What is a $TEM_{900}$ cavity radiation mode?

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

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 $\phi$).
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.