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Based on the scattering theory and the Green function method, a dynamical theory is given for calculating the difiraction of deeply-etched gratings with a stratifled structure substrate. The key of our method is that the patterned grating structure is considered as a perturbation to the unpatterned stratifled structure rather than to vacuum. Using the flrst-order Born approximation and in the Fresnel difiraction region, we obtain a simple analytical expression, which can be used to calculating the scattering intensity of deeply-etched circular binary Fresnel zone plates with a stratifled substrate (MDECBFZPs). The numerical results show that the focusing intensity at the foci of the MDCBFZP changes periodically with the etching depth and the thickness of the substrate fllm. Our results are in good agreement with FDTD simulations.

PERIODIC TRANSMISSION OF CIRCULAR BINARY FRESNEL ZONE PLATES WITH ETCHING DEPTH AND SUBSTRATE