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As a 2-D full-wave numerical algorithm in the time domain, the compact Finite Difference Time Domain ( FDTD ) is an efficient algorithm for eigenvalue analysis of optical waveguide system. However, the numerical dispersion accuracy and stability of fast algorithm need to be improved while simulating at high frequency. A novel high-order symplectic compact FDTD scheme is developed and validated for optical waveguide modal analysis. The stability condition and the numerical dispersion of schemes with fourth-order accuracy in temporal and spatial using the symplectic integrator and compact scheme are analyzed. By comparisons with other time-domain schemes, their stable and accurate performance is qualitatively verified. The proposed high-order SC-FDTD method can be used for efficiently simulating electrically large and longitudinally invariant optical devices since the reduction of simulation dimensionality and the novel high-order symplectic algorithm can greatly reduce the memory cost and the numerical dispersive errors.

The electromagnetic scattering problem over a wide incident angle can be rapidly solved by introducing the compressive sensing theory into the method of moments, whose main computational complexity is comprised of two parts: a few calculations of matrix equations and the recovery of original induced currents. To further improve the method, a novel construction scheme of measurement matrix is proposed in this paper. With help of the measurement matrix, one can obtain a sparse sensing matrix, and consequently the computational cost for recovery can be reduced by at least half. The scheme is described in detail, the analysis of computational complexity and numerical experiments are provided to demonstrate the effectiveness.

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