Large and negative Goos–Hänchen shift near the Brewster dip on reflection from weakly absorbing media

Abstract

Applying Artmann's formula to a light beam in the TM state of wave polarization, we show analytically the existence of a large and negative Goos-Hänchen shift near the angle of the Brewster dip on reflection from a weakly absorbing semi-infinite medium. The shift is opposite that in the case of total internal reflection, and it can be an order of magnitude larger than a wavelength if the absorption of the reflecting medium is sufficiently weak. Examples are given, and the detectibility of the shift is discussed.

Negative and positive lateral shift of a light beam reflected from a grounded slab

“…This phenomenon has been widely analyzed both theoretically [3][4][5][6][7][8][9] and experimentally [1,[10][11][12][13][14]. The investigation on the GH shift has been extended to other areas of physics, such as acoustics, quantum mechanics and plasma physics [15].…”

“…The GH shift is usually proportional to the penetration depth at the order of a wavelength. Many attempts have been made to achieve large lateral shifts (positive or negative) under different circumstances, such as absorbing media [4,9], atomic resonant absorptive vapors [12,16], resonant artificial structures [7,[17][18], negative-permittivity media [19][20], negatively refractive media [21][22][23][24][25][26][27][28], dielectric slabs [8,[29][30], multi-layered structures [6,[31][32]. Recently Li [8] found that the lateral shift of a light beam passing through a lossless transmitting slab could be negative due to the interference between the reflected waves from the slab's two interfaces.…”

Optical Effects Induced by Bloch Surface Waves in One-Dimensional Photonic Crystals

“…At the critical angle, the reflection coefficient varies rather smoothly and the values of the Goos-Hänchen effect turn out to be small. In contrast, it is possible to obtain significant values of the Goos-Hänchen shift at the angular vicinity of the Brewster angle [38], the edge of the photonic band gap in photonic crystals [39] and especially near the resonance of surface plasmons on a metal film [40]. Since the spectral-angular resonances of the BSW can be chosen to be substantially narrower than the resonances of surface plasmons in the visible spectral range, this caused an interest in the detection and research of the Goos-Hänchen effect near the resonance of the BSW.…”

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

“…But within the chosen frequency band (for example, 1.22ω p to 1.50ω p ) we can obtain a relatively large reflectance (for instance, ω=1.32ω p , |R| 2 =54.45×10 -3 ). It can be larger than that in weakly absorbing media [9], making it easier to detect. However, when the frequency is very high, the effect of the magnetic field vanishes, causing the zero reflection at the Brewster angle.…”

“…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].…”