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Nonlinear Guided Waves and Their Applications

Long-term storage of a soliton bit stream using phase-sensitive amplification

Antonio Mecozzi, William L. Kath, Prem Kumar, Christopher G. Goedde

Published Jan 1, 1995• 0 citations
Publisher

Abstract

Recently we have shown that stable soliton-like pulse propagation over ultra-long distances is possible in a nonlinear fiber line in which linear loss is balanced by periodic phase-sensitive (parametric) amplification.1 In such a line the length scale over which pulse evolution occurs is significantly increased beyond a soliton period because of the attenuation of phase variations across the pulse’s profile by the amplifiers. Here we examine the effects of quantum noise in the context of a storage ring for a bit stream of soliton-like pulses. We show that the one’s (soliton pulses) are asymptotically stable and the noise on the zero’s of the bit stream (absence of a soliton) is bounded. Moreover, we present evidence that the soliton-soliton interaction and Raman self-frequency shift are efficiently suppressed by the phase-sensitive amplifiers (PSA’s). The effects of direct timing noise and cubic dispersion in the fiber could also be decreased by using a pulsed pump (gain modulation) for the PSA’s.

DOI
10.1364/nlgw.1995.nfa12

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Recently we have shown that stable soliton-like pulse propagation over ultra-long distances is possible in a nonlinear fiber line in which linear loss is balanced by periodic phase-sensitive (parametric) amplification.1 In such a line the length scale over which pulse evolution occurs is significantly increased beyond a soliton period because of the attenuation of phase variations across the pulse’s profile by the amplifiers. Here we examine the effects of quantum noise in the context of a storage ring for a bit stream of soliton-like pulses. We show that the one’s (soliton pulses) are asymptotically stable and the noise on the zero’s of the bit stream (absence of a soliton) is bounded. Moreover, we present evidence that the soliton-soliton interaction and Raman self-frequency shift are efficiently suppressed by the phase-sensitive amplifiers (PSA’s). The effects of direct timing noise and cubic dispersion in the fiber could also be decreased by using a pulsed pump (gain modulation) for the PSA’s.
We study the possibility of employing phase-sensitive parametric amplifiers to compensate for losses incurred by solitons propagating in optical fibers. As phase-sensitive amplification is free from the excess spontaneous noise associated with laser amplifiers, the only quantum noise source in such a system arises from the fiber losses. In addition, under phase-sensitive amplification, fluctuations in the soliton frequency are squeezed to one half of the vacuum level, thus producing a negligible contribution to the fluctuations in the soliton arrival time. This greatly reduces the Gordon–Haus jitter of the solitons. The performance of the phase-sensitive amplifier is compared with that of alternative noise-reduction schemes employing phase-insensitive amplifiers and spectral filters as well as with the limits on long-distance data transmission imposed by quantum mechanics.
In optical communication systems, Phase Sensitive Amplifier (PSA) is well known for its superior noise performance in the sub-quantum limit. Therefore, PSAs are highly suitable for long haul transmission systems where amplification and regeneration is critical. In this paper, we analyze the gain performance of a single pump non-degenerate PSA operating in the quadratic gain regime. The variation of gain characteristics with pump power and fiber length has been discussed. It could be seen that for a 5km long fiber, increasing of pump power above 4W subjected to the increasing of amplifier gain while maintaining the relative phase at a stable constant value of 0.001 rad. Therefore, by fine tuning parameters like fiber nonlinearity, pump power and fiber length, a phase stabilized gain performance of the PSA could be achieved when it is operating in the quadratic gain regime.
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.
Classical optical solitons propagate in optical fibers without temporal or spectral distortion as a result of a balance between phase shifts due to group velocity dispersion and those due to nonlinear self-phase modulation. This balance is achieved by the proper choice of pulse shape and duration for a given pulse energy. The quantum fluctuations associated with a coherent soliton do not undergo stationary propagation, however, and a number of effects are predicted, including the evolution of vacuum noise associated with the input coherent pulse into squeezed fluctuations and the temporal spreading of the soliton pulse because of dispersion acting on quantum fluctuations of the pulse frequency.
Recent theoretical work predicts that the quantum-limited noise figure of a x(3)-based fiber-optical parametric amplifier operating as a phase-insensitive in-line amplifier or as a wavelength converter exceeds the standard 3-dB limit at high gain. The degradation of the noise figure is caused by the excess noise added by the unavoidable Raman gain and loss occurring at the signal and the converted wavelengths. We present detailed experimental evidence in support of this theory through measurements of the gain and noise-figure spectra for phase-insensitive parametric amplification and wavelength conversion in a continuous-wave amplifier made from 4.4 km of dispersion-shifted fiber. The theory is also extended to include the effect of distributed linear loss on the noise figure of such a long-length parametric amplifier and wavelength converter.