Abstract

Phase modulated sub-picosecond pulses are converted by a time-to-space processor to quasi-monochromatic spatial beams that are spatially demultiplexed and coherently detected in real-time. The time-to-space processor, based on sum-frequency generation (SFG), serves as a serial-to-parallel converter, reducing the temporal bandwidth of the ultrashort pulse to match the bandwidth of optoelectronic receivers. As the SFG process is phase preserving, we demonstrate homodyne coherent detection of phase modulated temporal pulses by mixing the demultiplexed SFG beam with a narrow linewidth local oscillator (LO) resulting in single-shot phase detection of the converted pulses at a balanced detector. Positively and negatively phase-modulated signal pulses are individually detected and LO shot noise limited operation is achieved. This demonstration of real-time demultiplexing followed by single-shot full-field detection of individual pulses, highlights the potential of time-to-space conversion for ultrahigh bit rate optical communications and data processing applications.

© 2014 Optical Society of America

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    [Crossref] [PubMed]

2014 (1)

2013 (2)

2012 (4)

E. Palushani, H. C. Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18(2), 681–688 (2012).
[Crossref]

R. Essiambre and R. W. Tkach, “Capacity trends and limits of optical communications networks,” Proc. IEEE 100(5), 1035–1055 (2012).
[Crossref]

K.-Y. Wang, K. G. Petrillo, M. A. Foster, and A. C. Foster, “Ultralow-power all-optical processing of high-speed data signals in deposited silicon waveguides,” Opt. Express 20(22), 24600–24606 (2012).
[Crossref] [PubMed]

D. Shayovitz, H. Herrmann, W. Sohler, R. Ricken, C. Silberhorn, and D. M. Marom, “High resolution time-to-space conversion of sub-picosecond pulses at 1.55μm by non-degenerate SFG in PPLN crystal,” Opt. Exp. 20(24), 27388–27395 (2012).
[Crossref]

2011 (3)

D. Shayovitz and D. M. Marom, “High-resolution, background-free, time-to-space conversion by collinearly phase-matched sum-frequency generation,” Opt. Lett. 36(11), 1957–1959 (2011).
[Crossref] [PubMed]

H. C. H. Mulvad, E. Palushani, H. Hu, H. Ji, M. Lillieholm, M. Galili, A. T. Clausen, M. Pu, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed optical serial-to-parallel dataconversion by time-domain optical Fouriertransformation in a silicon nanowire,” Opt. Exp. 19(26), B825–B835 (2011).
[Crossref]

J. K. Fischer, R. Ludwig, L. Molle, C. Schmidt-Langhorst, A. Galperin, T. Richter, C. C. Leonhardt, A. Matiss, and C. Schubert, “High-speed digital coherent based on parallel optical sampling,” J. Lightwave Technol. 29(4), 378–385 (2011).
[Crossref]

2010 (2)

2006 (1)

2003 (2)

T. Miyazaki and F. Kubota, “Simultaneous Demultiplexing and Clock Recovery for 160-Gb/s OTDM Signal Using a Symmetric Mach-Zehnder Switch in Electrooptic Feedback Loop,” IEEE Photon. Technol. Lett. 15(7), 1008–1010 (2003).
[Crossref]

J.-H. Chung and A. M. Weiner, “Real-time detection of femtosecond optical pulse sequences via time-to-space conversion in the lightwave communications band,” J. Lightwave Technol. 21(12), 3323–3333 (2003).
[Crossref]

2002 (1)

2001 (2)

D. M. Marom, D. Panasenko, P.-C. Sun, and Y. Fainman, “Linear and nonlinear operation of a time-to-space processor,” J. Opt. Soc. Am. A 18(2), 448–458 (2001).
[Crossref] [PubMed]

D. M. Marom, D. Panasenko, P.-C. Sun, Y. T. Mazurenko, and Y. Fainman, “Real-time spatial–temporal signal processing with optical nonlinearities,” IEEE J. Sel. Top. Quantum Electron. 7(4), 683–693 (2001).
[Crossref]

2000 (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000).
[Crossref]

1998 (1)

1997 (1)

1996 (1)

1995 (1)

K. I. Kang, I. Glesk, T. G. Chang, P. R. Prucnal, and R. K. Boncek, “Demonstration of all-optical Mach-Zehnder demultiplexer,” Opt. Lett. 31(9), 749–750 (1995).

1994 (1)

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64(3), 270–272 (1994).
[Crossref]

1993 (1)

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A Terahertz Optical Asymmetric Demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5(7), 787–790 (1993).
[Crossref]

Banyai, W. C.

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64(3), 270–272 (1994).
[Crossref]

Beliaev, A. G.

Bloom, D. M.

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64(3), 270–272 (1994).
[Crossref]

Boerner, C.

Boncek, R. K.

K. I. Kang, I. Glesk, T. G. Chang, P. R. Prucnal, and R. K. Boncek, “Demonstration of all-optical Mach-Zehnder demultiplexer,” Opt. Lett. 31(9), 749–750 (1995).

Buckley, B. W.

Bulla, D. A. P.

Chang, T. G.

K. I. Kang, I. Glesk, T. G. Chang, P. R. Prucnal, and R. K. Boncek, “Demonstration of all-optical Mach-Zehnder demultiplexer,” Opt. Lett. 31(9), 749–750 (1995).

Chizhov, S. A.

Choi, D.-Y.

Chujo, W.

Chung, J.-H.

Clausen, A. T.

E. Palushani, H. C. Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18(2), 681–688 (2012).
[Crossref]

H. C. H. Mulvad, E. Palushani, H. Hu, H. Ji, M. Lillieholm, M. Galili, A. T. Clausen, M. Pu, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed optical serial-to-parallel dataconversion by time-domain optical Fouriertransformation in a silicon nanowire,” Opt. Exp. 19(26), B825–B835 (2011).
[Crossref]

Eggleton, B. J.

Essiambre, R.

R. Essiambre and R. W. Tkach, “Capacity trends and limits of optical communications networks,” Proc. IEEE 100(5), 1035–1055 (2012).
[Crossref]

Fainman, Y.

Ferber, S.

Fischer, J. K.

Foster, A. C.

Foster, M. A.

Galili, M.

E. Palushani, H. C. Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18(2), 681–688 (2012).
[Crossref]

H. C. H. Mulvad, E. Palushani, H. Hu, H. Ji, M. Lillieholm, M. Galili, A. T. Clausen, M. Pu, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed optical serial-to-parallel dataconversion by time-domain optical Fouriertransformation in a silicon nanowire,” Opt. Exp. 19(26), B825–B835 (2011).
[Crossref]

T. D. Vo, H. Hu, M. Galili, E. Palushani, J. Xu, L. K. Oxenløwe, S. J. Madden, D.-Y. Choi, D. A. P. Bulla, M. D. Pelusi, J. Schröder, B. Luther-Davies, and B. J. Eggleton, “Photonic chip based transmitter optimization and receiver demultiplexing of a 1.28 Tbit/s OTDM signal,” Opt. Express 18(16), 17252–17261 (2010).
[Crossref] [PubMed]

Galperin, A.

Glesk, I.

K. I. Kang, I. Glesk, T. G. Chang, P. R. Prucnal, and R. K. Boncek, “Demonstration of all-optical Mach-Zehnder demultiplexer,” Opt. Lett. 31(9), 749–750 (1995).

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A Terahertz Optical Asymmetric Demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5(7), 787–790 (1993).
[Crossref]

Godil, A. A.

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64(3), 270–272 (1994).
[Crossref]

Herrmann, H.

Hu, H.

E. Palushani, H. C. Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18(2), 681–688 (2012).
[Crossref]

H. C. H. Mulvad, E. Palushani, H. Hu, H. Ji, M. Lillieholm, M. Galili, A. T. Clausen, M. Pu, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed optical serial-to-parallel dataconversion by time-domain optical Fouriertransformation in a silicon nanowire,” Opt. Exp. 19(26), B825–B835 (2011).
[Crossref]

T. D. Vo, H. Hu, M. Galili, E. Palushani, J. Xu, L. K. Oxenløwe, S. J. Madden, D.-Y. Choi, D. A. P. Bulla, M. D. Pelusi, J. Schröder, B. Luther-Davies, and B. J. Eggleton, “Photonic chip based transmitter optimization and receiver demultiplexing of a 1.28 Tbit/s OTDM signal,” Opt. Express 18(16), 17252–17261 (2010).
[Crossref] [PubMed]

Hvam, J. M.

H. C. H. Mulvad, E. Palushani, H. Hu, H. Ji, M. Lillieholm, M. Galili, A. T. Clausen, M. Pu, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed optical serial-to-parallel dataconversion by time-domain optical Fouriertransformation in a silicon nanowire,” Opt. Exp. 19(26), B825–B835 (2011).
[Crossref]

Ip, E. M.

Jalali, B.

Jeppesen, P.

E. Palushani, H. C. Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18(2), 681–688 (2012).
[Crossref]

H. C. H. Mulvad, E. Palushani, H. Hu, H. Ji, M. Lillieholm, M. Galili, A. T. Clausen, M. Pu, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed optical serial-to-parallel dataconversion by time-domain optical Fouriertransformation in a silicon nanowire,” Opt. Exp. 19(26), B825–B835 (2011).
[Crossref]

Ji, H.

H. C. H. Mulvad, E. Palushani, H. Hu, H. Ji, M. Lillieholm, M. Galili, A. T. Clausen, M. Pu, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed optical serial-to-parallel dataconversion by time-domain optical Fouriertransformation in a silicon nanowire,” Opt. Exp. 19(26), B825–B835 (2011).
[Crossref]

Kahn, J. M.

Kan’an, A. M.

Kane, M.

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A Terahertz Optical Asymmetric Demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5(7), 787–790 (1993).
[Crossref]

Kang, K. I.

K. I. Kang, I. Glesk, T. G. Chang, P. R. Prucnal, and R. K. Boncek, “Demonstration of all-optical Mach-Zehnder demultiplexer,” Opt. Lett. 31(9), 749–750 (1995).

Kauffman, M. T.

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64(3), 270–272 (1994).
[Crossref]

Koyamada, Y.

Kroh, M.

Kubota, F.

T. Miyazaki and F. Kubota, “Simultaneous Demultiplexing and Clock Recovery for 160-Gb/s OTDM Signal Using a Symmetric Mach-Zehnder Switch in Electrooptic Feedback Loop,” IEEE Photon. Technol. Lett. 15(7), 1008–1010 (2003).
[Crossref]

Leonhardt, C. C.

Lillieholm, M.

H. C. H. Mulvad, E. Palushani, H. Hu, H. Ji, M. Lillieholm, M. Galili, A. T. Clausen, M. Pu, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed optical serial-to-parallel dataconversion by time-domain optical Fouriertransformation in a silicon nanowire,” Opt. Exp. 19(26), B825–B835 (2011).
[Crossref]

Ludwig, R.

Luther-Davies, B.

Madden, S. J.

Madni, A. M.

Marembert, V.

Marom, D. M.

Matiss, A.

Mazurenko, Y. T.

Miyazaki, T.

T. Miyazaki and F. Kubota, “Simultaneous Demultiplexing and Clock Recovery for 160-Gb/s OTDM Signal Using a Symmetric Mach-Zehnder Switch in Electrooptic Feedback Loop,” IEEE Photon. Technol. Lett. 15(7), 1008–1010 (2003).
[Crossref]

Molle, L.

Mulvad, H. C.

E. Palushani, H. C. Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18(2), 681–688 (2012).
[Crossref]

Mulvad, H. C. H.

H. C. H. Mulvad, E. Palushani, H. Hu, H. Ji, M. Lillieholm, M. Galili, A. T. Clausen, M. Pu, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed optical serial-to-parallel dataconversion by time-domain optical Fouriertransformation in a silicon nanowire,” Opt. Exp. 19(26), B825–B835 (2011).
[Crossref]

Oxenløwe, L. K.

E. Palushani, H. C. Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18(2), 681–688 (2012).
[Crossref]

H. C. H. Mulvad, E. Palushani, H. Hu, H. Ji, M. Lillieholm, M. Galili, A. T. Clausen, M. Pu, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed optical serial-to-parallel dataconversion by time-domain optical Fouriertransformation in a silicon nanowire,” Opt. Exp. 19(26), B825–B835 (2011).
[Crossref]

T. D. Vo, H. Hu, M. Galili, E. Palushani, J. Xu, L. K. Oxenløwe, S. J. Madden, D.-Y. Choi, D. A. P. Bulla, M. D. Pelusi, J. Schröder, B. Luther-Davies, and B. J. Eggleton, “Photonic chip based transmitter optimization and receiver demultiplexing of a 1.28 Tbit/s OTDM signal,” Opt. Express 18(16), 17252–17261 (2010).
[Crossref] [PubMed]

Palushani, E.

E. Palushani, H. C. Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18(2), 681–688 (2012).
[Crossref]

H. C. H. Mulvad, E. Palushani, H. Hu, H. Ji, M. Lillieholm, M. Galili, A. T. Clausen, M. Pu, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed optical serial-to-parallel dataconversion by time-domain optical Fouriertransformation in a silicon nanowire,” Opt. Exp. 19(26), B825–B835 (2011).
[Crossref]

T. D. Vo, H. Hu, M. Galili, E. Palushani, J. Xu, L. K. Oxenløwe, S. J. Madden, D.-Y. Choi, D. A. P. Bulla, M. D. Pelusi, J. Schröder, B. Luther-Davies, and B. J. Eggleton, “Photonic chip based transmitter optimization and receiver demultiplexing of a 1.28 Tbit/s OTDM signal,” Opt. Express 18(16), 17252–17261 (2010).
[Crossref] [PubMed]

Panasenko, D.

D. M. Marom, D. Panasenko, P.-C. Sun, Y. T. Mazurenko, and Y. Fainman, “Real-time spatial–temporal signal processing with optical nonlinearities,” IEEE J. Sel. Top. Quantum Electron. 7(4), 683–693 (2001).
[Crossref]

D. M. Marom, D. Panasenko, P.-C. Sun, and Y. Fainman, “Linear and nonlinear operation of a time-to-space processor,” J. Opt. Soc. Am. A 18(2), 448–458 (2001).
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H. C. H. Mulvad, E. Palushani, H. Hu, H. Ji, M. Lillieholm, M. Galili, A. T. Clausen, M. Pu, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed optical serial-to-parallel dataconversion by time-domain optical Fouriertransformation in a silicon nanowire,” Opt. Exp. 19(26), B825–B835 (2011).
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J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A Terahertz Optical Asymmetric Demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5(7), 787–790 (1993).
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D. M. Marom, D. Panasenko, P.-C. Sun, Y. T. Mazurenko, and Y. Fainman, “Real-time spatial–temporal signal processing with optical nonlinearities,” IEEE J. Sel. Top. Quantum Electron. 7(4), 683–693 (2001).
[Crossref]

D. M. Marom, D. Panasenko, P.-C. Sun, and Y. Fainman, “Linear and nonlinear operation of a time-to-space processor,” J. Opt. Soc. Am. A 18(2), 448–458 (2001).
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H. C. H. Mulvad, E. Palushani, H. Hu, H. Ji, M. Lillieholm, M. Galili, A. T. Clausen, M. Pu, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed optical serial-to-parallel dataconversion by time-domain optical Fouriertransformation in a silicon nanowire,” Opt. Exp. 19(26), B825–B835 (2011).
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[Crossref]

D. M. Marom, D. Panasenko, P.-C. Sun, Y. T. Mazurenko, and Y. Fainman, “Real-time spatial–temporal signal processing with optical nonlinearities,” IEEE J. Sel. Top. Quantum Electron. 7(4), 683–693 (2001).
[Crossref]

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H. C. H. Mulvad, E. Palushani, H. Hu, H. Ji, M. Lillieholm, M. Galili, A. T. Clausen, M. Pu, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed optical serial-to-parallel dataconversion by time-domain optical Fouriertransformation in a silicon nanowire,” Opt. Exp. 19(26), B825–B835 (2011).
[Crossref]

D. Shayovitz, H. Herrmann, W. Sohler, R. Ricken, C. Silberhorn, and D. M. Marom, “High resolution time-to-space conversion of sub-picosecond pulses at 1.55μm by non-degenerate SFG in PPLN crystal,” Opt. Exp. 20(24), 27388–27395 (2012).
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E. Palushani, T. Richter, R. Ludwig, C. Schubert, H. C. H. Mulvad, A. T. Clausen, and L. K. Oxenløwe, “OTDM-to-WDM Conversion of Complex Modulation Formats by Time-Domain Optical Fourier Transformation,” Proc. Opt. Fiber Commun. (OFC) 2012, paper OTh3H.2.
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Time-to-space conversion concept. Time domain information is converted to a spatial image with the temporal coordinate t mapped linearly to a spatial coordinate x. Note that in our experimental setup the signal and reference beams propagate collinearly in the nonlinear crystal, whereas here they are shown at crossed angles for clarity. The dashed line in the OTDM pulse stream represents an empty bit slot.
Fig. 2
Fig. 2 Experimental setup for time-to-space conversion with coherent detection (MLL, mode-locked laser; OPO, optical parametric oscillator; PM, phase modulator; G1/G2, diffraction grating; f, Fourier lens; DM, dichroic mirror; Cyl., cylindrical lens; FC, fiber collimator; PD, photodetector). Note that the SFG beam fiber collimator can be laterally translated to detect different spatially demultiplexed pulse images. The spectral filtering block represents a diffraction grating – Fourier lens – spatial filter setup. A high voltage amplifier (not shown) was used to amplify the RF signal driving the phase modulator. Dashed lines represent electrical connections. Inset: dispersed signal and reference beams at the PPLN. No second harmonic components were generated for the signal and reference in the crystal due to phase matching bandwidth limitation of the PPLN.
Fig. 3
Fig. 3 Time-to-space converted SFG spectrum (blue) and local oscillator spectrum (green). Each spectrum is centered at 810 nm and has a −3dB bandwidth of approximately 0.1 nm (~50 GHz). The measurements were made by alternately coupling the SFG and LO light from one of the −3 dB fiber coupler outputs into an optical spectrum analyzer set to0.1 nm resolution.
Fig. 4
Fig. 4 Coherent detection of time-to-space converted phase modulated pulses. (a) Oscilloscope trace showing the balanced photodetector signal (blue) and the 500 kHz sinusoidal driving signal applied to the phase modulator (red). The phase modulator driving signal shown was taken from the monitor output of the high voltage amplifier which was used to drive the phase modulator. (b), (c)and (d) Close-ups of individual pulses detected at various phases (note the nanosecond time scale).The sampling windows used to derive the data shown in Fig. 5 are represented by green rectangles; the window amplitude varies from zero to one in a square wave fashion. The location on the oscilloscope trace of each close-up is indicated by a green dashed circle in (a).The waveforms seen in (b) are due to ringing by the 350 MHz bandwidth balanced detector, which degrades the quality of the phase-demodulated signal as can be seen in (a). However negative and positive demodulated pulses can clearly be seen in (c) and (d) respectively. Note that due to a residual fixed phase on the LO, there is an offset between the phase modulator driving signal phase and the phase of the received signal.
Fig. 5
Fig. 5 Time window sampled and averaged photodetector signal. (a) Time domain representation showing the average photovoltage for each pulse (magenta dots) with a sine curve fit to the data points (blue line). (b) Frequency domain representation of the sampled signal, found by taking the Fourier transform of the photovoltage data points in (a). Peak at 500 KHz modulation apparent.

Equations (2)

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U out ( x,t )=w( c( t t 0 ) α )w( ct α )s( αx c t 0 )r( αx c )exp( j( ω S + ω R )t )
s( t )= k p( tk t 0 )exp( j f RF t )

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