26 April 2018 Simulation of light propagation in the thin-film waveguide lens
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In this paper we investigate the solution of the problem of modeling the propagation of electromagnetic radiation in three-dimensional integrated optical structures, such as waveguide lenses. When propagating through three-dimensional waveguide structures the waveguide modes can be hybridized, so the mathematical model of their propagation must take into account the connection of TE- and TM-mode components. Therefore, an adequate consideration of hybridization of the waveguide modes is possible only in vector formulation of the problem. An example of three-dimensional structure that hybridizes waveguide modes is the Luneburg waveguide lens, which also has focusing properties.

If the waveguide lens has a radius of the order of several tens of wavelengths, its variable thickness at distances of the order of several wavelengths is almost constant. Assuming in this case that the electromagnetic field also varies slowly in the direction perpendicular to the direction of propagation, one can introduce a small parameter characterizing this slow varying and decompose the solution in powers of the small parameter. In this approach, in the zeroth approximation, scalar diffraction problems are obtained, the solution of which is less resource-consuming than the solution of vector problems. The calculated first-order corrections of smallness describe the connection of TE- and TM-modes, so the solutions obtained are weakly-hybridized modes.

The formulation of problems and methods for their numerical solution in this paper are based on the authors' research on waveguide diffraction on a lens in a scalar formulation.
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M. D. Malykh, M. D. Malykh, D. V. Divakov, D. V. Divakov, L. A. Sevastianov, L. A. Sevastianov, A. L. Sevastianov, A. L. Sevastianov, } "Simulation of light propagation in the thin-film waveguide lens", Proc. SPIE 10717, Saratov Fall Meeting 2017: Laser Physics and Photonics XVIII; and Computational Biophysics and Analysis of Biomedical Data IV, 1071711 (26 April 2018); doi: 10.1117/12.2315898; https://doi.org/10.1117/12.2315898

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