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Physical Review A

Influence of higher-order photon absorption on bistable-soliton propagation and switching

Richard H. Enns, S. S. Rangnekar

Published Sep 1, 1991• 3 citations
Publisher

Abstract

The effect of weak higher-order photon absorption on bistable-soliton propagation and switching in a fiber whose intensity-dependent refractive index is described by the linear-plus-smooth-step model is investigated numerically. The choice of model allows the application of the adiabatic assumption and a clear analytic interpretation of all of the observed results.

DOI
10.1103/physreva.44.3373

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The effect of weak higher-order photon absorption on bistable-soliton propagation and switching in a fiber whose intensity-dependent refractive index is described by the linear-plus-smooth-step model is investigated numerically. The choice of model allows the application of the adiabatic assumption and a clear analytic interpretation of all of the observed results.
Recently, we predicted1) that partial sample switching can occur in a system showing resonatorless optical bistability due to induced absorption. For an increasing intensity of the incident light, a stepwise propagation of the kink in the excitation profile takes place. In the meantime, the corresponding modulation of the transmitted light has been observed in sharp-cut color filters2). Here, we present an in-depth study of the structure, formation and motion of the kinks. We supplement and expand our original numerical investigations1) by detailed analytical studies. We show that the kink profile may be approximated by a soliton structure if the diffusion of the excitation density is taken into account. Furthermore, we present some simple estimates for the kink propagation.
The authors study analytically and numerically the effect of a periodic perturbation in the index of refraction of a nonlinear optical medium. Using a one-dimensional model for monochromatic waves incident on the medium, they find that near resonance between the perturbation and the modulation of the electric field there can be a significant enhancement of optical bistability in the low intensity regime. In particular, they discuss in detail the case of the primary resonance, which is responsible for the most significant effects, and show how one can optimize the bistability curve for the implementation of an optical switch, based on the information provided by the resonance structure.
Accurate modeling of optical nonlinearities is crucial to describe macroscopic laser propagation in a medium, including sum frequency generation, spectral broadening due to self-phase modulation, various ionization processes and soliton formation. For incident laser light the response of the medium is given by the induced polarization of the microscopic system. The polarization is usually expanded in a Taylor series for the electric field amplitude, which is truncated after the first non-linear term being of third order for isotropic media. A third-order nonlinearity leads to the well-known optical Kerr effect, where the refractive index of the medium becomes intensity dependent via n = n0+ n2I. This leads to an inherent problem when modeling laser propagation in two or more spatial dimensions, linked to the formal divergence (n2> 0) of the refractive index for increasing intensity.
Recent experimental results on edge-filtered (also referred to as low- and high-pass filters) subpicosecond optical solitons have raised a number of theoretical questions concerning the origin of the reduced photon- number fluctuations. One of the main experimental results was that for long fibers, on the order of 100 soliton periods, the measured photon-number squeezing increased with propagation distance in contrast with theoretical calculations for picosecond solitons at that time. Here I present theoretical results on photon statistics of edge-filtered subpicosecond optical solitons. The numerical simulations include coupling to phonons via a Raman interaction, in addition to the electronic Kerr nonlinearity, and are in good agreement with the experimental data over the range of propagation distances investigated so far. The theoretical results clearly show that the phenomena observed are not related to long fiber propagation but to the Raman self-frequency shift and should be more clearly observable using cooled fiber.
It is known that two-wave coupling in photorefractive crystal may result in an intensity-dependent phase shift as well as energy transfer between the two waves without phase crosstalk. In a sense, this kind of phase shift is similar to the intensity-dependent refractive-index effects in Kerr media. Consequently, optical bistability can be established in an optical cavity with a photorefractive crystal. We formulate the model and get the expected bistable transmission with numerical simulations. Several cases, including that of the codirectional coupling and the contradirectional coupling, are considered. The effects of the photorefractive crystal’s distribution absorption and the spatial phase shift between the index grating and the light interference pattern in the crystal on the nonlinear transmission characteristics have also been studied. It is interesting to note that the output of the pumping wave is dependent on the cavity intensity and thus shows bistable behavior with respect to the cavity input as well.