arXiv subjects

Dmitry A. Bykov

Publications and source records attributed to Dmitry A. Bykov.

25 records · Page 2Linked to original sources

arXiv2018

$ω{\rm-}k_x$ Fano line shape in photonic crystal slabs

We study the resonant properties of photonic crystal slabs theoretically. An $ω{\rm-}k_x$ Fano line shape that approximates the transmission (reflection) spectrum is obtained. This approximation, being a function of light's frequency and in-plane wave vector, generalizes the conventional Fano line shape. Two particular approximations, parabolic and hyperbolic, are obtained and investigated in detail, taking into account the symmetry of the structure, the reciprocity, and the energy conservation. The parabolic approximation considers a single resonance at normal incidence, while the hyperbolic one takes into account two modes, the symmetric and the antisymmetric. Using rigorous simulations based on the Fourier modal method we show that the hyperbolic line shape provides a better approximation of the transmission spectrum. By deriving the causality conditions for both approximations, we show that only the hyperbolic one provides causality in a relativistic sense.

physics.optics↗

arXiv2018

First-order optical spatial differentiator based on a guided-mode resonant grating

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.

physics.optics↗

arXiv2018

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 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. The method is suitable for designing continuous piecewise-smooth optical surfaces. The design of refractive optical elements transforming beams with circular cross-section to variously shaped (rectangular, triangular, and cross-shaped) beams with plane wavefront is discussed. The presented numerical simulation results confirm high efficiency of the designed optical elements.

physics.optics↗

arXiv2018

Spatial differentiation and integration of optical beams in a slab waveguide by a single dielectric ridge

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 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. At the considered parameters of the structure and incidence geometry, neither "parasitic" out-of-plane scattering nor polarization conversion occurs. The presented rigorous numerical simulation results confirm high-quality differentiation and integration. We demonstrate that by choosing the quality factor of the resonance, one can achieve the required tradeoff between the differentiation (or integration) quality and the amplitude of the resulting beam. The proposed integrated structure may find application in ultrafast all-optical analog computing and signal processing systems.

physics.optics↗

arXiv2017

Two-groove narrowband transmission filter integrated in a slab waveguide

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 transmittance are achieved at resonant conditions. Width and location of the transmittance peak can be controlled by changing the widths of the grooves and of the ridge, respectively. The proposed filter may find application in waveguide-integrated spectrometers.

physics.optics↗

arXiv2017

On the use of the Fourier modal method for calculation of localized eigenmodes of integrated optical resonators

We propose the generalization of the Fourier modal method aimed at calculating localized eigenmodes of integrated optical resonators. The method is based on constructing the analytic continuation of the structure's scattering matrix and calculating its poles. The method allows one to calculate the complex frequency of the localized mode and the corresponding field distribution. We use the proposed method to calculate the eigenmodes of rectangular dielectric block located on metal surface. We show that excitation of these modes by surface plasmon-polariton (SPP) results in resonant features in the SPP transmission spectrum. The proposed method can be used to design and investigate optical properties of integrated and plasmonic optical devices.

physics.optics↗

arXiv2012

Numerical methods for calculating poles of the scattering matrix with applications in grating theory

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. A new iterative method for computing the 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 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.

cond-mat.other↗