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Physical Review A

Multimode quantum theory of nonlinear propagation in optical fibers

Aruto Hosaka, Taiki Kawamori, Fumihiko Kannari

Published Nov 17, 2016• 9 citations
Publisher

Abstract

We theoretically reveal the potential of the parallelism of squeezed state generation by nonlinear pulse propagation in an optical fiber. Starting from a nonlinear Schr\"odinger equation coupling with phonon modes that cause Raman noise, we develop a multimode quantum theory of nonlinear propagation in an optical fiber. Based on our proposed method, we numerically simulate fiber nonlinear propagation in two conditions: solitonlike and zero-group-delay-dispersion (zero-GVD) propagation. As a result, we find that zero-GVD propagation enables the large-scale parallel generation of squeezed states relative to solitonlike propagation owing to the broadband phase matching of the four-wave mixing process.

DOI
10.1103/physreva.94.053833

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We theoretically reveal the potential of the parallelism of squeezed state generation by nonlinear pulse propagation in an optical fiber. Starting from a nonlinear Schr"odinger equation coupling with phonon modes that cause Raman noise, we develop a multimode quantum theory of nonlinear propagation in an optical fiber. Based on our proposed method, we numerically simulate fiber nonlinear propagation in two conditions: solitonlike and zero-group-delay-dispersion (zero-GVD) propagation. As a result, we find that zero-GVD propagation enables the large-scale parallel generation of squeezed states relative to solitonlike propagation owing to the broadband phase matching of the four-wave mixing process.
This paper presents a theory for quantum light propagation in a single-mode fiber which includes the effects of the Kerr nonlinearity, group-velocity dispersion, and linear loss. The theory reproduces the results of classical self-phase modulation, quantum four-wave mixing, and classical solution physics, within their respective regions of validity. It demonstrates the crucial role played by the Kerr-effect material time constant, in limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any quantized input field. Operator moment equations - approximated, numerically, via a terminated cumulant expansion - are used to obtain results for homodyne-measurement noise spectra when dispersion is negligible. More complicated forms of these equations can be used to incorporate dispersion into the noise calculations.
In this dissertation, multimode optical fibers (MMFs) have been studied as a robust and practical platform for nonlinear optics and quantum optics applications, where by experimental investigations and theoretical calculations we present the quantum and nonlinear virtue of MMFs as a versatile tool for future applications. Our investigations can be summarized in three parts: At first, we have investigated stimulated Raman scattering (SRS) in a long MMF, where more than 20 orders of cascaded Raman peaks have been generated. Observation of beam clean-up despite the highly multimode nature of the fiber and such strong nonlinear interaction despite the large fiber core size are distinguishable results of our work. Next, we have studied four-wave mixing (FWM) via intermodal phase-matching in both step-index and graded-index MMFs (GIMFs). A rigorous and general approach in the theoretical study is presented where some of the commonly used, yet inaccurate approximations are avoided. Experimentally, FWM side-bands with minimal contamination from SRS, and residual pump photons have been generated from quantum vacuum and amplified more than 11 orders of magnitude. Finally, in the last part of this dissertation, we have done a theoretical study of photon-pair generation in a multimode optical fiber (both step-index and GIMF) via intermodal-FWM as a source of state-engineered photon-pairs.
Squeezed light, in which the quantum noise in one amplitude component is reduced below the vacuum level, has been generated using parametric processes. The starting point described here is the nonlinear Schrodinger equation which models light propagating through optical fibers. When such a dispersive nonlinear medium with a third-order susceptibility is pumped with an optical beam, squeezing can result. It is found that the degree of squeezing oscillates as a function of fiber length in the normal dispersion regime, whereas in the anomalous dispersion regime, it grows exponentially with fiber length. Examination of squeezing near the fiber’s zero dispersion wavelength shows that odd-order dispersive terms have no effect on squeezing. However, small values of higher-order even terms have significant effects on squeezing. In practice, high-frequency components of the squeezing spectrum are difficult to obtain. However, it is shown that a cross-correlation technique may be used to explore the frequency dependence of the squeezing spectrum.
Generation of light with nonclassical properties, such as squeezed light, has gathered a lot of attention because of possible uses in such areas as quantum state engineering, quantum imaging, continuous variable quantum computing, and detection of gravitational waves. Squeezed light is generally produced by transporting light through a nonlinear medium. One such media is Kerr-nonlinear optical fibres. We aim to find the parameters for a fibre polarization squeezing setup by studying the dependencies of quantum noise suppression on the duration of the pulse and the input power. This is performed by modeling the light field propagation using the split-step Fourier method to numerically solve the stochastic nonlinear Schrödinger equation obtained by using the Wigner representation. This equation includes such physical effects as damping, quantum loss noise, dispersion, Kerr and Raman nonlinearities, and stochastic Raman noise.
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.