This paper presents a numerical study of the quasi-resonant absorption of TE-polarized waves by a periodic structure of the metal-dielectric grating type on a dielectric substrate. The parameters of such a metal-dielectric grating, in particular the period, are chosen in such a way that no waveguide resonance occurs in the grating. The absence of resonance is evidenced by low fields at grating boundaries with homogeneous dielectric media. The quasi-resonant interaction is manifested under the condition that the real part of the zeroth harmonic of the Fourier series expansion of the dielectric permittivity of the grating medium is equal to zero. This condition determines the grating filling factor which is much less than unity. The absorption, reflection, and transmission coefficients have been calculated as a function of grating thickness at the working wavelengths of 405 nm and 1064 nm. The corresponding dependences have an oscillatory character, and local absorption and transmission maxima occur at the same wavelength. The maximum of absorption, the minimum of reflection, and the maximum of transmission are observed near the wavelength of 405 nm at the grating thickness of 510 nm. It is typical of resonance phenomena in periodic structures. However, such an absorption resonance is spectrally quite broad. The fields at the grating boundaries with homogeneous dielectric media are close to the amplitude of the incident wave. The spectral characteristics of the studied structure also have an oscillatory character at the grating thickness of 625 nm and at the working wavelength of 1064 nm. Such an oscillatory character allows us to assume that the processes occurring in the studied structure are similar to the processes in the Fabry-Perot interferometer, in which there is a small absorption. Reducing the grating period leads to the decrease in the number of oscillations in the spectral characteristics. These spectral characteristics approach the spectral characteristics of the three-layer structure. Therefore, if the grating period is much less than the wavelength, then such a grating can be replaced by an equivalent multilayer structure in which metal and dielectric alternate in series. It will have approximately the same spectral characteristics.
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