ABSTRACT
A successful polarization analysis requires the integration of many science models for the physics of thin films, reflection, refraction, gratings, crystals, stress, scattering, diffraction, and more. For an accurate polarization ray trace of an optical system, everything which makes a significant contribution to the polarization, thin films, reflection, refraction, gratings, crystals, stress, scattering, diffraction, and more, needs to be included. In conventional ray tracing, optical systems are defined only by the materials and shape of the optical elements. Polarization analysis requires additional information not commonly used in conventional analysis. Thin films prescriptions, thicknesses and indices must be specified and assigned to surfaces. For diffraction gratings, the ruling profile is needed, and then rigorous coupled wave analysis can be performed at each ray intercept; unfortunately the complex RCWA algorithm slows the calculation by orders of magnitude per ray intercept. For elements with stress, the three-dimensional stress distribution must be calculated with finite element molding simulations or measured data, then rays traced through the gradient index birefringence. For liquid crystal cells, the three-dimensional director distribution of the director is calculated from the electric field distribution and the liquid crystal’s elastic coefficients, then is used for calculating the complex amplitude transmittance.
The antireflection and other thin film structures generate a multiplicity of partial waves propagating in the forward and reverse directions. To improve transmission, these partial waves must substantially constructively interfere in the forward direction and destructively interfere in the reverse direction. This blurs our bedrock concept of optical path length; OPL becomes a multi-valued function. The phase remains well defined and is uniquely measured by an interferometer. Similarly, light transmitting through a sequence of anisotropic materials generates a set of two, four, eight, or more partial waves, each with a different OPL. Retardance is simple to define for a single crystal waveplate, but more difficult in such general circumstances. The polarization ray tracing program can use ray trees to track the multiplicity of rays, and mode combination algorithms with interpolation to calculated fields in the exit pupil. The amplitude image is represented as an amplitude response matrix, and its Fourier transform is the optical transfer matrix, which represents the optical system’s frequency response to cosinusoidal Stokes parameters objects.
Polarization ray tracing methods and polarization aberration methods are compared for a Cassegrain telescope. Aberration theory has strengths in the simplicity of the aberration representation, representation of the aberration with a small number of parameters, the ability to describe how performance scales with numerical aperture and object size, and the ability to pinpoint at which surfaces aberration is arising and suggest methods for polarization aberration balancing. The strength of ray tracing is its ability to analyze arbitrary systems and to provide (nearly) exact answers. The aberration approach can lead to powerful design rules to assist in making optical design tradeoffs.
