I'm a little confused regarding the maths of TE and TM modes.
Solving the following system for TE (which derives from Ey(x, z, t) = Em(x) = exp[i(ωt-βz)] ):
Asin(px) + Bcos(px) , -d/2 < x <d/2
Cexp(-qx), x>d/2
Dexp(qx), x<-d/2
we conclude in two types of solutions for TE modes: symmetric...