Boundary conditions and time domain electromagnetic waves

[Born2bwire]

I need the field distributions. A transmission line model won't fit because I'm looking for TE and TM modes on a coaxial cable, semi-infinite, with 2 dielectrics: one lossy and the other lossless. And I need distributions of field because I need to find the best way to place some receivers for a very very specific application.

PS: I didnt say in any moment I want a dumped wave on lossless medium. You said so.

Then what is the difficulty that you are having? Why do you keep complaining that the lossless medium will not allow a damped solution?

 

[ashade]

Then what is the difficulty that you are having? Why do you keep complaining that the lossless medium will not allow a damped solution?

Because dumped and undumped solutions cannot equal for all t. Therefore, continuous tangential electric field is not guarateed in the boundary of both media.

 

[Born2bwire]

Because dumped and undumped solutions cannot equal for all t. Therefore, continuous tangential electric field is not guarateed in the boundary of both media.

They are equal because one wave is the source for the other. As I explained previously, a wave that transitions from a lossy to a lossless region has already been attenuated by its passage through the lossy region. A wave that goes from lossless to lossy will become attenuated as it travels into the lossy region. But the wave isn't going to decay until it is traveling in the lossy media. The causality of the problem and the fact that you are working with waves what you are forgetting here. Think of what happens if you were to send a wave pulse down your lossless section of your waveguide and it hits the the lossy dielectric section.

In addition, the analysis of the boundary conditions that I gave in post #19 demonstrates the general case that you are discussing using a plane wave solution. If you convert it from the time-harmonic form to the time domain form the wave solutions match the same conditions that you stipulated in your OP. That is, the left-hand side is dependent upon a sinusoidal function demonstrating the spatial and time phase dependence multiplied by what is equivalently an exponentially decaying function in time (by virtue of the constant dispersion curve relating the wave number with frequency and the phase velocity of the wave). The right hand side will be just a sinusoidal function with a spatial and time dependence.