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: ptan(pd/2) = q and asymmetric: pcot(pd/2) = -q. What is different for the above solutions for TM? I have a hard time determining that. I think it has something to do with the dielectric constant, but I'm not quite sure. I can elaborate on any maths you ask for. Also sorry for the quality of my post, it is my first one.