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Journal of Modern Optics

Reflection and refraction of light at saturating active boundaries

Mohammad Azadeh, Lee W. Casperson

Published Jan 1, 1997• 4 citations
Publisher

Abstract

This study deals with the topic of reflection and refraction of light from the boundary of a high-gain saturating laser amplifier. Expressions for the electric field and intensity reflection and transmission coefficients are obtained for the case of a wave in a uniform dielectric that is incident normally on a nonlinear saturating active medium. Bistability effects are predicted even for the simplest case of zero frequency detuning from the line centre of the saturating transition.

DOI
10.1080/09500349708232897

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This study deals with the topic of reflection and refraction of light from the boundary of a high-gain saturating laser amplifier. Expressions for the electric field and intensity reflection and transmission coefficients are obtained for the case of a wave in a uniform dielectric that is incident normally on a nonlinear saturating active medium. Bistability effects are predicted even for the simplest case of zero frequency detuning from the line centre of the saturating transition.
Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].
A rigorous solution is given in the plane-wave approximation for the boundary problem of light reflection from the interface between an isotropic medium and a photorefractive crystal with drift-diffusion nonlinearity. The possibility of realizing hysteresis reflection or optical bistability in the system under certain conditions is shown. Analytical expressions are obtained that describe the hysteresis behavior of reflectivity as a function of the angle of incidence or the strength of a constant external electric field applied to the crystal. The results of the study are of interest for the development of devices controlling laser radiation.
Bistable laser amplifiers are attractive for potential application in optical switching because of very low input optical requirement, high extinction ratio and the presence of optical gain. Optical bistability (OB) arises from gain saturation and the associated nonlinear refraction combined with the effect of feedback in the laser cavity. We present the experimental results of bistable characteristics for the case of a 1.55 /spl mu/m symmetric Fabry-Perot (F-P) laser amplifier with uncoated facets. This paper reports a particularly rich variety of behaviour for reflected signals. Three main forms of hysteresis loops are observed on reflection. The hysteresis loop changes from anticlockwise to clockwise hysteresis in the optical input-output characteristic when the drive current or initial phase detuning is changed. The butterfly hysteresis loop is observed experimentally at optical input power as low as 260 /spl mu/W for a drive current equal to 90% of the lasing threshold. The dependence of the optical bistability on drive current, initial phase detuning and injected optical power has been investigated. In the bistable light output-initial phase detuning characteristic, the optimum frequency is shifted downward with an increase in the injected power or the drive current. All measurements are in good agreement with an analytical model.
The rigorous solution in the plane-wave approximation of the light reflection boundary problem for the interface the isotropic medium - photorefractive crystal with the drift- diffusion nonlinearity mechanism is given. The possibility of the realization of the hysteresis light reflection phenomenon in this case under certain conditions is shown. The analytical expressions describing hysteresis behavior of the reflectivity as a function of the angle of incidence or that of the external electric field strength applied to the crystal are derived. By changing the value and sign of the applied electric field it is possible to transfer system from the total reflection state to the transmission state and vice versa. The obtained results are attractive for the elaboration of the possible devices for laser radiation control and optical information processing.
We study the behavior of light waves at an interface between linear and photorefractive media, where the incident wave propagates from the linear side. We find bistable behavior of the reflection coefficient as a function of the incident angle at incident wave directions in the vicinity of the critical angle for total internal reflection. The analysis is based on approximations in the photorefractive-process equations, for which an analytical plane-wave solution for the boundary problem is found. In this regime an exponentially decaying evanescent field induces a uniform change of the refractive index. The limitation of this solution is also studied by a numerical analysis.