Optical computation of the Laplace operator at oblique incidence using a multilayer metal-dielectric structure.

We investigate the possibility of the optical computation of the Laplace operator in the oblique incidence geometry using a layered structure consisting of a set of homogeneous thin films. For this, we develop a general description of the diffraction of a three-dimensional linearly polarized optical beam by a layered structure at oblique incidence. Using this description, we derive the transfer function of a multilayer structure consisting of two three-layer metal-dielectric-metal structures and possessing a second-order reflection zero with respect to the tangential component of the wave vector of the incident wave.

Analytical design of flat-top transmission filters composed of several resonant structures.

Resonant properties of composite structures consisting of several identical resonant structures (e.g. multilayer thin-film structures or guided-mode resonance gratings) separated by phase-shift layers are investigated theoretically.

Resonant properties of composite structures consisting of several resonant diffraction gratings.

We theoretically and numerically investigate resonant optical properties of composite structures consisting of several subwavelength resonant diffraction gratings separated by homogeneous layers. Using the scattering matrix formalism, we demonstrate that the composite structure comprising N gratings has a multiple transmittance zero of the order N. We show that at the distance between the gratings satisfying the Fabry-Pérot resonance condition, an (N - 1)-degenerate bound state in the continuum (BIC) is formed.

Planar two-groove optical differentiator in a slab waveguide.

We propose a simple planar optical differentiator consisting of two grooves on the surface of a slab waveguide. The studied differentiator operates in reflection and enables temporal and spatial differentiation of optical pulses and beams propagating in the waveguide. The differentiation is associated with the excitation of an eigenmode localized at the ridge located between the grooves.

Analytical description of 3D optical pulse diffraction by a phase-shifted Bragg grating.

Diffraction of a three-dimensional (3D) spatiotemporal optical pulse by a phase-shifted Bragg grating (PSBG) is considered. The pulse diffraction is described in terms of signal transmission through a linear system with a transfer function determined by the reflection or transmission coefficient of the PSBG. Resonant approximations of the reflection and transmission coefficients of the PSBG as functions of the angular frequency and the in-plane component of the wave vector are obtained.

Spatiotemporal pulse shaping using resonant diffraction gratings.

We propose a new theoretical model describing spatiotemporal transformations of two-dimensional optical pulses by resonant diffraction gratings. The diffraction of the pulse is described in terms of a linear system. Simple analytical approximations for the transfer function and the impulse response of the system are derived.