# Polarization of E-M waves, basic concept question

So I searched around a bit on SE for an answer to this question, didn't find exactly what I was looking for.

When it comes to polarization of E-M waves (and subsequently, light), does it suffice to say the following:

• E-M waves have a particular direction of propagation, and we know that the oscillating electric and magnetic fields must both be perpendicular to the direction of travel
• I visualize this by holding out my right hand with my fingers straight and my thumb perpendicular
• The direction I "push" with my palm is the direction of wave travel and my fingers represent the electric field and my thumb the magnetic field

Under this premise, could I simply use my left hand to represent the other way this works, ie. polarization? My logic is that the electric field and magnetic field are still both perpendicular to the wave travel direction but now are "flipped". Is this an overly simplified approach?

(Context: Deriving Planck's formula and there's a factor of two in determining number of modes for a 3D E-M wave in a cavity with perfectly reflective walls, held in thermoequilibrium- the factor of 2 supposedly comes from polarization)

• Generally the fluctuating magnetic part of the wave field must be orthogonal to the wave propagation direction (i.e., $\mathbf{k} \cdot \delta \mathbf{B}$ = 0) but the electric field oscillations can be parallel (e.g., electrostatic waves or $\mathbf{k} \times \delta \mathbf{E}$ = 0). If it is a plane EM wave, then yes both fields are treated as orthogonal to the propagation direction. – honeste_vivere Oct 22 '16 at 17:40
• The origin and (lack of) fundamentalness of [right hand rules](right hand rule) (RHRs) have been discussed on the site more than a few times. The choice of right- or left-handedness for cross-products is a convention which does not effect experimental observables, but instead determines how certain figures are labeled because RHRs always appear in pairs. For instance the force between two parallel current carrying wires is determined by using a RHR to find the field near one due to the other and another RHR to determine the force on the wire due to the field. It all comes out in the wash. – dmckee --- ex-moderator kitten Oct 22 '16 at 17:57
• Are you asking if one sense of polarization is right-handed (E, B, k) and the other left-handed (B, E, k)? If that's the question, the answer is "no". – garyp Oct 22 '16 at 18:07
• I honestly didn't know that the electric field could be parallel to the direction of propagation. That's interesting. Also, I am aware the LHR and RHR are just conventions but I was looking for a simple way to describe what I was thinking. – Michael Burt Oct 23 '16 at 19:44

In a linearly polarized plane electromagnetic wave with a wave vector $\vec k$ and the electric field vector $\vec E$ giving the polarization direction, the magnetic field is given by the cross product $$\vec B=\frac{\vec k/|\vec k|×\vec E}{Z_0}$$ where $Z_0=\sqrt{\mu_0/\epsilon_0}$ is the free space wave impedance. The convention of the orientation of the cross product vector $\vec c=\vec a×\vec b$ is the right hand rule: When the forefinger of the right hand points in the direction of $\vec a$ and the middle finger in the direction of $\vec b$, then the vector $\vec c$ is coming out of the thumb. Using a left hand orientation would not give a different linear polarization. Circular polarized waves, however, have a right-handed or left-handed $\vec E$ and $\vec B$ field vector rotation, where $\vec E$ and $\vec B$ are always at right angles according to the above cross product.