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IEEE Photonics Technology Letters

Four-Wave-Mixing-Based Phase-Sensitive Amplification of Pulsed Signal in Fibers

Xiaosheng Xiao, Perry Ping Shum, Elham S. Nazemosadat, Changxi Yang

Published Feb 9, 2009• 4 citations
Publisher

Abstract

The four-wave-mixing-based phase-sensitive amplification of pulsed signals is analytically investigated, taking into account the pump depletion and the self- and cross-phase modulation (SPM and XPM) effects of the pumps and signals. Formulas for output phase and power are derived. It is found that, for a single-pulse signal input, the SPM/XPM of the signal will cause frequency chirping to the output; for a pulse-sequence, the amplitude-fluctuation of the input signal will destroy the phase regeneration through the SPM/XPM. In addition, the amplified signal pulse will initially be compressed and distorted, and then it will get broadened due to pump-depletion.

DOI
10.1109/lpt.2009.2012400

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An investigation is reported of the characteristic features of a four-wave mixing of a chirped signal with bandwidth- limited pump waves in a resonant medium modeled by a two- level scheme. Analytic estimates are obtained and a numerical analysis is made of the combined influence of various mechanisms (spatial phase matching, a finite nonlinear response time, and phase cross-modulation) on the spectral composition and on the temporal behavior of the fourth pulse. Conditions are found for achieving, with practically undetectable distortions, phase conjugation of a chirped signal accompanied by shortening of the pulse envelope and narrowing of the spectrum of the phase- conjugate wave.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 28, 1998•0 citations
The four-wave-mixing-based phase-sensitive amplification of pulsed signals is analytically investigated, taking into account the pump depletion and the self- and cross-phase modulation (SPM and XPM) effects of the pumps and signals. Formulas for output phase and power are derived. It is found that, for a single-pulse signal input, the SPM/XPM of the signal will cause frequency chirping to the output; for a pulse-sequence, the amplitude-fluctuation of the input signal will destroy the phase regeneration through the SPM/XPM. In addition, the amplified signal pulse will initially be compressed and distorted, and then it will get broadened due to pump-depletion.
The four-wave mixing (FWM)-based phase sensitive amplification (PSA) with pulsed signal input is investigated. A set of exact analytical solutions for the output amplitude and phase of PSA is derived, taking into account the pump depletion and the self- and cross-phase modulation (SPM and XPM) from pumps, signal and idler. Simplified analytical expression of output idler power is obtained, which shows that, the amplified signal/idler pulse will be compressed firstly due to the phase distortion of input signal, then will be broadened due to pump-depletion.
Optical amplification in optical fibers by means of degenerate four-wave mixing (DFWM) is studied by classical equations. A balanced interferometer is used to mix and separate the signal and the pump. Exact solutions are obtained even with pump depletion. If the cross-phase modulation is small, the signal power gain varies as the square of the pump self-phase shift. This gain can be sizable for moderate fiber lengths and laser powers, before the onset of stimulated Raman scattering. We have experimentally verified these calculations with a Sagnac interferometer, comprising a 300 m long polarization-preserving fiber, emitting pulses with 100-200 W peak power and 100-200 nsec duration. We have measured a signal power gain of 22 (13.3 dB); this value correlated well with a pump self-phase shift of 3π/2 measured in a separate two-wavelength experiment. This system can be used for squeezing fluctuations of the signal quadrature which is not amplified. We have performed a classical derivation of squeezing, based upon a geometrical study of the transformation of the signal phasor. The results are in agreement with those of more elaborate quantum-mechanical derivations.
The noise properties of phase sensitive amplifiers based on degenerate four-wave mixing in optical fibers are studied taking into account the quantum noise amplification, the amplitude and phase noise properties of the pump sources. An analytical tool is presented for the direct calculation of the amplifier noise figure also verified by extensive numerical simulations. The signal power dependence of noise figure is both analytically and numerically accented. The need for high speed and precise phase locking is also revealed in order to diminish the effect of phase noise on the noise properties of the amplifier.
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.
Summary form only given. When a signal propagates through a transmission line, it is deteriorated by amplitude and phase noise, which reduces its signal-to-noise ratio (SNR) [1]. According to Shannon's theory, the SNR determines the maximum spectral efficiency. It is therefore necessary to limit the noise [3]. For this purpose, one can use phase sensitive amplifiers (PSA) instead of phase insensitive amplifiers (PIA) like Erbium-doped fiber amplifiers. PSAs amplify only one phase quadrature of the signal while deamplifying the other, thanks to a required phase relationship between the pump and the signal. This unique property, known as phase-squeezing, allows to obtain noise figures (NF) as low as 0 dB whereas PIAs, based on stimulated emission, cannot be go below the 3 dB quantum limit [2]. Moreover, the phase-squeezing property of PSAs can be used for quantum communication or even in metrology [1]. PSA can be realized with χ(2)material through degenerate parametric amplification [2]. The large spectral separation between the pump and the signal makes it very easy to filter out the pump after amplification. A ± 11 dB amplification with a sub-quantum NF and a regeneration of a DPSK signal was experimentally performed in LiNbO3 [3]. A fiber based approach would however be preferable for telecommunication purposes. PSA's based on four wave-mixing have been demonstrated, but the long length and the difficulty to separate pump from the signal [1] hinders its practical implementation. Here we present the first demonstration of a PSA based on periodically poled silica fiber (PPSF). This design has the advantage of all-fiber devices as well as simple pump filtering. The experimental set-up is depicted in Figure 1. A 20 mW CW fiber laser at 1550 nm is sent through a 99:1 coupler to be divided into a signal and a pump. The pump is modulated into 1 ns wide pulses with a repetition rate of 50 MHz. It is then amplified and frequency doubled in a PPLN crystal. The peak power of the 775 nm pump pulses reaches 10W. The pump and CW signal are then combined in a WDM and sent through a 30 cm long PPSF [4] where the signal undergoes parametric amplification. A second WDM is used to separate the pump from the amplified signal. The wave plates and the polarization controller in the pump path, allow to simultaneously control the polarization of the pump and the power in the fundamental mode of the PPSF (at 775 nm the fibre is slightly multimode). The relative phase between the pump and signal is controlled by fine tuning the frequency of the laser via a built-in piezo.
An investigation is reported of the characteristic features of a four-wave mixing of a chirped signal with bandwidth- limited pump waves in a resonant medium modeled by a two- level scheme. Analytic estimates are obtained and a numerical analysis is made of the combined influence of various mechanisms (spatial phase matching, a finite nonlinear response time, and phase cross-modulation) on the spectral composition and on the temporal behavior of the fourth pulse. Conditions are found for achieving, with practically undetectable distortions, phase conjugation of a chirped signal accompanied by shortening of the pulse envelope and narrowing of the spectrum of the phase- conjugate wave.