Can't quite grasp idea of Unpolarized Light, TE-TM Polarization

[SmashtheVan]

So Polarization of light has always really bugged me. Linear polarization is simple. I understand Elliptical and Circular as well; the Electric Field vector changes as the Ex and Ey(or Ex and Ez, etc) functions grow and recede, periodically. This is easy to show as the propagation of a singular wave/photon packet(I like to call them wavons, just to have some fun)

Now, for Unpolarized light, if I try to think in terms of a "random variable" function for Ex and Ey, I think, well, it looks like the resultant E field is accelerating/decelerating constantly from one instant to the next, shouldn't there be some outside force needed to provide that change? My other thought is that instead of talking about "Unpolarized Light" as a "wavon" with a randomly fluctuating field, we should instead think of Unpolarized Light as a beam of infinitesimal light beams, each of a different polarization(say linear, at different angles due to initial conditions upon emission from a source), such that at any instant the resultant E field summation is random...is this second line of thought at all correct?

2nd question:

I am working through a book for a training course for my job(in optics, of course), in which polarization is termed either TM or TE(transverse magnetic/electric), and I have no clue what this means. My interpretation of the textbook makes me think they're implying a part of the Electric Field is traveling in the same plane as the Magnetic field, which I know Maxwell would disapprove of. I also gather that these definitions are only relevant in relation to an interface of reflection/refraction. I guess I just want to know a better definition for TM/TE, and how exactly they relate to said optical interface. The book is written by the professor, so some things are explained very hazily, and its been a long time since my class on Hecht's text

Thanks!

 

[zen loki]

First, it is entirely correct to think of unpolarized light as a sum of different polarizations, much like white light is the sum of all visible frequencies. No one polarization dominates, so we call it unpolarized.

As for TM/TE/TEM this happens only in an electrically conducting cavity, thus bypassing the ordinary rules we all know EM wave propagation because electric charge is involved. TEM in particular only happens in a coaxial cable. The best place to start reading about this, as well as one of the best EM texts out there, is Griffeth's Introduction to Electrodynamics.

 

[chrisbaird]

1) You don't need infinitesimal beams or randomly fluctuating E fields to get unpolarized light. Just take a horizontally polarized sine wave and add a vertically polarized sine wave with the same frequency and traveling in the same direction as the first, but make the vertical one out of phase from the horizontal one by a random phase factor. Depending on the phase factor, the total field can point in any direction perpendicular to the propagation direction. With a random phase difference, the polarization direction becomes random and, voila, you have unpolarized light. Note that in monochromatic unpolarized light, the E field components do not dance around all crazy - they are still oscillating in sine waves.

2) In waveguides, the fields can have a component in the direction of propagation (as opposed to completely transverse waves [TEM] in free space). This does not violate Maxwell's equations. Transverse Magnetic (TM) implies that the electric field is not transverse to the direction of propagation, but has a component in this direction. Similarly, Transverse Electric (TE) has a magnetic component in the direction of propagation.

In the context of reflection/refraction at a material interface, transverse magnetic may refer to when the magnetic field is perpendicular to the plane of incidence. In this case, the electric field is still transverse to the direction of propagation (free-space plane waves are hitting the interface), but the electric field is not transverse to the plane of incidence (rather, it lies in or is parallel to the plane of interface).