Optimizing Weak Measurements to Detect Angular Deviations

Abstract

Optimizing weak measurements to detect angular deviationsW e analyze and compare the angular deviations for an optical beam reflected by and transmitted through a dielectric triangular prism. The analytic expressions derived for the angular deviations hold for arbitrary incidence angles. For incidence approaching the internal and external Brewster angles, the angular deviations transverse magnetic waves present the same behavior leading to the well-known giant Goos-Hänchen angular shift. For incidence near the critical angle a new region of large shift is seen both for transverse magnetic and transverse electric waves. While a direct measuring procedure is better in the vicinity of the Brewster region, a weak measurement breaks off the giant Goos-Hänchen effect, preserving the amplification in the critical region. We discuss under which conditions it is possible to optimize the amplification and we also determine when a weak measurement is preferred to a direct measuring procedure.

Incidence angles maximizing the Goos-Haenchen shift in seismic data analysis

“…Deviations from geometrical optics are not restricted to lateral displacements. Indeed, the spatial GH shift has an angular analogous effect [25][26][27]. This effect has recently been observed in optical experiment for incidence in the resonant Brewster region [28], by using a transverse electric wave to decouple the polarization from the propagation dynamics of the beam [29], and by the weak measurement technique [30].…”

“…While the spatial GH shift is essentially due to the phase of the Fresnel reflection coefficient, the angular effect is mainly connected to the amplitude of the Fresnel reflection coefficient. Consequently, it is the breaking of symmetry in the optical beam wave number distribution induced by the Fresnel reflection coefficient to cause the angular deviation [27]. Such a breaking of symmetry can also be seen for acoustic (scalar) waves when the reflection Zoeppritz coefficient rapidly changes, see Fig.…”

“…2-4 and thus this effect is not restricted to the vector nature of light. Of particular interest, it could be, for example, to examine the Rayleigh waves influence on acoustic beams at liquid-solid interfaces [31,32] in view of the double peak reflected beam recently discussed in Optics [27].…”

Lateral shifts and angular deviations of Gaussian optical beams reflected by and transmitted through dielectric blocks: A tutorial review

“…In 2016, Santana et al made the first weak measurement experiment in order to investigate the composite Goos-Hänchen shift [42]. In 2015, Araújo, De Leo, and Maia presented their study on how weak measurements of the Goos-Hänchen shift in the critical region could suffer axial deformations [43], due to the symmetry breaking of the beam in the region, and, in 2017, a paper by the same authors made a comparative analysis of weak measurements versus direct measurements of angular deviations near the Brewster and critical regions, evaluating the efficiency of the amplification technique [44]. Finally, in an accepted, but yet unpublished paper, Maia et al investigated the effect of the Goos-Hänchen phase in weak measurements [45].…”

Giant Goos-Hänchen shifts in non-Hermitian dielectric multilayers incorporated with graphene

“…Since the Goos-Hänchen (GH) shift was first observed experimentally by Goos and Hänchen in 1947 [1], many efforts have been devoted into the theoretical and experimental studies of the effect [2][3][4][5][6][7][8][9][10]. The GH shift may manifest a spatial or angular shift [11][12][13][14], which could occur individually or simultaneously at the interface of two materials with different permittivities [15]. GH shifts have been reported in various systems, including dielectric slab [16,17], metamaterials [18], graphene [19,20], phase-conjugate mirrors [21], and photonic crystals (PCs) [22][23][24].…”