Engineering Harmonic Content in Diffractive Optical Elements

Diffraction gratings produce a number of diffraction orders, which relative intensity is directly related to the grating profile. Continuous blazed phase-only gratings have the greatest efficiency onto a single first order [1], but they are difficult to fabricate. In more common binary amplitude or binary phase gratings, numerous diffracted harmonic orders are produced [2]. Dammann gratings are of interest because they produce equal intensities in a given number of selected orders [3]. They are designed by subdividing each grating period into regions with phases 0 or

π

radians. In order to increase their efficiency, different studies were conducted in the field of the so called fan-out arrays, extensively developed in the late 80’s [4]. More recently, Romero and Dickey further extended and provided a general framework for the design of optimal fan-out phase elements [5,6], by extending a previous study on the optimal triplicator [7]. The method provides an analytical optimal solution for designing a grating with a set of target diffraction orders. The calculation involves optimization of two numerical variables for each target order, and results in a single function that generates a periodic diffraction grating with continuous phase modulation levels.