Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers

Eigenvalue equations for solving full-vector modes of optical waveguides are formulated using Yee-mesh-based finite difference algorithms and incorporated with perfectly matched layer absorbing boundary conditions. The established method is thus able to calculate the complex propagation constants and the confinement losses of leaky waveguide modes. Proper matching of dielectric interface conditions through the Taylor series expansion of the fields is adopted in the formulation to achieve high numerical accuracy. The method is applied to the study of the holey fiber with triangular lattice, the two-core holey fiber, and the air-guiding photonic crystal fiber.