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arXiv:physics/0408104 · Physical Review E

Squared-field amplitude modulus and radiation intensity nonequivalence within nonlinear slabs

Alberto Lencina, Pablo Vaveliuk

Published May 25, 2005• 7 citations
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Abstract

This paper presents an approach to wave propagation inside the Fabry-Pérot framework. It states that the time-averaged Poynting vector modulus can be nonequivalent to the squared-field amplitude modulus. This fact permits the introduction of a kind of nonlinear medium whose nonlinearity is proportional to the time-averaged Poynting vector modulus. Its transmittance is calculated and found to differ from that obtained for a Kerr medium, whose nonlinearity is proportional to the squared-field amplitude modulus. The latter emphasizes the nonequivalence of these magnitudes. A space-time symmetry analysis shows that the Poynting nonlinearity should be possible only in noncentrosymmetric materials.

DOI
10.1103/physreve.71.056614

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This paper presents an approach to wave propagation inside the Fabry-Pérot framework. It states that the time-averaged Poynting vector modulus can be nonequivalent to the squared-field amplitude modulus. This fact permits the introduction of a kind of nonlinear medium whose nonlinearity is proportional to the time-averaged Poynting vector modulus. Its transmittance is calculated and found to differ from that obtained for a Kerr medium, whose nonlinearity is proportional to the squared-field amplitude modulus. The latter emphasizes the nonequivalence of these magnitudes. A space-time symmetry analysis shows that the Poynting nonlinearity should be possible only in noncentrosymmetric materials.
A theoretical analysis on wave propagation and optical properties of slabs with light-induced free charge carriers within a Fabry-Pérot framework is presented. The key of the analysis is to attack the wave propagation problem in terms of the time-averaged Poynting vector modulus within the medium through an alternative approach. This fact allows coupling the microscopic (free charge rate) and macroscopic (electromagnetic field evolution) equations self-consistently by means of the nonlinear permittivity and conductivity, which, in turn, depend on the time-averaged Poynting vector modulus. Thereby, the transmittance, reflectance, and absorptive power are derived as functions of the pump intensity and medium thickness. Bistable behavior is found at relatively high excitation intensity for positive values of the nonlinear permittivity coefficient. The bistability enhances for increasing values of such coefficient and weakens for increasing values of nonlinear photoconductivity coefficient. On the contrary, for negative nonlinear permittivity coefficient, bistability does not appear possessing these media mirrorlike behavior. Some possible applications are suggested.
In this paper we study propagation of electromagnetic waves in media with an imaginary Kerr-type nonlinearity. We show numerically that the slowly varying envelope approximation can still be used. It is proved that theoretical problems described by this type of differential equations are Hamiltonian systems. This characteristic is used to predict the variation of the electromagnetic field in the nonlinear material. Furthermore, we find a closed expression for the electromagnetic waves in a nonlinear medium with a linear absorption and an imaginary Kerr-type nonlinearity, for both a localized and a diffusive nonlinearity. Calculating the transmission probability of light through a Fabry-P\'erot structure shows that the introduction of an imaginary Kerr-type nonlinearity describes an intensity-dependent optical gain or absorption in a nonlinear medium. This system also shows bistable behavior comparable to real Kerr-type nonlinear materials. \textcopyright{} 1996 The American Physical Society.
We theoretically study multiple scattering of monochromatic light by a collection of spheres that can freely move in a background medium. The spheres contain an optical nonlinearity of the Kerr type. Employing diagrammatic methods we construct the iterative solution of the nonlinear scalar wave equation that describes the electromagnetic radiation field inside the sacttering medium. The ensuing diagrammatic series for the amplitude of the radiation field is averaged over all possible configurations of the scatterers. Subsequently, it is proved that the average amplitude satisfies a nonlinear equation that is the counterpart of the usual Dyson equation. For the case of point scatterers that do not absorb light we obtain solutions of our nonlinear Dyson equation. They predict that as a result of auto-Kerr and backscattering effects, the system can become unstable. Furthermore, we find that it is possible to bleach the scatterers. Finally, the influence of nonlinear absorption on the average amplitude is investigated.
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We apply a recently developed scheme for electromagnetic field quantization in dispersive and absorbing dielectrics to calculate the effects of perpendicular propagation through a finite-temperature dielectric slab on the properties of an incident pulse of light. The theory applies to incident pulses of nonclassical light and also reproduces the results for classical pulses in the appropriate limit. The transmitted pulse is assumed to be measured by a detector that receives radiation only from the direction normal to the slab surfaces. The Poynting vector of the transmitted light includes contributions from the incident pulse, whose shift in peak position and additional broadening or narrowing are determined, and from the thermal emission of the slab, which tends to a black-body form in the appropriate limits.