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

Abstract

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.

Low profile dual band slotted-patch antenna for WIMAX applications

“…FDTD time-stepping formulas constitute the discretization (in space and time) of Maxwell's equations on a discrete three-dimensional mesh in a Cartesian xyz coordinate system are mentioned in [8]. A perfectly matched layer (PML) with the following impedance matching condition is applied to bound the 3-D computational window of microstrip patch antenna configuration [9][10][11].…”

Crucial Parameters of Photonic-Crystal Holes within Photonic-Crystal VCSEL DBR

“…The boundary conditions are assumed in the form of the absorbing Perfectly Matched Layers. [2] For the z axis along the direction of light propagation, the above mathematical manipulations lead to the following wave equations for the electric and the magnetic fields [1]:…”

Comparative study of several time-domain methods for optical waveguide analyses

“…Before comparing TD methods, we preliminarily investigate two treatments of modeling the waveguide grating. First, we calculate the grating by the WB-TD-BPM with the IFD2, taking into account an arbitrary position of the dielectric interface between the sampling points [22], [23], in which the grating structure is correctly modeled (for the FDTD, an arbitrary dielectric interface can also be modeled by a combination of the boundary condition and one-sided difference operator [37]- [39] or by an index averaging technique [40]). Next, we analyze the grating using the WB-TD-BPM under the assumption that each region in one grating period has the same length: Λ + = Λ − = 0.31895 µm.…”

“…However, as far as we know, there is no application of the higher order FD scheme considering the boundary condition at a dielectric interface to the FDTD (although the second-order FDTD has been developed for an arbitrary dielectric interface [37]- [39], the corresponding fourth-order FDTD has not yet been developed). Therefore, we do not investigate FDTDs based on the higher order scheme.…”