used in the EOM in order to reduce the number sorption of laser light by the optical elements,the primary de- of surface reflections.Three separate pairs of electrodes,each sign consideration was finding optics with lower absorption.19 with its own resonant LC circuit,are placed across the crystal Both the EOM and the FI were replaced for Enhanced LIGO. in series,producing the three required sets of RF sidebands: Only minor changes were made to the MC and MMT.A de- 24.5 MHz,33.3 MHz,and 61.2 MHz.A diagram is shown in tailed layout of the Enhanced LIGO IO is shown in Figure 3. Fig.4.Reference 23 contains further details about the modu- lator architecture. A.Electro-optic modulator design We replaced the commercially made New Focus 4003 B.Mode cleaner design resonant phase modulator of Initial LIGO with an in-house The MC is a suspended 12.2 m long triangular ring cavity EOM design and construction.Both a new crystal choice and with finesseF=1280 and free spectral range of 12.243 MHz. architectural design change allow for superior performance. The three mirror architecture was selected over the standard The Enhanced LIGO EOM design uses a crystal of ru- two mirror linear filter cavity because it acts as a polarization bidium titanyl phosphate (RTP),which has at most 1/10 the absorption coefficient at 1064 nm of the lithium nio- bate (LiNbO3)crystal from Initial LIGO.At 200 W the RTP TABLE I.Comparison of selected properties of the Initial and Enhanced should produce a thermal lens of 200 m and higher order LIGO EOM crystals,LiNbO3,and RTP,respectively.RTP was preferred for Enhanced LIGO because of its lower absorption,superior thermal properties, mode content of less than 1%,compared to the 3.3 m lens and similar electro-optic properties. the LiNbO3 produces at 10 W.The RTP has a minimal risk of damage,because it has both twice the damage threshold of Units LiNbO3 RTP LiNbOa and is subjected to a beam twice the size of that in Ini- tial LIGO.RTP and LiNbO3 have similar electro-optic coeffi- Damage threshold MW/cm2 280 >600 <5000 cients.Also,RTP's dn/dT anisotropy is 50%smaller.Table I Absorption coeff.at 1064 nm ppm/cm <500 Electro-optic coeff.(n2r33) pm/V 306 239 compares the properties of most interest of the two crystals. dnldT 10-6K 5.4 2.79 We procured the RTP crystals from Raicol and packaged dn-ldT 10-6K 37.9 9.24 them into specially designed,custom-built modulators.The Reuse of AlP Publishing content is subject to the terms at:https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 183.195251.60:Fi.22Apr2016 00:54:10

033109-4 Dooley et al. Rev. Sci. Instrum. 83, 033109 (2012) FIG. 3. Enhanced LIGO Input Optics optical and sensing configuration. The HAM1 (horizontal access module) vacuum chamber is featured in the center, with locations of all major optics superimposed. HAM2 is shown on the right, with its components. These tables are separated by 12 m. The primary beam path, beginning at the pre-stabilized laser and going to the power recycling mirror, is shown in red as a solid line, and auxiliary beams are different colors and dotted. The MMTs, MCs, and steering mirror (SM) are suspended; all other optics are fixed to the seismically isolated table. The laser and sensing and diagnostic photodiodes are on in-air tables. IO, and accommodated up to four times the power of Initial LIGO. Also, the design was a prototype for handling the 180 W laser planned for Advanced LIGO. Because the adverse thermal properties of the Initial LIGO IO (beam drift, birefringence, and lensing) are all attributable primarily to absorption of laser light by the optical elements, the primary design consideration was finding optics with lower absorption.19 Both the EOM and the FI were replaced for Enhanced LIGO. Only minor changes were made to the MC and MMT. A detailed layout of the Enhanced LIGO IO is shown in Figure 3. A. Electro-optic modulator design We replaced the commercially made New Focus 4003 resonant phase modulator of Initial LIGO with an in-house EOM design and construction. Both a new crystal choice and architectural design change allow for superior performance. The Enhanced LIGO EOM design uses a crystal of rubidium titanyl phosphate (RTP), which has at most 1/10 the absorption coefficient at 1064 nm of the lithium niobate (LiNbO3) crystal from Initial LIGO. At 200 W the RTP should produce a thermal lens of 200 m and higher order mode content of less than 1%, compared to the 3.3 m lens the LiNbO3 produces at 10 W. The RTP has a minimal risk of damage, because it has both twice the damage threshold of LiNbO3 and is subjected to a beam twice the size of that in Initial LIGO. RTP and LiNbO3 have similar electro-optic coeffi- cients. Also, RTP’s dn/dT anisotropy is 50% smaller. Table I compares the properties of most interest of the two crystals. We procured the RTP crystals from Raicol and packaged them into specially designed, custom-built modulators. The crystal dimensions are 4 × 4 × 40 mm and their faces are wedged by 2.85◦ and anti-reflection (AR) coated. The wedge serves to separate the polarizations and prevents an etalon effect, resulting in a suppression of amplitude modulation. Only one crystal is used in the EOM in order to reduce the number of surface reflections. Three separate pairs of electrodes, each with its own resonant LC circuit, are placed across the crystal in series, producing the three required sets of RF sidebands: 24.5 MHz, 33.3 MHz, and 61.2 MHz. A diagram is shown in Fig. 4. Reference 23 contains further details about the modulator architecture. B. Mode cleaner design The MC is a suspended 12.2 m long triangular ring cavity with finesse F = 1280 and free spectral range of 12.243 MHz. The three mirror architecture was selected over the standard two mirror linear filter cavity because it acts as a polarization TABLE I. Comparison of selected properties of the Initial and Enhanced LIGO EOM crystals, LiNbO3, and RTP, respectively. RTP was preferred for Enhanced LIGO because of its lower absorption, superior thermal properties, and similar electro-optic properties.19 Units LiNbO3 RTP Damage threshold MW/cm2 280 >600 Absorption coeff. at 1064 nm ppm/cm <5000 <500 Electro-optic coeff. (n3 zr33) pm/V 306 239 dny/dT 10−6/K 5.4 2.79 dnz/dT 10−6/K 37.9 9.24 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 183.195.251.6 On: Fri, 22 Apr 2016 00:54:10

033109-5 Dooley et al. Rev.Sci.Instrum.83,033109(2012) 7 mm 22 mm 2.85 deg s-polarization p-polarization electrodes loss input(● C crystal FIG.4.Electro-optic modulator design.(a)The single RTP crystal is sandwiched between three sets of electrodes that apply three different modulation fre- quencies.The wedged ends of the crystal separate the polarizations of the light.The p-polarized light is used in the interferometer.(b)A schematic for each of the three impedance matching circuits of the EOM.For the three sets of electrodes,each of which creates its own C a capacitor is placed parallel to the LC circuit formed by the crystal and a hand-wound inductor.The circuits provide 50 input impedance on resonance and are housed in a separate box from the crystal. filter and because it eliminates direct path back propagation to dition,trade-offs between optical efficiency in the forward di- the laser.24 A pick-off of the reflected beam is naturally facil- rection,optical isolation in the backwards direction,and feasi- itated for use in generating control signals.A potential down- bility of physical access of the return beam for signal use were side to the three mirror design is the introduction of astig- considered.The result is that the Enhanced LIGO FI needed a matism,but this effect is negligible due to the small opening completely new architecture and new optics compared to both angle of the MC. the Initial LIGO FI and commercially available isolators. The MC has a round-trip length of 24.5 m.The beam Figure 5 shows a photograph and a schematic of the waist has a radius of 1.63 mm and is located between the two Enhanced LIGO FI.It begins and ends with low absorption 45 flat mirrors,MC1 and MC3(see Figure 3).A concave calcite wedge polarizers (CWPs).Between the CWPs is a third mirror,MC2,18.15 m in radius of curvature,forms the thin film polarizer(TFP),a deuterated potassium dihydrogen far point of the mode cleaner's isosceles triangle shape.The phosphate (DKDP)element,a half-wave plate (HWP),and a power stored in the MC is 408 times the amount coupled in, Faraday rotator.The rotator is made of two low absorption equivalent to about 2.7 kW in Initial LIGO and at most 11 kW terbium gallium garnet(TGG)crystals sandwiching a quartz for Enhanced LIGO.The peak irradiances are 32 kW/cm2 and rotator(QR)inside a 7-disc magnet with a maximum field 132 kW/cm2 for Initial LIGO and Enhanced LIGO,respec- strength of 1.16 T.The forward propagating beam upon pass- tively. ing through the TGG,QR,TGG,and HWP elements is rotated The MC mirrors are 75 mm in diameter and 25 mm thick. by+22.5°-67.5°+22.5°+22.5°=0°.n the reverse direc-. The substrate material is fused silica and the mirror coating is tion,the rotation through HWP,TGG,QR,TGG is -22.5 made of alternating layers of silica and tantala.In order to +22.5°+67.5°+22.5°=90°.The TGG crystals are non-- reduce the absorption of light in these materials and therefore reciprocal devices while the QR and HWP are reciprocal. improve the transmission and modal quality of the beam in the MC,we removed particulate by drag wiping the surface 1.Thermal birefringence of the mirrors with methanol and optical tissues.The MC was otherwise identical to that in Initial LIGO. Thermal birefringence is addressed in the Faraday rota- tor by the use of the two TGG crystals and one quartz rota- tor rather than the typical single TGG.25 In this configuration, any thermal polarization distortions that the beam experiences C.Faraday isolator design while passing through the first TGG rotator will be mostly un- The Enhanced LIGO FI design required not only the use done upon passing through the second.The multiple elements of low absorption optics,but additional design choices to mit- in the magnet required a larger magnetic field than in Initial igate any residual thermal lensing and birefringence.In ad- LIGO.The 7-disc magnet is 130 mm in diameter and 132 mm Reuse of AlP Publishing content is subject to the terms at:https://publishing.aip.org/authors/rights-and-permissions.Download to IP:183.195.251.6 On:Fri.22 Apr 2016 00:54:10

033109-5 Dooley et al. Rev. Sci. Instrum. 83, 033109 (2012) FIG. 4. Electro-optic modulator design. (a) The single RTP crystal is sandwiched between three sets of electrodes that apply three different modulation frequencies. The wedged ends of the crystal separate the polarizations of the light. The p-polarized light is used in the interferometer. (b) A schematic for each of the three impedance matching circuits of the EOM. For the three sets of electrodes, each of which creates its own Ccrystal, a capacitor is placed parallel to the LC circuit formed by the crystal and a hand-wound inductor. The circuits provide 50 input impedance on resonance and are housed in a separate box from the crystal. filter and because it eliminates direct path back propagation to the laser.24 A pick-off of the reflected beam is naturally facilitated for use in generating control signals. A potential downside to the three mirror design is the introduction of astigmatism, but this effect is negligible due to the small opening angle of the MC. The MC has a round-trip length of 24.5 m. The beam waist has a radius of 1.63 mm and is located between the two 45◦ flat mirrors, MC1 and MC3 (see Figure 3). A concave third mirror, MC2, 18.15 m in radius of curvature, forms the far point of the mode cleaner’s isosceles triangle shape. The power stored in the MC is 408 times the amount coupled in, equivalent to about 2.7 kW in Initial LIGO and at most 11 kW for Enhanced LIGO. The peak irradiances are 32 kW/cm2 and 132 kW/cm2 for Initial LIGO and Enhanced LIGO, respectively. The MC mirrors are 75 mm in diameter and 25 mm thick. The substrate material is fused silica and the mirror coating is made of alternating layers of silica and tantala. In order to reduce the absorption of light in these materials and therefore improve the transmission and modal quality of the beam in the MC, we removed particulate by drag wiping the surface of the mirrors with methanol and optical tissues. The MC was otherwise identical to that in Initial LIGO. C. Faraday isolator design The Enhanced LIGO FI design required not only the use of low absorption optics, but additional design choices to mitigate any residual thermal lensing and birefringence. In addition, trade-offs between optical efficiency in the forward direction, optical isolation in the backwards direction, and feasibility of physical access of the return beam for signal use were considered. The result is that the Enhanced LIGO FI needed a completely new architecture and new optics compared to both the Initial LIGO FI and commercially available isolators. Figure 5 shows a photograph and a schematic of the Enhanced LIGO FI. It begins and ends with low absorption calcite wedge polarizers (CWPs). Between the CWPs is a thin film polarizer (TFP), a deuterated potassium dihydrogen phosphate (DKDP) element, a half-wave plate (HWP), and a Faraday rotator. The rotator is made of two low absorption terbium gallium garnet (TGG) crystals sandwiching a quartz rotator (QR) inside a 7-disc magnet with a maximum field strength of 1.16 T. The forward propagating beam upon passing through the TGG, QR, TGG, and HWP elements is rotated by +22.5◦ − 67.5◦ +22.5◦ +22.5◦ = 0◦. In the reverse direction, the rotation through HWP, TGG, QR, TGG is −22.5◦ +22.5◦ +67.5◦ +22.5◦ = 90◦. The TGG crystals are nonreciprocal devices while the QR and HWP are reciprocal. 1. Thermal birefringence Thermal birefringence is addressed in the Faraday rotator by the use of the two TGG crystals and one quartz rotator rather than the typical single TGG.25 In this configuration, any thermal polarization distortions that the beam experiences while passing through the first TGG rotator will be mostly undone upon passing through the second. The multiple elements in the magnet required a larger magnetic field than in Initial LIGO. The 7-disc magnet is 130 mm in diameter and 132 mm Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 183.195.251.6 On: Fri, 22 Apr 2016 00:54:10

033109-6 Dooley et al. Rev.Sci.Instrum.83,033109(2012) rejected reverse to ISC table (s-pol) B TFP DKDP QR magnet aperture in (p-pol) out 888 (p-pol) aperture CWP TGG HWP CWP 36in. rejected input (s-pol) beam dump FIG.5.Faraday isolator photograph and schematic.The FI preserves the polarization of the light in the forward-going direction and rotates it by 90 in the reverse direction.Light from the MC enters from the left and exits at the right towards the interferometer.It is ideally p-polarized,but any s-polarization contamination is promptly diverted ~10 mrad by the CWP and then reflected by the TFP and dumped.The p-polarized reflected beam from the interferometer enters from the right and is rotated to s-polarized light which is picked-off by the TFP and sent to the Interferometer Sensing and Control (ISC)table.Any imperfections in the Faraday rotation of the interferometer return beam results in p-polarized light traveling backwards along the original input path. long and placed in housing 155 mm in diameter and 161 mm reflected direction.and thermal beam drift.The CWPs have long.The TGG diameter is 20 mm. very high extinction ratios (>10)and high transmission (>99%)contributing to good optical efficiency and isola- 2.Thermal lensing tion performance.However,the angle separating the exiting Thermal lensing in the FI is addressed by including orthogonal polarizations of light is very small,on the order DKDP,a negative dn/dT material,in the beam path.Ab- of 10 mrad.This small angle requires the light to travel rela- sorption of light in the DKDP results in a de-focusing of tively large distances before we can pick off the beams needed the beam,which partially compensates for the thermal fo- for interferometer sensing and control.In addition,thermally cusing induced by absorption in the TGGs.26.27 The optical induced index of refraction gradients due to the 4.95 wedge path length (thickness)of the DKDP is chosen to slightly angle of the CWPs result in thermal drift.However,the CWPs over-compensate the positive thermal lens induced in the for the Enhanced LIGO FI have a measured low absorption of TGG crystals,anticipating other positive thermal lenses in the 0.0013 cm-1 with an expected thermal lens of 60 m at 30 W system. and drift of less than 1.3 urad/W.19 The advantages of the thin film polarizer over the calcite 3.Polarizers wedge polarizer are that it exhibits negligible thermal drift when compared with CWPs and it operates at the Brewster The polarizers used (two CWPs and one TFP)each of- angle of 55,thus diverting the return beam in an easily ac- fer advantages and disadvantages related to optical efficiency cessible way.However,the TFP has a lower transmission than in the forward-propagating direction,optical isolation in the the CWP.about 96%,and an extinction ratio of only 103. Reuse of AIP Publishing content is subject to the terms at:https://publishing.aip.org/authors/rights-and-permissions.Download to IP:183.195.251.6 On:Fri,22 Apr 2016 00:54:10

033109-6 Dooley et al. Rev. Sci. Instrum. 83, 033109 (2012) FIG. 5. Faraday isolator photograph and schematic. The FI preserves the polarization of the light in the forward-going direction and rotates it by 90◦ in the reverse direction. Light from the MC enters from the left and exits at the right towards the interferometer. It is ideally p-polarized, but any s-polarization contamination is promptly diverted ∼10 mrad by the CWP and then reflected by the TFP and dumped. The p-polarized reflected beam from the interferometer enters from the right and is rotated to s-polarized light which is picked-off by the TFP and sent to the Interferometer Sensing and Control (ISC) table. Any imperfections in the Faraday rotation of the interferometer return beam results in p-polarized light traveling backwards along the original input path. long and placed in housing 155 mm in diameter and 161 mm long. The TGG diameter is 20 mm. 2. Thermal lensing Thermal lensing in the FI is addressed by including DKDP, a negative dn/dT material, in the beam path. Absorption of light in the DKDP results in a de-focusing of the beam, which partially compensates for the thermal focusing induced by absorption in the TGGs.26, 27 The optical path length (thickness) of the DKDP is chosen to slightly over-compensate the positive thermal lens induced in the TGG crystals, anticipating other positive thermal lenses in the system. 3. Polarizers The polarizers used (two CWPs and one TFP) each offer advantages and disadvantages related to optical efficiency in the forward-propagating direction, optical isolation in the reflected direction, and thermal beam drift. The CWPs have very high extinction ratios (>105) and high transmission (> 99%) contributing to good optical efficiency and isolation performance. However, the angle separating the exiting orthogonal polarizations of light is very small, on the order of 10 mrad. This small angle requires the light to travel relatively large distances before we can pick off the beams needed for interferometer sensing and control. In addition, thermally induced index of refraction gradients due to the 4.95◦ wedge angle of the CWPs result in thermal drift. However, the CWPs for the Enhanced LIGO FI have a measured low absorption of 0.0013 cm−1 with an expected thermal lens of 60 m at 30 W and drift of less than 1.3 μrad/W.19 The advantages of the thin film polarizer over the calcite wedge polarizer are that it exhibits negligible thermal drift when compared with CWPs and it operates at the Brewster angle of 55◦, thus diverting the return beam in an easily accessible way. However, the TFP has a lower transmission than the CWP, about 96%, and an extinction ratio of only 103. Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 183.195.251.6 On: Fri, 22 Apr 2016 00:54:10

033109-7 Dooley et al. Rev.Sci.Instrum.83,033109(2012) Thus,the combination of CWPs and a TFP combines We present in this section detailed measurements of the the best of each to provide a high extinction ratio (from the IO performance during Enhanced LIGO.Specific measure- CWPs)and ease of reflected beam extraction(from the TFP). ments and results presented in figures and the text come from The downsides that remain when using both polarizers are Livingston;performance at Hanford was similar and is in- that there is still some thermal drift from the CWPs.Also the cluded in tables summarizing the results. transmission is reduced due to the TFP and to the fact that there are 16 surfaces from which light can scatter. A.Optical efficiency 4.Heat conduction The optical efficiency of the Enhanced LIGO IO from Faraday isolators operating in a vacuum environment suf- EOM to recycling mirror was 75%,a marked improvement fer from increased heating with respect to those operating in over the approximate 60%that was measured for Initial LIGO.A substantial part of the improvement came from the air.Convective cooling at the faces of the optical components is no longer an effective heat removal channel,so proper heat discovery and subsequent correction of a 6.5%loss at the sec- sinking is essential to minimize thermal lensing and depo- ond of the in-vacuum steering mirrors directing light into the larization.It has been shown that Faraday isolators carefully MC (refer to Fig.3).A 45 reflecting mirror had been used for aligned in air can experience a dramatic reduction in isola- a beam with an 8 angle of incidence.Losses attributable to tion ratio(>10-15 dB)when placed in vacuum.28 The dom- the MC and FI are described in Subsections V A 1 and V A 2. inant cause is the coupling of the photoelastic effect to the A summary of the IO power budget is found in Table II. temperature gradient induced by laser beam absorption.Also of importance is the temperature dependence of the Verdet 1.Mode cleaner losses constant-different spatial parts of the beam experience dif- ferent polarization rotations in the presence of a temperature The MC was the greatest single source of power loss in gradient.29 both Initial and Enhanced LIGO.The MC visibility, To improve heat conduction away from the Faraday rota- V= Pin -Prefl tor optical components,we designed a housing for the TGG (1) and quartz crystals that provided improved heat sinking to the Pin Faraday rotator.We wrapped the TGGs with indium foil that where Pin is the power injected into the MC and Prea the made improved contact with the housing and we cushioned power reflected,was 92%.Visibility reduction is the result the DKDP and the HWP with indium wire in their aluminum of higher order mode content of Pin and mode mismatch into holders.This has the additional effect of avoiding the devel- the MC.The visibility was constant within 0.04%up to 30 W opment of thermal stresses in the crystals,an especially im- input power at both sites,providing a positive indication that portant consideration for the very fragile DKDP. thermal aberrations in the MC and upstream were negligible. 88%of the light coupled into the MC was transmitted. D.Mode-matching telescope design 2.6%of these losses were caused by poor AR coatings on the second surfaces of the 45 MC mirrors.The measured surface The mode matching into the interferometer (at microroughness of o<0.4 nm 31 caused scatter losses of Livingston)was measured to be at best 90%in Initial [4mms<22 ppm per mirror inside the MC,or a total of LIGO.Because of the stringent requirements placed on the 2.7%losses in transmission. LIGO vacuum system to reduce phase noise through scat- Another source of MC losses is via absorption of heat tering by residual gas,standard opto-mechanical translators by particulates residing on the mirror's surface.We measured are not permitted in the vacuum;it is therefore not possible the absorption with a technique that makes use of the fre- to physically move the mode matching telescope mirrors quency shift of the thermally driven drumhead eigenfrequen- while operating the interferometer.Through a combination cies of the mirror substrate.32 The frequency shift directly of needing to move the MMTs in order to fit the new FI correlates with the MC absorption via the substrate's change on the in-vacuum optics table and additional measurements and models to determine how to improve the coupling,a new set of MMT positions was chosen for Enhanced LIGO. TABLE II.Enhanced LIGO IO power budget.Errors are +1%,except for the TFP loss whose error is +0.1%.The composite MC transmission is the Fundamental design considerations are discussed in Ref.30. percentage of power after the MC to before the MC and is the product of the MC visibility and transmission.Initial LIGO values,where known,are V.PERFORMANCE OF THE ENHANCED LIGO INPUT included in parentheses and have errors of several percent. OPTICS Livingston Hanford The most convincing figure of merit for the IO perfor- mance is that the Enhanced LIGO interferometers achieved MC visibility 92% 97% low-noise operation with 20 W input power without thermal MC transmission 88% 90% Composite MC transmission 81%(72%) 87% issues from the IO.Additionally,the IO were operated suc- FI transmission 93%(86%) 94%(86%) cessfully up to the available 30 W of power.(Instabilities with TFP loss 4.0% 2.7% other interferometer subsystems limited the Enhanced LIGO IO efficiency (PSL to RM) 75%(60%) 82% science run operation to 20 W.) Reuse of AlP Publishing content is subject to the terms at:https://publishing.aip.org/authors/rights-and-permissions. D0wmlo8 d to IP:183.195251.60m:Fi.22Apr2016 00:54:10

033109-7 Dooley et al. Rev. Sci. Instrum. 83, 033109 (2012) Thus, the combination of CWPs and a TFP combines the best of each to provide a high extinction ratio (from the CWPs) and ease of reflected beam extraction (from the TFP). The downsides that remain when using both polarizers are that there is still some thermal drift from the CWPs. Also the transmission is reduced due to the TFP and to the fact that there are 16 surfaces from which light can scatter. 4. Heat conduction Faraday isolators operating in a vacuum environment suffer from increased heating with respect to those operating in air. Convective cooling at the faces of the optical components is no longer an effective heat removal channel, so proper heat sinking is essential to minimize thermal lensing and depolarization. It has been shown that Faraday isolators carefully aligned in air can experience a dramatic reduction in isolation ratio (>10-15 dB) when placed in vacuum.28 The dominant cause is the coupling of the photoelastic effect to the temperature gradient induced by laser beam absorption. Also of importance is the temperature dependence of the Verdet constant—different spatial parts of the beam experience different polarization rotations in the presence of a temperature gradient.29 To improve heat conduction away from the Faraday rotator optical components, we designed a housing for the TGG and quartz crystals that provided improved heat sinking to the Faraday rotator. We wrapped the TGGs with indium foil that made improved contact with the housing and we cushioned the DKDP and the HWP with indium wire in their aluminum holders. This has the additional effect of avoiding the development of thermal stresses in the crystals, an especially important consideration for the very fragile DKDP. D. Mode-matching telescope design The mode matching into the interferometer (at Livingston) was measured to be at best 90% in Initial LIGO. Because of the stringent requirements placed on the LIGO vacuum system to reduce phase noise through scattering by residual gas, standard opto-mechanical translators are not permitted in the vacuum; it is therefore not possible to physically move the mode matching telescope mirrors while operating the interferometer. Through a combination of needing to move the MMTs in order to fit the new FI on the in-vacuum optics table and additional measurements and models to determine how to improve the coupling, a new set of MMT positions was chosen for Enhanced LIGO. Fundamental design considerations are discussed in Ref. 30. V. PERFORMANCE OF THE ENHANCED LIGO INPUT OPTICS The most convincing figure of merit for the IO performance is that the Enhanced LIGO interferometers achieved low-noise operation with 20 W input power without thermal issues from the IO. Additionally, the IO were operated successfully up to the available 30 W of power. (Instabilities with other interferometer subsystems limited the Enhanced LIGO science run operation to 20 W.) We present in this section detailed measurements of the IO performance during Enhanced LIGO. Specific measurements and results presented in figures and the text come from Livingston; performance at Hanford was similar and is included in tables summarizing the results. A. Optical efficiency The optical efficiency of the Enhanced LIGO IO from EOM to recycling mirror was 75%, a marked improvement over the approximate 60% that was measured for Initial LIGO. A substantial part of the improvement came from the discovery and subsequent correction of a 6.5% loss at the second of the in-vacuum steering mirrors directing light into the MC (refer to Fig. 3). A 45◦ reflecting mirror had been used for a beam with an 8◦ angle of incidence. Losses attributable to the MC and FI are described in Subsections VA1 and VA2. A summary of the IO power budget is found in Table II. 1. Mode cleaner losses The MC was the greatest single source of power loss in both Initial and Enhanced LIGO. The MC visibility, V = Pin − Prefl Pin , (1) where Pin is the power injected into the MC and Prefl the power reflected, was 92%. Visibility reduction is the result of higher order mode content of Pin and mode mismatch into the MC. The visibility was constant within 0.04% up to 30 W input power at both sites, providing a positive indication that thermal aberrations in the MC and upstream were negligible. 88% of the light coupled into the MC was transmitted. 2.6% of these losses were caused by poor AR coatings on the second surfaces of the 45◦ MC mirrors. The measured surface microroughness of σrms < 0.4 nm 31 caused scatter losses of [4πσrms/λ] 2 < 22 ppm per mirror inside the MC, or a total of 2.7% losses in transmission. Another source of MC losses is via absorption of heat by particulates residing on the mirror’s surface. We measured the absorption with a technique that makes use of the frequency shift of the thermally driven drumhead eigenfrequencies of the mirror substrate.32 The frequency shift directly correlates with the MC absorption via the substrate’s change TABLE II. Enhanced LIGO IO power budget. Errors are ±1%, except for the TFP loss whose error is ±0.1%. The composite MC transmission is the percentage of power after the MC to before the MC and is the product of the MC visibility and transmission. Initial LIGO values, where known, are included in parentheses and have errors of several percent. Livingston Hanford MC visibility 92% 97% MC transmission 88% 90% Composite MC transmission 81% (72%) 87% FI transmission 93% (86%) 94% (86%) TFP loss 4.0% 2.7% IO efficiency (PSL to RM) 75% (60%) 82% Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 183.195.251.6 On: Fri, 22 Apr 2016 00:54:10

033109-8 Dooley et al. Rev.Sci.Instrum.83,033109(2012) 0.6 0.4 0 f=28164Hz(MC1) -0.4 f-28209Hz(MC2) 0.6 f-28237Hz(MC3) 0 20 25 Time(h) 0.5 0.5 5 10 15 20 25 5 10 15 20 25 Time (h) FIG.6.Data from the MC absorption measurement post drag-wiping.Power into the MC was cycled between0.9 W and 5.1 Wat 3-h intervals (bottom frame) and the change in frequency of the drumhead mode of each mirror was recorded (top frame).The ambient temperature(middle frame)was also recorded in order to correct for its effects. in Young's modulus with temperature,dy/dT.A finite ele- 2.Faraday isolator losses ment model(COMSOL Ref.33)was used to compute the ex- pected frequency shift from a temperature change of the sub- The FI was the second greatest source of power loss with strate resulting from the mirror coating absorption.The mea- its transmission of 93%.This was an improvement over the sured eigenfrequencies for each mirror at room temperature 86%transmission of the Initial LIGO FI.The most lossy ele- ment in the FI is the thin film polarizer,accounting for 4%of are 28164 Hz,28209 Hz,and 28237 Hz,respectively. We cycled the power into the MC between 0.9 W and total losses.The integrated losses from AR coatings and ab- 5.1 W at 3-h intervals,allowing enough time for a thermal sorption in the TGGs,CWPs,HWP,and DKDP account for characteristic time constant to be reached.At the same time, the remaining 3%of missing power. we recorded the frequencies of the high Q drumhead mode peaks as found in the mode cleaner frequency error signal, heterodyned down by 28 kHz(see Figure 6).Correcting for B.Faraday isolation ratio ambient temperature fluctuations,we find a frequency shift The isolation ratio is defined as the ratio of power in- of 0.043,0.043,and 0.072 Hz/W.As a result of drag-wiping cident on the FI in the reverse direction (the light reflected the mirrors,the absorption decreased for all but one mirror,as from the interferometer)to the power transmitted in the re- shown for both Hanford and Livingston in Table III. verse direction and is often quoted in decibels:isolation ratio =10log10(Pin-reverse/Pout-reverse).We measured the isolation ra- tio of the FI as a function of input power both in air prior to TABLE III.Absorption values for the Livingston and Hanford mode installation and in situ during Enhanced LIGO operation. cleaner mirrors before (in parentheses)and after drag wiping.The precision To measure the in-vacuum isolation ratio,we misaligned is土10%. the interferometer arms so that the input beam would be promptly reflected off of the 97%reflective recycling mirror. Mirror Livingston Hanford This also has the consequence that the FI is subjected to twice MCI 2.1ppm(18.7Ppm) 5.8(6.1Ppm) the input power.Our isolation monitor was a pick-off of the MC2 2.0 ppm (5.5 ppm) 7.6(23.9Ppm) backwards transmitted beam taken immediately after trans- MC3 3.4 ppm (12.8 ppm) 15.6(12.5ppm) mission through the FI that we sent out of a vacuum chamber viewport.Refer to the "isolation check beam"in Fig.3.The Reuse of AlP Publishing content is subject to the terms at:https://publishing.aip.org/authors/rights-and-permissions.Download to IP:183.195.251.6 On:Fri.22 Apr 2016 00:54:10

033109-8 Dooley et al. Rev. Sci. Instrum. 83, 033109 (2012) 0 5 10 15 20 25 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 Mode Freq Shift (Hz) Time (h) 0 5 10 15 20 25 0.5 0 0.5 BSC1&3 dT (F) 0 5 10 15 20 25 0 2 4 6 PMC ( W) Time (h) f=28164 Hz (MC1) f=28209 Hz (MC2) f=28237 Hz (MC3) FIG. 6. Data from the MC absorption measurement post drag-wiping. Power into the MC was cycled between 0.9 W and 5.1 W at 3-h intervals (bottom frame) and the change in frequency of the drumhead mode of each mirror was recorded (top frame). The ambient temperature (middle frame) was also recorded in order to correct for its effects. in Young’s modulus with temperature, dY/dT. A finite element model (COMSOL Ref. 33) was used to compute the expected frequency shift from a temperature change of the substrate resulting from the mirror coating absorption. The measured eigenfrequencies for each mirror at room temperature are 28164 Hz, 28209 Hz, and 28237 Hz, respectively. We cycled the power into the MC between 0.9 W and 5.1 W at 3-h intervals, allowing enough time for a thermal characteristic time constant to be reached. At the same time, we recorded the frequencies of the high Q drumhead mode peaks as found in the mode cleaner frequency error signal, heterodyned down by 28 kHz (see Figure 6). Correcting for ambient temperature fluctuations, we find a frequency shift of 0.043, 0.043, and 0.072 Hz/W. As a result of drag-wiping the mirrors, the absorption decreased for all but one mirror, as shown for both Hanford and Livingston in Table III. TABLE III. Absorption values for the Livingston and Hanford mode cleaner mirrors before (in parentheses) and after drag wiping. The precision is ±10%. Mirror Livingston Hanford MC1 2.1 ppm (18.7 ppm) 5.8 (6.1 ppm) MC2 2.0 ppm (5.5 ppm) 7.6 (23.9 ppm) MC3 3.4 ppm (12.8 ppm) 15.6 (12.5 ppm) 2. Faraday isolator losses The FI was the second greatest source of power loss with its transmission of 93%. This was an improvement over the 86% transmission of the Initial LIGO FI. The most lossy element in the FI is the thin film polarizer, accounting for 4% of total losses. The integrated losses from AR coatings and absorption in the TGGs, CWPs, HWP, and DKDP account for the remaining 3% of missing power. B. Faraday isolation ratio The isolation ratio is defined as the ratio of power incident on the FI in the reverse direction (the light reflected from the interferometer) to the power transmitted in the reverse direction and is often quoted in decibels: isolation ratio = 10log10(Pin-reverse/Pout-reverse). We measured the isolation ratio of the FI as a function of input power both in air prior to installation and in situ during Enhanced LIGO operation. To measure the in-vacuum isolation ratio, we misaligned the interferometer arms so that the input beam would be promptly reflected off of the 97% reflective recycling mirror. This also has the consequence that the FI is subjected to twice the input power. Our isolation monitor was a pick-off of the backwards transmitted beam taken immediately after transmission through the FI that we sent out of a vacuum chamber viewport. Refer to the “isolation check beam” in Fig. 3. The Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 183.195.251.6 On: Fri, 22 Apr 2016 00:54:10

033109-9 Dooley et al. Rev.Sci.Instrum.83,033109(2012) 90 300 3 20 10 ×in-air data O in-vacuum data -Fl pitch 10 15 20 25 30 35 40 45 50 -Fl yaw power in Faraday [W) MC Ditch (x10) -MC yaw (x10) input power FIG.7.Faraday isolator isolation ratio as measured in air prior to installation and in sin in vacuum.The isolation worsens by a factor of 6 upon placement 5000 5500 6000 6500 7000 7500 8000 time [secl of the FI in vacuum.The linear fits to the data show a constant in-air isolation 200 ratio and an in-vacuum isolation ratio degradation of 0.02 dB/W. ◇FI pitch ◆Fl yaw 150 MC pitch o MC yaw in air measurement was done similarly,except in an optics lab 100 0 with a reflecting mirror placed directly after the FI. Figure 7 shows our isolation ratio data.Most notably,we observe an isolation decrease of a factor of six upon plac- ing the FI in vacuum,a result consistent with that reported by Ref.28.In air the isolation ratio is a constant 34.46+0.04 dB from low power up to 47 W,and in vacuum the isolation ratio 10 20 40 50 60 is 26.5 dB at low power.The underlying cause is the absence of cooling by air convection.If we attribute the loss to the FIG.8.Mode cleaner and Faraday isolator thermal drift data.(a)Angular TGGs,then based on the change in TGG polarization rota- motion of the beam at the MC waist and FI rotator as the input power is tion angle necessary to produce the measured isolation drop stepped.The beam is double-passed through the Faraday isolator,so it expe- riences twice the input power.(b)Average beam angle per power level in the of 8 dB and the temperature dependence of the TGG's Verdet MC and FI.Linear fits to the data are also shown.The slopes for MC yaw, constant,we can put an upper limit of 11 K on the crystal tem- MC pitch,FI yaw,and FI pitch,respectively,are 0.0047,0.44.1.8,and 3.2 perature rise from air to vacuum.Furthermore,a degradation urad/W. of 0.02 dB/W is measured in vacuum. upper limit on the drift experienced by the reflected beam is C.Thermal steering about 100 urad.This is a 30-fold reduction with respect to the initial LIGO FI and represents a fifth of the beam's divergence We measured the in situ thermal angular drift of both the beam transmitted through the MC and of the reflected beam angle,6div =490 urad. from the FI with up to 25 W input power.Just as for the iso- lation ratio measurement,we misaligned the interferometer arms so that the input beam would be promptly reflected off of D.Thermal lensing the recycling mirror.The Faraday rotator was thus subjected We measured the profiles of both the beam transmitted to up to 50 W total and the MC to 25 W. through the mode cleaner and the reflected beam picked off Pitch and yaw motion of the MC transmitted and inter- by the FI at low (~1 W)and high (~25 W)input powers to ferometer reflected beams were recorded using the quadrant assess the degree of thermal lensing induced in the MC and photodiode (QPD)on the IO table and the RF alignment de- FI.Again,we misaligned the interferometer arms so that the tectors on the Interferometer Sensing and Control table(see input beam would be promptly reflected off the recycling mir- Fig.3).There are no lenses between the MC waist and its ror.We picked off a fraction of the reflected beam on the Inter- measurement QPD,so only the path length between the two ferometer Sensing and Control table and of the mode cleaner were needed to calibrate in radians the pitch and yaw sig- transmitted beam on the IO table (refer to Fig.3).placed nals on the OPD.The interferometer reflected beam,however. lenses in each of their paths,and measured the beam diam- passes through several lenses.Thus,ray transfer matrices and eters at several locations on either side of the waists created the two alignment detectors were necessary to determine the by the lenses.A change in the beam waist size or position as Faraday drift calibration. a function of laser power indicates the presence of a thermal Figure 8 shows the calibrated beam steering data.The an- lens. gle of the beam out of the MC does not change measurably as As seen in Figs.9 and 10,the waists of the two sets of a function of input power in yaw(4.7 nrad/W)and changes by data are collocated:no thermal lens is measured.For the FI, only 440 nrad/W in pitch.For the FL we record a beam drift the divergence of the low and high power beams differs,in- originating at the center of the Faraday rotator of 1.8 urad/W dicating that the beam quality degrades with power.The M2 in yaw and 3.2 urad/W in pitch.Therefore,when ramping the factor at 1 W is 1.04 indicating the beam is nearly perfectly a input power up to 30 W during a full interferometer lock,the TEMoo mode.At 25 W,M2 increases to 1.19,corresponding Reuse of AlP Publishing content is subject to the terms at:https://publishing.aip.org/authors/rights-and-permissions.Download to IP:183.195.251.6 On:Fri.22 Apr 2016 00:54:10

033109-9 Dooley et al. Rev. Sci. Instrum. 83, 033109 (2012) 0 5 10 15 20 25 30 35 40 45 50 0 10 20 30 40 power in Faraday [W] Faraday isolation ratio [dB] in−air data in−vacuum data FIG. 7. Faraday isolator isolation ratio as measured in air prior to installation and in situ in vacuum. The isolation worsens by a factor of 6 upon placement of the FI in vacuum. The linear fits to the data show a constant in-air isolation ratio and an in-vacuum isolation ratio degradation of 0.02 dB/W. in air measurement was done similarly, except in an optics lab with a reflecting mirror placed directly after the FI. Figure 7 shows our isolation ratio data. Most notably, we observe an isolation decrease of a factor of six upon placing the FI in vacuum, a result consistent with that reported by Ref. 28. In air the isolation ratio is a constant 34.46 ± 0.04 dB from low power up to 47 W, and in vacuum the isolation ratio is 26.5 dB at low power. The underlying cause is the absence of cooling by air convection. If we attribute the loss to the TGGs, then based on the change in TGG polarization rotation angle necessary to produce the measured isolation drop of 8 dB and the temperature dependence of the TGG’s Verdet constant, we can put an upper limit of 11 K on the crystal temperature rise from air to vacuum. Furthermore, a degradation of 0.02 dB/W is measured in vacuum. C. Thermal steering We measured the in situ thermal angular drift of both the beam transmitted through the MC and of the reflected beam from the FI with up to 25 W input power. Just as for the isolation ratio measurement, we misaligned the interferometer arms so that the input beam would be promptly reflected off of the recycling mirror. The Faraday rotator was thus subjected to up to 50 W total and the MC to 25 W. Pitch and yaw motion of the MC transmitted and interferometer reflected beams were recorded using the quadrant photodiode (QPD) on the IO table and the RF alignment detectors on the Interferometer Sensing and Control table (see Fig. 3). There are no lenses between the MC waist and its measurement QPD, so only the path length between the two were needed to calibrate in radians the pitch and yaw signals on the QPD. The interferometer reflected beam, however, passes through several lenses. Thus, ray transfer matrices and the two alignment detectors were necessary to determine the Faraday drift calibration. Figure 8 shows the calibrated beam steering data. The angle of the beam out of the MC does not change measurably as a function of input power in yaw (4.7 nrad/W) and changes by only 440 nrad/W in pitch. For the FI, we record a beam drift originating at the center of the Faraday rotator of 1.8 μrad/W in yaw and 3.2 μrad/W in pitch. Therefore, when ramping the input power up to 30 W during a full interferometer lock, the 5000 5500 6000 6500 7000 7500 8000 −300 −200 −100 0 100 200 300 time [sec] angle [urad] 5000 5500 6000 6500 7000 7500 8000 0 5 10 15 20 25 30 input power [ W] FI pitch FI yaw MC pitch (x10) MC yaw (x10) input power 0 10 20 30 40 50 60 −50 0 50 100 150 200 power in MC and FI [W] angle [urad] FI pitch FI yaw MC pitch MC yaw FIG. 8. Mode cleaner and Faraday isolator thermal drift data. (a) Angular motion of the beam at the MC waist and FI rotator as the input power is stepped. The beam is double-passed through the Faraday isolator, so it experiences twice the input power. (b) Average beam angle per power level in the MC and FI. Linear fits to the data are also shown. The slopes for MC yaw, MC pitch, FI yaw, and FI pitch, respectively, are 0.0047, 0.44, 1.8, and 3.2 μrad/W. upper limit on the drift experienced by the reflected beam is about 100 μrad. This is a 30-fold reduction with respect to the initial LIGO FI and represents a fifth of the beam’s divergence angle, θ div = 490 μrad. D. Thermal lensing We measured the profiles of both the beam transmitted through the mode cleaner and the reflected beam picked off by the FI at low (∼1 W) and high (∼25 W) input powers to assess the degree of thermal lensing induced in the MC and FI. Again, we misaligned the interferometer arms so that the input beam would be promptly reflected off the recycling mirror. We picked off a fraction of the reflected beam on the Interferometer Sensing and Control table and of the mode cleaner transmitted beam on the IO table (refer to Fig. 3), placed lenses in each of their paths, and measured the beam diameters at several locations on either side of the waists created by the lenses. A change in the beam waist size or position as a function of laser power indicates the presence of a thermal lens. As seen in Figs. 9 and 10, the waists of the two sets of data are collocated: no thermal lens is measured. For the FI, the divergence of the low and high power beams differs, indicating that the beam quality degrades with power. The M2 factor at 1 W is 1.04 indicating the beam is nearly perfectly a TEM00 mode. At 25 W, M2 increases to 1.19, corresponding Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 183.195.251.6 On: Fri, 22 Apr 2016 00:54:10

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上海交通大学：《探索物质微观世界》课程教学资源（补充材料）引力波_Thermal effects in the Input Optics of the Enhanced Laser Interferometer Gravitational Wave Observatory interferometers