# What is the difference between the structure of plane and circularly polarized light?

"If the polarization of all the electromagnetic waves in a light beam can be made so that each of the electric or magnetic field vector to have the same orientation, then the light beam is said to be polarized. Because of this, there is then a unique plane which contains all the directions of the electric or magnetic field along with the light rays. This type of polarization is referred to as plane polarization or linear polarization."

I understand that even for polarized light, there still exists an electric and magnetic field vector, which oscillate 90 degrees to each other. From this definition, would circularly polarized light just be plane polarized light that has passed a quarter-wave plate and has the electric and magnetic field vectors 90 degrees (1/4 cycle) out of phase, resulting in a "resultant" wave that is circling around?

• Polarization has nothing to do with changing a phase difference between electric and magnetic fields, just between their own components – user234190 Aug 19 '19 at 10:30

## 1 Answer

The electric and magnetic field vectors of a transverse electromagnetic wave are always at right angles to each other and in phase (for waves in a vacuum or non-conducting medium), whatever the state of polarisation. The polarisation state refers to the direction of the electric field vector, from which the magnetic field vector can always be inferred.

One way of thinking about polarisation is to note that it is always possible to deconstruct a transverse wave travelling in some particular direction into the sum of two separate components that are linearly polarised in orthogonal directions (e.g. see https://en.wikipedia.org/wiki/Polarization_(waves)#Polarization_state).

Thus we can construct a wave by adding two electromagnetic waves (of the same frequency and amplitude) but with the electric fields at right angles to each other and a common direction of wave motion.

If the two waves have zero phase difference, then they sum to give plane polarised light. The resultant electric field vector oscillates back and forth in a line at 45 degrees to the oscillation directions of the two contributing electric fields. This and the direction of wave motion defines a plane of polarisation.

If they have a phase difference of $$\pm \pi/2$$, then when they sum, the resultant E-field vector is of constant magnitude, but its direction rotates around. This is circularly polarised light. The tip of the resultant electric field vector draws out a circle when viewed along the direction of wave motion, or a helix when viewed in three dimensions, with its axis the direction of wave motion.

For an arbitrary phase difference the tip of the resultant electric field vector traces out an ellipse. i.e. Elliptically polarised light.

Play around with this Geogebra App that I wrote in order to model and explain this scenario. You can control the amplitude, frequency and phase difference of the two waves.

• Thank you for the answer. But I am still unsure, whether the "two electromagnetic waves" are magnetic and electric field vectors. We cannot simply "add" two EM waves, when they are already polarized. What physically/actually happens in linear and circular polarization? – HirG Aug 19 '19 at 8:38
• @JosephGoto I think there is a fundamental misunderstanding. The Electric and magnetic fields are always in phase (in vacuum or a non-conducting medium). Polarisation refers to the electric field vector only. The magnetic field vector is at 90 degrees and in phase. – Rob Jeffries Aug 19 '19 at 10:58
• I also don't know what you mean by "We cannot simply "add" two EM waves, when they are already polarized."? Yes, you can. That is the principle of superposition. – Rob Jeffries Aug 19 '19 at 11:05
• I meant, how can we add 2 EM waves for just one polarized wave? Circular polarized light waves are apparently "two perpendicular components" that are quarter cycle out of phase, but I do not understand what these "two components" are. A polarized wave only has one electric field and another magnetic field, how can we add two electric fields together when we are talking about only one polarized EM wave? – HirG Aug 19 '19 at 12:41
• @JosephGoto any transverse EM wave can be represented as the sum of two arbitrary orthogonal polarisation states. Electric and magnetic fields are vectors and sum as vectors. In the same way that the vector $\hat{i} + \hat{j}$ is the sum of $\vec{a} = \hat{i}$ and $\vec{b} = \hat{j}$, i.e. the sum of two orthogonal vectors. – Rob Jeffries Aug 19 '19 at 13:34