How to distinguish TE and TM in a multilayer film?

[niubiworker]

Most photonic crystal slabs are symmetric along the z-direction (with the xy-plane as the periodic plane), but now I want to design a multilayer structure (such as air, silicon, silicon dioxide, air), where the periodicity remains in the xy-plane or along a line-defect waveguide in a certain direction. Clearly, the symmetry in the z-direction is broken in this multilayer structure. Can I still use the mpb function TE-yodd to distinguish between TE or TM modes?Thank you very much!

[stevengj]

No. In this case there is no z mirror plane, and hence no strict symmetry classification in z.

Even when there is a strict z=0 mirror symmetry plane, the even/odd modes are not purely TE/TM polarized. See also this figure from our book:

However, if you have another mirror symmetry plane, you can use that. For example, for a line defect along the x direction, you may have a y=0 mirror-symmetry plane, and you can use that to help you classify the modes.