Efficiency of Gaussian light beam transformation into a waveguide mode of a plane dielectric layer under frustrated total internal reflection

Theory of Gaussian Beam Diffraction by a Transmission Dielectric Grating

“…In order to use this method for description of radiation beams for various diffraction orders, one needs to relate their angular spectra at the output of a grating with spectrum of the initial Gaussian diffracting beam. If before inclined incidence on a grating, this beam covers the distance L 0 from the waist, then its Fourier-spectrum on the surface of a grating has the form [12,19]:…”

“…(40) with the multiplier x. The integral (41) plays an important part in the theory of Gaussian beam propagation through multilayer dielectric media [12], and therefore, we present the result of its calculation in a general form:…”

“…Behavior of the solution, described by the analytical expressions (40) and ( 43), essentially depends on the value Q n (43b). If it is great in magnitude, which is provided by a small value of the derivative Γ n over a spectrum of a Gaussian beam, this function permits a simple asymptotic expansion [12], whose substitution into Eq. ( 40) yields the Gaussian function (34).…”

“…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].…”