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Optics Express

Optimization of the conversion efficiency and evaluation of the noise figure of an optical frequency converter based on a dual-pump fiber phase sensitive amplifier

Debanuj Chatterjee, Yousra Bouasria, Fabienne Goldfarb, Y. Hassouni, Fabien Bretenaker

Published Oct 19, 2022• 6 citations
Publisher

Abstract

We propose a new architecture of phase sensitive optical frequency converter based on dual-pump phase sensitive amplification in a highly nonlinear fiber. This frequency converter allows generation of extra tones through nonlinear four-wave mixing between two strong pumps and an input tone. The frequency channel to which the input tone is converted can be chosen by adjusting the phase of the input signal. The conversion efficiency and extinction ratio of this frequency converter are predicted and optimized and its noise figure is calculated using a numerical approach based on the nonlinear Schrödinger equation. A semi-classical noise figure calculation for this approach was used and validated using an analytical fully quantum calculation based on the multi-wave model.

DOI
10.1364/oe.471087

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We propose a new architecture of phase sensitive optical frequency converter based on dual-pump phase sensitive amplification in a highly nonlinear fiber. This frequency converter allows generation of extra tones through nonlinear four-wave mixing between two strong pumps and an input tone. The frequency channel to which the input tone is converted can be chosen by adjusting the phase of the input signal. The conversion efficiency and extinction ratio of this frequency converter are predicted and optimized and its noise figure is calculated using a numerical approach based on the nonlinear Schrödinger equation. A semi-classical noise figure calculation for this approach was used and validated using an analytical fully quantum calculation based on the multi-wave model.
Phase-sensitive amplification (PSA) based on nonlinear parametric interaction provides low-noise amplification such that the noise figure can be 0 dB in principle. However, when an optical fiber is used as a nonlinear medium for PSA, multiple four-wave-mixing (FWM) processes other than the PSA process are induced, which can degrade the PSA noise performance, especially in dual-pump PSA with a narrow signal-pump wavelength separation. This paper investigates the influence of multiple FWM processes on quantum noise of dual-pump PSA in an optical fiber. The noise figure is calculated using quantum-mechanical operators, considering multiple FWM processes with the PSA process. Calculation examples are also presented, which indicate that the noise figure is degraded by 0.2–0.4 dB from the ideal 0 dB, depending on the signal-pump wavelength separation and fiber parameters.
We have experimentally achieved a gain extinction ratio (GER) of 30 dB at 21.75 dBm pump power in a dual-pump phase sensitive amplifier based on highly nonlinear fiber, which is more efficient than what we predict with the conventional three-wave model. We point out that high-order sidebands play a key role. Then we scrutinize the trajectories of the output signal vector in the complex plane with increasing nonlinear phase shift and understand the roll-over behavior of GER versus pump power curve. We found that the phase "flip" of the output signal occurs around the largest GER. Adjusting design parameters, we show how to improve GER.
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.
We theoretically and experimentally study the principle of phase-sensitive frequency conversion in a highly-nonlinear fiber using three pump waves. This mechanism, originally demonstrated with four continuous-wave pumps and a signal wave, is based on four-wave mixing and enables to convert the two quadrature components of the signal to different frequencies. In this work, we derive a set of two simple equations to describe this mechanism and find analytic solutions. We show that only three pumps are required, instead of four as originally proposed. We give simple relations to determine the initial conditions for the power levels and the phases of the pumps. To validate this approach, we perform an experimental demonstration of the three-pump scheme and find excellent agreement with the theory.
Optical parametric amplifiers rely on second-order susceptibility (three-wave mixing) or third-order susceptibility (four-wave mixing) in a nonlinear process where the energy of incoming photons is not changed (elastic scattering). In the latter case, two pump photons are converted to a signal and to an idler photon. Under certain conditions, related to the phase evolution of the waves involved, this conversion can be very efficient, resulting in large amplification of an input signal. As the nonlinear process can be very fast, all-optical applications aside from pure amplification are also possible. If the amplifier is implemented in an optical input-phase-sensitive manner, it is possible to amplify a signal wave without excess noise, i.e., with a noise figure of 0 dB. In this paper, we will provide the fundamental concepts and theory of such amplifiers, with a focus on their implementation in highly nonlinear optical fibers relying on four-wave mixing. We will discuss the distinctions between phase-insensitive and phase-sensitive operation and include several experimental results to illustrate their capability. Different applications of parametric amplifiers are also discussed, including their use in optical communication links.
A semi-classical seven-wave model is developed to investigate the noise performances of a degenerate dual-pump phase-sensitive amplifier. This approach takes into account the transfer to the signal, through multiple four-wave mixing processes, of the vacuum fluctuations injected into high-order waves. This effect leads to a degradation of the noise figure of the amplifier with respect to the 0 dB value predicted by the usual three-wave model. However, it is proved that a careful choice of the fiber dispersion allows us to use high-order waves to enhance the signal gain without degrading the noise figure above 1 dB.