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arXiv:quant-ph/0412096 · Physical Review A

Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: Numerical study

Edouard Brainis, David Amans, Serge Massar

Published Feb 14, 2005• 35 citations
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Abstract

We study scalar and vector modulation instabilities induced by the vacuum fluctuations in birefringent optical fibers. To this end, stochastic coupled nonlinear Schr\"odinger equations are derived. The stochastic model is equivalent to the quantum field operators equations and allows for dispersion, nonlinearity, and arbitrary level of birefringence. Numerical integration of the stochastic equations is compared to analytical formulas in the case of scalar modulation instability and nondepleted pump approximation. The effect of classical noise and its competition with vacuum fluctuations for inducing modulation instability is also addressed.

DOI
10.1103/physreva.71.023808

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We study scalar and vector modulation instabilities induced by the vacuum fluctuations in birefringent optical fibers. To this end, stochastic coupled nonlinear Schr"odinger equations are derived. The stochastic model is equivalent to the quantum field operators equations and allows for dispersion, nonlinearity, and arbitrary level of birefringence. Numerical integration of the stochastic equations is compared to analytical formulas in the case of scalar modulation instability and nondepleted pump approximation. The effect of classical noise and its competition with vacuum fluctuations for inducing modulation instability is also addressed.
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In this Letter we introduce a novel equation addressing the effect of quantum noise in optical fibers with arbitrary frequency-dependent nonlinear profiles. To the best of our knowledge, such an endeavor has not been undertaken before despite the growing relevance of fiber optics in the design of new quantum devices. We show that the stochastic generalized nonlinear Schrödinger equation, derived from a quantum theory of optical fibers, leads to unphysical results such as a negative photon number and the appearance of a dominant anti-Stokes sideband when applied to this kind of waveguides. Starting from a recently introduced master-equation approach to propagation in fibers, we derive a novel stochastic photon-conserving nonlinear Schrödinger equation suitable for modeling arbitrary nonlinear profiles, thus greatly enhancing the study of fiber-based quantum devices.
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Presents an analytical model which describes the dynamics of the modulation instability in a nonlinear, dispersive, homogeneously broadened and nonsaturable fiber amplifiers. The general case of arbitrary detuning between the laser frequency and the resonance frequency and arbitrary bandwidth of the amplifying transition is treated. The model accounts both for the gain dispersion and for the gain-induced, near resonant refractive index dispersion, Simple closed form expressions for the combined gain coefficients of the Stokes and anti-Stokes frequencies are obtained.
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.