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Journal of Lightwave Technology

Polarization-Independent Phase-Sensitive Amplification

Abel Lorences-Riesgo, Peter A. Andrekson, Magnus Karlsson

Published Apr 4, 2016• 15 citations
Publisher

Abstract

We thoroughly analyze the requirements on the signal and idler state of polarizations (SOPs) for achieving maximum amplification in phase-sensitive amplifiers (PSAs). These requirements are described using a Jones-space description as well as a Stokes-space description. Our analysis includes the cases of polarization-diverse and vector PSAs, and in each type of PSA, we also consider the signal-degenerate and the non-degenerate schemes. We observe that the relation between the signal and idler SOPs to achieve maximum phase-sensitive (PS) amplification can be described similarly in polarization-diverse and in vector PSAs. Moreover, both types of PSAs are polarization-dependent, which means that PSAs do require polarization-tracking schemes when being implemented in a realistic optical-transmission scenario. We therefore evaluate how polarization tracking of the signal and the idler SOPs can overcome the theoretical polarization dependence of both polarization-diverse and vector PSAs. We find that only one polarization tracker for either the signal or idler SOP is necessary for achieving polarization-independent PS amplification when considering the general case of dual-polarization (DP) modulated signals. This polarization tracker requires the control of three degrees of freedom which describe a general polarization rotation. For single-polarization (SP) modulated signals, the polarization tracker can rotate both the signal and the idler SOPs simultaneously which eliminates the need for splitting the signal and the idler before the PSA. Moreover, only two degrees of freedom for the polarization tracker are necessary in this case. When considering degenerate schemes, a polarization tracker with two degrees of freedom is sufficient to achieve maximum PS amplification of DP binary phase-shift keying (BPSK) signals in both vector and polarization diverse PSAs. For the case of SP-BPSK signals, a polarization-diverse PSA can perform polarization-independent amplification by controlling the relative phase between the pumps, whereas a polarization tracker with only one degree of freedom is necessary in the case of vector PSAs.

DOI
10.1109/jlt.2016.2550051

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We thoroughly analyze the requirements on the signal and idler state of polarizations (SOPs) for achieving maximum amplification in phase-sensitive amplifiers (PSAs). These requirements are described using a Jones-space description as well as a Stokes-space description. Our analysis includes the cases of polarization-diverse and vector PSAs, and in each type of PSA, we also consider the signal-degenerate and the non-degenerate schemes. We observe that the relation between the signal and idler SOPs to achieve maximum phase-sensitive (PS) amplification can be described similarly in polarization-diverse and in vector PSAs. Moreover, both types of PSAs are polarization-dependent, which means that PSAs do require polarization-tracking schemes when being implemented in a realistic optical-transmission scenario. We therefore evaluate how polarization tracking of the signal and the idler SOPs can overcome the theoretical polarization dependence of both polarization-diverse and vector PSAs. We find that only one polarization tracker for either the signal or idler SOP is necessary for achieving polarization-independent PS amplification when considering the general case of dual-polarization (DP) modulated signals. This polarization tracker requires the control of three degrees of freedom which describe a general polarization rotation. For single-polarization (SP) modulated signals, the polarization tracker can rotate both the signal and the idler SOPs simultaneously which eliminates the need for splitting the signal and the idler before the PSA. Moreover, only two degrees of freedom for the polarization tracker are necessary in this case. When considering degenerate schemes, a polarization tracker with two degrees of freedom is sufficient to achieve maximum PS amplification of DP binary phase-shift keying (BPSK) signals in both vector and polarization diverse PSAs. For the case of SP-BPSK signals, a polarization-diverse PSA can perform polarization-independent amplification by controlling the relative phase between the pumps, whereas a polarization tracker with only one degree of freedom is necessary in the case of vector PSAs.
This work is devoted to the characterization of vector phase-sensitive amplifiers and processors. A detailed analysis of degenerate vector phase-sensitive amplifier (PSA) is performed.The gain and phase-sensitive extinction ratio are theoretically analyzed using three-wave theory. Experiments and simulation results confirm the validity of this three-wave theory. The influence of polarization-mode dispersion is also evaluated, showing that aligning the pump polarizations at the fiber input is essential in order to achieve the theoretically predicted results. The scheme is also compared to the degenerate scalar PSA scheme. At the same pump power, the vector PSA has lower gain but also less influence from higher-order idlers and lower pump depletion due to FWM between the pumps. Using the degenerate vector PSA, phase-sensitive (PS) amplification of dual-polarization (DP) binary phase-shift keying (BPSK) signals was demonstrated. To the best of our knowledge, this was the first demonstration of a DP-modulated signal with large net phase-sensitive gain. Furthermore, we also demonstrated that this scheme can phase regenerate the signal. The same scheme was also used for a different purpose: quadrature decomposition into two cross-polarized waves. We demonstrated demultiplexing of quadrature phase-shift keying (QPSK) signal into two cross-polarized BPSK signals by the operating the amplifier in phase-insensitive mode. The design of a novel phase-locked loop scheme enabled stable operation and negligible penalty in the decomposition.
We investigate the possibility of obtaining phase-sensitive amplification (PSA) in a fiber-optic parametric amplifier (OPA), with gain independent of the state of polarization of the input signal, i.e., polarization-independent amplification. We consider both a single OPA with two orthogonal pumps and a polarization-diversity scheme. In either case, PSA with maximum gain is possible, provided that the signal and idler are in suitably matched polarization states; this condition is naturally satisfied by the output fields of an upstream polarization-insensitive amplifier of the same type. Two polarization-multiplexed signals can then be simultaneously amplified in the PSA. The low noise figure can also be obtained with these types of PSA. However, in general, this favorable situation is not maintained if the signal and idler states of polarization drift together due to birefringence fluctuations in a transmission fiber preceding the PSA.
We comprehensively investigate a degenerate vector phase-sensitive amplifier (PSA). We determine the gain dependence on the relative phase and polarization angle between the pumps and the degenerate signal wave. The vector PSA is experimentally shown to be sensitive to the pump states of polarization (SOP) due to polarization mode dispersion in the fiber. However, the scheme performance agrees well with theory under specific pump SOPs and we achieve an on-off gain over 10 dB with a small deviation from the theoretically expected results. In comparison to the scalar scheme, the proposed vector scheme has larger tolerance for pump depletion due to four-wave mixing between pumps and generation of higher-order idlers.
We propose and experimentally demonstrate a phase-sensitive optical processor, capable of generating two codirectional and π-phase-shifted phase-sensitive amplifiers (PSAs) in a single device. Phase-sensitive operation is obtained by polarization mixing a phase-locked signal/idler pair generated in a degenerate dual-pump vector parametric amplifier based on four-wave mixing in a highly nonlinear fiber. We refer to this configuration as a polarization assisted PSA and demonstrate some of the applications that it may find. First, we experimentally demonstrate the regeneration of a binary phase shift keying signal in a system that requires only a very low nonlinear phase shift of 0.35 rad. Second, we decompose a quadrature phase shift keying (QPSK) signal into its in-phase and quadrature components. While application to a QPSK signal is shown in our demonstration, we demonstrate numerically that any complex modulation format signal can be decomposed using this approach. Finally, we use our processor to regenerate QPSK signals in a single nonlinear device.