Reflective Characteristics of Spatially-Bounded Laser Beam by Rugate coating

Based on the transfer matrix analysis and discrete Fourier transform, the reflective characteristics of a spatially-bounded laser beam by a Rugate coating are investigated. The spatial intensity distribution and reflectance efficiency of the reflected beam are formulated. When the central vector of the laser beam satisfies the coating's Bragg law, the spatial intensity distributions of the diffracted beam with the change of the coating's parameters are simulated. The results show that with the decrease of the thickness, the increase of the period, or the decrease of the relative permittivity modulation, the spatial intensity distributions of the reflected beam in the incidence plane are broadened compared with those of incident beam, while those perpendicular to the incidence plane are not. And the reflectance efficiencies decrease. Among these three parameters, the relative permittivity modulation and thickness influence the reflectance characteristics a lot, while the period influences the reflectance characteristics a little. It means that when the thickness decreases, or modulation decreases, the Rugate coating has finer angular selective characteristics and less angular selectivity bandwidth. The results are instructive for the design and application of Rugate coating.