ADVANCED OPTICAL TECHNIQUES FOR LASER-INTERFEROMETRIC GRAVITATIONAL-WAVE DETECTORS

By I. KUERR

CONTENTS DUAL RECYCLING INTRODUCTION TO RECYCLING POWER RECYCLING SIGNAL RECYCLING AND RSE DETECTION OF THE SIGNAL BY MODULATION METHODS COMMON TECHNIQUES FOR MODELLING INTERFEROMETERS MODULATED LIGHT AND SIDEBANDS PHASE MODULATION AMPLITUDE MODULATION FREQUENCY MODULATION DESCRIPTION OF MIRRORS AND BEAMSPLITTERS TREATMENT OF ‘LENGTHS’ AND ‘TUNINGS’ INTERNAL, EXTERNAL AND SCHNUPP MODULATION INTERNAL MODULATION IN THE SIDEBAND PICTURE EXTERNAL MODULATION SCHNUPP MODULATION SIMULATION TOOLS THE INTERFEROMETER MODEL STATIC RESPONSE FREQUENCY RESPONSE: AN INTRODUCTION SIMULATING THE E?ECTS OF GRAVITATIONAL WAVES COMPUTATION OF THE FREQUENCY RESPONSE DEMODULATION PHASE ? AND RECONSTRUCTION OF THE SIGNAL TWO MIXERS ONE MIXER LOSS IN SNR BY USING ONLY ONE MIXER SIGNAL RECYCLING: FREQUENCY RESPONSE ‘BROADBAND’ AND ‘DETUNED’ TRANSFER FUNCTION AND SIGNAL-TO-NOISE RATIO SIGNAL SIDEBAND TRANSFER FUNCTION SCHNUPP MODULATION SIDEBAND THROUGHPUT CONTROL OF SIGNAL RECYCLING PR CAVITY LOOP ERROR SIGNAL ACTUATOR KEEPING THE PR CAVITY RESONANT IN THE SIMULATION MICHELSON CONTROL ERROR SIGNAL WITHOUT SIGNAL RECYCLING ERROR SIGNAL WITH DUAL RECYCLING ACTUATOR AND LOOP ?LTER SR MIRROR CONTROL POWER RECYCLING GAIN IN DUAL RECYCLING LOCK ACQUISITION OTHER STABLE STATES OPERATION OF DUAL RECYCLING INITIAL ALIGNMENT AND ADJUSTMENTS CON?RMATION OF DUAL RECYCLING NOISE BEHAVIOUR OF THE DUAL RECYCLED PROTOTYPE CONTRAST IMPROVEMENT AND ‘MODE HEALING’ E?ECT 1 10 DETUNED SIGNAL RECYCLING 1 10 1 FREQUENCY RESPONSE OF DETUNED SIGNAL RECYCLING 1 10 1 1 SIGNAL TRANSFER FUNCTION 1 10 1 2 SCHNUPP SIDEBAND THROUGHPUT 1 10 1 3 TRANSFER FUNCTION OF THE INTERFEROMETER 1 10 2 CONTROL OF DETUNED DUAL RECYCLING 1 10 3 EXPERIMENTAL DEMONSTRATION OF DETUNED DUAL RECYCLING 1 11 MUST PR AND SR CAVITY HAVE DI?ERENT LENGTHS? AUTOALIGNMENT INTRODUCTION MISALIGNMENTS IN THE MODE PICTURE DETECTION OF MISALIGNMENTS FABRY-PEROT CAVITY MICHELSON INTERFEROMETER MACH-ZEHNDER ALIGNMENT MISALIGNMENTS CAUSED BY INDIVIDUAL COMPONENTS PR CAVITY COMPUTATION OF LENS SYSTEMS EXPERIMENTAL SETUP QUADRANT PHOTODETECTORS AUXILIARY BEAM-STEERING LOOPS AUTOMATIC ALIGNMENT LOOPS ACTUATORS LOOP ?LTERS AUXILIARY SIGNALS FOR NORMALIZATION ALIGNMENT LOOPS FOR MICHELSON AND PR CAVITY SPOT POSITIONS ON END MIRRORS LOCK ACQUISITION AND ERROR CHECKING NOISE SPECTRA DARK FRINGE CONTRAST 2 10 ALIGNMENT ERROR SIGNALS FOR GEO 600 2 10 1 RAY-TRACING PROGRAM 2 10 2 THE GEO 600 POWER RECYCLING CAVITY 2 10 3 THE GEO 600 MODECLEANER CAVITIES CHAPTER WILL BE USED THROUGHOUT TO IDENTIFY DIRECTIONS AS SEEN FROM THE BEAMSPLITTER ‘NORTH’ AND ‘EAST’ REPRESENT THE LONG ARMS; THE LIGHT FROM THE LASER IS INJECTED FROM THE ‘WEST’, AND ‘SOUTH’ REPRESENTS THE DETECTION PORT IN THE DARK FRINGE CONDITION, ALL LIGHT INCIDENT ON THE BEAMSPLITTER WILL BE RE?ECTED BACK TO WHERE IT CAME FROM, AS SHOWN IN FIGURE 1 1 THIS IS TRUE FOR LIGHT COMING FROM EITHER THE WEST OR THE SOUTH DIRECTIONS IN FIGURE 1 1 THIS MODEL IS SIMPLI?ED IN THAT IT NEGLECTS VARIOUS OPERATIONAL FACTORS, FOR EXAMPLE: THE INEVITABLE OPTICAL LOSSES IN THE ARMS WILL LIMIT THE AMOUNT OF RE?ECTED LIGHT TO A FRACTION LESS THAN UNITY ANY ASYMMETRY BETWEEN THE ARMS AND IN PARTICULAR, ANY DEVIATION OF THE END MIRRORS FROM THEIR IDEAL SHAPE, WILL LIMIT THE CONTRAST OF THE MICHELSON IN OTHER WORDS, A CERTAIN FRACTION OF THE LIGHT FROM EACH ARM WILL ?ND NO COMPONENT FROM