Todd Ballen, Graduate Student Researcher Siamak Makki, Graduate Student Researcher Eric Shields, Graduate Student Researcher David Sklenicka, Graduate Student Researcher Richard G. Solstad, Graduate Student Researcher Qiwen Zhan, Graduate Student Researcher
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"Optical Anti-Aliasing Filters Based on Complementary Golay Codes," J.R. Leger, J. Schuler, N. Morphis, and R. Knowlden, University of Minnesota Supercomputing Institute Research Report UMSI 99/37, March 1999. |
Many micro-optical elements have feature sizes where geometrical optical and scalar diffraction theory is not valid, which makes rigorous solution of Maxell's equations necessary. These researchers have written a MATLAB code based on the rigorous coupled wave (RCW) method to simulate two-dimensional periodic structures. The micro-optical structure is approximated by slicing down to many dielectric slabs. More than one hundred slabs are required to simulate continuous micro-optical structures accurately. The Fast Fourier Transform (FFT) algorithm is applied to each slab to calculate the eigenmodes. For each slab, a one-dimensional FFT of 212 elements is used for convergence and a 200 ¥ 200 matrix is solved to find the eigenfunctions. Then, system matrix is obtained by matching EM boundary conditions at interfaces between every two adjacent slabs. The final system matrix has a size around 40,000 ¥ 40,000. By solving this system matrix, the EM field distribution inside and outside of the elements can be obtained. For some calculations, iterations up to one hundred times are also necessary.
These researchers have improved their two-dimensional RCW model to simulate the EM field for micro-optical element. They can now apply plane wave incident with any polarization state, while it was limited to TE and TM mode before. They are also able to apply the RCW model to more complex periodic structures. A new approach to study non-periodic structure using RCW is proposed and under current study. This new approach might be extended to study the properties of three-dimensional structures. A finite-difference-time-domain algorithm for three-dimensional structure is now under development and will be tested. Using these algorithms, these researchers investigated some optical properties of sub-wavelength structures and obtained many useful results.
X (left), Y (center), and Z (right) components of polarization at the focal point of a high-numerical aperature lens. The fields are calculated using a Richards and Wolf model of vector diffraction.
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