Abstract

Recent progress in low-noise optical amplification and signal processing has raised prospects of practical devices operating below the conventional quantum limit. We review the basic principles, practical implementation, and performance of such devices. In particular, we focus on the operation and limitations of χ(3)-based nonlinear platforms, such as silica high-confinement fiber. Classified by the parametric process application, we discuss the use of low-noise parametric mixers as optical amplifiers, phase regenerators, wavelength converters, and signal multicasters.

© 2013 Optical Society of America

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2013 (6)

2012 (19)

M. A. Ettabib, L. Jones, J. Kakande, R. Slavík, F. Parmigiani, X. Feng, F. Poletti, G. M. Ponzo, J. A. Shi, M. N. Petrovich, W. H. Loh, P. Petropoulos, and D. J. Richardson, “Phase sensitive amplification in a highly nonlinear lead-silicate fiber,” Opt. Express 20, 1629–1634 (2012).
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E. Myslivets, B. P. P. Kuo, N. Alic, and S. Radic, “Generation of wideband frequency combs by continuous-wave seeding of multistage mixers with synthesized dispersion,” Opt. Express 20, 3331–3344 (2012).
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R. Slavík, A. Bogris, J. Kakande, F. Parmigiani, L. Grüner-Nielsen, R. Phelan, J. Vojtěch, P. Periklis, D. Syvridis, and D. J. Richardson, “Field-trial of an all-optical PSK regenerator/multicaster in a 40  Gbit/s, 38 channel DWDM transmission experiment,” J. Lightwave Technol. 30, 512–520 (2012).
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R. Slavík, J. Kakande, P. Petropoulos, and D. J. Richardson, “Processing of optical combs with fiber optic parametric amplifiers,” Opt. Express 20, 10059–10070 (2012).
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M. Asobe, T. Umeki, and O. Tadanaga, “Phase sensitive amplification with noise figure below the 3 dB quantum limit using CW pumped PPLN waveguide,” Opt. Express 20, 13164–13172 (2012).
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S. Turitsyn, M. Sorokina, and S. Derevyanko, “Dispersion-dominated nonlinear fiber-optic channel,” Opt. Lett. 37, 2931–2933 (2012).
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Z. Tong, A. O. J. Wiberg, E. Myslivets, B. P. P. Kuo, N. Alic, and S. Radic, “Spectral linewidth preservation in parametric frequency combs seeded by dual pumps,” Opt. Express 20, 17610–17619 (2012).
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B. P.-P. Kuo, J. M. Fini, L. Grüner-Nielsen, and S. Radic, “Dispersion-stabilized highly-nonlinear fiber for wideband parametric mixer synthesis,” Opt. Express 20, 18611–18619 (2012).
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Z. Tong, A. O. J. Wiberg, E. Myslivets, B. P. P. Kuo, N. Alic, and S. Radic, “Broadband parametric multicasting via four-mode phase-sensitive interaction,” Opt. Express 20, 19363–19373 (2012).
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C. Lundström, B. Corcoran, M. Karlsson, and P. A. Andrekson, “Phase and amplitude characteristics of a phase-sensitive amplifier operating in gain saturation,” Opt. Express 20, 21400–21412 (2012).
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T. Umeki, H. Takara, Y. Miyamoto, and M. Asobe, “3  dB signal-ASE beat noise reduction of coherent multi-carrier signal utilizing phase sensitive amplification,” Opt. Express 20, 24727–24734 (2012).
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M. A. Ettabib, F. Parmigiani, X. Feng, L. Jones, J. Kakande, R. Slavík, F. Poletti, G. M. Ponzo, J. Shi, M. N. Petrovich, W. H. Loh, P. Petropoulos, and D. J. Richardson, “Phase regeneration of DPSK signals in a highly nonlinear lead-silicate W-type fiber,” Opt. Express 20, 27419–27424 (2012).
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M. E. Marhic, “Noise figure of hybrid optical parametric amplifiers,” Opt. Express 20, 28752–28757 (2012).
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S. Radic, “Parametric signal processing,” IEEE J. Sel. Top. Quantum Electron. 18, 670–680 (2012).
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Z. Tong, C. Lundström, P. A. Andrekson, M. Karlsson, and A. Bogris, “Ultra-low noise, broadband phase-sensitive amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 18, 1016–1032 (2012).
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M. Annamalai and M. Vasilyev, “Phase-sensitive multimode parametric amplification in a parabolic-index waveguide,” IEEE Photon. Technol. Lett. 24, 1949–1952 (2012).
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N. V. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Noiseless optical amplifier operating on hundreds of spatial modes,” Phys. Rev. Lett. 109, 043602 (2012).
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R. Slavík, A. Bogris, F. Parmigiani, J. Kakande, M. Westlund, M. Sköld, L. Grüner-Nielsen, R. Phelan, D. Syvridis, P. Petropoulos, and D. J. Richardson, “Coherent all-optical phase and amplitude regenerator of binary phase-encoded signals,” IEEE J. Sel. Top. Quantum Electron. 18, 859–869 (2012).
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A. Szabó, B. J. Puttnam, D. Mazroa, S. Shinada, and N. Wada, “Investigation of an all-optical black-box PPLN-PPLN phase regenerator,” IEEE Photon. Technol. Lett. 24, 2087–2089 (2012).
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2011 (17)

J. Kakande, R. Slavík, F. Parmigiani, A. Bogris, D. Syvridis, L. Grüner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics 5, 748–752 (2011).
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R. S. Tucker and K. Hinton, “Energy consumption and energy density in optical and electronic signal processing,” IEEE Photon. J. 3, 821–833 (2011).
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A. Zavatta, J. Fiurášek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states.” Nat. Photonics 5, 52–60 (2011).
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A. O. J. Wiberg, C.-S. Brès, A. Danicic, E. Myslivets, and S. Radic, “Performance of self-seeded parametric multicasting of analog signals,” IEEE Photon. Technol. Lett. 23, 1570–1572 (2011).
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H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Wavelength translation across 210  nm in the visible using vector Bragg scattering in a birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 23, 109–111 (2011).
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B. J. Puttnam, D. Mazroa, S. Shinada, and N. Wada, “Large phase sensitive gain in periodically-poled lithium-niobate with high pump power,” IEEE Photon. Technol. Lett. 23, 426–428 (2011).
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Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
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G. Li, “Optical communications: amplifying to perfection,” Nat. Photonics 5, 385–386 (2011).
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C. Brès, S. Zlatanovic, A. O. J. Wiberg, and S. Radic, “Reconfigurable parametric channelized receiver for instantaneous spectral analysis,” Opt. Express 19, 3531–3541 (2011).
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Z. Tong, C. Lundström, M. Karlsson, M. Vasilyev, and P. A. Andrekson, “Noise performance of a frequency nondegenerate phase-sensitive amplifier with unequalized inputs,” Opt. Lett. 36, 722–724 (2011).
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T. Umeki, O. Tadanaga, A. Takada, and M. Asobe, “Phase sensitive degenerate parametric amplification using directly-bonded PPLN ridge waveguides,” Opt. Express 19, 6326–6332 (2011).
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C. J. McKinstrie, N. Alic, Z. Tong, and M. Karlsson, “Higher-capacity communication links based on two-mode phase-sensitive amplifiers,” Opt. Express 19, 11977–11991 (2011).
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C. Lundström, Z. Tong, M. Karlsson, and P. A. Andrekson, “Phase-to-phase and phase-to-amplitude transfer characteristics of a nondegenerate-idler phase-sensitive amplifier,” Opt. Lett. 36, 4356–4358 (2011).
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M. Pu, H. Hu, H. Ji, M. Galili, L. K. Oxenløwe, P. Jeppesen, J. M. Hvam, and K. Yvind, “One-to-six WDM multicasting of DPSK signals based on dual pump four-wave mixing in a silicon waveguide,” Opt. Express 19, 24448–24453 (2011).
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B. J. Puttnam, D. Mazroa, S. Shinada, and N. Wada, “Phase-squeezing properties of non-degenerate PSAs using PPLN waveguides,” Opt. Express 19, B131–B139 (2011).
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S. Sygletos, P. Frascella, S. K. Ibrahim, L. Grüner-Nielsen, R. Phelan, J. O’Gorman, and A. D. Ellis, “A practical phase sensitive amplification scheme for two channel phase regeneration,” Opt. Express 19, B938–B945 (2011).
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B. P. P. Kuo, E. Myslivets, N. Alic, and S. Radic, “Wavelength multicasting via frequency comb generation in a bandwidth-enhanced fiber optical parametric mixer,” J. Lightwave Technol. 29, 3515–3522 (2011).
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2010 (14)

Z. Tong, A. Bogris, M. Karlsson, and P. A. Andrekson, “Full characterization of the signal and idler noise figure spectra in single-pump fiber optical parametric amplifiers,” Opt. Express 18, 2884–2893 (2010).
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J. Kakande, C. Lundström, P. A. Andrekson, Z. Tong, M. Karlsson, P. Petropoulos, F. Parmigiani, and D. J. Richardson, “Detailed characterization of a fiber-optic parametric amplifier in phase-sensitive and phase-insensitive operation,” Opt. Express 18, 4130–4137 (2010).
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C. Brès, A. O. Wiberg, B. P. P. Kuo, J. M. Chavez Boggio, C. F. Marki, N. Alic, and S. Radic, “Optical demultiplexing of 320  Gb/s to 8×40  Gb/s in single parametric gate,” J. Lightwave Technol. 28, 434–442 (2010).
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A. Bogris, D. Syvridis, and C. Efstathiou, “Noise properties of degenerate dual pump phase sensitive amplifiers,” J. Lightwave Technol. 28, 1209–1217 (2010).
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Z. Tong, A. Bogris, C. Lundström, C. J. McKinstrie, M. Vasilyev, M. Karlsson, and P. A. Andrekson, “Modeling and measurement of noise figure in a cascaded non-degenerate phase-sensitive parametric amplifier,” Opt. Express 18, 14820–14835 (2010).
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Z. Tong, C. J. McKinstrie, C. Lundström, M. Karlsson, and P. A. Andrekson, “Noise performance of optical fiber transmission links that use non-degenerate cascaded phase-sensitive amplifiers,” Opt. Express 18, 15426–15439 (2010).
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C. J. McKinstrie, M. Karlsson, and Z. Tong, “Field-quadrature and photon-number correlations produced by parametric process,” Opt. Express 18, 19792–19823 (2010).
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S. A. Diddams, “The evolving optical frequency comb,” J. Opt. Soc. Am. B 27, B51–B60 (2010).
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H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105, 093604 (2010).
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C.-S. Brès, A. O. J. Wiberg, B. P. P. Kuo, E. Myslivets, N. Alic, B. Stossel, and S. Radic, “Low distortion multicasting of an analog signal by self-seeded parametric mixer,” IEEE Photon. Technol. Lett. 22, 332–334 (2010).
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N. El Dahdah, D. S. Govan, M. Jamshidifar, N. J. Doran, and M. E. Marhic, “1  Tb/s DWDM long-haul transmission employing a fiber optical parametric amplifier,” IEEE Photon. Technol. Lett. 22, 1171–1173 (2010).
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G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).
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R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
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M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4, 786–791 (2010).
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2009 (4)

C.-S. Brès, A. O. J. Wiberg, B. P. P. Kuo, N. Alic, and S. Radic, “Wavelength multicasting of 320  Gb/s channel in self-seeded parametric amplifier,” IEEE Photon. Technol. Lett. 21, 1002–1004 (2009).
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E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett. 21, 1807–1809 (2009).
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G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photon. 1, 279–307 (2009).
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K. J. Lee, F. Parmigiani, S. Liu, J. Kakande, P. Petropoulos, K. Gallo, and D. Richardson, “Phase sensitive amplification based on quadratic cascading in a periodically poled lithium niobate waveguide,” Opt. Express 17, 20393–20400 (2009).
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2008 (10)

E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16, 753–791 (2008).
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Y. Park, T. Ahn, and J. Azaña, “Stabilization of a fiber-optic two-arm interferometer for ultra-short pulse signal processing applications,” Appl. Opt. 47, 417–421 (2008).
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C. J. McKinstrie, S. J. van Enk, M. G. Raymer, and S. Radic, “Multicolor multipartite entanglement produced by vector four-wave mixing in a fiber,” Opt. Express 16, 2720–2739 (2008).
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H. Kamada, M. Asobe, T. Honjo, H. Takesue, Y. Tokura, Y. Nishida, O. Tadanaga, and H. Miyazawa, “Efficient and low-noise single-photon detection in 1550  nm communication band by frequency upconversion in periodically poled LiNbO3 waveguides,” Opt. Lett. 33, 639–641 (2008).
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M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion trimming in a reconfigurable wavelength selective switch,” J. Lightwave Technol. 26, 73–78 (2008).
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R. Tang, P. S. Devgan, V. S. Grigoryan, P. Kumar, and M. Vasilyev, “In-line phase-sensitive amplification of multi-channel CW signals based on frequency non-degenerate four-wave-mixing in fiber,” Opt. Express 16, 9046–9053 (2008).
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E. Lantz and F. Devaux, “Parametric amplification of images: from time gating to noiseless amplification,” IEEE J. Sel. Top. Quantum Electron. 14, 635–647 (2008).
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L. Lopez, N. Treps, B. Chalopin, C. Fabre, and A. Maître, “Quantum processing of images by continuous wave optical parametric amplification,” Phys. Rev. Lett. 100, 013604 (2008).
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S. Radic, “Parametric amplification and processing in optical fibers,” Laser Photon. Rev. 2, 498–513 (2008).
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2007 (5)

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2005 (12)

K. Croussore, I. Kim, Y. Han, C. Kim, and G. Li, “Demonstration of phase regeneration of DPSK signals based on phase-sensitive amplification,” Opt. Express 13, 3945–3950 (2005).
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C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes,” Opt. Express 13, 4986–5012 (2005).
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D. Dahan and G. Eisenstein, “Tunable all optical delay via slow and fast light propagation in a Raman assisted fiber optical parametric amplifier: a route to all optical buffering,” Opt. Express 13, 6234–6249 (2005).
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M. V. Vasilyev, “Distributed phase-sensitive amplification,” Opt. Express 13, 7563–7571 (2005).
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C. McKinstrie, J. Harvey, S. Radic, and M. Raymer, “Translation of quantum states by four-wave mixing in fibers,” Opt. Express 13, 9131–9142 (2005).
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R. Tang, J. Lasri, P. S. Devgan, V. Grigoryan, P. Kumar, and M. Vasilyev, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express 13, 10483–10493 (2005).
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H. Maeda, G. Funatsu, and A. Naka, “Ultra-long-span 500  km 16×10  Gbit/s WDM unrepeatered transmission using RZ-DPSK format,” Electron. Lett. 41, 34–35 (2005).
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R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan, and P. Kumar, “In-line frequency-nondegenerate phase-sensitive fiber-optical parametric amplifier,” IEEE Photon. Technol. Lett. 17, 1845–1847 (2005).
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R. Tang, P. Devgan, V. S. Grigoryan, and P. Kumar, “Inline frequency-non-degenerate phase-sensitive fibre parametric amplifier for fibre-optic communication,” Electron. Lett. 41, 1072–1074 (2005).
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S. Radic and C. J. McKinstrie, “Optical amplification and signal processing in highly nonlinear optical fiber,” IEICE Trans. Electron. E88-C, 859–869 (2005).
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S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437, 116–120 (2005).
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A. Mosset, F. Devaux, and E. Lantz, “Spatially noiseless optical amplification of images,” Phys. Rev. Lett. 94, 223603 (2005).
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2004 (7)

2003 (3)

T. Torounidis, H. Sunnerud, P. O. Hedekvist, and P. A. Andrekson, “Amplification of WDM signals in fiber-based optical parametric amplifiers,” IEEE Photon. Technol. Lett. 15, 1061–1063 (2003).
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C. McKinstrie, S. Radic, and C. Xie, “Parametric instabilities driven by orthogonal pump waves in birefringent fibers,” Opt. Express 11, 2619–2633 (2003).
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Y. Yamamoto and K. Inoue, “Noise in amplifiers,” J. Lightwave Technol. 21, 2895–2915 (2003).
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2002 (6)

V. E. Perlin and H. G. Winful, “Optimizing the noise performance of broadband WDM systems with distributed Raman amplification,” IEEE Photon. Technol. Lett. 14, 1199–1201 (2002).
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K. Inoue and T. Mukai, “Experimental study on noise characteristics of a gain-saturated fiber optical parametric amplifier,” J. Lightwave Technol. 20, 969–974 (2002).
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K. Uesaka, K. K.-Y. Wong, M. E. Marhic, and L. G. Kazovsky, “Wavelength exchange in a highly nonlinear dispersion-shifted fiber: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 8, 560–568 (2002).
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M. N. Islam, “Raman amplifiers for telecommunications,” IEEE J. Sel. Top. Quantum Electron. 8, 548–559 (2002).
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J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
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C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8, 538–547 (2002).
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2001 (2)

2000 (4)

D. M. Baney, P. Gallion, and R. S. Tucker, “Theory and measurement techniques for the noise figure of optical amplifiers,” Opt. Fiber Technol. 6, 122–154 (2000).
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H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Sel. Top. Quantum Electron. 6, 1325–1331 (2000).
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F. Devaux and E. Lantz, “Gain in phase sensitive parametric image amplification,” Phys. Rev. Lett. 85, 2308–2311 (2000).
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W. Imajuku, A. Takada, and Y. Yamabayashi, “Inline coherent optical amplifier with noise figure lower than 3  dB quantum limit,” Electron. Lett. 36, 63–64 (2000).
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1999 (6)

W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3  dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35, 1954–1955 (1999).
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D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. 24, 984–986 (1999).
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E. Desuvire, “Comments on ‘The noise figure of optical amplifiers’,” IEEE Photon. Technol. Lett. 11,620–621 (1999).
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L. H. Sahasrabuddhe and B. Mukherjee, “Light trees: optical multicasting for improved performance in wavelength routed networks,” IEEE Commun. Mag. 37(2), 67–73 (1999).
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1998 (4)

H. A. Haus, “The noise figure of optical amplifiers,” IEEE Photon. Technol. Lett. 10, 1602–1604 (1998).
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M. Movassaghi, M. K. Jackson, V. M. Smith, and W. J. Hallam, “Noise figure of erbium-doped fiber amplifiers in saturated operation,” J. Lightwave Technol. 16, 812–817 (1998).
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A. Takada and W. Imajuku, “In-line optical phase-sensitive amplifier employing pump laser injection-locked to input signal light,” Electron. Lett. 34, 274–276 (1998).
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W. Imajuku and A. Takada, “Error-free operation of in-line phase-sensitive amplifier,” Electron. Lett. 34, 1673–1674 (1998).
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1997 (3)

W. Imajuku and A. Takada, “In-line phase-sensitive amplifier with optical-PLL-controlled internal pump light source,” Electron. Lett. 33, 2155–2156 (1997).
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P. K. Lam, T. C. Ralph, E. H. Huntington, and H.-A. Bachor, “Noiseless signal amplification using positive electro-optic feedforward,” Phys. Rev. Lett. 79, 1471–1474 (1997).
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1996 (2)

1995 (5)

L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995).
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1994 (6)

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L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, B. Pálsdóttir, S. Dasgupta, D. Richardson, C. Lundström, S. L. Olsson, and P. A. Andrekson, “Brillouin suppressed highly nonlinear fibers,” in European Conference and Exhibition on Optical Communication, OSA Technical Digest (Optical Society of America, 2012), paper We.1.F.1.

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J. Kakande, P. Petropoulos, and D. J. Richardson, “Fiber optical parametric amplification of optical combs for enhanced performance and functionality,” in European Conference and Exhibition on Optical Communication, OSA Technical Digest (Optical Society of America, 2011) paper Th.11.LeCervin.5.

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Figures (24)

Figure 1
Figure 1

Phase space plot of coherent state light after (a) phase-insensitive amplification and (b) phase-sensitive amplification.

Figure 2
Figure 2

Typical frequency configurations of TWM processes: (a) one-mode parametric amplification, (b) two-mode parametric amplification, and (c) two-mode upconversion.

Figure 3
Figure 3

Typical frequency configurations of FWM processes: (a) one-mode parametric amplification, including the fully degenerate case (left) and the nondegenerate pump condition (right), (b) two-mode parametric processes including MI, PC, and BS, and (c) the four-mode parametric scheme.

Figure 4
Figure 4

Practical techniques to generate phase- and frequency-locked optical waves at different wavelengths: (a) opto-electronic-modulation-based sideband generation, (b) phase-insensitive parametric amplification, and (c) mode-locked-laser-based optical frequency comb.

Figure 5
Figure 5

(a) Experimental setup of a typical one-mode PSA based on PPLN waveguides, as reported in [80]. ECLD, external-cavity laser diode; Mod, modulator; PLL, phase-locking loop; DPA, degenerate parametric amplification; SHG, second-harmonic generation; PZT, piezoelectric transducer; PD, photodetector. (b) Amplification and deamplification spectra at the PSA output. Reproduced with permission from [80] (© 2012, Optical Society of America), images courtesy of Masaki Asobe, NTT Photonics Laboratories.

Figure 6
Figure 6

Experimental setup of a “black-box” BPSK/DPSK phase and amplitude regenerator based on a one-mode PSA scheme. Reprinted by permission from Nature Publishing Group, Macmillan Publishers Ltd: Nat. Photonics 4, 690-695 (2010) [103], www.nature.com. Image courtesy of Radan Slavík and David Richardson, University of Southampton.

Figure 7
Figure 7

Measured bit-error-rate curves and eye diagrams before and after PSA regeneration. Reprinted by permission from Nature Publishing Group, Macmillan Publishers Ltd: Nat. Photonics 4, 690-695 (2010) [103], www.nature.com. Image courtesy of Radan Slavík and David Richardson, University of Southampton.

Figure 8
Figure 8

Measured optical spectrum of a low-noise frequency conversion based on two-mode BS. Reproduced with permission from [138] (© 2006, Optical Society of America).

Figure 9
Figure 9

Measured optical spectrum of a conventional phase-insensitive, dispersion-shifted-fiber-based FOPA with (phase-sensitive mode, blue curve) or without a 15 m midstage SMF (phase-insensitive mode, black curve). Reproduced with permission from [160] (© 2005, Optical Society of America), image courtesy of Renyong Tang and Prem Kumar, Northwestern University.

Figure 10
Figure 10

Principle of a two-mode copier–PSA-amplified fiber transmission link. Reproduced with permission from [169] (© 2012, Optical Society of America).

Figure 11
Figure 11

Experimental setup of a copier–PSA link, with the input spectra shown in the insets. NFA, noise figure analyzer; PM, phase modulator; PC, polarization controller; TDL, tunable delay line; VOA, variable optical attenuator; TX, transmitter; PRBS, pseudo-random bit sequence [173].

Figure 12
Figure 12

(a) Measured link NF curves of different link schemes with 0 dB net gain. (b) Measured output spectra of the PIA-based and copier–PIA-based links [173].

Figure 13
Figure 13

(a) Measured average BER of each WDM channel versus received signal power by using an EDFA or a PSA as a preamplifier. (b) Comparison of BER performance of three measured links, in which PSA was considered as an in-line amplifier [173].

Figure 14
Figure 14

(a) Measured PSA (signal and idler, separately) and PIA NFs as a function of the input signal power at 26.5 dB PSA gain (20.7 dB PIA gain). (b) Measured PSA gain and NF spectra [173].

Figure 15
Figure 15

Upper figure: Q -factor penalty versus launched signal power in different transmission link schemes (with 80 km SMF). Lower figure: constellation diagrams at the receiver for + 16 dBm input signal power for (a) an EDFA, (b) the copier–PIA, and (c) the copier–PSA condition. Reproduced with permission from [180] (© 2012, Optical Society of America), image courtesy of Samuel L. I. Olsson and Peter A. Andrekson, Chalmers University of Technology.

Figure 16
Figure 16

Measured phase-to-phase transfer functions (upper row) and output constellation diagrams (lower row) of a two-mode PSA with different signal-to-idler power ratio at its input. Reproduced with permission from [201] (© 2012, Optical Society of America).

Figure 17
Figure 17

(a) Optical spectrum of a frequency comb with phase-sensitive amplification (black) or with pump off (red). (b) Spectral comparison of a frequency comb with phase-insensitive and phase-sensitive amplification. Clear spectral equalization ( 2.5 dB ripple) as well as low-noise amplification ( 6 dB optical SNR improvement) compared to the phase-insensitive amplification has been observed. Reproduced with permission from [206] (© 2012, Optical Society of America), image courtesy of Radan Slavík, University of Southampton.

Figure 18
Figure 18

Optical (a) input and (b) output spectra of a four-mode fiber-based PSA in the copier–PSA configuration. Reproduced with permission from [210] (© 2012, Optical Society of America), image courtesy of Thomas Richter and Peter A. Andrekson, Chalmers University of Technology.

Figure 19
Figure 19

Simulated NF and CE as functions of HNLF length in a multicasting parametric device, with (a) no dispersion and (b) a small normal dispersion (ZDW is 1590 nm and dispersion slope is 0.002 ps / nm 2 / km ), respectively. See [221] for detailed parameters. Reproduced with permission from [221] (© 2013, Optical Society of America).

Figure 20
Figure 20

Principle of ultralow-noise spectral replication/frequency multicasting via a four-mode phase-sensitive process, relying on normal-dispersion-induced localization of parametric noise coupling. Reproduced with permission from [224] (© 2012, Optical Society of America).

Figure 21
Figure 21

Experimental setup of the four-mode PSA-based spectral signal replication. ECL, external-cavity laser; PC, polarization controller; PS, phase shifter; MZM, Mach–Zehnder modulator; PM, phase modulator; DFB, distributed feedback laser; TDL, tunable delay line. Reproduced with permission from [224] (© 2012, Optical Society of America).

Figure 22
Figure 22

(a) Measured (zoomed in) output spectra and (b) conversion efficiency of each sideband (copy) for different input schemes. Reproduced with permission from [224] (© 2012, Optical Society of America).

Figure 23
Figure 23

Simulated CE and NF spectra of a four-mode phase-sensitive and a phase-insensitive multicasting mixer, respectively. About 12 dB CE increase as well as below 3 dB combined NF can be observed in the phase-sensitive mode. System parameters were chosen to mimic the experimental setup used in [224].

Figure 24
Figure 24

Principles of frequency multicasting to preprocess ultrahigh-speed optical signals in a real-time manner: (a) high-resolution copy-and-sample-all analog-to-digital-conversion preprocessor, reproduced with permission from [229] (© 2012, Optical Society of America), (b) wideband RF channelizing, reproduced with permission from [231] (© 2011, Optical Society of America), and (c) high-rate digital signal multiplexing and demultiplexing. (© 2012 IEEE. Reprinted, with permission, from S. Radic, IEEE Sel. Top. Quantum Electron. 18, 670–680 (2012) [232]).

Equations (48)

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NF = SNR in SNR out ,
SNR = I s 2 δ I s 2 ,
SNR shot = I shot 2 q Δ v ,
NF G < 1 = SNR in SNR out = I in I out = 1 / G .
Δ N ^ 1 2 Δ N ^ 2 2 1 16 ( 1 G 1 G 2 ) 2 ,
B l = m [ μ l m ( A m + n m ) + ν l m ( A m * + n m * ) ] ,
B = μ ( A + n ) + ν ( A * + n * ) .
B = e j θ r { ( | μ | + | ν | ) Re [ A r ] + ( | μ | | ν | ) Im [ A r ] } ,
[ B s B i ] = [ μ ν ν * μ * ] [ A s + n s A i + n i ] ,
[ B s B i * ] = [ μ ν ν * μ * ] [ A s + n s A i * + n i * ] ,
A + = ( A s + n s ) + ( A i + n i ) 2 , A = ( A s + n s ) ( A i + n i ) 2 .
B + = μ A + + ν A + * ,
B = μ A ν A * ,
B + = e j θ r { ( | μ | + | ν | ) Re [ A + ] + ( | μ | | ν | ) Im [ A + ] } ,
B = e j θ r { ( | μ | + | ν | ) Im [ A ] + ( | μ | | ν | ) Re [ A ] } ,
B s = μ A s + ν A s * + μ n s + ν n i * ,
B i = μ A s + ν A s * + μ n i + ν n s * .
δ I in _ s , i 2 / Δ v = 2 q R | A s | 2 ,
δ I out _ s , i 2 / Δ v = 2 R 2 | A s | 2 | μ + ν | 2 h v s , i ( | μ | 2 + | ν | 2 ) ,
NF s , i = | μ | 2 + | ν | 2 ( | μ | + | ν | ) 2 .
NF c NF s + NF i NF s · | A s | 2 + | A i | 2 | A s | 2 ,
B s = μ A s + ν A s + μ n s + ν n i ,
B i = μ A s + ν A s + μ n i + ν n s .
[ B s B s ] = [ τ s ρ s ρ s * τ s * ] [ A s + N s n s ] [ B i B i ] = [ τ i ρ i ρ i * τ i * ] [ A i + N i n i ] ,
[ B s B i ] = [ T s 0 0 T i ] [ A s + N s A i + N i ] + [ 1 T s n s 1 T i n i ] .
NF Copier + Loss + PSA 1 + G 2 2 ,
NF PIA + Loss + PIA 1 + 2 G 2 ,
[ B 1 * B 1 + B 2 * B 2 + ] = [ μ 11 μ 12 μ 13 μ 14 μ 21 μ 22 μ 23 μ 24 μ 31 μ 32 μ 33 μ 34 μ 41 μ 42 μ 43 μ 44 ] [ A 1 * + n 1 * A 1 + + n 1 + A 2 * + n 2 * A 2 + + n 2 + ] = [ 1 j γ P z j γ P z j γ P z j γ P z j γ P z 1 + j γ P z j γ P z j γ P z j γ P z j γ P z 1 j γ P z j γ P z j γ P z j γ P z j γ P z 1 + j γ P z ] [ A 1 * + n 1 * A 1 + + n 1 + A 2 * + n 2 * A 2 + + n 2 + ] ,
B l = m μ l , m * A + m μ l , m + * A * + m μ l , m * n m + m μ l , m + * n m + * ,
B l + = m μ l + , m + A + m μ l + , m A * + m μ l + , m + n m + + m μ l + , m n m * ,
NF l ± = m | μ l ± , m + | 2 + m | μ l ± , m | 2 ( m | μ l ± , m + | + m | μ l ± , m | ) 2 .
B l = m μ l , m * A + m μ l , m + * A + m μ l , m * n m + m μ l , m + * n m + ,
B l + = m μ l + , m + A + m μ l + , m A + m μ l + , m + n m + + m μ l + , m n m .
a ^ = X ^ 1 + j X ^ 2 ,
b ^ = Y ^ 1 + j Y ^ 2 .
Y ^ 1 = G 1 X ^ 1 + N ^ 1 ,
Y ^ 2 = G 2 X ^ 2 + N ^ 2 ,
[ a ^ , a ^ ] = 1 ,
[ b ^ , b ^ ] = 1 .
[ X ^ 1 , X ^ 2 ] = j / 2 ,
[ Y ^ 1 , Y ^ 2 ] = j / 2 .
[ N ^ 1 , N ^ 2 ] = j 2 ( 1 G 1 G 2 ) .
Δ N ^ 1 2 Δ N ^ 2 2 1 4 | [ N ^ 1 , N ^ 2 ] | 2 = 1 16 ( 1 G 1 G 2 ) 2 ,
Δ Y ^ i 2 = G Δ X ^ i 2 + Δ N ^ i 2 ,
NF PIA = X ^ i 2 / Δ X ^ i 2 Y ^ i 2 / Δ Y ^ i 2 = Δ Y ^ i 2 1 4 G 2 1 G .
NF PSA = X ^ i 2 / Δ X ^ i 2 Y ^ i 2 / Δ Y ^ i 2 1 ,
RIN = δ I 2 σ shot 2 I 2 ,
NF = 1 G + P in ( S out S in ) 2 h v I out 2 ,

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