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I am reading a paper by Serge Haroche stating the cavity they use sustains a Gaussian mode of the e.m. field called $TEM_{900}$. I understand what Gaussian means. I found this explaining what TEM means, but if I am working in a cavity, what is the "direction of propagation"? And above all, why three indices instead of two?

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"why three indices instead of two" It's a three-dimensional cavity, right? –  dmckee Jan 22 '13 at 19:20
    
Yes, but looking at the wikipedia page, it only uses two. Now i'm noticing that it's for laser beams. Perhaps the two things are interconnected, i.e. when I have a stationary field in a cavity, then no direction of propagation => three indices? –  Bzazz Jan 22 '13 at 19:26
    
I think that the laser modes in the wikipedia article are not bounded in the beam direction, so there is no quantization in that direction--which cooresponds to the $z$ direction in my (rather incomplete) answer. –  dmckee Jan 22 '13 at 19:33
    
Yes, exactly what I was thinking about. It wasn't difficult after all. Thanks. –  Bzazz Jan 22 '13 at 19:35
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1 Answer

up vote 1 down vote accepted

The solutions for a electric field in a perfectly conductive cylindrical cavity separate into the form $$ E(r,\phi,z) = R(r)\Phi(\phi)Z(z)\quad ,$$ and quantize in each of the coordinate directions (periodic boundary conditions on $\phi$).

Likewise of the magnetic field.

The "T" in "TEM" is "transverse, which means that the intensity of the two fields must have the same dependence on the coordinates.

Accordingly we can label the modes with a set of three integers.

The thing I can't recall off the top of my head is the numbering scheme. Is it $(\text{radial},\text{angular},\text{longitudinal})$ or $(\text{longitudinal},\text{radial},\text{angular})$ which matters in your case. There may be a hint in the text.

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It says it's gaussian. It also describes the cavity, but it means little to me. However, don't worry too much. –  Bzazz Jan 22 '13 at 19:48
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