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Journal of Applied Physics

Theory of Saturable Reflection

James D. Macomber, Neil R. Kestner

Published Jul 1, 1969• 4 citations
Publisher

Abstract

The theory of the effect of optical saturation upon the reflectance of a plane slab (irradiated by a linearly polarized monochromatic electromagnetic wave of constant amplitude at normal incidence) is developed. The absorbing centers within the slab are described by means of the density matrix, and the electromagnetic field is described by Maxwell's equations. For simplicity's sake, it is assumed that only two quantum states (characterized by a transition dipole moment μ and relaxation times T1 and T2) at exact resonance with the electromagnetic wave are necessary to describe the absorption process. The coupling between waves travelling in opposite directions is provided by Fresnel reflection at the boundaries of the slab. Only the steady-state solutions are found.

DOI
10.1063/1.1658168

Related papers

Laws of optics at high irradiance I Steady-state theory of a saturable slab*

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The ancient laws developed by Snell, Bouguer, Lambert, Fresnel, and Beer, describing the reflection, absorption, and transmission of light by a plane slab of absorbing materials, are applicable only at low irradiances. We have developed new laws that apply at irradiances sufficiently high to produce partial optical saturation of the chromophoric atoms, ions, or molecules of the slab. The radiation field is treated in accordance with the characteristic matrix method of Abelès, based upon Maxwell’s equations. The chromophores are treated in accordance with the optical analogs to the Bloch equations, based upon quantum-statistical mechanics. Our results are presented in the form of an algorithm, by means of which the optical properties are initially estimated assuming no saturation. These properties are then used to compute the field intensities within the medium, and these field intensities are employed in the computation of estimates for the saturated properties. Successive iterations of this procedure are used until the calcuated fields and properties are self-consistent. We show for the first time how to calculate the influence of optical saturation upon the reflectance and angle of refraction of an absorbing sample, and how the method of characteristic matrices can be employed in a problem in nonlinear optics. In addition, the effects of the divergence and finite width of the incident beam, of the cell windows, and the interaction of the forward- and backward-traveling waves to produce a spatial variation in the saturation within the sample, are all treated correctly. The results may therefore be of use to those who wish to design a practical optical memory for a computer, using bistable saturable Fabry-Perot interferometers.

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Possibility for observation of the narrow resonances of the saturated absorption and dispersion

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Summary form only given. Results are presented of theoretical studies into the resonances of the saturated absorption and saturated dispersion in an external absorption cell. The theory has been worked out by means of combining methods of mathematical theory of diffraction and quantum mechanical method for computing the polarization of active media. This made it possible for the first time to find a self-consisting spatial solution of the density matrix equation for the two-level system and the Helmholtz equation for electromagnetic field and to solve the problem of propagation of two counterpropagating monochromatic waves though an absorbing nonlinear medium taking into consideration the transverse transit-time effect.

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The propagation of laser light a few wavelengths inside a saturable absorber is theoretically studied. Computed steady-state solutions of the Maxwell–Bloch equations that describe the unidimensional propagation of a plane monochromatic wave, without introducing the slowly varying envelope approximation, show how saturation effects can influence this propagation. This can even lead to the appearance of a self-reflected wave inside the absorber because of the refractive-index changes that are induced by nonlinear coupling. One finds a close relation between the failure of the slowly varying envelope approximation and the presence of the self-reflected wave.

Journal of the Optical Society of America B•Nov 1, 1987•29 citations

Reflection of a Plane Wave at the Boundary of a Saturable Absorber: Normal Incidence

L. Roso, M. Ll. Pons

The absorption and reflection of a plane wave at the interface of a linear dielectric and a very dense saturable absorber is studied in situations where the linear refractive index has an imaginary part that is much bigger than its real part. In this domain of parameters, computed results calculated without the use of the slowly varying envelope approximation show the presence of a self-reflected wave that eventually might lead to a bistable reflectivity.

Journal of Modern Optics•Oct 1, 1990•8 citations
The theory of the effect of optical saturation upon the reflectance of a plane slab (irradiated by a linearly polarized monochromatic electromagnetic wave of constant amplitude at normal incidence) is developed. The absorbing centers within the slab are described by means of the density matrix, and the electromagnetic field is described by Maxwell's equations. For simplicity's sake, it is assumed that only two quantum states (characterized by a transition dipole moment μ and relaxation times T1 and T2) at exact resonance with the electromagnetic wave are necessary to describe the absorption process. The coupling between waves travelling in opposite directions is provided by Fresnel reflection at the boundaries of the slab. Only the steady-state solutions are found.
The ancient laws developed by Snell, Bouguer, Lambert, Fresnel, and Beer, describing the reflection, absorption, and transmission of light by a plane slab of absorbing materials, are applicable only at low irradiances. We have developed new laws that apply at irradiances sufficiently high to produce partial optical saturation of the chromophoric atoms, ions, or molecules of the slab. The radiation field is treated in accordance with the characteristic matrix method of Abelès, based upon Maxwell’s equations. The chromophores are treated in accordance with the optical analogs to the Bloch equations, based upon quantum-statistical mechanics. Our results are presented in the form of an algorithm, by means of which the optical properties are initially estimated assuming no saturation. These properties are then used to compute the field intensities within the medium, and these field intensities are employed in the computation of estimates for the saturated properties. Successive iterations of this procedure are used until the calcuated fields and properties are self-consistent. We show for the first time how to calculate the influence of optical saturation upon the reflectance and angle of refraction of an absorbing sample, and how the method of characteristic matrices can be employed in a problem in nonlinear optics. In addition, the effects of the divergence and finite width of the incident beam, of the cell windows, and the interaction of the forward- and backward-traveling waves to produce a spatial variation in the saturation within the sample, are all treated correctly. The results may therefore be of use to those who wish to design a practical optical memory for a computer, using bistable saturable Fabry-Perot interferometers.
Propagation of laser light through a saturable absorber is theoretically studied. Computed steady state solutions of the Maxwell equations describing the unidimensional propagation of a plane monochromatic wave without introducing the slowly-varying envelope approximation are presented showing how saturation effects can influence the absorption of the field. At a certain range of refractive index and extintion coefficients, computed solutions display a very susprising behaviour, and a self-reflected wave appears inside the absorber. This can be useful for a new kind of biestable device, similar to a standard bistable cavity but with the back mirror self-induced by the light.
Summary form only given. Results are presented of theoretical studies into the resonances of the saturated absorption and saturated dispersion in an external absorption cell. The theory has been worked out by means of combining methods of mathematical theory of diffraction and quantum mechanical method for computing the polarization of active media. This made it possible for the first time to find a self-consisting spatial solution of the density matrix equation for the two-level system and the Helmholtz equation for electromagnetic field and to solve the problem of propagation of two counterpropagating monochromatic waves though an absorbing nonlinear medium taking into consideration the transverse transit-time effect.
The propagation of laser light a few wavelengths inside a saturable absorber is theoretically studied. Computed steady-state solutions of the Maxwell–Bloch equations that describe the unidimensional propagation of a plane monochromatic wave, without introducing the slowly varying envelope approximation, show how saturation effects can influence this propagation. This can even lead to the appearance of a self-reflected wave inside the absorber because of the refractive-index changes that are induced by nonlinear coupling. One finds a close relation between the failure of the slowly varying envelope approximation and the presence of the self-reflected wave.