Light Propagation in Williams Domains as Analyzed Numerically by Geometrical Optics

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Abstract
We have studied Williams Domain (WD) patterns in detail by observing tomograms with a polarizing optical microscope, confirming the following characteristic features: (1) there are two types of real images, upper and lower; (2) the spacings between the neighboring imaginary image lines are not uniform; and (3) when the focussing plane of the objective is moved above the upper real image or under the imaginary image, the sharp image line splits into two. By taking into account the ray deflection from the wave front normal as well as the focussing effect, we have calculated numerically the characteristic distribution of phase (optical path length) as well as intensity. The results can reproduce the tomograms observed here and the photographs taken by Sato et al. holographically, showing directly the optical path length as the interference fringe patterns.