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

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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.