Rigorous analysis of grazing-angle scattering of electromagnetic waves in periodic gratings

Abstract

Grazing-angle scattering (GAS) is a type of Bragg scattering of waves in slanted non-uniform periodic gratings, when the diffracted order satisfying the Bragg condition propagates at a grazing angle with respect to the boundaries of a slablike grating. Rigorous analysis of GAS of bulk TE electromagnetic waves is undertaken in holographic gratings by means of the enhanced T-matrix algorithm. A comparison of the rigorous and the previously developed approximate theories of GAS is carried out. A complex pattern of numerous previously unknown resonances is discovered and analysed in detail for gratings with large amplitude, for which the approximate theory fails. These resonances are associated not only with the geometry of GAS, but are also typical for wide transmitting gratings. Their dependence on grating amplitude, angles of incidence and scattering, and grating width is investigated numerically. Physical interpretation of the predicted resonances is linked to the existence and the resonant generation of special new eigenmodes of slanted gratings. Main properties of these modes and their field structure are discussed. Structure and solutionsConsider an isotropic medium with a volume, uniform, holographic grating represented by sinusoidal variations of the dielectric permittivity ( Fig. 1):

Grazing-angle scattering of electromagnetic waves in gratings with varying mean parameters: Grating eigenmodes

“…It will be discussed in detail below. At this stage we shall only mention that the presented resonances (figure 2(a)) are not related to GAS, since GAS resonances do not exist in narrow gratings [1,2] (for more detail see It can be seen that increasing the grating amplitude so that the grating width becomes just larger than L c ( figure 2 (b)) results in the appearance of extremely high and sharp resonances just below θ 21r which is the GAS resonant angle in the same structure, but with zero variations in the mean permittivity (for figure 2 (b), θ 21r ≈ 89.22 • [1,2]). The rightmost resonant maximum in figure 2 (b) (i.e.…”

“…It is realized when the scattered wave (+1 diffracted order for first-order GAS [1,2,4], or +2 order for second-order GAS [3]) propagates almost parallel to the front grating boundary, that is at a grazing angle to this boundary. Thus, GAS is intermediate between extremely asymmetrical scattering (EAS) (which occurs when the scattered wave propagates parallel to the grating boundaries [58]) and conventional Bragg scattering in reflecting or transmitting gratings (where the scattered wave propagates at a significant angle with respect to the grating boundaries).…”

“…One of the most unexpected features of the GAS resonance is that it strongly increases in height and sharpness with increasing grating amplitude and/or grating width [14]. A physical explanation for this resonant behaviour with respect to angle of scattering has been related to resonant generation of a special new type of grating eigenmodes that are guided by the grating in the absence of any conventional guiding effect in the structure [2,3]. 1…”

Resonant coupling between bulk waves and guided modes in a dielectric slab with a thick holographic grating

“…This effect rapidly increases with increasing grating amplitude (compare figures 6(a) and 6(b)). Eventually, when the grating amplitude becomes sufficiently large, the structures of the guided modes substantially change, and they may be transformed into grating eigenmodes [7,8,9,10]. Note also that the effect of the grating is more pronounced for lower slab modes (compare the curves in figures 6(a) and 6(b)).…”

“…This demonstrates that these modes can exist in the absence of the grating. Therefore they cannot be a type of grating eigenmode [7,8,9,10] but must simply be the conventional guided modes of the dielectric slab. This has also been confirmed by considering the field distributions in the grating and slab at the resonant frequency detunings.…”