polarization of light

BeauGeste

So from what I understand, right handed circularly polarized light has angular momentum +1,
left handed circularly polarized light has angular momentum -1.
What is the angular momentum of linear polarized light?

Claude Bile

Are you referring to the angular momentum of a photon with circular polarisation? Or are you referring to the angular momentum of a classical wave?

Also, when you say +1, what quantity are you referring to, the angular momentum itself (in which case you should denote units) or the quantum number associated with angular momentum?

Claude.

BeauGeste

i guess i'm referring to the quantum number of the photon. but i'm interested in the classical answer too if there is one.

Claude Bile

For a single photon, the quantum number for angular momentum must be +/- 1, sometimes we say that the photon has spin +/- 1.

For a collection of photon with linear polarisation, we can regard half has having spin +1 and half as having spin -1 (with spin +1 corresponding to left hand and spin -1 corresponding to right hand circular polarisation). The average angular momentum from a group of linearly polarised photons is therefore 0.

Claude.

Meir Achuz

There is actually a mismatch between the definition of circular polalrization
(R and L) and the photon spin direction. The photons of R polarized light are actually left handed. That is they have negative helicity, or spin component
of -hbar (or -1 in units where hbar is absent). The reason for this difference is that opticians define the rotation of the E vector as you look toward the light. Particlelists define the spin of the photon in the direction of advance of the light.

Classical light is the case when the number of photons is so large that the amplitude seems continuous. The angular momentum of classical L polarized light of a pure frequency would be n hbar, where n is the number of photons.

Voltage

Sorry if I ought to start a new thread with this, but can anybody tell me:

Can a single photon exhibit linear polarisation?

What's the difference between polarization plane and polarization?

BeauGeste

I thought that non polarized light would have avg. ang. mom. of 0, because it is have left handed and half right handed. It seems that linear polarized light is a different situation. You see what I'm saying?

Claude Bile

Voltage - The polarisation of an EM wave is typically defined as the direction of the E-field vector, with the polarisation plane being the plane defined by the E-field vector and the wave-vector, k.

Voltage, BeauGeste - The question of whether a single photon can possess a linear polarisation pushes the edge of my knowledge to be honest. While a single photon must possess angular momentum of +/- h-bar units, a photon can exist in a superposition of two states with the photon having a 50% probability of becoming either RH or LH polarised when a "measurement" is performed. You could perhaps call a photon in such a superposition of states a single photon with linear polarisation. You could similarly regard an unpolarised photon as being in a superposition of two orthogonal linearly polarised states. (I would recommend asking this question again in the QM forums, you will most likely get a more accurate answer there.)

The bottom line though is that a photon MUST have a momentum of either +/- h-bar units.

Claude.

Creator

Classically, BeauGeste, it is different because you are not dealing with discrete particles but with continuous electric field amplitudes. Classically, circular polarization is composed of two linear polarized waves (of equal amplitude) oriented orthogonal to each other which are simply out of phase by 90 degrees.
The resulting superposition of the electric fields creates a continuosly rotating electric field vector thru space.

This can be seen experimentally simply by sending linear polarized light through a 'quarter wave' plate, creating circular polarized light.

Of course, classically, I don't think linear polarized waves have a net angular moment, but rather have a transverse oscillating field which can been seen in the effect on charges in matter as the wave passes through.
And they do have linear momentum (as per the Poyting vector) in the direction of propogation.

Creator

"Never eat more than you can lift" - Ms. Piggy

Voltage

Many thanks Claude and Creator.

Milind_shyani

I would like to know first of alll what is right handed circularly polarized light and left handed circularly polarized light ??

Voltage

Are we talking about them being out of phase by 90 degrees in a left handed direction or a right handed direction? Like by +90 or -90 degrees, perhaps better expressed as 90 degrees or 270 degrees?

Creator

Here's a brief discription with diagrams so you can better visualize.

http://hyperphysics.phy-astr.gsu.edu...t/polclas.html

...

Voltage

Creator: many, many thanks.

Creator

No problem Voltage.

I guess, in light of BeauGeste's original question, I ought to address the angular momentum question classically also.

Notice in my first post to him I mentioned (as did Claude) it is only the direction of the electric field vector, E, that defines polarization; but this says nothing of the angular momentum.

Not so well known is the fact that, classically, standard Maxwell equations show there should be NO angular momentum vector directed along the direction of propogation ......however, this directly contradicts laser experiments which reveal angular momentum is transferred to objects in the path of circularly polarized light.

Just thought that ought to be mentioned.....

Creator

-Honk if you like peace and quiet.-

Weimin

I'm following the link creator provided, here

http://hyperphysics.phy-astr.gsu.edu...t/polclas.html

According to this picture in the link below, we are looking to the light that is coming toward us. The text says:

If this wave were approaching an observer, it electric vector would appear to be roting counterclockwise. This is called right-circular polarized.

http://hyperphysics.phy-astr.gsu.edu...pho/polcir.gif

But right after that, it says:

If while looking at the source, the electric vector of the light coming toward you appears to be rotating clockwise, the light is said to be right-circularly polarized

That appears to be contrary!

Creator

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:
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Good catch Weimin; its probably a typo.

Creator