A Two-Component Compact 2-D FDFD Method for Waveguide Structures with ARPACK

A two-component compact two-dimensional (2-D) finite difference frequency domain (FDFD) method is proposed based on the four-component FDFD method. The new method eliminates the transverse magnetic field components of the four-component method. The 2-D FDFD method can be concluded as a sparse eigenvalue problem. In the new method, the order of the eigenvalue problem is reduced by half, so the new method is more efficient. Moreover, the new eigenvalue problem can be solved by ARPACK directly with the largest real part strategy.