Our eventual objective is to optimize designs for a given set of nominal dimensions and layout constraints. Mode shapes are calculated in the time-domain by applying an approximate TM mode to one end face of a long 3D symmetric model with radiation or symmetry conditions on the other faces. Shape of the stable mode that arrives approximately 12 wavelengths from the illuminated end is then measured. Thus, we use the finite element model as a waveguide filter. These experiments are done for a number of cross-sections and the effective index is calculated to insure that modes are trapped.
Leaky modes are also apparent by their gradual amplitude decay.
Mode shapes calculated in this manner are illustrated in Figure 1 for a 1.75 x 3.0 micron cross-section. The effective index is 3.33. Waveguide height is the critical dimension in these 3D experiments. Free-space wavelength is 10 microns and effective index of the mode is 3.33. The smaller Ey and Ez fields are scaled by a factor of 2.0 over Ex.