# Training Videos

## Directional Couplers

This is a continuation from the previous tutorial - grating waveguide couplers. Directional couplers are multiple-waveguide couplers used for codirectional coupling. They can be used in many different applications, including power splitters, optical switches, wavelength filters, and polarization selectors. We consider in this tutorial two-channel directional couplers, which consist of two parallel waveguides, as shown schematically in figure 4 below.  Figure 4. Schematic diagram of (a) a two-channel directional coupler and (b) its index profile assuming two step-index waveguides on the same substrate. The coupler is symmetric if $$n_a=n_b=n_1$$ and $$d_a=d_b=d$$. For simplicity, we consider only the case where each...

## Grating Waveguide Couplers

This is a continuation from the previous tutorial - two-mode coupling. Grating waveguide couplers have many useful applications and are one of the most important kinds of waveguide couplers. They consist of periodic fine structures that form gratings in waveguides. The gratings in a waveguide can be either periodic index modulation or periodic structural corrugation. Periodic index modulation can be permanently written in a waveguide by periodically modulating the doping concentration in the waveguide medium, for example, or it can be created by an electro-optic, acousto-optic, or nonlinear optical effect. In the latter case, the grating can be time dependent...

## Two-Mode Coupling

This is a continuation from the previous tutorial - coupled-mode theory. In most applications, we are interested in the coupling between two modes. This includes coupling between two modes in the same waveguide, such as that in a periodic waveguide, or coupling between two parallel waveguides, such as that in a directional coupler. For coupling between two modes, the coupled-mode equations can be written in a simple form that can be solved analytically. In this tutorial, we consider the general formulation and general solutions for this important case of two-mode coupling. The characteristics of specific couplers are discussed in later...