Multilayer waveguides: efficient numerical analysis of general structures

Abstract

Abstruct-An efficient numerical method is presented for accurately determining the real and/or complex propagation constants of guided modes and leaky waves in general multilayer waveguides. The method is applicable to any lossless and/or lossy (dielectric, semiconductor, metallic) waveguide structure. The method is based on the argument principle theorem and is capable of extracting all of the zeros of any analytic function in the complex plane. It is applied in the present work to solving the multilayer waveguide dispersion equation derived from the well known thin-film transfer matrix theory. Excellent agreement is found with seven previously published results and with results from two limiting cases where the propagating constants can be obtained analytically.

Accuracy of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities

“…However, even for large values of the re− fractive index contrast the error still tends to the value of the local truncation error observed for the homogenous medium, if the mesh size is sufficiently small. In order to study the consequences of a rather compli− cated dependence of the local truncation error on the mesh size on the calculation of the propagation constants of opti− cal waveguides we selected three standard structures [20] and calculated their propagation constants using the two selected 3−point FD approximations [5,19] and compared it with reference values obtained using an analytical ap− proach [21]. Structure 1 is a GaAs based symmetrical slab waveguide.…”

Propagation Characteristics of Multilayer Hybrid Insulator-Metal-Insulator and Metal-Insulator-Metal Plasmonic Waveguides

“…Here we perform the zero-search using a two step approach. Firstly, an algorithm is used to find the minima of the absolute value of dispersion function F. The F function for TM-polarized mode (supported by the SPP wave) is defined as follows [24]: Spatial length, describes the spatial extent of the propagating mode by the distance between the points in the cladding and substrate regions where the electric field decays to 1/e of its peak value. Spatial length, in another words, is the physical length of the propagating mode and is a descriptor representing the integration ability of a plasmonic waveguide and is written as: …”

Substrate-embedded and flip-chip-bonded photodetector polymer-based optical interconnects: analysis, design, and performance

“…3 as function of for both TE and TM incident guided modes and for both m and m free-space wavelengths. From this figure it can be seen that the reflected power depends exponentially on and is negligible for detector-waveguide separations m. Using the APM method [12], the radiation coupling coefficient can also be determined. This is shown in Fig.…”

“…The power that can radiate into the cover (air) area (for ) can be neglected since those leaky modes will not be strongly excited at the interface. The radiation coupling coefficient can be calculated using the argument principle method (APM) [12], [13]. The latter method is a rigorous mathematical technique based on complex analysis [14] and is capable of finding the zeros (leaky-mode propagation constants ) of any analytic function (the waveguide dispersion relation) in the complex plane.…”

“…If the desired order along the direction forms an angle with respect to the -axis, then the grating vector components and are given by (9) (10) where , with , and is the effective index of the waveguide incident mode for . After and are defined, the period and the slant angle of the grating can be determined by the equations (11) (12) In practice the angle , which means that the diffracted power is propagating along the -axis. Using the leaky-mode approach in conjunction with the rigorous coupled-wave analysis, the radiation coupling coefficient can be calculated.…”