Nonspecular effects on reflection from absorbing media at and around Brewster's dip

Abstract

We show that, for a TM (or p-state) Gaussian beam incident onto an absorbing medium at and around Brewster's dip, the reflected beam always remains Gaussian and undergoes a Goos-Hänchen-like (GH) shift, an angular shift, a focal shift, and a beam-waist modification, provided that the beam is sufficiently collimated that the third-order change of the (logarithmic) reflection coefficient can be ignored in the angular range of beam divergence. For weak absorption, not only are a large negative GH shift and an odd-functioned-like focal shift with greater magnitude found but also the angular shift, though small by itself, is shown to give an even larger lateral net shift at a distance beyond the Rayleigh range.

Loss-induced transition of the Goos-Hänchen effect for metals and dielectrics

“…The maximum GH shift for a high-loss metal occurs at the second extremum, similarly to the dielectric case. In the dielectric case the transition from the high-loss to the low-loss regime is less striking; however, one can generally see a broadening of the resonance on transition from the low-loss to the intermediate loss regime [3,4]. On increasing the loss further we reach the high-loss regime in which the resonance seems to become narrower again (see Figure 2(c)) and the maximum of the GH shift moves closer to grazing incidence; here, for high-loss dielectrics, the analytic formulae from [4] are no longer valid.…”

“…The Goos-Hänchen (GH) shift is a displacement of a reflected beam of light if compared to an ideal, geometric reflection [1] and has been studied for a wide range of materials, including semiconductors [2,3,4], photonic crystals [5] and negative refractive media [6]. The GH shift has also been investigated for various different material compositions such as multi-layered and periodic structures [7] and finite width slabs [8].…”

“…With the exception of [2] this distinction is also commonly seen in the literature where authors focus on either dielectrics or metals to study the GH shift. Within the context of the GH shift it is helpful to consider the ratio ε i /|ε r | [4], and a medium is said to be 'low-loss' if ε i /|ε r | 1 and 'high-loss' if ε i /|ε r | 1. We also introduce the notion of 'intermediate-loss' to describe materials with ε i /|ε r | ≈ 1.…”

“…Dielectrics have been studied in the low-loss regime [3] as well as for intermediate losses [2]. It has been shown that the analytical expression for the dielectric GH shift obtained in the low-loss case also holds for intermediate-loss dielectrics with an acceptable error [4].…”

Positively and negatively large Goos–Hänchen lateral displacements from a symmetric gyrotropic slab

“…In this situation, the displacement is usually positive and in the forward direction, i.e., in the same direction of the component of the incident wave vector along the interface. Recently there are some studies on negative GH shifts in different systems: strongly reflecting and attenuating media such as metal at IR frequencies [3,4], non-absorbing [5], weakly absorbing interfaces [6][7][8][9][10], slabs [11], metallic gratings [12], transparent dielectric slabs [13], dielectric slabs backed by a metal [14], photonic crystals [15], and left-handed materials [16][17][18]. Among them there are some reports on large lateral shift near Brewster or pseudo-Brewster angle upon reflection from a weakly absorbing medium [9,10,17,18].…”