# E.A. BezusImage Processing Systems Institute, Russian Academy of Sciences · Diffractive Optics Laboratory

E.A. Bezus

PhD (Candidate of Sciences)

## About

125

Publications

7,985

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1,792

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Introduction

Additional affiliations

September 2009 - present

September 2009 - present

Education

July 2009 - March 2012

September 2003 - February 2009

## Publications

Publications (125)

We develop a method for calculating the eikonal function (or the phase function) of the light field, ensuring the formation of a prescribed irradiance distribution in the geometrical optics approximation. In the proposed method, the problem being solved is formulated in a semi-discrete form as a problem of the maximization of a concave function. Fo...

We consider a version of the supporting quadric method for designing freeform mirrors that generate prescribed irradiance distributions in the near field. The method is derived for a general case of an incident beam with an arbitrary wavefront. As an example, for a practically important special case of a plane incident wavefront, we design a freefo...

This erratum includes a necessary additional reference for the article [J. Opt. Soc. Am. A38, 855 (2021)JOAOD60740-323210.1364/JOSAA.425379].

We propose and theoretically and numerically investigate integrated high-contrast diffraction gratings for surface electromagnetic waves. We consider two platforms for the on-chip gratings: surface plasmon-polaritons propagating along metal-dielectric interfaces and Bloch surface waves propagating along interfaces of photonic crystals. We demonstra...

We propose a simple integrated resonant structure for the Bloch surface wave platform, which consists of two subwavelength grooves patterned on the surface of a one-dimensional dielectric photonic crystal. We demonstrate that the investigated structure can operate in a parasitic-scattering-free regime and, in this case, provide unity transmittance...

In the geometrical optics approximation, we consider a method for calculating a refractive optical element with two freeform surfaces, which transforms an incident beam with a plane wave-front into an output beam with a required wavefront and generating a required illuminance distribution. As examples, optical elements forming given illuminance dis...

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...

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 eiko...

We propose and theoretically and numerically investigate integrated diffraction gratings for the Bloch surface wave (BSW) platform, which have subwavelength or near-subwavelength period. We demonstrate that, in the oblique incidence geometry of a transverse-electric polarized BSW and with a properly chosen band gap configuration of the photonic cry...

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)10.1364/OE.398990] proposed...

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 equ...

Optical properties of a resonant trilayer metal-dielectric-metal (MDM) structure that consists of an upper metal layer, a dielectric layer, and a metal substrate are investigated. Using a multiple wave interference model, we prove that the reflection coefficient of the MDM structure may strictly vanish. The existence of a reflectance zero makes it...

The development and investigation of novel photonic structures for the differentiation of optical signals, which are considered as promising building blocks for the optoelectronic information processing devices, has attracted considerable attention in recent years. In this tutorial, we discuss the optical computation of the spatial derivatives of t...

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 subwavel...

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. Using the scattering matrix formalism, we analytically demonstrate that, at properly chosen thicknesses of the phase-shift layers,...

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-pola...

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-Ne...

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...

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...

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 f...

It has been experimentally shown that a rigid polyimide Kapton film of submillimeter thickness is sufficiently transparent in the frequency range of 1.2–3 THz and can be used for splitting surface plasmon polaritons (SPPs) propagating along a flat conducting surface. The transmittance T and reflectance R measured for SPPs excited by a free-electron...

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 t...

We demonstrate that dielectric slab waveguides terminated with a dielectric ridge (i.e. with a slab waveguide segment having a greater thickness) support high-Q resonances and bound states in the continuum (BICs). The resonances and BICs take place at oblique incidence of TE-polarized guided modes in the total internal reflection geometry, when all...

Photonic bound states in the continuum (BICs) are eigenmodes with an infinite lifetime, which coexist with a continuous spectrum of radiating waves. BICs are not only of great theoretical interest but also have a wide range of practical applications, e.g. in the design of optical resonators. Here, we study this phenomenon in a new integrated nanoph...

A method for calculating a “spectral” diffractive lens, which ensures the preservation of the focal position at several prescribed wavelengths is proposed. The method is based on minimizing the function characterizing the difference between the complex transmission functions of the spectral lens for given wavelengths and the complex transmission fu...

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,...

We propose and theoretically and numerically investigate narrowband integrated filters consisting of identical resonant dielectric ridges on the surface of a single-mode dielectric slab waveguide. The proposed composite structures operate near a bound state in the continuum (BIC) and enable spectral filtering of transverse-electric-polarized guided...

We discuss the development of a software package, which enables simulating and analyzing the diffraction of a plane electromagnetic wave on a multilayer diffraction grating with. The main functional requirements to the system are formulated. The architectural solution of the implemented software including the main functional and logical layers of t...

A problem of calculating a refractive surface that forms a required irradiance distribution in the far field in the case of a plane illuminating beam is considered. We show that this problem can be formulated as a mass transportation problem. The specific form of the cost function for this problem is obtained. It is shown that with a certain choice...

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. Using the scattering matrix formalism, we analytically demonstrate that, at properly chosen thicknesses of the phase-...

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 propose two simple planar structures that enable spatial differentiation of the profile of optical beams propagating in a slab waveguide. The differentiator operating in transmission consists of a single subwavelength dielectric ridge on the surface of a slab waveguide. The differentiator operating in reflection consists of two grooves on the su...

We propose and theoretically and numerically investigate narrowband integrated filters consisting of identical resonant dielectric ridges on the surface of a single-mode dielectric slab waveguide. The proposed composite structures operate near a bound state in the continuum (BIC) and enable spectral filtering of transverse-electric-polarized guided...

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....

Resonant properties of composite structures consisting of several identical resonant diffractive structures (e.g. multilayer thin-film structures or guided-mode resonance gratings) separated by phase-shift layers are investigated theoretically. Using the scattering matrix formalism, we analytically demonstrate that, at properly chosen thicknesses o...

We present simple yet extremely accurate coupled-wave models describing the formation of bound states in the continuum (BICs) in one-dimensional periodic guided-mode resonant gratings consisting of a slab waveguide layer with a binary grating attached to one or both of its interfaces. Using these models, we obtain simple closed-form expressions pre...

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...

Photonic bound states in the continuum (BICs) are eigenmodes with an infinite lifetime, which coexist with a continuous spectrum of radiating waves. BICs are not only of great theoretical interest, but have a wide range of practical applications, e.g. in the design of optical resonators. Here, we study this phenomenon in a new integrated nanophoton...

We present simple yet extremely accurate coupled-wave models describing the formation of bound states in the continuum (BICs) in 1D-periodic guided-mode resonant gratings (GMRGs) consisting of a slab waveguide layer with a binary grating attached to one or both of its interfaces. Using these models, we obtain simple closed-form expressions predicti...

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 (BI...

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...

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 surfac...

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 o...

Diffraction of slab waveguide modes on a dielectric ridge located on the waveguide surface is studied. Calculations, based on aperiodic rigorous coupled-wave analysis, demonstrate the existence of sharp resonant features in the reflectance and the transmittance spectra occurring at oblique incidence of TE-polarized waveguide mode on the ridge. Angu...

We present a simple and compact integrated narrowband filter that enables spectral or spatial filtering of optical radiation propagating in a slab waveguide. The filter consists of two grooves on the waveguide surface and constitutes an integrated analogue of the so-called W-type structure. The filtering is performed in transmission at oblique inci...

Terahertz (THz) surface plasmons (SPs) can be effectively used in THz communication lines, information processing devices, spectroscopic measurements of submicron dielectric layers, and metal surface quality control. Such applications necessitate implementation of various optical schemes, including splitting of THz SPs on the guiding surface. This...

In this work, diffraction efficiency and scattering and absorption losses in dielectric Bragg gratings for surface plasmon polaritons (SPP) are numerically studied using the Fourier modal method. It is shown that the main reason behind the low efficiency of such Bragg reflectors is the out-of-plane parasitic scattering of SPP at the grating ridges....

In the present work, we numerically study the performance (reflectance and scattering /absorption losses) of dielectric Bragg gratings for surface plasmon polaritons using a rigorous coupled-wave analysis technique. We demonstrate that the main reason behind the low efficiency of such Bragg reflectors is the parasitic out-of-plane scattering of SPP...

An optical differentiator based on a three-layer resonant structure with a W-shaped refractive index profile is proposed. The differentiation operation is performed in reflection and is associated with the resonant excitation of an eigenmode of the structure localized in the central layer. The presented results of numerical simulations demonstrate...

We investigate the diffraction of 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)...

We propose a method for designing refractive optical elements for collimated beam shaping. 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...

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 tran...

We show that a very simple structure consisting of a single subwavelength dielectric ridge on the surface of a slab waveguide enables spatial differentiation and integration of the profile of optical beams propagating in the waveguide. The differentiation and integration operations are performed in transmission and in reflection, respectively, at o...

We present an experimental demonstration of a subwavelength diffraction grating performing spatial differentiation of the transverse profile of a 3D optical beam. The experimental results are in agreement with the presented analytical model suggesting that the differentiation is performed in transmission at oblique incidence and is associated with...

We present a method for calculating a spectral multifocal diffractive lens that forms a given set of fixed-position foci at multiple operating wavelengths. It is based on minimizing a function represented as a squared absolute value of difference between the complex amplitudes of beams formed by the relief of a spectral lens at the given wavelength...

We consider the derivation of a dispersion relation of Bloch surface waves supported by interfaces between a semi-infinite one-dimensional photonic crystal and a homogeneous medium. From the derived dispersion relation, we obtain an explicit analytical expression that defines the relationship between the propagation constant and the thickness of th...

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 complex transmission...

A diffractive structure for the generation of high-frequency interference patterns of evanescent electromagnetic waves based on the interference of the “volume” modes of 1D dielectric photonic crystal at Fabry-Perot resonances is proposed. The obtained results may find application in the design of novel devices for near-field interference photolith...

We propose a simple integrated narrowband filter consisting of two grooves on the surface of a slab waveguide. Spectral filtering is performed in transmission at oblique incidence due to excitation of an eigenmode of the structure localized at a ridge cavity between the grooves. For the considered parameters, strictly zero reflectance and unity tra...

The problem of calculation of the light field eikonal function providing focusing into a prescribed region is formulated as a variational problem and as a Monge–Kantorovich mass transportation problem. It is obtained that the cost function in the Monge–Kantorovich problem corresponds to the distance between a point of the source region (in which th...

We present an iterative method for calculating complex-frequency eigenmodes of photonic crystal slabs with 1D periodicity based on the aperiodic Fourier modal method. By comparison with the known methods, we show that the proposed method is e cient for studying resonant properties of long-period photonic crystal slabs and di raction gratings. We de...

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 a...

In this work, we study numerically and theoretically phase-shifted Bragg gratings (PSBG) for Bloch surface waves (BSW) propagating along the interfaces between a 1D photonic crystal and a homogeneous medium. The studied on-chip structure consists of a set of dielectric ridges located on the photonic crystal surface constituting two symmetrical onch...

A diffraction structure for generating high-frequency interference patterns of evanescent electromagnetic waves based on the interference of “volume” modes of dielectric photonic crystals at Fabry-Perot resonances is discussed. For the prediction of the angular locations of the Fabry-Perot resonances, a simple approach for the description of diffra...

Bloch surface waves (BSWs) supported by the interfaces between a photonic crystal and a homogeneous medium are considered as a prospective information carrier in integrated photonic circuits. In the present work, we study the application of on-chip phase-shifted Bragg gratings for spatial differentiation of BSW beams. The presented simulation resul...

Interference patterns of Bloch surface waves with a period that is significantly less than the wavelength of incident radiation are formed using dielectric diffraction gratings located on the surface of photonic crystal. The simulation based on electromagnetic diffraction theory is used to demonstrate the possibility of high-quality interference pa...