how to analyze bend transmission line, and can use to bend the optical transmission

As we all know, we can transmit electrical signals use 2 wire transmission line system.
From the field view, we transmit TEM mode EM wave useing the 2 wire transmission line system.
However, the textbook analyze the situation of straightline transmission of the wave.
If we bend the 2 wire transmission line system, the signal propagate direction will also bend.
How can we analyze this situation use the Maxwell equations and boardary conditions? I have thought many years, and not get the answer.

and can we use the 2 wire transmission line system change the optical light propagate direction? the optical light can also be TEM mode.
Thanks in advance.

I think this is a interesting problem.
Let us discuss!

could any nice guy give some expalnation?
you will be the genius!

You should probably post such a question on the electromagnetic board. But, in general, if you consider the electric and magnetic fields to the left of such a bend, and the fields to the right of such a bend, it is obvious that there is some minor perturbation going on right at the bend. To get the field patterns to match up, you would have to postulate various non-propagating field modes (often called evanescent modes). Far away from the bend, those non-propagating fields have died down and can no longer be detected. But right at the bend, there are there, and storing energy reactively.

There are a number of papers that compute lumped element models for such a bend. They simulate the evanescent mangnetic energy with things like series inductances, and the evanescent electrical energy with things like shunt capacitances. So, for a tem analysis where the next perturbation is far enough away, you can simulate a bend with those lumped element models.

---------- Post added at 15:35 ---------- Previous post was at 14:54 ----------

http://www.google.com/url?sa=t&rct=j...oyyA59A_mUptYg

why wavelength so important?

Wavelength is important because, because as frequency increases, your wavelength decreases thus, you cannot use standard circuit analysis to analyse circuit lines.

The transmission line is design to study circuit lines at high frequencies, because the behaviour of circuitry is different when you apply a high frequency signal to it, which always applies in the case of electromagnetic propagation.

let us discuss!
I think this is a interesting problem.