Non-steady-state extremely asymmetrical scattering of waves in periodic gratings

Abstract

Extremely asymmetrical scattering (EAS) is a highly resonant type of Bragg scattering with a strong resonant increase of the scattered wave amplitude inside and outside the grating. EAS is realized when the scattered wave propagates parallel to the grating boundaries. We present a rigorous algorithm for the analysis of non-steady-state EAS, and investigate the relaxation of the incident and scattered wave amplitudes to their steady-state values. Non-steady-state EAS of bulk TE electromagnetic waves is analyzed in narrow and wide, slanted, holographic gratings. Typical relaxation times are determined and compared with previous rough estimations. Physical explanation of the predicted effects is presented.

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

“…, within which the steady-state regime of scattering is reached [7,16]. Here, τ is the relaxation time for a particular resonance [7,16], and c is the speed of light in vacuum.…”

“…Here, τ is the relaxation time for a particular resonance [7,16], and c is the speed of light in vacuum. Resonant generation of the conventional modes guided by a slab with a holographic grating occurs (figure 2 (a)) when lc for the corresponding resonance is noticeably larger than the distance l ref = L/ cos(θ 21 ) that the bulk wave in the slab travels between two successive reflections.…”

“…Resonant generation of the conventional modes guided by a slab with a holographic grating occurs (figure 2 (a)) when lc for the corresponding resonance is noticeably larger than the distance l ref = L/ cos(θ 21 ) that the bulk wave in the slab travels between two successive reflections. For example, for figure 2 (a), the analysis developed in [16] …”

“…The larger the relaxation time, the stronger is the resonance and the longer is the distance that the corresponding eigenmode can propagate without noticeable decay (due to leakage) along the grating. The relaxation time can be determined using the method based on the Fourier analysis of the incident pulse [16]. As mentioned above, during the relaxation time τ, the scattered wave propagates the distance l c ≈ τ cǫ −1/2 along the grating, which should approximately be equal to the distance that the corresponding eigenmode can propagate along the grating in the absence of the incident wave.…”

“…As mentioned above, during the relaxation time τ, the scattered wave propagates the distance l c ≈ τ cǫ −1/2 along the grating, which should approximately be equal to the distance that the corresponding eigenmode can propagate along the grating in the absence of the incident wave. For example, the results of [16] suggest that a resonance of about 100E 00 high should usually correspond to an l c value of about several tens of centimetres. It is important to understand that the predicted new eigenmodes of a guiding slab with a grating are generically associated with scattering.…”