Simulation of guided modes (eigenmodes) and synthesis of a thin-film generalised waveguide Luneburg lens in the zero-order vector approximation

Propagation of a guided mode (eigenmode) through an integrated optical generalised waveguide Luneburg lens is numerically simulated for the first time in terms of the previously obtained analytical solution of the vector electrodynamic problem in a smoothly irregular four-layer integrated optical 3D waveguide. The dispersion relation for a four-layer continuously irregular integrated optical 3D waveguide is calculated within the approximations of the asymptotic method of comparison waveguides and the method of adiabatic modes, in particular, taking into account the shift of the propagation constants of quasi-TE and quasi-TM modes. A generalised waveguide Luneburg lens with a full aperture is synthesised in the zero-order approximation. The results of numerical simulation demonstrate, on the one hand, a very good coincidence of the solution to the stated problem obtained in the approximation of the method of comparison waveguides with the previous results, and, on the other hand, advantages of our method: more rigorous solution of the problem, more complete consideration of its physical peculiarities, and higher accuracy of calculations. Another undoubted advantage of the analytical method proposed here is that it can be used to analyse similar structures fabricated of dielectrics, magnetics, and metamaterials, including nonlinear materials, in a wide range of electromagnetic wavelengths.