2020 International Conference on Information Technology and Nanotechnology (ITNT)
One-dimensional photonic crystals (PCs) consisting of alternating homogeneous dielectric layers a... more One-dimensional photonic crystals (PCs) consisting of alternating homogeneous dielectric layers are considered as a promising platform for integrated photonic systems, since they can support Bloch surface waves (BSWs; surface electromagnetic waves propagating along an interface of a PC), which can be used as information carriers in such integrated systems. Here, we study the parasitic scattering losses arising upon diffraction of BSWs on a dielectric ridge located on the surface of the PC. We demonstrate that under certain conditions imposed on the BSW angle of incidence and the PC parameters (thicknesses and refractive indices of the PC layers), the parasitic scattering losses can be completely eliminated.
Photonic devices performing required temporal and spatial transformations of optical signals are ... more Photonic devices performing required temporal and spatial transformations of optical signals are of great interest for a wide range of applications including all-optical information processing and analog optical computing. Among the most important operations of analog optical processing are the operations of temporal and spatial differentiation. Various types of resonant photonic structures performing these operations were previously proposed, such as phase-shifted Bragg gratings and other multilayer structures, resonant diffraction gratings, and nanoresonators. In the current work, we present an overview of our recent results dedicated to the design of resonant nanophotonic structures for optical implementation of various differential operators including integrated structures for Bloch surface waves and guided modes. A special attention is paid to a simple planar (integrated) optical differentiator consisting of two identical grooves on the surface of a dielectric slab waveguide (t...
We propose a horizontally symmetrical three-layer dielectric structure composed of a high-index c... more We propose a horizontally symmetrical three-layer dielectric structure composed of a high-index central (core) layer surrounded by two identical low-index cladding layers, which acts as an optical differentiator in reflection. If the refractive index of the surrounding medium is greater that the refractive index of the cladding layers, the spectra of the considered structure may exhibit resonant features associated with the excitation of a leaky mode localized at the central layer. At resonant conditions, the reflection coefficient will vanish at certain values of frequency and angle of incidence, which enables the differentiation of the incident optical pulse. We theoretically justify that this three-layer structure can perform temporal differentiation (differentiation of an incident optical pulse envelope), spatial differentiation (differentiation of an optical beam profile) and the so-called “spatiotemporal differentiation” (differentiation of an optical signal envelope along a c...
We study on-chip spectral filters comprising several dielectric ridges placed on a single-mode di... more We study on-chip spectral filters comprising several dielectric ridges placed on a single-mode dielectric slab waveguide. The investigated filters work in reflection and carry out spectral filtering of obliquely incident TE-polarized modes of the waveguide. We show that by choosing the widths of the grooves separating the adjacent ridges, one can obtain nearly rectangular reflectance peaks using just a few ridges. The proposed filters are promising for the design of novel integrated spectral filters, sensors and optical computing devices.
We consider a guided-mode resonant grating, the period of which slowly varies in the direction of... more We consider a guided-mode resonant grating, the period of which slowly varies in the direction of the periodicity. Optical properties of this structure are investigated rigorously using the Fourier modal method and the scattering matrix formalism. By simulating the diffraction of a plane wave on the considered structure, we demonstrate that it can be used as a linear variable filter (LVF). We also investigate how the line shape of the resonances depends on the rate of the variation of the period. The considered structure can find application in novel multi- and hyperspectral optical systems.
Resonant properties of composite structures consisting of several identical resonant structures (... more 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, composite structures comprising two or four resonant diffractive structures with a Lorentzian transmittance profile optically implement second- and third-order Butterworth filters, respectively, and enable achieving flat-top transmission spectra with steep slopes and low sidebands. We also show that composite structures consisting of three or four second-order Butterworth filters can accurately approximate fourth- or fifth-order Butterworth filters, respectively. The theoretical results are confirmed by rigorous simulations of composite structures consisting of simple three-layer resonant structures.
One-dimensional photonic crystals (PCs) consisting of alternating homogeneous dielectric layers a... more One-dimensional photonic crystals (PCs) consisting of alternating homogeneous dielectric layers are considered as a promising platform for integrated photonic systems, since they can support Bloch surface waves (BSWs; surface electromagnetic waves propagating along an interface of a PC), which can be used as information carriers in such integrated systems. Here, we study the parasitic scattering losses arising upon diffraction of BSWs on a dielectric ridge located on the surface of the PC. We demonstrate that under certain conditions imposed on the BSW angle of incidence and the PC parameters (thicknesses and refractive indices of the PC layers), the parasitic scattering losses can be completely eliminated.
This work is the first experimental demonstration of the fact that a polyimide kapton film of sub... more This work is the first experimental demonstration of the fact that a polyimide kapton film of submillimetre thickness can effectively split THz SPs. Measurements of the transmission and reflection coefficients of SPs on gold-ZnS layer plane structures using monochromatic terahertz $\lambda=130\ \mu\mathrm{m})$ radiation of the Novosibirsk free-electron laser have shown good accordance with theoretical and numerical calculations.
The paper focused on the design problem of a refracting surface forming a prescribed irradiance d... more The paper focused on the design problem of a refracting surface forming a prescribed irradiance distribution in the far field in the case of a plane incident beam. We give the formulation of this problem as a mass transfer problem (MTP) and obtain the cost function for the MTP. We propose effective design method of a refracting surface based on MTP. We give the example of calculating of the refractive surface which forms a chessboard pattern.
We present a method for designing lenses with two aspherical surfaces having minimal Fresnel loss... more 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. Simple analytical approximations are also obtained for the lens profiles.
We propose and numerically investigate integrated high-contrast gratings (HCGs) for surface plasm... more 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. The presented results may find application in two-dimensional optical circuits for steering the SPP propagation.
We consider a method for designing stigmatic lenses implementing required ray mappings. A ray map... more 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. As examples, we design stigmatic lenses satisfying the Abbe sine condition, the Herschel's condition, and the constant angular magnification condition.
Hybrid methods combining the geometrical-optics and diffraction-theory methods enable designing d... more 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. For solving the maximization problem, a gradient method is used, with analytical expressions obtained for the gradient. In contrast to geometrical-optics approaches based on solving the Monge-Ampére equation using finite difference methods, the proposed method enables generating irradiance distributions defined on disconnected regions with non-smooth boundaries. As an example, we calculate an eikonal function, which provides the generation of a "discontinuous" irradiance distribution in the form of a hexagram. It is shown that the utilization of the hybrid approach, in which the obtained geometrical-optics solution is used as a starting point in iterative Fourier transform algorithms, enables designing DOEs with a quasi-regular or piecewise-smooth microrelief structure. The calculation results are confirmed by the results of experimental investigations of a DOE generating a hexagram-shaped irradiance distribution.
We propose a method for designing diffractive lenses having a fixed-position focus at several pre... more 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. The simulation results of the calculated lenses confirm high efficiency of the proposed method. For experimental verification of the design method, we fabricate using direct laser writing and experimentally investigate an SDL operating at five wavelengths. The presented experimental results confirm the efficiency of the proposed method in practical problems of designing SDLs. The obtained results may find applications in the design and fabrication of novel flat diffractive lenses with reduced chromatic effects.
We propose a method for designing optical elements with two freeform refracting surfaces generati... more 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. Using the proposed approach, we design optical elements generating uniform square-shaped irradiance distributions in the far- and near-field. The designed elements are very compact (the height-to-source ratio is only 1.6) and, while providing a high lighting efficiency of 89%, generate highly uniform distributions (the ratio between minimum and average irradiance values in the prescribed square-shaped region exceeds 0.9).
It has been experimentally shown that a rigid polyimide Kapton film of submillimeter thickness is... more 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 laser radiation (λ=130µm) in “gold–ZnS layer–air” flat structures are in good agreement with the results of numerical simulations obtained using the rigorous coupled-wave analysis technique. Transmittance of the SPPs decreases slightly when the layer gets thicker. To minimize the SPP radiative losses emerging due to diffraction of the SPPs on the impedance discontinuity, the Kapton film should be placed normal to the guiding surface and brought in good contact with it (the gap must be less than λ/2). The performed experiments clearly demonstrated Kapton films to be very promising for SPP beam splitting in large-scale terahertz SPP devices.
We propose a multiscale approach for designing mirrors generating prescribed irradiance distribut... more 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. As an example requiring a mesh of this size, we design a mirror generating a grayscale image of A. Einstein on a zero background. The proposed multiscale approach is general and can be applied to a wide range of inverse problems of nonimaging optics.
Photonic bound states in the continuum (BICs) are eigenmodes with an infinite lifetime, which coe... more 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 nanophotonic element consisting of a single dielectric ridge terminating an abruptly ended slab waveguide. This structure can be considered as an on-chip analog of the Gires-Tournois interferometer (GTI). We demonstrate that the proposed integrated structure supports high-Q phase resonances and robust BICs. We develop a simple but extremely accurate coupled-wave model that clarifies the physics of BIC formation and enables predicting BIC locations. The developed model shows that the studied BICs are topologically protected and describes the strong phase resonance effect that occurs when two BICs with opposite topological charges annihilate.
2020 International Conference on Information Technology and Nanotechnology (ITNT)
One-dimensional photonic crystals (PCs) consisting of alternating homogeneous dielectric layers a... more One-dimensional photonic crystals (PCs) consisting of alternating homogeneous dielectric layers are considered as a promising platform for integrated photonic systems, since they can support Bloch surface waves (BSWs; surface electromagnetic waves propagating along an interface of a PC), which can be used as information carriers in such integrated systems. Here, we study the parasitic scattering losses arising upon diffraction of BSWs on a dielectric ridge located on the surface of the PC. We demonstrate that under certain conditions imposed on the BSW angle of incidence and the PC parameters (thicknesses and refractive indices of the PC layers), the parasitic scattering losses can be completely eliminated.
Photonic devices performing required temporal and spatial transformations of optical signals are ... more Photonic devices performing required temporal and spatial transformations of optical signals are of great interest for a wide range of applications including all-optical information processing and analog optical computing. Among the most important operations of analog optical processing are the operations of temporal and spatial differentiation. Various types of resonant photonic structures performing these operations were previously proposed, such as phase-shifted Bragg gratings and other multilayer structures, resonant diffraction gratings, and nanoresonators. In the current work, we present an overview of our recent results dedicated to the design of resonant nanophotonic structures for optical implementation of various differential operators including integrated structures for Bloch surface waves and guided modes. A special attention is paid to a simple planar (integrated) optical differentiator consisting of two identical grooves on the surface of a dielectric slab waveguide (t...
We propose a horizontally symmetrical three-layer dielectric structure composed of a high-index c... more We propose a horizontally symmetrical three-layer dielectric structure composed of a high-index central (core) layer surrounded by two identical low-index cladding layers, which acts as an optical differentiator in reflection. If the refractive index of the surrounding medium is greater that the refractive index of the cladding layers, the spectra of the considered structure may exhibit resonant features associated with the excitation of a leaky mode localized at the central layer. At resonant conditions, the reflection coefficient will vanish at certain values of frequency and angle of incidence, which enables the differentiation of the incident optical pulse. We theoretically justify that this three-layer structure can perform temporal differentiation (differentiation of an incident optical pulse envelope), spatial differentiation (differentiation of an optical beam profile) and the so-called “spatiotemporal differentiation” (differentiation of an optical signal envelope along a c...
We study on-chip spectral filters comprising several dielectric ridges placed on a single-mode di... more We study on-chip spectral filters comprising several dielectric ridges placed on a single-mode dielectric slab waveguide. The investigated filters work in reflection and carry out spectral filtering of obliquely incident TE-polarized modes of the waveguide. We show that by choosing the widths of the grooves separating the adjacent ridges, one can obtain nearly rectangular reflectance peaks using just a few ridges. The proposed filters are promising for the design of novel integrated spectral filters, sensors and optical computing devices.
We consider a guided-mode resonant grating, the period of which slowly varies in the direction of... more We consider a guided-mode resonant grating, the period of which slowly varies in the direction of the periodicity. Optical properties of this structure are investigated rigorously using the Fourier modal method and the scattering matrix formalism. By simulating the diffraction of a plane wave on the considered structure, we demonstrate that it can be used as a linear variable filter (LVF). We also investigate how the line shape of the resonances depends on the rate of the variation of the period. The considered structure can find application in novel multi- and hyperspectral optical systems.
Resonant properties of composite structures consisting of several identical resonant structures (... more 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, composite structures comprising two or four resonant diffractive structures with a Lorentzian transmittance profile optically implement second- and third-order Butterworth filters, respectively, and enable achieving flat-top transmission spectra with steep slopes and low sidebands. We also show that composite structures consisting of three or four second-order Butterworth filters can accurately approximate fourth- or fifth-order Butterworth filters, respectively. The theoretical results are confirmed by rigorous simulations of composite structures consisting of simple three-layer resonant structures.
One-dimensional photonic crystals (PCs) consisting of alternating homogeneous dielectric layers a... more One-dimensional photonic crystals (PCs) consisting of alternating homogeneous dielectric layers are considered as a promising platform for integrated photonic systems, since they can support Bloch surface waves (BSWs; surface electromagnetic waves propagating along an interface of a PC), which can be used as information carriers in such integrated systems. Here, we study the parasitic scattering losses arising upon diffraction of BSWs on a dielectric ridge located on the surface of the PC. We demonstrate that under certain conditions imposed on the BSW angle of incidence and the PC parameters (thicknesses and refractive indices of the PC layers), the parasitic scattering losses can be completely eliminated.
This work is the first experimental demonstration of the fact that a polyimide kapton film of sub... more This work is the first experimental demonstration of the fact that a polyimide kapton film of submillimetre thickness can effectively split THz SPs. Measurements of the transmission and reflection coefficients of SPs on gold-ZnS layer plane structures using monochromatic terahertz $\lambda=130\ \mu\mathrm{m})$ radiation of the Novosibirsk free-electron laser have shown good accordance with theoretical and numerical calculations.
The paper focused on the design problem of a refracting surface forming a prescribed irradiance d... more The paper focused on the design problem of a refracting surface forming a prescribed irradiance distribution in the far field in the case of a plane incident beam. We give the formulation of this problem as a mass transfer problem (MTP) and obtain the cost function for the MTP. We propose effective design method of a refracting surface based on MTP. We give the example of calculating of the refractive surface which forms a chessboard pattern.
We present a method for designing lenses with two aspherical surfaces having minimal Fresnel loss... more 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. Simple analytical approximations are also obtained for the lens profiles.
We propose and numerically investigate integrated high-contrast gratings (HCGs) for surface plasm... more 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. The presented results may find application in two-dimensional optical circuits for steering the SPP propagation.
We consider a method for designing stigmatic lenses implementing required ray mappings. A ray map... more 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. As examples, we design stigmatic lenses satisfying the Abbe sine condition, the Herschel's condition, and the constant angular magnification condition.
Hybrid methods combining the geometrical-optics and diffraction-theory methods enable designing d... more 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. For solving the maximization problem, a gradient method is used, with analytical expressions obtained for the gradient. In contrast to geometrical-optics approaches based on solving the Monge-Ampére equation using finite difference methods, the proposed method enables generating irradiance distributions defined on disconnected regions with non-smooth boundaries. As an example, we calculate an eikonal function, which provides the generation of a "discontinuous" irradiance distribution in the form of a hexagram. It is shown that the utilization of the hybrid approach, in which the obtained geometrical-optics solution is used as a starting point in iterative Fourier transform algorithms, enables designing DOEs with a quasi-regular or piecewise-smooth microrelief structure. The calculation results are confirmed by the results of experimental investigations of a DOE generating a hexagram-shaped irradiance distribution.
We propose a method for designing diffractive lenses having a fixed-position focus at several pre... more 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. The simulation results of the calculated lenses confirm high efficiency of the proposed method. For experimental verification of the design method, we fabricate using direct laser writing and experimentally investigate an SDL operating at five wavelengths. The presented experimental results confirm the efficiency of the proposed method in practical problems of designing SDLs. The obtained results may find applications in the design and fabrication of novel flat diffractive lenses with reduced chromatic effects.
We propose a method for designing optical elements with two freeform refracting surfaces generati... more 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. Using the proposed approach, we design optical elements generating uniform square-shaped irradiance distributions in the far- and near-field. The designed elements are very compact (the height-to-source ratio is only 1.6) and, while providing a high lighting efficiency of 89%, generate highly uniform distributions (the ratio between minimum and average irradiance values in the prescribed square-shaped region exceeds 0.9).
It has been experimentally shown that a rigid polyimide Kapton film of submillimeter thickness is... more 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 laser radiation (λ=130µm) in “gold–ZnS layer–air” flat structures are in good agreement with the results of numerical simulations obtained using the rigorous coupled-wave analysis technique. Transmittance of the SPPs decreases slightly when the layer gets thicker. To minimize the SPP radiative losses emerging due to diffraction of the SPPs on the impedance discontinuity, the Kapton film should be placed normal to the guiding surface and brought in good contact with it (the gap must be less than λ/2). The performed experiments clearly demonstrated Kapton films to be very promising for SPP beam splitting in large-scale terahertz SPP devices.
We propose a multiscale approach for designing mirrors generating prescribed irradiance distribut... more 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. As an example requiring a mesh of this size, we design a mirror generating a grayscale image of A. Einstein on a zero background. The proposed multiscale approach is general and can be applied to a wide range of inverse problems of nonimaging optics.
Photonic bound states in the continuum (BICs) are eigenmodes with an infinite lifetime, which coe... more 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 nanophotonic element consisting of a single dielectric ridge terminating an abruptly ended slab waveguide. This structure can be considered as an on-chip analog of the Gires-Tournois interferometer (GTI). We demonstrate that the proposed integrated structure supports high-Q phase resonances and robust BICs. We develop a simple but extremely accurate coupled-wave model that clarifies the physics of BIC formation and enables predicting BIC locations. The developed model shows that the studied BICs are topologically protected and describes the strong phase resonance effect that occurs when two BICs with opposite topological charges annihilate.
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Papers by Evgeni Bezus