Everything you always wanted to know about cascaded parametric amplifiers,
but were afraid to ask
Colin J. McKinstrie
Bell Laboratories, Alcatel-Lucent
Abstract
I will review briefly the properties of optical amplifiers and attenuators, and how they
affect the information carried by signals. I will then describe in detail the properties of
cascaded parametric amplifiers and transmission links, and explain why such links are
signal-phase-insensitive, but have noise figures that are 6-dB lower than standard phaseinsensitive links.
Biography
Colin J. McKinstrie received a BSc degree from the University of Glasgow in 1981
(mathematics and physics) and a PhD degree from the University of Rochester in 1986
(plasma physics). From 1985 to 1988 he was a Postdoctoral Fellow of Los Alamos National Laboratory, where he was associated with the Applied Physics Division and the
Center for Nonlinear Studies. In 1988 Dr McKinstrie returned to the University of Rochester as a Professor of Mechanical Engineering and a Scientist in the Laboratory for Laser
Energetics. While there, his main research interests were laser fusion and nonlinear fiber
optics. Since 2001 Dr McKinstrie has been a Member of the Technical Staff at Bell Laboratories, where his research concerns the amplification and transmission of optical
pulses in communication systems, and applications of parametric devices in quantum information science.
Everything you always wanted to know about cascaded
parametric amplifiers, but were afraid to ask
C. J. McKinstrie
Bell Labs, Alcatel-Lucent, Holmdel, NJ 07733
mckinstrie@alcatel-lucent.com
Abstract: I will review briefly the properties of optical amplifiers and attenuators, and how they affect the information carried by signals. I will
then describe in detail the properties of cascaded parametric amplifiers and
transmission links, and explain why such links are signal-phase-insensitive,
but have noise figures that are 6-dB lower than standard phase-insensitive
links.
OCIS codes: 060.2320 fiber optics amplifiers and oscillators; 060.2360 fiber optics links
and subsystems; 190.4380 nonlinear optics, four-wave mixing; 270.2500 fluctuations, relaxation and noise.
Summary
The properties of optical amplifiers and attenuators will be reviewed briefly [1-4].
Two-mode parametric amplifiers are signal-phase-insensitive (PI) if one input amplitude
is nonzero, in which case the input (signal) is amplified. They are phase-sensitive (PS) if
both inputs are nonzero, in which case in-phase (signal and idler) sidebands are amplified, whereas out-of-phase sidebands are de-amplified. Two-mode attenuators are always
PI because the input loss mode is a vacuum state. The noise figure (NF) of an optical device is the input signal-to-noise ratio (SNR) divided by the output SNR. It is a figure of
demerit. In the high-gain regime, the NF of a PI amplifier is 2 (3 dB), because the output
signal inherits fluctuations from both (coherent-state and vacuum) inputs. The noise figure of an attenuator equals its loss factor L, because the coherent signal is diminished,
whereas the signal (quadrature) fluctuations remain constant. In contrast, the NF of a PS
amplifier is 1.2 (-3 dB). The sideband amplitudes combine constrictively, so their powers
are increased by a factor of 4G (where G is the PI gain), whereas the sideband fluctuations combine incoherently, so the noise powers are increased by a factor of only 2G.
Hence, the SNRs of the output sidebands are 3-dB lower than those of the input sidebands.
Standard communication systems are based on single-carrier-frequency signals,
which are amplified in a PI manner. However, if one uses a PI parametric amplifier to
copy an input signal (amplify the signal and generate a frequency-shifted idler), one has
the two inputs required to operate another amplifier in a PS manner [5,6]. Because the
first amplifier is PI, so also is composite (cascaded parametric) amplifier. Hence, in the
high-gain regime, the NF of the composite device cannot be lower than 3 dB. However, if
the amplifiers are separated by a fiber link (attenuator), operating the second amplifier in
a PS manner reduces the NF of the link by 6 dB (L/2 instead of 2L). This NF reduction
corresponds to a 2-bit/s-Hz increase in the information capacity of the link [7,8]. In a recent landmark experiment, a NF reduction of 5.5 dB was observed [9,10].
Bibliography
[1] C. J. McKinstrie et al., “Quantum noise properties of parametric processes,” Opt.
Express 13, 4986 (2005).
[2] M. Vasilyev, “Distributed phase-sensitive amplification,” Opt. Express 13, 7563
(2005).
[3] C. J. McKinstrie et al., “Field-quadrature and photon-number fluctuations produced
by parametric processes,” Opt. Express 18, 19792 (2010).
[4] C. J. McKinstrie and J. P. Gordon, “Field fluctuations produced by parametric processes in fibers,” IEEE J. Sel. Top. Quantum Electron. (available online).
[5] R. Tang, et al., “Gain characteristics of a frequency nondegenerate phase-sensitive
fiber-optic parametric amplifier with phase self-stabilized output,” Opt. Express 13,
10483 (2005).
[6] J. Kakande, et al., “Detailed characterization of a fiber-optic parametric amplifier in
phase-sensitive and phase-insensitive operation,” Opt. Express 18, 4130 (2010).
[7] C. J. McKinstrie and N. Alic, “Information efficiencies of parametric devices,” IEEE
J. Sel. Top. Quantum Electron. (available online).
[8] C. J. McKinstrie et al., “Higher-capacity communication links based on phasesensitive parametric amplifiers,” Opt. Express 19, 11977 (2011).
[9] Z. Tong et al., “Noise performance of optical transmission links that use nondegenerate cascaded parametric amplifiers, Opt. Express 18, 15426 (2010).
[10] Z. Tong et al., “Toward ultra-sensitive optical links enabled by low-noise phasesensitive amplifiers,” Nat. Photon. 5, 430 (2011).