The Wiener-Hopf technique [13-16] is known as a powerful approach for analyzing electromagnetic wave problems associated with canonical geometries rigorously, and can be applied efficiently to problems of the diffraction by specific periodic structures such as gratings.
As an example of infinite periodic structures with non-plane boundaries, Das Gupta  analyzed the plane wave diffraction by a half-plane with sinusoidal corrugation by means of the Wiener-Hopf technique together with the perturbation method.
As mentioned earlier, we have already analyzed the diffraction problem involving the same grating geometry for the E-polarized plane wave incidence using the Wiener-Hopf technique together with the perturbation method [32,33].
In this paper, we have analyzed the diffraction by a finite sinusoidal grating for the H-polarized plane wave incidence using the Wiener-Hopf technique combined with the perturbation method.
It contains all the significant topics of EM wave technology, from the finite element method, boundary element method, point-matching method, mode matching method, the spatial network method, the equivalent source method, the geometrical theory of diffraction, the Wiener-Hopf technique
, asymptotic expansion techniques and beam propagation method to spectral domain method.
We'll use methods of the theory of singular integral equations [2,3,5,7], boundary value problems , and the Wiener-Hopf technique .
Further we'll apply the Wiener-Hopf technique to the equation (2.6) and write it in a convenient form:
Methods based on Wiener-Hopf technique for the solution of partial differential equations.