What do scientists mean when they talk about two-dimensional photon gas in Photon BEC?

Question

In a photon BEC, people are talking that cavity consisting of $2$ highly reflective mirrors make the photon gas $2$ dimensional by freezing out one wavevector $k_z$, which stays constant:
$$
k_z=npi/L
$$
where $L$ is cavity length and $n=7$. What does $2$ dimensional photon gas mean then? It means that photons then can move only in $x$ and $y$ direction or it means it can have only changing values of $k_x$ and $k_y$? In other words, is it $2$ dimensional in space or in $k$-space?
This is a screenshot from original paper (Nature $468$, $545$–$548$ ($2010$)):

SuperCiocia · Answer

It is a 2D system because the cavity is very short and has a large free spectral range, much larger than thermal energy. If the energy associated with the trapping potential along $z$ is $hbaromega_z$, then $hbar omega_z / (k_{mathrm{B}} T) gg 1$.
You can change $omega_z$ to $k_z$ with the dispersion relationship.
Since there is not enough energy to be able to excite motion along $z$, the $z$ degree of freedom is frozen. Everything moves only in the transverse direction. In real space.
It should be noted that this is a 2D system, but it is a harmonic potential. BEC in a homogeneous 2D potential is not possible, as discussed in my answer to your other question about photon BECs.

What do scientists mean when they talk about two-dimensional photon gas in Photon BEC?

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