Optical Waveguide Mode Profile

Question

SE, I have a question about a mode profile chart from Synopsis RSOFT. After following an example silicon Y-Splitter waveguide below with the waveguide width = 0.45um and height=0.22 um , I simulated the Ex, and Hy mode profile of the splitter, but I do not know how to read this graph.

I always thought waveguide modes are only integers and are related to the standing waves inside of the waveguide. What am I missing here. Also what causes the shape of the mode profile, especially the Ex mode?

Answer 1

The transverse electric field will not be continuous across the boundary because the Si and cladding have different polarizabilities. The discontinuity you see does not indicate a higher-order mode but rather results from the induced surface charge (think Gauss’ Law). If you’d like to see a continuous field profile, plot $\mathbf{D}$ instead, which takes into account the polarizability. Or, you could plot the $x$-component field in the $y$ direction.