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Solving arbitrary resonant structures with an efficient eigen-based MRTD formulation

Numerical computation of a high-Q resonant structure may pose as a challenge for its requirements computation time and memory. Circumvent the problem, we developed an eigen-based formulation, called the "Spatial Multi-Resolution Time-Domain (SPATIAL-MRTD) method, based on the recently developed MRTD method. In it, wavelets are used to expand the electromagnetic fields in spatial domain while the time differentials are kept with the Maxwell's equations. The final formulation is a sparse eigenvalue problem. By applying the sparse matrix techniques, resonant frequencies and modes are obtained effectively and efficiently. Like MRTD, low number of spatial grid points (as low as two points per wavelength) is required. Unlike MRTD, direct recursive time-marching calculations are not needed. As a result, the method is numerical-instability free. In addition, no post-simulation data-processing, such as discrete Fourier Transform, is required.