The Quasi-optical Equation in a Medium with Weak Dissipation
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ICAL OPTICS
The Quasi-optical Equation in a Medium with Weak Dissipation N. N. Rosanova, b, * a
b
Ioffe Institute, St. Petersburg, 194021 Russia Vavilov State Optical Institute, St. Petersburg, 199053 Russia *e-mail: [email protected]
Received February 2, 2020; revised February 2, 2020; accepted March 16, 2020
Abstract—The form of a quasi-optical equation for a pulse of quasi-monochromatic radiation propagating in a homogeneous or one-dimensionally inhomogeneous linear medium with dissipation is analyzed. For a layer of an inhomogeneous medium, the effective parameters of an equivalent homogeneous medium are obtained. Keywords: quasi-optical approximation, dissipative effects DOI: 10.1134/S0030400X20080305
The quasi-optical approximation and the equation were proposed about 75 years ago [1, 2] and then became a firmly established part not only of original articles, but also of reviews, textbooks, and monographs [3–8], covering a wide range of optical, radiophysical, acoustic and other wave processes. Nevertheless, these questions still remain relevant due to a wide variety of media with significantly different material relations. Among recent publications, we note the version of the quasi-optical equation for smoothly inhomogeneous media with spatial dispersion that was proposed and used in [9, 10]. The quasi-optical approximation is applicable to quasi-monochromatic and quasi-plane-wave radiation. As applied to optics, the main idea of the approximation is to represent the total electric field strength as a product of a slowly varying envelope (on the scale of the inverse frequency and wavelength of the reference, carrier component) by a rapidly changing phase factor [1–10]. However, as was shown in [11], for a layer of a medium with at least weak absorption, this approach does not allow one to take into account the simple fact that waves that propagate normally to the boundaries of the layer have a lower total absorption than obliquely propagating waves (angular selectivity of absorption). This circumstance leads to the situation that ordinary diffraction in media with absorption is complemented by a kind of diffusion, which gives rise to peculiar phenomena of dichroism (understood here as the dependence of absorption on the direction of wave propagation) [12, 13]. For wide-aperture laser systems dissipation in which is present in the form of both absorption and gain, the indicated angular selectivity of losses seems to be a fundamental factor. Its influence is especially pronounced for topological
structures of light with wavefront singularities [8, 14– 16]. This communication generalizes and supplements the previous work [11]. An analysis of the pulsed regime and taking into account the longitudinal inhomogeneity of the medium are new aspects. The results can also be regarded as a substantiation of the statement of the problem of topologically three-dimensional solitons [14–16]. We begin our consideration with the case of propagation of pulses and radiation beams close to a monochromatic plane wave in a ho
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