Abstract
We propagate partially coherent light through discontinuous surfaces and analyze the optical effects in phase space. The discontinuous surfaces are classified into two types, those with discontinuity in space and those with discontinuity in slope. Results are discussed based on the Wigner function. This approach explains the performance of segmented elements during the transition from the refractive into the diffractive regime. At first the diffraction effects generated by a single discontinuity (e.g. a phase step and a linear axicon) are investigated. Later on we discuss surfaces with periodic discontinuities, e.g. gratings, to study the formation of multiple diffracted orders. A kinoform lens is given as a further example to visualize the change from pure refraction to diffraction. Moreover, we present the beam homogenizing effect in phase space generated by lens arrays.
Highlights
The Wigner function was first proposed by Wigner [1] in 1932 as a quasi-probability distribution to describe quantum mechanics in phase space
In this work we focus on light beams of spatial partial coherence, and propagate the beam through discontinuous surfaces
At first we introduce an important parameter Δφ to denote the optical path difference generated by a phase step (Fig. 2c)
Summary
The Wigner function was first proposed by Wigner [1] in 1932 as a quasi-probability distribution to describe quantum mechanics in phase space. There are several remarkable advantages of using the Wigner function for analyzing optical systems It describes optical signals simultaneously in spatial frequency and space. This idea resembles the concepts of angle and position in geometrical optics. Making use of this property we are able to propagate light in phase space with the ray transfer matrix ( known as ABCD matrix) [5, 6]. The Wigner function is able to represent a partially coherent beam in a straightforward way [7]. It visualizes the degree of coherence in phase space as the angular extent.
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