Semiconductor waveguides: analysis of optical propagation in single rib structures and directional couplers

Investigation of Polymer Optical Waveguide Devices

“…Total switching occurs when 8 = 3 1/2 rc/2L [15,86,87]. This can be verified by the substitution of 8 = 3 1/2 TC/2L into Eqs.…”

“…This i referred to as directional coupling. The eigenmodes of the coupling region consist of one symmetric and one antisymmetric mode [15,24,25,27,28,[86][87][88][89]. Treatment of waveguide coupling can be performed by coupled-mode theory [15,27,28,86].…”

“…Assume that the waveguides are not too close, so that the overlap integral of the mode functions will be small [15,27,28,86]. With a single input to waveguide 1, Pii = 1 and Pi2 = 0, the output power from waveguides 1 and 2 are given as [15,27,28,86,87] Poi…”

High order matched interface and boundary methods for the Helmholtz equation in media with arbitrarily curved interfaces

“…2(a), these auxiliary points are chosen to be ðx iÀ2 ; C À2 Þ; ðx iÀ1 ; C À1 Þ; ðx i ; C 0 Þ; ðx iþ1 ; C 1 Þ, and ðx iþ2 ; C 2 Þ. After two u derivatives being accurately estimated, the 1D MIB iterative procedure can be used to discretize jump conditions (26) and H y on each auxiliary point will be interpolated along y line by using five Cartesian nodes exclusively from one side of the interface C. Both positive and negative sides can be used in principle. However, for the present study, it has been found that grid nodes from X À give a better result because the eigenfunctions decay exponentially in X þ .…”

“…In the past two decades, numerous numerical methods have been proposed to solve optical waveguides, including finite difference method [26], finite element method [19], pseudospectral method [3], discontinuous Galerkin method [8], and so on. The general trend in the field has been to move from the scalar methods which solve a single field component to the the full-vectorial methods that solve more than one field components simultaneously.…”