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The scattering characteristics of the periodic surface of infinite and finite media are investigated in detail. The Fourier expression of the scattering field of the periodic surface is obtained in terms of Huygens’s principle and Floquet’s theorem. Using the extended boundary condition method (EBCM) and T-matrix method, the scattering amplitude factor is solved, and the correctness of the algorithm is verified by use of the law of conservation of energy. The scattering cross section of the periodic surface in the infinitely long region is derived by improving the scattering cross section of the finite period surface. Furthermore, the effects of the incident wave parameters and the geometric structure parameters on the scattering of the periodic surface are analyzed and discussed. By reasonable approximation, the scattering calculation methods of infinite and finite long surfaces are unified. Besides, numerical results show that the dielectric constant of the periodic dielectric surface has a significant effect on the scattering rate and transmittance. The period and amplitude of the surface determine the number of scattering intensity peaks, and, together with the incident angle, influence the scattering intensity distribution.

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In this paper, the scattering characteristics an infinite dielectric periodic surface are investigated in detail. The Fourier expression of scattering field of the periodic surface is obtained by using the Rayleigh hypothesis and the Floquet theorem. Using the extended boundary condition method and the T-matrix method, the scattering amplitude factor is solved, and the correctness of the algorithm is verified by use of the law of energy conservation. The scattering cross section of the periodic surface in the infinitely long region is derived by improving the formula of the finite one as its length is increased. Furthermore, the effects of the incident wave parameters and geometric structure parameters on the scattering of the periodic surface are analyzed and discussed. The results show that the period and amplitude of the surface corrugations determine the number of scattering intensity peaks, and influence the scattering intensity distribution with permittivity significantly.