Determination of PDH Modulation Frequency

This article by Daisuke TATSUMI from the National Astronomical Observatory of Japan discusses the determination of PDH modulation frequencies in the context of frequency domain interferometer simulation. The content focuses on the intricacies of selecting the appropriate modulation frequency for accurate simulation results. It delves into the significance of this parameter and its impact on the overall simulation process. The author's insights shed light on the importance of understanding and implementing modulation frequencies effectively in this simulation software.

• PDH Modulation Frequency
• Interferometer Simulation
• Frequency Domain
• Astronomical Observatories

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Uploaded on Mar 05, 2025 | 0 Views

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1. Determination of PDH Modulation Frequency Daisuke TATSUMI National astronomical observatory of Japan finesse: Frequency domain INterfErometer Simulation SoftwarE http://www.gwoptics.org/finesse/ #----------------------------------------------------------------------- # pdh-signal.kat test file for Finesse 1.1 # (Error signal of the Pound-Drever-Hall signal) # # http://www.gwoptics.org/finesse/ # 01.11.2013 # # The "#" is used for comment lines. # # # m1 m2 # .-----. .-. .-. # | | | | . . . . . . . . . . | | # --> n1 | EOM | n2 n3 | | n4 . s_cav # | | | | . . . . . . . . . . | | # `-----' | | | | # `-' `-' #------------------------------------------------------------------ . n5 | |

2. l i1 1 0 n0 # laser P=1W f_offset=0Hz s s0 1 n0 n1 mod eo1 30M 0.1 3 pm n1 n2 # phase modulator f_mod=15MHz # midx=0.1 order=1 s s1 1 n2 n3 # a Fabry-Perot cavity m m1 0.92 0.08 0 n3 n4 # mirror R=0.92 T=0.08 phi=0 s s_cav 0.037474 n4 n5 # space L=37.474mm m m2 0.9995 0.0005 0 n5 dump # mirror R=0.9995 T=0.0005 phi=0 pd1 inphase 30M 0 n3 # photo diode + mixer # f_demod=15MHz phase=0 pd1 quadrature 30M 90 n3 # photo diode + mixer # f_demod=15MHz phase=90degrees xaxis m2 phi lin -90 90 400 # xaxis: tune mirror m2 # from -90 to 90 (400 steps) yaxis abs # plot `as is'

3. FSR (Free Spectral Range) FSR = c /2L c: light speed L: cavity length FSR = 4GHz --> L = c /2 /FSR = 37.474 mm Finesse ? ?1?2 1 ?1?2 ? ~ r1= sqrt(R1) = sqrt(0.92) = 0.95917 r2= sqrt(R2) = sqrt(0.9995) = 0.99975 Finesse = 74.8998 FWHM of the cavity FWHM = FSR / finesse = 4 GHz / 75 = 53.4 MHz

4. > ./finesse SHG.param [INPUT] Length= 3.747400e-02 R1= 9.200000e-01 L1 = 0.000000e+00 R2 = 9.995000e-01 L2 = 0.000000e+00 [OUTPUT] Finesse = 74.8998 FSR = 4.000006e+09 FSR/Finesse = 5.340477e+07 Gain = 4.742051e+01 Reflectivity = 0.97629 Transmissivity = 2.371025e-02 > ./finesse SHG.param [INPUT] Length= 3.747400e-02 R1= 9.200000e-01 L1 = 1.000000e-04 R2 = 9.995000e-01 L2 = 1.000000e-04 [OUTPUT] Finesse = 74.8998 FSR = 4.000006e+09 FSR/Finesse = 5.340477e+07 Gain = 4.736123e+01 Reflectivity = 0.97629 Transmissivity = 1.894449e-02

6. < FWHM = 60 MHz PDH signal get lower than that of optimal.