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

Abstract

A highly unusual pattern of strong multiple resonances for bulk electromagnetic waves is predicted and analysed numerically in thick periodic holographic gratings in a slab with the mean permittivity that is larger than that of the surrounding media. This pattern is shown to exist in the geometry of grazing-angle scattering (GAS), that is when the scattered wave (+1 diffracted order) in the slab propagates almost parallel to the slab (grating) boundaries. The predicted resonances are demonstrated to be unrelated to resonant generation of the conventional guided modes of the slab. Their physical explanation is associated with resonant generation of a completely new type of eigenmodes in a thick slab with a periodic grating. These new slab eigenmodes are generically related to the grating; they do not exist if the grating amplitude is zero. The field structure of these eigenmodes and their dependence on structural and wave parameters is analysed. The results are extended to the case of GAS of guided modes in a slab with a periodic groove array of small corrugation amplitude and small variations in the mean thickness of the slab at the array boundaries.

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

“…These modes can be guided by a slanted grating alone without conventional guiding effects in the structure [7,8,9]. At the same time, increasing the mean dielectric permittivity inside the grating region, i.e., assuming that the grating is formed in a guiding slab, results in a number of new modes propagating in the slab [10]. These modes have nothing to do with the conventional guided slab modes-they are generated at wrong angles of scattering and have an unusual field structure inside the slab [10].…”

“…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.…”

“…In particular, strong GAS resonances have been associated with the generation of a new type of mode in gratings and photonic crystals-grating eigenmodes [7,8,9,10]. These modes can be guided by a slanted grating alone without conventional guiding effects in the structure [7,8,9].…”

“…However, strong resonances of scattering at frequencies that are strongly detuned from the Bragg frequency normally occur at large grating amplitude (more than ≈ 10% of the mean permittivity in the grating) [9]. If the grating amplitude is reduced, the resonances disappear and eventually are replaced by resonances caused by the generation of conventional slab modes [10].…”

“…Grating eigenmodes are formed by all the diffracted orders interacting with each other inside the grating, and thus cannot exist in the absence of the grating [7,8,9,10]. They appear to be weakly coupled to the bulk incident wave, which results in strong resonances of scattering in the grating at angles that do not correspond to generation of the conventional guided modes [11].…”