To analyze our MZI devices we first have to model the individual components of the device. These include the strip waveguide, the bent waveguide, the y-branch splitter/combiner, and the surface grating coupler. Since we are evaluating our components' behaviour with respect to wavelength, we need to determine the parameters of these devices as a function of wavelength.
The strip waveguide is a rectangular silicon structure with a high index of refraction surrounded by a cladding region (either silicon dioxide or air) with a much lower index of refraction. This arrangement allows the waveguide to guide light using total internal reflection. We use the effective index method to determine the phase and group velocity of light propegating down the waveguide. The effective index method is a phenomenological approach to modeling, wherein the various parameters of the waveguide (geometry, material, etc.) and propegating mode (confinement, polarization, etc.) are combined into a single value, namely, the effective index neff. The effective index thus differs for modes where the polarization of the electric field is mainly parallel to the wafer, quasi-TE, vs. modes where the polarization of the electric field is manly perpendicular to the wafer, quasi-TM.
The effective index and group index are determined as a function of wavelength to determine the velocities of the phase fronts and guided energy, respectively.
Bent waveguides are a device in and of themselves, with distinct modes that differ from that of a straight waveguide. Because of this, there will be a mode-mismatch between a section of straight and a section of bent waveguide which is responsible for most of the loss when including a bent waveguide in one's design. Other sources of loss are regular propegation loss and radiated power, caused by coupling of light into higher order unguided modes.
The third component necessary to implement our MZI is the y-branch splitter / combiner. This device, when used as a splitter, divides the intensity of light on the input side equally into th