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A new multidomain pseudospectral frequency-domain (PSFD) method based on Legendre polynomials with a penalty scheme for studying electromagnetic wave scattering is presented. Scattered field calculation with accuracy on the order of 9 10  is obtained for a circular plasmonic cylinder. The method is further applied to demonstrate the scattering by a dielectric rectangular cylinder with sharp corners and by multiple circular plasmonic cylinders.

We propose a pseudospectral mode solver for optical waveguide mode analysis formulated by the frequency-domain Maxwell equations. Special attention is paid upon identifying the required boundary operator for the formulation and the relationships between the derived operator and the physical boundary conditions. These theoretical results are adopted into a Legendre pseudospectral multidomain computational framework to compute the propagation characteristics of optical waveguides. Numerical experiments are conducted, and the expected spectral convergence of the scheme is observed for smooth problems and for problems having field jumps at material interfaces. For dielectric waveguides with sharp corners, the spectral convergence is lost due to the singular nature of fields at the corner. Nevertheless, compared with other methods, the present formulation remains as an efficient approach to obtain waveguide modes. Index Terms-Frequency-domain Maxwell's equations, optical waveguides, penalty boundary conditions, pseudospectral methods, waveguide analysis. I. INTRODUCTION I N modal analysis for optical waveguides, the propagation constants and the associated field distributions of guided modes provide useful information in designing and operating optical guiding devices such as filters, switches, modulators, and fibers. To obtain these guiding characteristics, one needs to solve either Maxwell's equations or the vectorial Helmholtz Manuscript

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