# Polarization states of light in 2D

Hi,

I stumbled upon this dilemma in a homework problem which involved 2D photon gas (unphysical, I know). How many polarization states are there for EM-radiation confined to 2D? In 3D it's 2, but how does it work in 2D? An EM-wave propagating in the z-direction can have its E-component pointing in the x- or y-direction. But obviously that setup is not possible in 2D. Can a photon even propagate in two dimensions, or is this paradox just from the fact that Maxwell's equations (the cross products) don't really work in 2D?

The question is ill put. Of course one can imagine configurations where the e field is forced to swing in one plane only and you could call this 2D. But they probably want to be a smart *** and remind you that the linearly polarized plane wave always has a magnetic field perpendicular to the E field, so the answer is 1 or 0.

The question is ill put. Of course one can imagine configurations where the e field is forced to swing in one plane only and you could call this 2D. But they probably want to be a smart *** and remind you that the linearly polarized plane wave always has a magnetic field perpendicular to the E field, so the answer is 1 or 0.

Actually, the question came up in a statistical physics exercise, where we were asked to calculate the pressure of a photon gas confined to area A=L^2. And you need the number of polarization states when you change a sum to an integral. My theory is that the lecturer was lazy and just changed the dimension from 3 to 2 without considering the implications, because this problem is solved in 3D in the course book. :tongue:

DrDu
You can achieve this confinement by putting the photons between two metal plates. As long as the distance of the two plates is much smaller than the mean wavelength which is of order hc/kT, the thermodynamical problem is effectively two-dimensional. Try to work out the different solutions to the Maxwell equations.

Hi,

I stumbled upon this dilemma in a homework problem which involved 2D photon gas (unphysical, I know). How many polarization states are there for EM-radiation confined to 2D? In 3D it's 2, but how does it work in 2D? An EM-wave propagating in the z-direction can have its E-component pointing in the x- or y-direction. But obviously that setup is not possible in 2D. Can a photon even propagate in two dimensions, or is this paradox just from the fact that Maxwell's equations (the cross products) don't really work in 2D?

Of course light (both in the classical wave and quantum photon description) can propagate in 2D and even in "1D" - both cases can be experimentally realized, too. After all, this is what the wave guides are all about :-).

Googling with 2D or 1D light/photons will give you ample references.

Claude Bile
Since E, B and k must be mutually perpendicular (or at least have mutually perpendicular components), it is impossible to realise this scenario in anything less than 3D.

Claude.

Since E, B and k must be mutually perpendicular (or at least have mutually perpendicular components), it is impossible to realise this scenario in anything less than 3D.

Claude.

This is simply not the case in reality! First, the 2D and 1D cases refer (of course) to physical systems where the light is trapped and can propagate in one or two spatial directions only - mathematically exact 2D or 1D systems don't exist in Nature (although they have great theoretical value). It is easy to prevent the propagation of photons in a specific direction by optical traps.

Claude Bile