Magnetic field control of light is among the most intriguing methods for modulation of light intensity and polarization on sub-nanosecond timescales. The implementation in nanostructured hybrid materials provides a remarkable increase of magneto-optical effects. However, so far only the enhancement of already known effects has been demonstrated in such materials. Here we postulate a novel magneto-optical phenomenon that originates solely from suitably designed nanostructured metal-dielectric material, the so-called magneto-plasmonic crystal. In this material, an incident light excites coupled plasmonic oscillations and a waveguide mode. An in-plane magnetic field allows excitation of an orthogonally polarized waveguide mode that modifies optical spectrum of the magneto-plasmonic crystal and increases its transparency. The experimentally achieved light intensity modulation reaches 24%. As the effect can potentially exceed 100%, it may have great importance for applied nanophotonics. Further, the effect allows manipulating and exciting waveguide modes by a magnetic field and light of proper polarization.

Diffraction of a 3D optical beam on a multilayer phase-shifted Bragg grating (PSBG) is considered. It is shown that the PSBG enables optical computation of the spatial Laplace operator of the electromagnetic field components of the incident beam. The computation of the Laplacian is performed in reflection at normal incidence. As a special case, the parameters of the PSBG transforming the incident Gaussian beam into a Laguerre–Gaussian mode of order (1,0) are obtained. Presented numerical results demonstrate high quality of the Laplace operator computation and confirm the possibility of the formation of Laguerre–Gaussian mode. We expect the proposed applications to be useful for all-optical data processing.

We present a theoretical study of a new application of the phase-shifted Bragg grating (PSBG) as an optical spatial differentiator operating in reflection. We demonstrate that the PSBG allows to calculate the first-order spatial derivative at oblique incidence and the second-order derivative at normal incidence. As an example, the differentiator is numerically shown to be able to convert an input 2D Gaussian beam into a 2D Hermite–Gaussian mode. We expect the proposed application to be useful for all-optical data processing.

We present an experimental demonstration of a subwavelength diffraction grating performing first-order differentiation of the transverse profile of an incident optical beam with respect to a spatial variable. The experimental results are in a good agreement with the presented analytical model suggesting that the differentiation is performed in transmission at oblique incidence and is associated with the guided-mode resonance of the grating. According to this model, the transfer function of the grating in the vicinity of the resonance is close to the transfer function of an exact differentiator. We confirm this by estimating the transfer function of the fabricated structure on the basis of the measured profiles of the incident and transmitted beams. The considered structure may find application in the design of new photonic devices for beam shaping, optical information processing, and analog optical computing.

Waveguide and resonant properties of diffractive structures are often explained through the complex poles of their scattering matrices. Numerical methods for calculating poles of the scattering matrix with applications in grating theory are discussed and analyzed. A new iterative method for computing the scattering matrix poles is proposed. The method takes account of the scattering matrix form in the pole vicinity and relies upon solving matrix equations with use of matrix decompositions. Using the same mathematical approach, we also describe a Cauchy-integral-based method that allows all of the poles in a specified domain to be calculated. Calculation of the modes of a metal-dielectric diffraction grating shows that the iterative method proposed has the high rate of convergence and is numerically stable for large-dimension scattering matrices. An important advantage of the proposed method is that it usually converges to the nearest pole.

We investigate the diffraction of the guided modes of a dielectric slab waveguide on a simple integrated structure consisting of a single dielectric ridge on the surface of the waveguide. Numerical simulations based on aperiodic rigorous coupled-wave analysis demonstrate the existence of sharp resonant features and bound states in the continuum (BICs) in the reflectance and transmittance spectra occurring at the oblique incidence of a transverse-electric (TE)-polarized guided mode on the ridge. Using the effective index method, we explain the resonances by the excitation of cross-polarized modes of the ridge. Formation of the BICs are confirmed using a theoretical model based on coupled-wave theory. The model suggests that the BICs occur due to the coupling of quasi-TE and quasi-transverse-magnetic modes of the structure. Simple analytical expressions for the angle of incidence and the ridge width predicting the location of the BICs are obtained. The existence of high-$Q$ resonances and BICs enables using the considered integrated structure for sensing, transformation of optical signals, and enhancing nonlinear light–matter interactions. Due to the Lorentzian line shape of the resonances near the BICs, the structure is also promising for filtering applications.