Scalar-Based Analysis of Phase Gratings Etched in the Micro/nanofabrication Process

Abstract

The diffraction characteristics of several types of phase gratings often etched on the substrate by the micro/nanofabrication techniques are analytically explored using scalar-based analysis in this paper. The process of an incident wave being reflected or transmitted by the diffraction grating is regarded as a process of modulation, and the reflectance or transmittance can be unified as the modulation index. The mechanisms of phase modulation, amplitude modulation, and the amplitude–phase hybrid modulation in different situations are discussed. Analytical results indicate that the diffraction efficiency is directly determined by the phase difference of adjacent features, i.e., the cyclically distributed ridges and grooves that induce different phase and amplitude variations. The absolute phase grating with phase difference equivalent to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">$\pi$</tex-math></inline-formula> has the maximum diffraction efficiency among all types of gratings. The conclusions could, in general, provide guidance for the design and micro/nanofabrication of phase gratings for many diffraction-based applications of optical metrology or imaging.