The Method of Lines Analysis of TE Mode Propagation in Silica based Optical Directional Couplers

Optical directional couplers fabricated using planar light wave circuit (PLC) technology are versatile tools in integrated photonics devices. They have the advantages of small size, high consistency, ability for high volume production, and excellent possibility to be integrated with electronics circuits. Optical waveguide couplers are mainly utilized as power dividers, optical switches, and wavelength division multiplexers/de-multiplexers (WDM). A number of methods have been used to analyze directional couplers, such as coupled mode theory (CMT), the beam propagation method (BPM), the method of lines (MoL), finite-difference methods (FDM), and finite element methods (FEM). Among these numerical approaches, MoL is the simplest method to analyze mode propagation inside directional couplers because it has the advantages of very fast convergence and accurate solutions for one-dimensional structures. The objective of this study was to analyze the propagation of TE modes in optical directional couplers by using MoL. The parameters used, i.e. waveguide width, refractive index, and wavelength, were taken from the characteristics of silica-on-silicon directional couplers that were used in fabrication. MoL is considered a special finite-difference method, which discretizes a one- or two-dimensional wave equation in the transverse direction and uses an analytical solution for the propagation directions. Basically, MoL is a semi analytical numerical method with the advantages of numerical stability, computational efficiency, and calculation time reduction. Further, we explored the possibility of using directional couplers as optical switching devices.