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A recursive algorithm for a non-uniform 			amplitude beam propagating through a 			sub-wavelength grating is proposed in this 			paper. This method is based on Maxwell's 			equations and the continuity of the tangential 			components of the electric and magnetic field 			vectors, and gives an exact complete 			solution. And we illustrate a propagation of a 			Gaussian beam through a grating in detail.

A Recursive Algorithm for a Non-uniform Amplitude Beam Propagating Through a Sub-wavelength Grating