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

Abstract

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.