Abstract: A theoretical and numerical investigation was made of the optical implementation of the second-order spatial differentiation operation using a layered metal–dielectric structure at normal light beam inciden...
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We discuss two source vector fields of Poincare-beam type that can be looked upon as optical skyrmions, i.e. topological quasiparticles. We derive explicit analytical relationships that describe projections of a three...
We discuss two source vector fields of Poincare-beam type that can be looked upon as optical skyrmions, i.e. topological quasiparticles. We derive explicit analytical relationships that describe projections of a three-dimensional (3D) skyrmion vector field in the source plane and skyrmion numbers, which are shown to be proportional to the topological charges of constituent optical vortices of the Poincare beams. We also propose a new constructive formula as an effective tool for calculating the skyrmion number via normalized Stokes vector projections rather than skyrmion vector field projections. The skyrmion numbers calculated using the familiar and newly proposed formulae coincide. Numbers of each projection of a 3D skyrmion vector field are shown to comprise a third of the full skyrmion number. The theoretical conclusions are validated by a numerical simulation.
We propose a method for the design of diffractive neural networks (DNNs) for image classification, which takes into account the positioning errors (transverse shifts) of phase diffractive optical elements (DOEs) const...
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We propose a method for the design of diffractive neural networks (DNNs) for image classification, which takes into account the positioning errors (transverse shifts) of phase diffractive optical elements (DOEs) constituting the DNN. In this method, the error in solving the classification problem is represented by a functional depending on the phase functions of the DOEs and on random vectors describing the transverse shifts of the DOEs. The mathematical expectation of this functional is used as an error functional in the gradient method for calculating the DNN taking into account the transverse shifts of the DOEs. Explicit expressions are obtained for the derivatives of the error functional. It is shown that the calculation of the derivatives of this functional using the Monte Carlo method corresponds to the DNN training method, in which the DOEs have random transverse shifts. By using the proposed gradient method, DNNs are designed that are robust to transverse shifts of the DOEs and enable solving the problem of classifying handwritten digits at a visible wavelength. Numerical simulations demonstrate good performance of the designed DNNs at transverse shifts of up to 17 wavelengths.
We present a formulation of the supporting quadric method (SQM) taking into account diffraction effects and allowing one to calculate the phase function of a diffractive optical element (DOE) generating a prescribed i...
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We present a formulation of the supporting quadric method (SQM) taking into account diffraction effects and allowing one to calculate the phase function of a diffractive optical element (DOE) generating a prescribed intensity distribution. In the method, the DOE phase is represented as a piecewise smooth function constituted by the phase functions of lenses (quadrics) focusing the incident beam to the points of the required distribution. The quadric parameters are calculated using a gradient method minimizing an error function representing the difference between the generated and required intensity distributions. Importantly, we calculate the gradient of the error function with respect to the quadric parameters in the framework of the scalar diffraction theory (SDT) in an analytical form. The presented examples of DOE design demonstrate good performance of a hybrid approach based on using the geometrical-optics SQM solution as a starting point for the proposed SQM operating in the SDT framework.
We consider the design of cascaded diffractive optical elements (DOEs) for generating specified intensity distributions for several incident beams with different wavelengths. For each incident beam with a given wavele...
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We discuss polarizing kinoforms - diffractive optical elements that modulate only the polarization of incident light and form desired intensity distributions at a pregiven distance. The surface microrelief of such opt...
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We discuss polarizing kinoforms - diffractive optical elements that modulate only the polarization of incident light and form desired intensity distributions at a pregiven distance. The surface microrelief of such optical elements has the form of a binary curvilinear diffraction grating with a constant period less than a wavelength. The energy efficiency of the elements is equivalent to that of conventional multilevel phase kinoforms.
We study iterative algorithms for calculating two classes of diffractive optical elements: (1) those forming a set of concentric rings in the spatial spectrum plane, and (2) those forming non-diffracting beams with a ...
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We study iterative algorithms for calculating two classes of diffractive optical elements: (1) those forming a set of concentric rings in the spatial spectrum plane, and (2) those forming non-diffracting beams with a predetermined distribution of transverse intensity in the beam. The methods employ the representation of the desired function as a linear superposition of partial solutions to the Helmholtz equation in cylindrical coordinates.
We propose a procedure of calculation of diffractive optical elements (DOE) for formation of optical beams with a given intensity distribution in the transverse plane. We use the superposition of zero-order Bessel bea...
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We present a formulation of a fuzzy logic system (FLS) that can be used to construct nonparametric models of nonlinear processes, given only input-output data. In order to effectively construct such models, we discuss...
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We present a formulation of a fuzzy logic system (FLS) that can be used to construct nonparametric models of nonlinear processes, given only input-output data. In order to effectively construct such models, we discuss several design methods with different properties and features. We compare and illustrate systems designed with each one of the methods, using an example on the predictive modeling of a nonlinear dynamic (chaotic) system.
An iterative method in this paper reports the design of a phase diffractive optical element (DOE) that has a transmission function in the form of a linear combination of a finite number of Hadamard functions with diff...
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ISBN:
(纸本)0819423556
An iterative method in this paper reports the design of a phase diffractive optical element (DOE) that has a transmission function in the form of a linear combination of a finite number of Hadamard functions with different carrier spatial frequencies. If such a DOE is coupled with a spherical lens and illuminated by the light wave, the light intensities in desired points will be proportional to the squared modules of the expansion coefficients of that light field in terms of the Hadamard basis. It is found that 80% of the incident light energy is accounted for by the formation of the desired coefficients.
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