# A question about meaning of polarisation of light

Hi,

I have been spending the last week just to understand the meaning of polarisation of light. I think the books so I far I have seen are not following simple language and are making things complex or I have not seen so far a good book on this subject which simplified the things or perhaps I am not able to understand this completely, I may be missing some fined point.

Most of the books mention that in unpolarised light electric fied vector can be in any plane whereas in polarised light, E vector is restricted to just one plane.

Now let us consider light travelling along the x direction. Since light is A transverse wave, E vector can at most be in YZ plane. True, in the YZ plane, the E vector can be with any orientation, it can be along y axis, it can be along z axis, and it can be a combination of both. So in an unpolarised light, the E vector can be at one moment along y direction, at another it can be along z, and at yet another it can be a combination of both. But still, the E vector is in the YZ plane only. So I find that it is wrong to say that even in UNPOLARISED light, E vector can be in any plane - for example in this case, it can not be along the x axis, it can not be a combination of x and z or in other words, it can not be in the XZ plane - because still the E vector has to be perpendicular to the direction of light propagation. Polarised light can restrict E vector to only along y axis, or z axis or a combination of both.

The gist of my point is that since there can be only one plane perpendicular to a line, (YZ plane for x axis), and E has to be perpendicualr to the direction, E has to be always in the YZ plane.

Am I right? Please clarify. Thanks

Andy Resnick
Personally, I dislike the term "unpolarized", becasue at any instant of time the electric field is pointing in some particular direction. A better term is "randomly polarized", becasue that is more descriptive of the actual field vector.

Given a plane wave, propogating in the 'z' direction, the electric field always lies in the x-y plane. If the vector always lies in a particular direction (x-, y-, some angle to the x-axis, etc), it's linearly polarized light. If the electric field vector traces out a circle (or ellipse), it's circularly (or elliptically) polarized..

There are more exotic polarization states: radial and tangential for example. Also, if the wave is not a plane wave, defining the polarization can become difficult, especially for strongly focused light

ciao
marco

Andy, Thanks for the clarification. So to reconfirm, my understanding is right, for light moving forward in z direction, the E vector, by the definition of transverse nature, is restricted to be in x-y plane. The E field can be then,

E = A sin(wt-kz) i

Where E stands for the electric vector, and i stands for a unit vector in the x-y plane. In the case of randomly polarised vector, i changes with time - but still being restricted to the x-y plane.

Is this right?

Andy Resnick
Andy, Thanks for the clarification. So to reconfirm, my understanding is right, for light moving forward in z direction, the E vector, by the definition of transverse nature, is restricted to be in x-y plane. The E field can be then,

E = A sin(wt-kz) i

Where E stands for the electric vector, and i stands for a unit vector in the x-y plane. In the case of randomly polarised vector, i changes with time - but still being restricted to the x-y plane.

Is this right?

Well, I would hesitate to have the unit vector 'i' change in time. Better to write something like

E(t) = A sin(wt-kx) e(t), where e(t) is the direction of the electric field vector in time. Then, if you want to write down linear polarized states like u(t) = i, or u(t) = j, or even u(t) = 1/sqrt(2) (i + j), and for circular states you can write down other combinations. For randomly polarized, you'd have some funky definition for u(t) that make it look like a stochastic variable.

Is polarity a continuous property?

Hi,

I always thought that a single photon is by it self polarized with E=Asin(wt-kz) in a constant direction perpendicular to z. The polarization is said to be generated by the momentum (say of an electron that has fallen energetic levels), and thus stays constant. In a beam of polarized light the whole population of photons have the same unit vector, while in unpolarized light the many photons each have different polarity, which might seem random. This leads me to the question, is polarity of a beam a continuous property? Can a beam be partially polarized?
In addition I wondered, why can't a single photon (or a beam) be polarized in the direction of propagation?

Andy Resnick
A single photon is circularly polarized (helicity).

Beams can indeed be partially polarized: polarization is inherently a statistical property of light. The most general way to discuss polarization involves the "Poincare sphere". If light is fully polarized, the polarization state lies on the surface of the sphere. Randomly polarized light lies at the origin, and partially polarized states fill the interior volume.

Helicity corresponds to spin; it is possible to have angular momentum as well, this involves special types of propogating modes: donut or Bessel beams, usually created with an axicon or phase grating device. The indeterminancy of phase at the origin of these beams gives rise to a non-zero winding number, corresponding to (quantized) angular momentum.

Circularly polarized light will exert a torque on birefringent materials.

All this is for far-field paraxial beams. Strongly focused light and evanescent waves will have components of the electric field that lie along the direction of propogation (longitudinal modes). I don't know too much about that, other than it exists.