Abstract

A fundamental scheme is utilized to reformulate the full-vectorial beam-propagation methods (BPMs). First, the fundamental scheme is introduced into the Fresnel equations which are discretized using the Crank–Nicolson method (FCN-BPM). The present FCN-BPM has the advantage that the total number of arithmetic operations is extremely reduced when compared with the conventional CN-BPM, while maintaining identical accuracy. Next, the fundamental scheme is applied to the alternating-direction implicit BPM (FADI-BPM). The choice of the refractive index at each split step is discussed paying attention to the commutativity of coefficient matrices. With the present method, computation time is reduced to approximately 74% for the analysis of a mode-evolution-based $z$ -varying polarization converter. Power expression based on both electric and magnetic fields is also adopted to improve the power conservation. Finally, the present method is applied to the design of a short polarization converter. It is revealed that the use of a curvilinearly tapered core leads to an extinction ratio of more than 15 dB with a device length of $100\ \mu$ m, over a wide wavelength range from 1.2 to $1.7\ \mu$ m.

© 2014 IEEE

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