|
Modeling the properties of polarization modeling is of importance in both geometrical and physical optics modeling. Most of the geometrical theory is directly applicable to the physical optics calculations but there are special considerations in implementing polarization in diffraction codes and such effects as spatial filters and near-field diffraction can be treated which are difficult or impossible with geometrical calculations. The discussion of modeling is general but application to waveguide grating couplers for optical data storage is treated as an interesting special case. This paper discusses a program to add polarization properties to a physical optics code. Physical optics codes have been developed over the last 20 years to analyze lasers resonators and beam trains. The polarization features have been added to a general purpose diffraction code called GLAD [1]. The specific program supported by this research is optical data storage with a special application to waveguide grating couplers. Our objective is to treat all types of systems with polarization and diffraction aspects -- conventional and those with integrated optics components. The first decision to be made is whether to treat polarization with Jones or Mueller matrices. Physical optics calculations generally deal with strictly coherent light so a case may be made for using the simpler Jones matrices. A second argument is that it is best to proceed with the simpler Jones methods before attempting to implement the more complex 4-vector treatment. In beam propagation studies, we commonly use complex arrays ranging in size from 32 X 32 to 1024 X 1024 with the most common sizes being between 64 X 64 to 256 X 256. These matrices are propagated with standard Fourier optics propagators [2]. The information required for a physical analysis is clearly much greater than for a geometric optics ray trace, which may require only a few rays to at most several hundred. One must take somewhat more care to develop efficient procedures so that the tens of thousands to hundreds of thousands points can be treated efficiently. However, in our studies the diffraction propagation remains the most time consuming task. In Jones calculus treatment, it is only necessary to have two complex numbers per point, for example Es and Ep where s and p are orthogonal polarization states. We simply use two complex amplitude arrays. The wavelength is of course identical for both arrays and for isotropic materials the index is also the same. For slightly anisotropic materials, it still may be possible to treat propagation of both arrays identically with the addition of a phase lead or lag. Thus the propagation time is doubled. Not only do the two arrays share the same wavelength and (almost) the same index of refraction, the spatial subtense of the two arrays is (almost) the same. We can treat the case of anisotropic materials and propagation at arbitrary angle with respect to the OPTICAL axis, which can introduces shear of the two polarization states, an an incremental effect. Since the arrays subtend the same physical space, we can treat the polarization properties by putting the polarization operations inside the inner most loop as shown in Table 1. Commonly we have more than one optical beam and the outer loop is generally a scan over all optical beams present
|
