Diffraction efficiency of a generalized complex binary grating

Abstract

A generalized complex binary grating is a type of grating that permits control of four degrees of freedom: the two steps amplitudes that form the period, their relative phase and their widths' ratio. In this work, using the Fourier formalism, we derive an analytical expression for the diffraction efficiency of all the grating diffraction orders. The analytical expression depends on the four degrees of freedom. Our model agrees with the results reported in the literature for the special cases of phase-only and amplitude-only Ronchi gratings and some particular extensions. In addition, we study situations where the amplitudes and widths of the grating steps differ. In particular, for a grating with a relative phase difference of π radians, normalized steps amplitudes of 1 and 0.77, and width's ratios of 0.5 and 0.25, our experimental results validate the values predicted by our model. The model developed in this work will be valuable in designing high-precision diffractive gratings for particular specifications. In addition, it can be used to characterize spatial amplitude, phase and complex-amplitude modulators.