hi im facing a problem in finding solution of helmoltz equation for righttriangular waveguide. The real problem is of the finding the right boundary conditions I've searched on google but ive not find it. anyone here can help me?
I'm curious about the shape of the waveguide. Why a right triangle? My limited experience with these animals suggests the a completely symmetrical shape is necessary. The shapes tend to be circular, square, or rectangular. If you will, the symmetry lets the EM waveform contained inside "fit" the constraints of the waveguide with minimal loss to ohmic heating, etc. What frequency and waveform do you propose to send through a right triangular shape?
Shape of waveguide is looklike a right-angle triangle with two sides of equal lenght (let say "a") along x and y direction .And it is infinite in z direction. Its an home work assignment to calculate te and tm mode inside it. To find tm and te mode, boundary coditions are required,
Think about Electric field boundry conditions. E tangential must be continuous accross the boundry. D perpendicular must be continuous accross the boundry. Since there is not electric field in the metal E must be zero at the interface for these boundry conditions to be met.
for te mode Ez=0,and we sovle helmoltz equation for Hz, tangential component of Hz are zero on boundary i.e., 1) at x=0, 2)at y=0, 3)at x=a-y, 4)at y=a-x. by putting these boundary conditions i get Kc=(kx^2 +ky^2)^1/2 in form of x and y but i know that Kc must be a constant . this mean that there is some mistake in my understanding about the boundary condition. or there is some other way to solve this problem.
Here is a link with the correct answers but no derrivation (it was the first thing that came up on "triangular waveguide" in google). It has a bit of explanation, but not much...Maybe tonight I'll work up a a partial solution to help you get started on a derivation of the field equations. http://www.iop.org/EJ/article/0957-0233/10/3/003/mt10003l3.html Hopefully this gets you on the right track.
i ve seen that paper manytimes but its not solving my problem because The detailed derivation are not given and only final solution is there. It does not give any information about boundary conditions