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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Intra-Modal Phase-Sensitive Four-Wave Mixing in a Few-Mode Fiber

Valentine Gaudillat, Margaux Barbier, Laurent Bramerie, Mathilde Gay, Marianne Bigot-Astruc, Pierre Sillard, Yannick Dumeige, Christophe Peucheret

Published Jun 26, 2023• 0 citations
Publisher

Abstract

Phase-sensitive parametric processes based on four-wave mixing (FWM) in third-order nonlinear media are attractive for the demonstration of numerous functionalities including low-noise amplification, high-sensitivity detection and signal phase quantization with applications to e.g. communication and sensing [1]. Until now, such processes have been demonstrated exclusively in single-mode optical fibers and waveguides. Meanwhile, the exploitation of the spatial (transverse) dimension of waveguides is also being explored for such applications, for instance in order to provide a new multiplexing degree of freedom in telecommunications [2]. One open question is whether the use of phase-sensitive processes can be made compatible with optical fibers and waveguides supporting multiple spatial modes. Some (inter-modal) phase-sensitive processes have been numerically investigated in few-mode fibers (FMFs) [3]. However, to the best of our knowledge, no experimental demonstration of phase-sensitive processes in FMFs has been reported so far. In this work, we demonstrate experimentally intra-modal phase-sensitive FWM, separately in two modes ($\text{LP}_{01}$and$\text{LP}_{11}$), in a 2-km long step-index FMF [4] supporting 4 LP-modes at 1550 nm.

DOI
10.1109/cleo/europe-eqec57999.2023.10232196

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Phase-sensitive parametric processes based on four-wave mixing (FWM) in third-order nonlinear media are attractive for the demonstration of numerous functionalities including low-noise amplification, high-sensitivity detection and signal phase quantization with applications to e.g. communication and sensing [1]. Until now, such processes have been demonstrated exclusively in single-mode optical fibers and waveguides. Meanwhile, the exploitation of the spatial (transverse) dimension of waveguides is also being explored for such applications, for instance in order to provide a new multiplexing degree of freedom in telecommunications [2]. One open question is whether the use of phase-sensitive processes can be made compatible with optical fibers and waveguides supporting multiple spatial modes. Some (inter-modal) phase-sensitive processes have been numerically investigated in few-mode fibers (FMFs) [3]. However, to the best of our knowledge, no experimental demonstration of phase-sensitive processes in FMFs has been reported so far. In this work, we demonstrate experimentally intra-modal phase-sensitive FWM, separately in two modes (LP01\text{LP}_{01}LP01​andLP11\text{LP}_{11}LP11​), in a 2-km long step-index FMF [4] supporting 4 LP-modes at 1550 nm.
Parametric processes in materials presenting a second- or third-order nonlinearity have been widely used to demonstrate a wide range of all-optical signal processing functionalities, including amplification, wavelength conversion, regeneration, sampling, switching, modulation format conversion, optical phase conjugation, etc.. The recent evolution of optical fiber communication systems towards advanced modulation formats making use of the phase dimension, as well as polarization and, more recently, space-multiplexing, has created new requirements, as well as new opportunities, for parametric all-optical signal processing. In this presentation, we will review our recent results on the demonstration of all-optical parametric signal processing using different nonlinear platforms, including highly nonlinear optical fibers (HNLFs), silicon nanowires, and periodically-poled lithium niobate (PPLN) waveguides. In particular, we will show how phase-sensitive processes can be engineered to demonstrate phase-quadrature separation, which we have recently demonstrated in HNLFs and PPLN waveguides. Silicon nanowires are particularly attractive for signal processing thanks to their compact size, CMOS compatible fabrication process, degrees of freedom in dispersion engineering, and high nonlinear coefficient. However, the detrimental effect of free-carrier absorption induced by two-photon absorption has so far prevented them from being used for the demonstration of phase-sensitive processing. Thanks to the introduction of p-i-n junctions across silicon waveguides, we have recently been able to demonstrate phase-sensitive extinction ratios as high as 20 dB, allowing the phase regeneration of phase-modulated signals under continuous wave pumping operation. One of the well-known limitations of planar waveguide devices for all-optical signal processing is their inherent polarization sensitivity. We will show how the introduction of polarization-diversity circuits relying on efficient and wideband polarization splitters and rotators can overcome this limitation. Finally, we will also discuss the introduction of signal processing functionalities that are compatible with the novel dimension of space multiplexing. More specifically, we will show how mode-selective wavelength conversion based on four-wave mixing can be realized in a multimode silicon waveguide.
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.
The stagnating increase in data transmission capacity in optical communication systems combined with the ever growing demand of transmission bandwidth is leading to an impending capacity crunch, referring to the point in time after which the available bandwidth of the individual user starts to decrease. To postpone this point in time, existing technologies in terms of data transmission through optical fibers must be optimized and new degrees of freedom must be introduced to continue the exponential increase in available bandwidth; space-division multiplexing is believed to be the strongest candidate for another degree of freedom in transmission fibers. This thesis is two-fold: firstly, starting at Maxwell’s equations and basic principles of quantum mechanics, a semi-classical model of the noise properties of fiber optical parametric amplifiers and frequency converters is presented. The model accounts for multiple effects present in nonlinear fibers such as four-wave mixing, Raman scattering, distributed loss, and dispersion, and it is valid in the depleted pump regime. After validating the model against well-known results of quantum models, the model is used to predict the impacts of Raman noise, loss, and pump depletion on the noise properties of parametric frequency conversion and phase-insensitive and phase-sensitive parametric amplification. An important part of realizing space-division multiplexing is the ability of optical signal processing so the second part of this thesis addresses few-mode Raman fiber amplifiers and parametric amplifiers and frequency converters. A model of weak random linear mode coupling in the pump of a two-mode distributed Raman fiber amplifier is presented and it is shown that an amplification noise figure induced by mode coupling increases with the degree of mode coupling and that this tendency increases as the pump depletes. Also, a very low mode-dependent gain of 0.25 dB per 10 dB gain is experimentally demonstrated in a two-mode distributed Raman fiber amplifier by exciting the pump in a combination of two modes. A comprehensive model of four-wave mixing in two-mode fibers acvi counting for six simultaneous processes is derived, and the conversion efficiency from signal to idler in the four-wave mixing processes of phase conjugation and Bragg scattering in two two-mode fibers with different phase matching properties are experimentally investigated. A conversion efficiency of > −2.70 dB is demonstrated for Bragg scattering in the conversion of a signal in the LP01-mode to the idler in the LP11-mode; the signal-to-idler separation is ∼ 25 nm. Good qualitative agreement between experiments and theory is found for both processes in both fibers.
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.
The strong interest in space-division multiplexing of classical communication signals has resulted in development of optical fibers that support propagation of multiple modes. This has paved the way for progress in signal processing using multiple modes and four-wave mixing between these. More specifically, careful design and knowledge of optical properties of individual modes enables phase matching in four-wave mixing that is otherwise not possible with single-mode fibers. This enables signal processing using four-wave mixing between higher-order modes for e.g. frequency conversion over a wide bandwidth. In addition, processing and creation of quantum states has also been demonstrated using four-wave mixing, including generation of photon pairs. In this work we review recent progress in signal processing and generation of quantum states using four-wave mixing.