A simulation was investigated to better understand the impacts and effects of the additional technical noises on weak-light phase-locking for space laser interferometer. The result showed that the locking precision was limited by the phase readout noise when the laser frequency noise and clock jitter noise were removed, and this result was then confirmed by a benchtop experimental test. The required space laser interferometer noise floor was recovered from the simulation which proved the validity of the simulation program. © Published under licence by IOP Publishing Ltd.National Natural Science Foundation of China/61575209Chinese Academy of Sciences/XDB2303020

Dong, Y.H.

Jin, G.

Li, Y.Q.

Liu, H.S.

Luo, Z.R.

Journal of Physics Conference Series

Abstract
A simulation was investigated to better understand the impacts and effects of the additional technical noises on weak-light phase-locking for space laser interferometer. The result showed that the locking precision was limited by the phase readout noise when the laser frequency noise and clock jitter noise were removed, and this result was then confirmed by a benchtop experimental test. The required space laser interferometer noise floor was recovered from the simulation which proved the validity of the simulation program

Li,Y Q

Dong,Y H

Liu,H S

Luo,Z R

Jin,G

Institute Of Mechanics,Chinese Academy of Sciences

A simulation of weak-light phase-locking for space laser interferometer

Li, Y.

Dong, Y.

Liu, H.

Luo, Z.

MPG.PuRe

1Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Published under licence by IOP Publishing Ltd123456789011th International LISA Symposium  IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 840 (2017) 012049  doi :10.1088/1742-6596/840/1/012049      A simulation of weak-light phase-locking for space laser interferometer Y Q Li1, Y H Dong1,2, H S Liu1,2, Z R Luo4,5 and G Jin1,3 1 Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China; 2 University of Chinese Academy of Sciences, Beijing 100190, China; 3 School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China; 4 Leibniz Universität Hannover, Hannover 30167, Germany; 5 Max-Planck-Institude for Gravitational Physics, Hannover 30167, Germany * Corresponding author: gajin@imech.ac.cn  Abstract. A simulation was investigated to better understand the impacts and effects of the additional technical noises on weak-light phase-locking for space laser interferometer. The result showed that the locking precision was limited by the phase readout noise when the laser frequency noise and clock jitter noise were removed, and this result was then confirmed by a benchtop experimental test. The required space laser interferometer noise floor was recovered from the simulation which proved the validity of the simulation program.  1.  Motivation The space-borne gravitational wave (G.W.) antennas were designed to use space laser interferometers to detect the G.W. signal at the frequencies from 0.1 mHz to 1 Hz. The LISA (Laser Interferometer Space Antenna) mission, due to the long distance transmission and the finite aperture of the telescope, only very few fraction of the transmitted light (≈100 pW) can be received by the remote satellite [1]. A technique called‘weak-light phase-locking’ (WLPL) is adopted by the remote satellite and makes it a ‘phase-transponder’ with the local satellite [2]. In this paper, a simulation was performed to better understand the impacts and effects of the additional technical noises on WLPL for LISA. 2.  Investigation of noises To simulate WLPL for LISA in a systematic manner, the noise sources categorized have to be taken into account as the interferometric measurement system (IMS) noise and the acceleration noise. The IMS noise mainly includes shot noise, beam pointing noise, laser frequency noise, clock jitter noise and so on [3-7]. Since the simulation will be run in time series, the above LISA noises given by smooth function in ASD (Amplitude Spectral Density) should be converted into random noise in time domain. An algorism based on Fourier transform was invented to convert the Fig.1 Diagram of the LISA noise 2123456789011th International LISA Symposium  IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 840 (2017) 012049  doi :10.1088/1742-6596/840/1/012049      noise function into real time data with random characteristics.   3.  Condition and simulation  A simulation program using Matlab Simulink is established and the schematic diagram of the program is shown in Fig. 2. The transmitting light received by the remote satellite is represented by ‘add1’. A single frequency ‘G.W. signal’ (100 pm/√Hz at 30 mHz) is also added as an indicator to analyze the impacts of various noises. The slave laser in the remote satellite is given as ‘add2’. The slave laser and the received light “interfere” at ‘add3’ and the phase difference is sent to and read out by a phasemeter which is represented by ‘add4’. Then, the PID (Proportional-Integral-Derivative) controller is introduced to feedback control the slave laser to phase-locking the transmitting light.  Considering all of the noises in Fig.1, supposing the frequency noise and the clock jitter noise have been well suppressed by arm-locking, TDI (Time Delay Interferometer) and other post process technics. It could be seen from the Fig.3 that the out-of-loop signal is mainly limited by the readout noise and the in-loop signal is well below 10-12 m/√Hz. Under this situation, the ‘G.W. signal’ emerges out. An experimental demonstration is also performed in order to test the control scheme. The schematic diagram and the result of the experimental test are given in Fig. 4. Here, the beat frequency is 1 MHz, and the power of the slave laser and the master laser are about 1 mW. Limited by the readout noise and optical pathlength noise, the phase lock loop is working at nanometer level. It could be seen that the phase difference between the slave laser and the master laser is suppressed from 10-7 to 3×10-10 m/ √Hz at 1 mHz after the phase locking loop is turned on. This directly demonstrates the functionality of our control scheme.  4.  Results The result showed that the locking precision was limited by the phase readout noise when the laser frequency noise and clock jitter noise were removed, and this result was also confirmed by a benchtop experimental test. The required LISA noise floor was recovered from the simulation which proved the validity of the simulation program.  Fig.4 Schematic diagram (a) and result of the experimental test (b) Fig.3 ASD noise performance of the simulationFig.2 The Simulink model of WLPL3123456789011th International LISA Symposium  IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 840 (2017) 012049  doi :10.1088/1742-6596/840/1/012049      Acknowledgements This work was supported by the National Natural Science Foundation of China, Grant No. 61575209, and the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant No. XDB23030200.  References [1] Diekmann C et al 2009 J. Phys. Conf. Series 154 012020 [2] Esteban J J et al. 2011 Opt. Express 19 15937–15946 [3] Jennrich O 2009 Class. Quantum Grav. 26 153001 [4] Yu Y, Mitryk S and Mueller G 2014 Phys. Rev. D 90 062005 [5] Otto M, Heinzel G and Danzmann K 2012 Class. Quantum Grav. 29 205003 [6] Danzmann K et al 2011 Assessment Study Report ESA/SRE 54–72 [7] Heinzel G et al 2011 Class. Quantum Grav. 28 094008 

English

Institutionelles Repositorium der Leibniz Universität Hannover

This content has been downloaded from IOPscience. Please scroll down to see the full text.Download details:IP Address: 194.95.157.241This content was downloaded on 13/07/2017 at 10:27Please note that terms and conditions apply.A simulation of weak-light phase-locking for space laser interferometerView the table of contents for this issue, or go to the journal homepage for more2017 J. Phys.: Conf. Ser. 840 012049(http://iopscience.iop.org/1742-6596/840/1/012049)Home Search Collections Journals About Contact us My IOPscienceYou may also be interested in:Phase-Locking of the Internally Loss-Modulated Ring LaserToyokatsu Miyashita and Jun-ichi IkenoueWeak-light phase locking for LISAPaul W McNamaraTheory of laser array phase locking by Fourier couplingD V  Vysotskii, A P  Napartovich and V N  TroshchievaLasers: reminiscing and speculatingMichael BassMultiple-Beam Lateral-Shear InterferometerS. Mallick and M. RousseauThe `Equivalent Interferometer' in holographyG L RogersHolographic interferometer using spherical mirrorsA F Belozjerov and J E KouzilinA Modified Angle Measuring InterferometerKoshi TakashimaHigh-Fidelity, Weak-Light Polarization Gate Using Room-Temperature Atomic VaporL Deng, E W Hagley, Runbing Li et al.1Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Published under licence by IOP Publishing Ltd123456789011th International LISA Symposium  IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 840 (2017) 012049  doi :10.1088/1742-6596/840/1/012049      A simulation of weak-light phase-locking for space laser interferometer Y Q Li1, Y H Dong1,2, H S Liu1,2, Z R Luo4,5 and G Jin1,3 1 Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China; 2 University of Chinese Academy of Sciences, Beijing 100190, China; 3 School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China; 4 Leibniz Universität Hannover, Hannover 30167, Germany; 5 Max-Planck-Institude for Gravitational Physics, Hannover 30167, Germany * Corresponding author: gajin@imech.ac.cn  Abstract. A simulation was investigated to better understand the impacts and effects of the additional technical noises on weak-light phase-locking for space laser interferometer. The result showed that the locking precision was limited by the phase readout noise when the laser frequency noise and clock jitter noise were removed, and this result was then confirmed by a benchtop experimental test. The required space laser interferometer noise floor was recovered from the simulation which proved the validity of the simulation program.  1.  Motivation The space-borne gravitational wave (G.W.) antennas were designed to use space laser interferometers to detect the G.W. signal at the frequencies from 0.1 mHz to 1 Hz. The LISA (Laser Interferometer Space Antenna) mission, due to the long distance transmission and the finite aperture of the telescope, only very few fraction of the transmitted light (≈100 pW) can be received by the remote satellite [1]. A technique called‘weak-light phase-locking’ (WLPL) is adopted by the remote satellite and makes it a ‘phase-transponder’ with the local satellite [2]. In this paper, a simulation was performed to better understand the impacts and effects of the additional technical noises on WLPL for LISA. 2.  Investigation of noises To simulate WLPL for LISA in a systematic manner, the noise sources categorized have to be taken into account as the interferometric measurement system (IMS) noise and the acceleration noise. The IMS noise mainly includes shot noise, beam pointing noise, laser frequency noise, clock jitter noise and so on [3-7]. Since the simulation will be run in time series, the above LISA noises given by smooth function in ASD (Amplitude Spectral Density) should be converted into random noise in time domain. An algorism based on Fourier transform was invented to convert the Fig.1 Diagram of the LISA noise 2123456789011th International LISA Symposium  IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 840 (2017) 012049  doi :10.1088/1742-6596/840/1/012049      noise function into real time data with random characteristics.   3.  Condition and simulation  A simulation program using Matlab Simulink is established and the schematic diagram of the program is shown in Fig. 2. The transmitting light received by the remote satellite is represented by ‘add1’. A single frequency ‘G.W. signal’ (100 pm/√Hz at 30 mHz) is also added as an indicator to analyze the impacts of various noises. The slave laser in the remote satellite is given as ‘add2’. The slave laser and the received light “interfere” at ‘add3’ and the phase difference is sent to and read out by a phasemeter which is represented by ‘add4’. Then, the PID (Proportional-Integral-Derivative) controller is introduced to feedback control the slave laser to phase-locking the transmitting light.  Considering all of the noises in Fig.1, supposing the frequency noise and the clock jitter noise have been well suppressed by arm-locking, TDI (Time Delay Interferometer) and other post process technics. It could be seen from the Fig.3 that the out-of-loop signal is mainly limited by the readout noise and the in-loop signal is well below 10-12 m/√Hz. Under this situation, the ‘G.W. signal’ emerges out. An experimental demonstration is also performed in order to test the control scheme. The schematic diagram and the result of the experimental test are given in Fig. 4. Here, the beat frequency is 1 MHz, and the power of the slave laser and the master laser are about 1 mW. Limited by the readout noise and optical pathlength noise, the phase lock loop is working at nanometer level. It could be seen that the phase difference between the slave laser and the master laser is suppressed from 10-7 to 3×10-10 m/ √Hz at 1 mHz after the phase locking loop is turned on. This directly demonstrates the functionality of our control scheme.  4.  Results The result showed that the locking precision was limited by the phase readout noise when the laser frequency noise and clock jitter noise were removed, and this result was also confirmed by a benchtop experimental test. The required LISA noise floor was recovered from the simulation which proved the validity of the simulation program.  Fig.4 Schematic diagram (a) and result of the experimental test (b) Fig.3 ASD noise performance of the simulationFig.2 The Simulink model of WLPL3123456789011th International LISA Symposium  IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 840 (2017) 012049  doi :10.1088/1742-6596/840/1/012049      Acknowledgements This work was supported by the National Natural Science Foundation of China, Grant No. 61575209, and the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant No. XDB23030200.  References [1] Diekmann C et al 2009 J. Phys. Conf. Series 154 012020 [2] Esteban J J et al. 2011 Opt. Express 19 15937–15946 [3] Jennrich O 2009 Class. Quantum Grav. 26 153001 [4] Yu Y, Mitryk S and Mueller G 2014 Phys. Rev. D 90 062005 [5] Otto M, Heinzel G and Danzmann K 2012 Class. Quantum Grav. 29 205003 [6] Danzmann K et al 2011 Assessment Study Report ESA/SRE 54–72 [7] Heinzel G et al 2011 Class. Quantum Grav. 28 094008 

A simulation of weak-light phase-locking for space laser interferometer

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