# ModeOverlapΒΆ

This post process computes the overlap of scattered electromagnetic field with the modes obtained from a waveguide simulation. This information is for example of interested when computing the coupling efficiency of a light source into a waveguide or glass fiber, or in simulations of integrated photonic circuits, when transition behavior of multi port devices like split ring resonators, y-splitters or curved waveguides are analyzed.

The overlap of the -th scattered field with the -the waveguide mode on a plane port is defined by:

where is the corresponding magnetic field of the mode.

Note

The mode fields (as a result of a propagating mode problem) are orthonormal with respect to the above scalar product, that is

Therefore, the mode-wise incoupled power flux is given by

You can explicitly specify the port within the section Port. Otherwise, the boundary of the computational domain is automatically matched with the geometry of the waveguide simulation to find all matching ports where the overlap is computed. The header of the created table file contains the positions and outer normals of the found ports.

Note

The above semi-scalar product uses the holomorphic form of the Poynting vector. Up to a phase shift, the resulting coupling coefficients are the same for loss-free, non-active materials as when using a Poynting vector based scalar product (conjugate the magnetic field). The above mentioned mode-orthonormality is only true for damped materials or leaky modes, when using the holomorphic form.