Resonant cavity with non-resonant dielectric

[Leopold89]

Dear Forum,

I would like to ask, if a certain construction is possible:
I have something like coaxial cable, but instead of a conductor at the core I have a different dielectric. Now I want the resonance outside the core to still happen, but not inside the core.

Is this possible? Because I thought I could then just use the coaxial case, since the condition that the electric field has to be orthogonal to the surface is unchanged, but the simulation shows no resonance at all.

So am I missing one boundary condition? If yes, I don't know which.

 

[DaveE]

It would be good if you could explain your set up more. I'm not sure where "resonance" comes from, for example. I guess you are talking about waveguide transmission modes? There are TEM modes (like TEM_01*) that have a null in the center. But the standard modes will be altered by the dielectric change, of course.

 

[Leopold89]

Yes, I am talking about modes. Resonance comes from my cylindrical cavity. So I have a closed cylinder filled with one dielectric material and inside this cylinder another cylinder, with different radius and dielectric constant. Their height can be the same, but don't have to.

 

[DaveE]

There should be lots of stuff on the web. This sounds similar to a stepped index fiber. I found some potentially good stuff just searching for "cylindrical waveguide modes with dielectric step". But I'm too lazy to follow up, since it's not my problem, and I'd have to review EM for months to remember how to deal with it.

This, for example:
https://scholar.google.com/scholar?q=10.1109/50.848397

 

[Baluncore]

Yes, I am talking about modes. Resonance comes from my cylindrical cavity.

You are building a waveguide resonator, not a coaxial resonator.
A waveguide has a cutoff frequency.
You must increase the size of the waveguide, or increase the frequency, before you will see a resonant mode.

 

[DaveE]

Yes, I am talking about modes. Resonance comes from my cylindrical cavity. So I have a closed cylinder filled with one dielectric material and inside this cylinder another cylinder, with different radius and dielectric constant. Their height can be the same, but don't have to.

Do you mean you have concentric conducting cylinders, just like a coax cable?
A sketch would really help, we're not clairvoyant.

 

[Baluncore]

I have something like coaxial cable, but instead of a conductor at the core I have a different dielectric. Now I want the resonance outside the core to still happen, but not inside the core.

For resonance of a coaxial cavity, there must be an inner conductor with an equal and opposite current flow to the outer conductor.

Without that coaxial inner conductor, there must be some other form of signal coupling into the cavity, which must be sufficiently large to support some mode of resonance.

Coaxial systems with a central conductor and two different concentric dielectrics occur often. It is only when the system becomes asymmetric, non-coaxial, that the mathematics becomes difficult.

 

[Leopold89]

The paper is exactly what I asked for, thank you. Especially equation 22 $$E_z=C_m I_m(\alpha \rho)F_m$$ for dielectric tubes should be the answer, if I understand it correctly that the wave will get damped in the core the closer it gets to the center and in the second dielectric I will see a resonance.

Just to be sure, the dielectric constant can be any positive real number, including one smaller than 1, right? And secondly, what do I do if I should get $\epsilon_2 > \epsilon_1 > \bar\beta^2$?

P.S. I thought the electric field does have to be orthogonal on every surface, but the sum of the modified Bessel functions of first and second kind cannot fulfill this condition, right? So, why are they solutions?

 

[tech99]

I have something like coaxial cable, but instead of a conductor at the core I have a different dielectric. Now I want the resonance outside the core to still happen, but not inside the core.

The outer cylinder must be more than an electrical half wavelength in diameter to support waveguide modes. It looks as if you are wanting to use the TE01 mode and it is difficult to launch this mode.

 

[DaveE]

I am talking about modes. Resonance comes from my cylindrical cavity.

This is probably just a language or semantic thing, but, I wouldn't use the term resonance when discussing propagation modes. The distinction to me is mostly about energy storage. Propagation in a matched waveguide stops nearly immediately when the source is removed, not so with highly (Q>1) resonant systems.

A mismatched cable can be configured as a resonator, but the propagation modes will exist in any long waveguide, matched or not. So, it's confusing when you mix the two up in a "closed cylinder". There is resonance (I suppose), and there are propagation modes, but they aren't the same thing.

 

[DaveE]

The paper is exactly what I asked for, thank you. Especially equation 22 $$E_z=C_m I_m(\alpha \rho)F_m$$ for dielectric tubes should be the answer, if I understand it correctly that the wave will get damped in the core the closer it gets to the center and in the second dielectric I will see a resonance.

Just to be sure, the dielectric constant can be any positive real number, including one smaller than 1, right? And secondly, what do I do if I should get $\epsilon_2 > \epsilon_1 > \bar\beta^2$?

P.S. I thought the electric field does have to be orthogonal on every surface, but the sum of the modified Bessel functions of first and second kind cannot fulfill this condition, right? So, why are they solutions?

Sorry, nope, I'm not going to read that paper. This is your problem, not mine.