A Simple Analytic Approximation for the Refracted Field at Gaussian Beam Incidence upon a Boundary of Absorbing Medium

Abstract

An approximate analytic model is presented to describe spatial structure of refracted electromagnetic field arising at oblique incidence of a Gaussian beam on a plane boundary of an absorbing homogeneous medium. The analytic solution is obtained by asymptotic approximation of a Fourier field integral under the condition of great beam width in comparison with a wavelength (the geometrical-optics approximation). This model can be used also for approximate simulation of refracted field in the cases of beam incidence near the critical angle on transparent or absorbing (amplifying) refracting medium, if one artificially introduces the additional absorption (amplification), whose value is proportional to the ratio of the wavelength and the effective beam width. It is shown that the analytic model reflects the general features of refracted field at total internal reflection

Theory of Gaussian Beam Diffraction by a Transmission Dielectric Grating

“…(10) become great in absolute value, which provides sufficiently great values of eigenvalues σ 2 m of the matrix in the left hand side of Eq. (11). It causes noticeable decrease in the values of the mode amplitudes A ± m in a grating as solutions of Equation ( 20) and, correspondingly, decrease in the mode amplitudes in Eqs.…”

“…Figure 2 shows the real eigenvalues σ 2 m of the matrix in Eq. (11), computed for planar and relief gratings in the cases of TE polarization, as functions of the tangential propagation parameter β 0 of an incident wave (for the TM polarization, the given dependences appear similarly). The eigenvalues σ 2 m from Fig.…”

“…These are works devoted to the consideration of a rather specific case of Gaussian beam diffraction by volume thick gratings. Meanwhile, the effects of transverse spatial inhomogeneity of the initial light beams, which are usually insignificant, begin to play an important role under conditions when the field or part of it (one of the diffraction orders, for example) undergoes transition from the free propagation regime to the regime of total internal reflection at the boundaries of dielectric media, and inversely [10] (see also [11,12]). In this case, abrupt variations in intensities of all diffraction orders are observed in metallic and dielectric gratings (so-called Wood's anomalies) [1,13].…”

Refractive Index Determination for a Plane Dielectric Layer Using the Measurements of Transmitted Beam Intensity

“…However, scientific experience show, that as these formulae, as the formula (1) are valid for more general case, when radiation is presented by a spatially bounded beam or by superposition of waves with various frequencies from narrow bounded frequency region. Then, for the temporal ω and spatial β frequencies of propagation, one takes averaged values of these parameters over the temporal and spatial (angular) spectrum of incident field (see, for example, [16]). …”

Approximate analytical solution for waveguide excitation of a plane dielectric layer by a Gaussian beam at frustrated total internal reflection

“…From this point of view, the problem of change from the plane-wave model to the model of a spatially inhomogeneous light beams looks rather easy: one should take formulas obtained for one wave propagating in a system under consideration and integrate them formally over a propagation parameter [1,2,22]. However, the problem is that the received integrals are subject to calculation with an effort [23]. For example, actually under simple conditions of light beam propagation through one or two parallel dielectric interfaces, the field integrals can be computed only numerically, owing to nonlinear dependence of reflection and transmission coefficients on the parameter of plane-wave propagation [1,2].…”