Effects of fabrication errors on Talbot array illuminators

Abstract

Talbot array illuminators (TAI’s) were first proposed by Lohmann as a means of creating optical interconnections.1 TAI’s are phase gratings that, under coherent, plane wave illumination, give rise to 100% modulated, square wave field and irradiance patterns. These patterns bear a strong resemblance to the spatial structure of the phase grating itself (Figure 1). Such patterns are referred to as Lohmann images2 to distinguish them from Talbot images. Talbot images are replicas of the complex field distribution immediately behind a periodic structure. Talbot images occur at integer multiples of the Talbot distance ZT = 2d2/λ, where d is the grating period and λ is the wavelength of the illuminating radiation. By comparison, only a limited number of combinations of grating duty cycle w/d, phase depth ϕ, and propagation distance z will generate Lohmann images.