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Frontiers in Optics

Solitons Propagation in a Tandem Arrangement of Nonlinear Materials

Javier J. Sanchez-Mondragon, Miguel Torres-Cisneros, A. Alejo-Molina, José Amparo Andrade-Lucio, Jesus Escobedo-Alatorre, M. A. Basurto‐Pensado, Luz Antonio Aguilera-Cortés

Published Jan 1, 2006• 0 citations
Publisher

Abstract

A tandem is a periodically stratified medium, where the propagation of pulses, in particular nonlinear, have been recently studied. The ensuing Optical solitons reshaping results into a nonlinear modulation, that can be locally linearized as a perturbation near a soliton. We discuss two typical media, Two Level Atom and Kerr media.
DOI
10.1364/fio.2006.ftha6

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In this work we discuss the characteristics of the resonant pulse propagation through a sequence of two level atom media and in the presence of intensity dependent nonlinearities that occur in Kerr & photorefractive materials. The area theorem conveniently describe the evolution of the soliton eigenvalues through the stratified medium, an essential analytical tool lacking in the intensity dependent nonlinearities, thereof its understanding clarifies the general problem. We can conclude that rather than a mean soliton, we have a modulated solution.
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In this complement we discuss several examples of optical phenomena in media where the refractive index depends nonlinearly on the intensity , known as optical Kerr media. This nonlinear effect exists in all materials, even isotropic ones, like glass or fused silica, but it is particularly marked in certain physical systems to be exemplified in Section 7B.1. After investigating the propagation of light through such media in Section 7B.2, we shall discuss three applications of the optical Kerr effect (which can be studied in any order). We begin by describing a bistable optical system , when this nonlinear medium is inserted in a Fabry–Perot cavity (Section 7B.3). We then study phase conjugate mirrors and examine their potential applications in adaptive optics (Section 7B.4). Finally, we discuss certain effects occurring during the propagation of an isolated wave, bounded either transversely or temporally, in a Kerr medium, and describe self-focusing effects (Section 7B.5) and self-phase-modulation effects (Section 7B.6). In particular, we shall show that nonlinear effects and dispersion effects can compensate to produce stable structures known as solitons , which maintain their shape during propagation. Examples of third-order nonlinearities Nonlinear response of two-level atoms We begin by studying a simple case of a nonlinear interaction, namely a two-level quantum system under the effects of a plane wave.
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.
Coherent propagation of a circularly polarized pulse which is two-photon quasi-resonant with a medium of multi-level atoms is considered in the adiabatic following limit. The relevant pair of non-linear coupled partial differential equations are solved exactly for arbitrary pulse shapes. The development of the envelope and the phase of the pulse as it propagates through the medium is described analytically. Perturbation theoretical results are shown to apply only for small intensity or small distance of propagation or both. Qualitatively different results apply for higher intensities and longer distances of propagation. These include strong self-phase-modulation effects as well as reshaping of the pulse envelope.
We analyze the controlled behavior of light propagation in a stratified Kerr-nonlinear medium with its photonic band structure tuned by applying an external electric field. The transmittance T of light is significantly influenced by nonlinear effects induced by both the external field and the incident light. Transmission resonance (T = 1) is induced by two mechanisms, band-edge resonance and gap soliton resonance. The T?Eex graph has two turning points and consists of three solution branches. One unstable branch is located between the turning points, and connected with a stable solution branch at each turning point. As Eex increases and then decreases through the region of the turning points, the transition between the stable states on different branches produces optical bistability and hysteresis. As input light intensity grows, the upper stable solution branch separates itself from the unstable branch at the turning point, and both branches extend down to the ordinate axis at Eex = 0. We have greatly enhanced single-envelope solitons on the upper stable branch from the separation point to the line of zero external field.