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Physica D Nonlinear Phenomena

The effect of propagation nonlinearities on the information capacity of WDM optical fiber systems: cross-phase modulation and four-wave mixing

L. G. L. Wegener, Michelle L. Povinelli, Andrew G. Green, Partha P. Mitra, J. B. Stark, P. B. Littlewood

Published Dec 12, 2003• 44 citations
Publisher
DOI
10.1016/j.physd.2003.09.038

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We present a quantum theory for generating two-photon states by means of four-wave mixing in optical fiber. We start with an interaction Hamiltonian that can correctly describe all nonlinear interactions among the four waves present in the fiber, namely, the frequency non-degenerate pumps, signal, and idler, including the terms responsible for self-phase modulation (SPM), cross-phase modulation (XPM), and four-photon scattering (FPS). The exact form of this Hamiltonian is obtained through comparison between the classical and quantum equations of motion. The two-photon state is then calculated by means of first-order perturbation theory. It turns out that only the FPM and the pump SPM terms contribute to the formation of the two-photon state. The entangled nature of this state is verified in a coincidence counting experiment. The results of the theoretical calculation agree well with experimental data.
Part I of this thesis describes the theoretical and experimental aspects of a new area in coherent optics known as phase conjugate optics. By using nonlinear optical mixing techniques, the complex conjugate of an arbitrary incident monochromatic wave can be generated. In particular, the theory of the degenerate four-wave mixing technique is presented. Experimental observation of phase conjugate wave front generation in a liquid crystal material (MBBA) is described. The ability of the conjugate wave front to correct for phase aberration is demonstrated. The quantum mechanical origin of the nonlinear third order susceptibility responsible for the four-wave mixing process is illustrated in an atomic system. Because of a finite memory time of such an atomic system, the electromagnetic waves taking part in the mixing process need not occur simultaneously. The applications of the phase conjugation process to real-time information processing and the characteristics of a phase conjugate resonator are discussed in detail. The ability of an optical fiber to confine the propagation of electromagnetic waves over a long distance and within a small cross sectional area implies that large optical intensities can be maintained over a long " interaction length even at moderate incident optical power. Part II of this thesis describes some third order nonlinear optical phenomena that have been observed under this condition. Especially, phase conjugation by degenerate four-wave mixing in a fiber has been shown to require significantly less pumping power. The theoretical and experimental studies of four-wave mixing in a liquid-filled fiber are presented. Extensive experimental efforts have been devoted over the last few years to the study of stimulated Raman scattering and the oscillation of the Stokes radiation inside fibers. A detailed theoretical treatment will be given here to describe these effects. The analysis shows that pump depletion due to the nonlinear process is very important in describing the stimulated Raman scattering in low loss fibers and is the dominant saturation effect in a fiber Raman oscillator. Finally, the implications of nonlinear optical phenomena to fiber optic communication will be mentioned.
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.