arXiv subjects

Albert A. Mingazov

Publications and source records attributed to Albert A. Mingazov.

3 recordsLinked to original sources

arXiv2026

Second-order supporting quadric method for designing freeform refracting surfaces generating prescribed irradiance distributions

We consider the inverse problem of calculating a refracting surface that generates a prescribed irradiance distribution in the far field for a collimated incident beam. This problem can be formulated as a mass transportation problem (MTP) with a quadratic cost function. To solve this problem, we propose a version of the supporting quadric method (SQM), in which the calculation of the quadric parameters is reduced to the problem of minimizing a convex function. We obtain simple analytical expressions for the second derivatives of this function, making it possible to calculate the quadric parameters using second-order optimization methods. This allows us to refer to the proposed method as the second-order SQM. We demonstrate high efficiency of this approach by designing several optical surfaces that generate complex irradiance distributions. We also consider the application of the second-order SQM to nonimaging optics problems described by MTPs with a non-quadratic cost function.

physics.optics↗

arXiv2024

Topological properties of reflection zeros of optical differentiators based on layered metal-dielectric-metal structures

We investigate the topological properties of reflection zeros of three-layer structures consisting of a dielectric layer sandwiched between two metal layers, which can be used as optical differentiators. We show that the reflection zeros possess non-zero topological charges, which makes them topologically protected. With a small perturbation of the parameters of the structure (e.g., a change in one of the layer thicknesses), the reflection zero does not disappear, but shifts in the parameter space, i.e., appears at different wavelength and angle of incidence. We demonstrate that with a further parameter change, two zeros with opposite topological charges (+1 and -1) approach each other, merge, and then disappear. We believe that the obtained results give useful insight regarding the operation of layered metal-dielectric-metal structures possessing reflection zeros.

physics.optics↗

arXiv2023

How many parameters do we need to obtain a BIC in symmetric and asymmetric structures?

Photonic bound states in the continuum (BICs) are nonradiating eigenmodes of structures with open scattering channels. Most often, BICs are studied in highly symmetric structures with one open scattering channel. In this simplest case, the so-called symmetry-protected BICs can be found by tuning a single parameter, which is the light frequency. Another kind of BICs -- accidental BICs -- can be obtained by tuning two parameters. For more complex structures lacking certain symmetries or having several open scattering channels, more than two parameters might be required. In the present work, we propose an algebraic approach for computing the number of parameters required to obtain a BIC by expressing it through the dimension of the solution set of certain algebraic equations. Computing this dimension allows us to relate the required number of parameters with the number of open scattering channels without solving Maxwell's equations. We show that different relations take place when the scattering matrices describing the system are symmetric or asymmetric. The obtained theoretical results are confirmed by the results of rigorous electromagnetic simulations.

physics.optics↗