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Annual Meeting Optical Society of America

Photon pair correlations and the effect of Raman scattering noise in optical fibers

T. A. B. Kennedy, J. Stephens

Published Jan 1, 1992• 0 citations
Publisher

Abstract

The propagation of a quantized radiation field in a nonlinear optical fiber is investigated by using a quantum nonlinear Schrödinger equation with Raman scattering contributions.1 Wideband photon pair correlations generated via the optical Kerr effect and the role of group velocity dispersion and Raman scattering will be discussed. Specifically, the quantum correlations of up-shifted and downshifted sidebands in the modulational instability at terahertz frequency detuning from the pump lie outside the GAWBS region, but they are influenced by the low frequency region of the Raman gain curve, which introduces an asymmetry between the sidebands. The effects of this asymmetry on photon pair correlations and twin beams will be discussed.

DOI
10.1364/oam.1992.fnn6

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The propagation of a quasimonochromatic beam in an optical fiber may be unstable owing to phase-matched four-wave mixing. The phase matching may arise in a variety of ways, and the resulting instabilities are commonly referred to as modulational instabilities. Here I consider the cross-phase-modulational (XPM) instability arising in a high birefringence optical fiber in the normal dispersion (visible) regime when the pump is polarized at 45° to the principal axes of birefringence.1,2 Orthogonally polarized sidebands are generated along these axes. Phase matching arises from a balance between dispersion and the group velocity mismatch of the sidebands and dictates that the up-shifted sideband travels on the fast axis. The sidebands result in terahertz modulation of the pump and are interesting from the point of view of optical communications. From a quantum-statistical perspective, the quantum correlations, which develop as the sidebands are generated from quantum noise, are the focus of attention here.
Intrapulse quantum spectral correlation of photon numbers of a femtosecond optical pulse, which propagates a 5-m-long optical fiber, is presented in a matrix format for quantum noise study by numerical calculation. The calculation includes the higher-order optical effects such as intrapulse-stimulated Raman scattering and self-steepening effects, as well as self-phase modulation and group velocity dispersion. The quantum correlations between spectral components (spectral resolution of 0.7 nm) which evolve with the pulse energy are provided in a matrix format at soliton orders including the low orders, N=0.1N=0.1N=0.1 to 1.0 (a 0.1 step), to give the detailed properties of spectral correlation evolutions in the matrix format. It is shown that the photon-number correlations between spectral components near the pulse spectrum center form strong correlations of a square shape in the matrix, at a soliton order NNN ($\ensuremath{\le}$0.4), and then are redistributed into those between spectral components near the spectrum wings such that the cross-shaped correlation pattern in the matrix begin to be visible at N=0.5N=0.5N=0.5 before their further redistribution as $N\ensuremath{\rightarrow}1.0$. In addition, significant anticorrelations can be increasingly extended to be found between spectral components near the spectrum center as $N\ensuremath{\rightarrow}1.0$, leading to the expectation that the degree of photon-number squeezing by spectral filtering for subsolitons can be lower than that for solitons. Intrapulse-stimulated Raman scattering that starts to become visible at around N=0.6N=0.6N=0.6 produces an asymmetric correlation structure with respect to the spectrum center in the correlation matrices while the relevant pulse self-frequency shift becomes visible at $N\ensuremath{\ge}0.8$. The calculation presented indicates that the measurement of nonlinear effects which are not detectable distinctly at the classical level is possible at the quantum level.
We present a general quantum theory capable of describing photon statistics under the combined effects of four-wave mixing and Raman scattering inside optical fibers. Our theory is vectorial in nature and includes all polarization effects. Our analysis shows that spontaneous Raman scattering degrades the pair correlation in all cases but the extent of degradation depends on the pumping configuration employed. In a single-pump configuration, photon pairs can be created with polarization either parallel or orthogonal to the pump. Our results show that the orthogonal configuration can improve the extent of quantum correlation considerably over a broad bandwidth. In the case of a dual-pump configuration, we show that imbalance of two pump powers can be used to improve the quality of photon pairs. We show that orthogonally polarized pumps can generate photon pairs automatically in a polarization-entangled state. In particular, orthogonal pumping with circular polarizations produces such an entangled state with relatively high quality. We also quantify the quality of polarization entanglement as well as energy-time entanglement constructed using correlated photon pairs.
We investigate the impact of fiber birefringence and spontaneous Raman scattering on the properties of photon pairs that are generated by the spontaneous four-wave mixing process in birefringent fibers. Starting from the formulation of the theory of four-wave mixing, we show a theoretical model for a generated optical field with the consideration of the Raman scattering and a Gaussian-distributed pump. The theoretical model is then applied for deriving the closed expressions of the photon-pair spectral properties as a function of the fiber birefringence. Also, with the modeled Raman gain, we evaluate the reduction of the pair production rate due to the presence of the Raman effect as well as the contributions of the Raman-scattered photons over a broad wavelength range. The predictions are experimentally verified with a commercial polarization-maintaining fiber.