Approximate analysis of the diffraction efficiency of transmission phase holographic gratings with smooth non-sinusoidal relief [Articol]

Abstract

In the article is presented the electro-dynamic model and method for numerical analysis of the diffraction efficiency of thin holographic diffraction gratings. Self-developing holographic gratings are easy to fabricate and can provide relatively high diffraction efficiency. Some photosensitive materials, such as chalcogenide glassy semiconductors of doped As-S-Se-Sn system used in a photo-thermoplastic recording process demonstrate the ability of registration the relief-phase gratings with efficiency up to 40% in transmitted light. The efficiency is highly dependent on the grating profile shape (groove shape and depth). Theoretical analysis is performed using the method of spectral expansions for periodic lattices. Semi-analytical dependences of efficiency on parameters of lattices with arbitrary continuous profile, including experimentally measured one by AFM, are obtained. They allow without using cumbersome numerical calculations to obtain the optimal shape of the lattice profile with maximum efficiency in a given diffraction order. A satisfactory agreement between numerical calculations and experimental measurements is demonstrated. It is shown that the optimal shape of the lattice for maximum efficiency tends to that of a symmetrical binary grating for which the theoretical limiting value of efficiency is 40.5%.