Diffraction grating parameter retrieval using non-paraxial structured beams in coherent Fourier scatterometry

In recent years, a lot of works have been published that use parameter retrieval using Orbital Angular Momentum (OAM) beams. Most make use of the OAM of different Laguerre-Gauss modes. However, those specific optical beams are paraxial beams and this limits the regime in which they can be used. In this paper, we report on the first results on retrieving the geometric parameters of a diffraction grating by analysing the corresponding complex-valued (i.e., amplitude and phase) Helmholtz Natural Modes (HNM) spectra containing both the azimuthal (i.e., n) and radial (i.e., m) indices. HNMs are a set of orthogonal, non-paraxial beams with finite energy carrying OAM. We use the coherent Fourier scatterometry (CFS) setup to calculate the field scattered from the diffraction grating. The amplitude and phase contributions of each HNM are then obtained by numerically calculating the overlap integral of the scattered field with the different modes. We show results on the sensitivity of the HNMs to several grating parameters.

Generalized Kerker effect in PT-symmetric nanoantenna array

All-dielectric nanophotonics is a rapidly developing and practical alternative to plasmonics for nanoscale optics. The electric and magnetic Mie resonances in high-index low-loss dielectric nanoresonators can be engineered to exhibit unique scattering response. Recently, nanophotonic structures satisfying parity-time (PT) symmetry have been shown to exhibit novel scattering responses beyond what can be achieved from the conventional nanoresonators. The complex interference of the magnetic and electric Mie resonances and lattice modes excited in PT-symmetric nanoantenna arrays give rise to a scattering anomaly called lasing spectral singularity (SS), where the scattering coefficients tend to infinity. In our previous work [1], we demonstrated the existence of lasing spectral singularities in vertically stacked 2D GaInP PT-symmetric metasurface. In this paper, we analyze the direction-sensitive scattering response of the PT-symmetric GaInP metasurface by decomposing the total scattered field into the electric and magnetic multipoles. The far-field scattering response at the singularity is highly asymmetric for incidence from either the gain or loss side and can be tuned by changing the geometry. By analyzing the phase of even- and odd-parity higher order multipoles, we explain the observed scattering response over a broad parameter space in terms of generalized Kerker effect. The interference between the direction-dependent excitation of different order multipoles and the overall 2D-lattice resonance opens a route towards designing a special class of tunable sources exhibiting direction-sensitive emission properties.

Generalization of the Optical Theorem to an Arbitrary Multipole Excitation of a Particle near a Transparent Substrate

In the present paper, the generalization of the optical theorem to the case of a penetrable particle deposited near a transparent substrate that is excited by a multipole of an arbitrary order and polarization has been derived. In the derivation we employ classic Maxwell’s theory, Gauss’s theorem, and use a special representation for the multipole excitation. It has been shown that the extinction cross-section can be evaluated by the calculation of some specific derivatives from the scattered field at the position of the multipole location, in addition to some finite integrals which account for the multipole polarization and the presence of the substrate. Finally, the present paper considers some specific examples for the excitation of a particle by an electric quadrupole.

Nonlinear Cylindrical Markers Using Metamaterials

In this paper, the research of nonlinear cylindrical metastructure was obtained. An algorithm for finding the total field of a nonlinearly loaded perfectly conducting cylinder covered with a metamaterial (MM) layer based on Maxwell’s equations with nonlinear boundary conditions on the surface of nonlinear loads (NL) was developed. A software package implementing this algorithm was created. Based on the results of numerical calculations of the program, the scattering diagrams of a metal cylinder with NL, covered with a layer of MM at the fundamental, second, and third harmonics were obtained. The dependences of the harmonics of the scattered field on the parameters of nonlinear loads were also studied. With the help of numerical simulation using Ansys HFSS, the extract procedure of the effective parameters of cylindrical MM was realized. Based on the results of calculation and numerical simulation, a model of a nonlinear cylindrical structure of two radii was made and an experimental study was carried out. As a result of the experiment, the frequency characteristics of the metastructure were obtained at various angles of incidence of the wave. The results of numerical simulation were confirmed by the results of the experiment. It is shown that the use of the provided nonlinear cylindrical marker with metamaterial makes it possible to obtain the levels of the first and second harmonics in a scattered field of the same order. This structure can be used as a nonlinear marker in both military and civilian areas.

OPERATOR METHOD IN THE PROBLEM OF A PLANE ELECTROMAGNETIC WAVE DIFFRACTION BY AN ANNULAR SLOT IN THE PLANE OR BY A RING

Purpose: The problem of a plane electromagnetic wave diffraction by an annular slot in the perfectly conducting zero thickness plane is considered. As a dual problem, the problem of diffraction by a perfectly conducting zero thickness ring is also considered. The paper aims at developing the operator method for the axially symmetric structures placed in free space. Design/methodology/approach: The problem is considered in the spectral domain. The scattered field is expressed in terms of unknown Fourier amplitudes (spectral functions). The annular slot is given as a unity of two simple discontinuities, namely of a disk and a circular hole in the plane, which interact with each other. The Fourier amplitude of the scattered field is sought as a sum of two amplitudes, the Fourier amplitude of the field of currents on the disk and Fourier amplitude of the field of currents on the perfectly conducting plane with circular hole. The operator equations are written for these amplitudes, which take into account the electromagnetic coupling of the disk and the hole in the plane. The equations use the reflection operators of a single isolated disk and a single hole in the plane. They are supposed to be known and can be obtained for example by the method of moments.The reflection operators can have singularities. After transformations, the equations are obtained, which are equivalent to the Fredholm integral equations of second kind and they can be solved numerically. Findings: The operator equations relative to the Fourier amplitudes of the field scattered by the discussed structure are obtained. The far zone scattered field for an annular slot and a ring for different values of parameters are studied. Conclusions: The rigorous solution of the problem of the electromagnetic wave diffraction by an annular slot in the plane and by a circular ring is obtained. The problem is reduced to the Fredholm integral equations of second kind. The far field distribution for different parameters is studied. The developed approach is an effective instrument for a number of problems of antenna technique to be solved. Key words: circular hole; disk; annular slot; ring; operator method; diffraction

Direct Sampling for Recovering Sound Soft Scatterers from Point Source Measurements

In this paper, we consider the inverse problem of recovering a sound soft scatterer from the measured scattered field. The scattered field is assumed to be induced by a point source on a curve/surface that is known. Here, we propose and analyze new direct sampling methods for this problem. The first method we consider uses a far-field transformation of the near-field data, which allows us to derive explicit bounds in the resolution analysis for the direct sampling method’s imaging functional. Two direct sampling methods are studied, using the far-field transformation. For these imaging functionals, we use the Funk–Hecke identities to study the resolution analysis. We also study a direct sampling method for the case of the given Cauchy data. Numerical examples are given to show the applicability of the new imaging functionals for recovering a sound soft scatterer with full and partial aperture data.