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Acta Physica Sinica (Overseas Edition)

Quantum noise theory for the two-mode radiation fields in the nonlinear optical fiber with gain

Lu-Bi Deng, Qian Feng, Mingde Zhang, Yang Xiang-lin

Published Feb 1, 1994• 0 citations
Publisher

Abstract

We have studied the squeezing of the two-mode radiation fields in a nonlinear optical fiber with gain. The coupling nonlinear Schrödinger equations corresponding to the circularly polarized radiation fields with gain are derived by means of the method of path integrals. The minimized power spectra of the quantum noise of these fields are obtained with a first-order perturbation approximation in the frequency domain. Detailed numerical analyses of the results are performed and presented graphically, taking zero-dispersion, normal and anomalous dispersion into account.

DOI
10.1088/1004-423x/3/2/003

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We analyze the quantum dynamics of radiation propagating in a single mode optical fiber with dispersion, nonlinearity, and Raman coupling to thermal phonons. We start from a fundamental Hamiltonian that includes the principal known nonlinear effects and quantum noise sources, including linear gain and loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are treated. This allows quantum Langevin equations to be calculated, which have a classical form except for additional quantum noise terms. In practical calculations, it is more useful to transform to Wigner or +PPP quasi-probability operator representations. These result in stochastic equations that can be analyzed using perturbation theory or exact numerical techniques. The results have applications to fiber optics communications, networking, and sensor technology.
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Abstract In this report, we present a quantum theory describing the propagation of the electromagnetic radiation in a fiber in the presence of the third order dispersion coefficient. We obtained the quantum photon-polariton field, hence, we provide herein a coupled set of operator forms for the corresponding nonlinear Schrödinger equations when the third order dispersion coefficient is included. Coupled stochastic nonlinear Schrödinger equations were obtained by applying a positive P-representation that governs the propagation and interaction of quantum solitons in the presence of the third-order dispersion term. Finally, to reduce the fluctuations near solitons in the first approximation, we developed coupled stochastic linear equations.
We develop a quantum theory of propagation in dispersive nonlinear media via a quantized field theory and a coherent state expansion. The resulting stochastic nonlinear Schrodinger equation includes both quantum fluctuations and thermal noise due to refractive-index fluctuations in the medium. The theory can describe either cw propagation with dispersion or soliton propagation. In the cw case, enhanced squeezing occurs with anomalous dispersion. This is reduced by thermal noise, just as it is in the normal dispersion case. The noise-induced reduction in squeezing is more severe with normal dispersion owing to the intrinsic lack of phase matching in the normal dispersion regime. With anomalous dispersion, the cancellation of nonlinear by linear dispersion allows squeezing to occur over a wide bandwidth even in the presence of thermal fluctuations. Our theory is also able to treat soliton propagation in the anomalous dispersion case. A substantial degree of pulsed squeezing is obtained, and we point out that an optimal detection scheme requires a pulsed local oscillator. Results for the effects of thermal noise on soliton propagation are presented, in which case improvement is obtained by reducing the soliton time duration.