Vector algorithm for light transmission in subwavelength microstructure film

This paper put forward the conception of Sub-wavelength Micro-structure Film (SMF) firstly. The light transmission in multi-step SMF is then treated using vector theory. Eigen functions are expressed conveniently by piece-wise elementary functions instead of infinite series, making it both fast and accurate in solving eigen equations. Matrixes of mode conversion, reflection coefficients and transmission coefficients are introduced to obtain the electromagnetic wave amplitude matrix in each layer. A fast and steady recurrent formula to calculate the amplitude coefficient matrix is obtained by matching the modes. Rates of transmission and reflection of all the diffraction orders are therefore obtained for incident light wave of arbitrary polarization. The amounts of computer calculation are drastically decreased by using the method based on this paper. The program is steady and reliable and is implementable on PC. And, the program can treat the light transmission in multi-step SMF fast. Therefore, a fast, accurate, steady and simple algorithm is provided to design SMF elements with various particular properties.