# Polarization states of light in 2D

• Jopi
This I do not doubt, and I get that the direction of propagation (k) can be confined to 2D, but the direction of the E and B vectors cannot be coplanar (confined to the same 2D plane) by my understanding. Therefore you cannot express the system in anything less than 3D.

#### Jopi

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:

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.

Jopi said:
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.

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

Claude.

Claude Bile said:
Since E, B and k must be mutually perpendicular (or at least have mutually perpendicular components), it is impossible to realize 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.

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.

This I do not doubt, and I get that the direction of propagation (k) can be confined to 2D, but the direction of the E and B vectors cannot be coplanar (confined to the same 2D plane) by my understanding. Therefore you cannot express the system in anything less than 3D.

Claude.

## 1. What is polarization of light in 2D?

Polarization of light in 2D refers to the orientation of the electric field vector of a light wave, which can be described as a two-dimensional plane. This plane can be perpendicular, parallel, or at an angle to the direction of the light wave's propagation.

## 2. How is polarization of light in 2D different from 3D?

In 3D, the polarization of light refers to the orientation of the electric field vector in all three dimensions. In 2D, the polarization is limited to a two-dimensional plane, which can be visualized as a flat sheet or screen.

## 3. What are the types of polarization states in 2D?

The three main types of polarization states in 2D are linear, circular, and elliptical. Linear polarization occurs when the electric field vector is oscillating in one direction, while circular polarization occurs when the electric field vector rotates in a circular motion. Elliptical polarization is a combination of both linear and circular polarization.

## 4. How is polarization of light in 2D measured?

Polarization of light in 2D can be measured using a polarimeter, which is a device that measures the intensity of light passing through a polarizing filter. By rotating the polarizing filter, the polarization state of the light can be determined.

## 5. What are the applications of polarization of light in 2D?

Polarization of light in 2D has various applications in fields such as optics, astronomy, and telecommunications. It is used in polarized sunglasses to reduce glare, in 3D glasses to create depth perception, and in satellite communication to transmit and receive signals.