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.

Total absorption and coherent perfect absorption in metal-dielectric-metal resonators integrated into a slab waveguide.

We propose and investigate integrated metal-dielectric-metal (MDM) resonators operating with semi-guided waves (guided modes of dielectric slab waveguides). The MDM resonators are constituted by two metal strips "buried" in the waveguide core layer and separated by a dielectric waveguide segment. We theoretically prove and numerically demonstrate that by a proper choice of the mode incidence geometry, the widths of the metal strips, and the distance between them, it is possible to achieve either total absorption of the incident wave or coherent perfect absorption (in the case of symmetric incidence of two modes on the structure).

Designing stigmatic lenses with minimal Fresnel losses: erratum.

This erratum includes a necessary additional reference for the article [J. Opt. Soc.

Design of a stigmatic lens implementing a required ray mapping.

We consider a method for designing stigmatic lenses implementing required ray mappings. A ray mapping relates the angular coordinates of the rays at the image points with the angular coordinates of the rays coming from the object. The calculation of a stigmatic lens with a required ray mapping is reduced to solving an explicit ordinary differential equation.

Hybrid design of diffractive optical elements for optical beam shaping.

Hybrid methods combining the geometrical-optics and diffraction-theory methods enable designing diffractive optical elements (DOEs) with high performance due to the suppression of stray light and speckles and, at the same time, with a regular and fabrication-friendly microrelief. Here, we propose a geometrical-optics method for calculating the eikonal function of the light field providing the generation of a required irradiance distribution. In the method, the problem of calculating the eikonal function is formulated in a semi-discrete form as a problem of maximizing a concave function.

Supporting quadric method for designing refractive optical elements generating prescribed irradiance distributions and wavefronts.

We propose a method for designing a refractive optical element with two working surfaces transforming an incident beam with a plane wavefront into an output beam with prescribed irradiance distribution and a non-planar wavefront. The presented method generalizes the supporting quadric method [Opt. Express28, 22642 (2020)10.

Designing stigmatic lenses with minimal Fresnel losses.

We present a method for designing lenses with two aspherical surfaces having minimal Fresnel losses among the class of stigmatic lenses. Minimization of Fresnel losses is achieved by ensuring equal ray deviation angles on the lens surfaces. Calculation of lenses with minimal Fresnel losses is reduced to solving an explicit ordinary differential equation.

Broadband mirrors for surface plasmon polaritons using integrated high-contrast diffraction gratings.

We propose and numerically investigate integrated high-contrast gratings (HCGs) for surface plasmon polaritons (SPPs) propagating along metal-dielectric interfaces, which consist of periodically arranged silicon pillars located on the gold surface. We demonstrate that such on-chip HCGs can be used as broadband plasmonic mirrors, which have subwavelength footprint in the SPP propagation direction and mean reflectance exceeding 85% in a 200-nm-wide spectral range for both the cases of normal and oblique SPP incidence. In order to increase the HCG efficiency and design practically feasible structures, we utilize a parasitic scattering suppression technique based on the use of two-layer grating pillars.

Integrated Gires-Tournois interferometers based on evanescently coupled ridge resonators.

We propose integrated Gires-Tournois interferometers (GTIs) for guided modes of dielectric slab waveguides. The proposed GTIs consist of one or several dielectric ridge resonators separated by subwavelength-width grooves patterned into an abruptly terminated slab waveguide and operate at oblique incidence of the fundamental transverse-electric-polarized mode. The grooves act as partially reflective mirrors, whereas the end facet of the last ridge works in the total internal reflection regime and reflects all the incident radiation.

Optimization method for designing double-surface refractive optical elements for an extended light source.

We propose a method for designing optical elements with two freeform refracting surfaces generating prescribed non-axisymmetric irradiance distributions in the case of an extended light source. The method is based on the representation of the optical surfaces as bicubic splines and on the subsequent optimization of their parameters using a quasi-Newton method. For the fast calculation of the merit function, we propose an efficient version of the ray tracing method.

On the use of the supporting quadric method in the problem of designing double freeform surfaces for collimated beam shaping.

We propose a version of the supporting quadric method for calculating a refractive optical element with two working surfaces for collimated beam shaping. Using optimal mass transportation theory and generalized Voronoi cells, we show that the proposed method can be regarded as a gradient method of maximizing a concave function, which is a discrete analogue of the Lagrange functional in the corresponding mass transportation problem. It is demonstrated that any maximum of this function provides a solution to the problem of collimated beam shaping.

Multiscale approach and linear assignment problem in designing mirrors generating far-field irradiance distributions.

We propose a multiscale approach for designing mirrors generating prescribed irradiance distributions in the far field. Our design method is based on calculating a ray mapping from a Monge-Kantorovich mass transportation problem and on reducing this problem to a linear assignment problem (LAP). The proposed multiscale formulation of the LAP allows one to efficiently calculate freeform mirror surfaces defined on meshes with a size of up to at least 1000×1000.

Design and fabrication of freeform mirrors generating prescribed far-field irradiance distributions.

We consider a method for designing freeform mirrors generating prescribed irradiance distributions in the far field. The method is based on the formulation of the problem of calculating a ray mapping as a Monge-Kantorovich mass transportation problem and on the reduction of the latter problem to a linear assignment problem. As examples, we design freeform mirrors generating a uniform irradiance distribution in a rectangular region and a complex chessboard-shaped distribution.

Design of diffractive lenses operating at several wavelengths.

We propose a method for designing diffractive lenses having a fixed-position focus at several prescribed wavelengths, which we refer to as spectral diffractive lenses (SDLs). The method is based on minimizing an objective function describing the deviation of the complex transmission functions of the spectral lens at the operating wavelengths from the complex transmission functions of diffractive lenses calculated separately for each of these wavelengths. As examples, SDLs operating at three, five, and seven different wavelengths are designed.

Optimal mass transportation problem in the design of freeform optical elements generating far-field irradiance distributions for plane incident beam.

We consider the problem of calculating a refracting surface generating a prescribed irradiance distribution in the far field in the case of a plane incident beam. We demonstrate that this problem can be formulated as a mass transportation problem (MTP) and obtain the cost function for the MTP. It is shown that with a special choice of coordinates, the cost function becomes quadratic.

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.

Optimal mass transportation and linear assignment problems in the design of freeform refractive optical elements generating far-field irradiance distributions.

We consider the problem of calculating a refractive surface generating a prescribed irradiance distribution in the far field in the case of a point light source. We show that this problem can be formulated as a mass transportation problem with a non-quadratic cost function. A method for calculating the refractive surface is proposed, which is based on reducing the problem of calculating an integrable ray mapping to finding a solution to a linear assignment problem.

Linear assignment problem in the design of freeform refractive optical elements generating prescribed irradiance distributions.

We consider the problem of calculating the eikonal function defined on a certain curved surface from the condition of generating a prescribed irradiance distribution on a target surface. We show that the calculation of the "ray mapping" corresponding to the eikonal function is reduced to the solution of a linear assignment problem (LAP). We propose an iterative algorithm for calculating a refractive optical surface from the condition of generating a prescribed near-field irradiance distribution in a non-paraxial case.

Spatial integration and differentiation of optical beams in a slab waveguide by a dielectric ridge supporting high-Q resonances.

We show that a very simple structure consisting of a single subwavelength dielectric ridge on the surface of a slab waveguide enables spatial integration and differentiation of the profile of optical beams propagating in the waveguide. The integration and differentiation operations are performed in reflection and in transmission, respectively, at oblique incidence of the beam impinging on the ridge. The implementation of these operations is associated with the resonant excitation of a cross-polarized eigenmode of the ridge.

Designing double freeform surfaces for collimated beam shaping with optimal mass transportation and linear assignment problems.

We propose a method for designing refractive optical elements for collimated beam shaping in the geometrical optics approximation. In this method, the problem of finding a ray mapping is formulated as a linear assignment problem, which is a discrete version of the corresponding mass transportation problem. A method for reconstructing optical surfaces from a computed discrete ray mapping is proposed.

Design of an axisymmetrical refractive optical element generating required illuminance distribution and wavefront.

The design of an axisymmetrical refractive optical element transforming a given incident beam into an output beam with prescribed illuminance distribution and wavefront is considered. The wavefront of the output beam is represented by the eikonal function defined in a certain plane behind the optical element. The design of the optical element is reduced to the solution of two explicit ordinary differential equations of the first order.

Beam shaping with a plano-freeform lens pair.

It has been shown in [Arch. Rational Mechanics and Analysis 201, 1013 (2011)]. Such approach provides a rigorous methodology for designing freeform optics for irradiance redistribution.

Multifocal diffractive lens generating several fixed foci at different design wavelengths.

We propose a method for designing multifocal diffractive lenses generating prescribed sets of foci with fixed positions at several different wavelengths. The method is based on minimizing the difference between the complex amplitudes of the beams generated by the lens microrelief at the design wavelengths, and the functions of the complex transmission of multifocal lenses calculated for these wavelengths. As an example, a zone plate generating three fixed foci at three different wavelengths was designed, fabricated, and experimentally investigated.