This paper proposes three techniques to reduce the time required to calculate single diffraction efficiencies or a series of diffraction efficiencies obtained from rigorous coupled-wave analysis algorithms. These are a technique using the properties of the Toeplitz matrix, a technique for reducing the number of variables in a function of Fourier coefficients, and a technique for using parallel computing. On the example of tasks on plotting the dependences of the diffraction efficiency of two-layer two-relief sawtooth microstructures with antireflection coatings on the angle of incidence of radiation, it is shown that using the properties of Toeplitz matrices can significantly reduce the calculation time. Parallel computing also reduces the calculation time, but it uses more RAM.
The harmonic sawtooth microstructure allows the diffractive lens to operate with polychromatic radiation, in particular, with the radiation of RGB LEDs, but only with restrictions due to axial color and specific field curvature. Its reason is the jump in the working diffraction order with an increase of the wave angle of incidence. The permissible wave angles of incidence at the microstructure were estimated using the example of a harmonic diffractive lens made of crown-like plastic E48R.
Based on a complete system of boundary conditions for an electromagnetic field incident on a periodic structure, an algorithm is presented that allows you to convert such a system, leaving only the unknown amplitudes of the transmitted diffraction orders. The method underlying the algorithm belongs to the family of Fourier-space methods so devices and fields are represented as a sum of spatial harmonics. It is shown that the results of calculating the diffraction efficiency obtained using this approach completely coincide with the results obtained in the framework of the enhanced transmittance matrix approach and the scattering matrix approach. The dependences of diffraction efficiency on the wavelength and angle of incidence of the microstructure obtained by this method are presented. These results are consistent with the conclusions made in earlier studies, based on a different approach in the framework of a rigorous coupled-wave analysis.
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