# Optical rotation and linear basis set

1. ### galvin452

15
If I have a 45 degree linear polarized light which I then circularly polarize using a 1/4 wave plate and put this through an optical rotary crystal and then using the equivalent 1/4 wave plate but in the reverse oriention, will I get back a 45 degree linear polarized light?

Put another way, as circular polarized light can use a linear basis set 90 degrees out of phase, can the angle of the linear basis set with respect to the 1/4 wave plate orientation be rotated by the optical rotary crystal (while the phase remains circular) or is the basis set orientation always fixed?

I would think the basis set orientation is fixed but just want to make sure.

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3. ### Claude Bile

1,479
There is no reason why the basis set orientation ought to be fixed. By my understanding the optical rotary crystal can rotate the linear basis set. I'd go through the Jones algebra to be sure though.

Claude.

4. ### galvin452

15
For a linear basis set, one can take each individual linear orientation basis as two oppositely rotating basis set so that each orthogonal linear basis is rotated by the difference between the right and left index of refraction. This would rotate the basis set as you indicated. The amount of rotation dependent on the difference between the left and right rotary index of refraction.

However if one uses a circular basis set the light is totally right circularly (or left circularly depending on the 1/4 wave plate fast slow axis orientation) polarized when entering the optical rotary crystal. Lets assume right circularly polarized, so at best it could only interact with the right index of refraction having no left component. So the right circular polarized light's reorientation would only be the result of the right rotary index of refraction.

That is to say we would get two different results depending on the basis set used.

Where is the mistake?

5. ### galvin452

15
I can't find the Jones matix is for an optical rotary crystal? Do you know it?

6. ### Andy Resnick

5,744
For a linear rotator (say, sugar water), the Jones matrices are: [[cos(δ/2)+icos(2θ)sin(δ/2) isin(2θ)sin(δ/2)], [isin(2θ)sin(δ/2) cos(δ/2)-icos(2θ)sin(δ/2)]] for cartesian basis states and [[cos(δ/2) i*exp(i2θ)sin(δ/2)], [i*exp(-i2θ)sin(δ/2) cos(δ/2)]] for circular basis states, where θ is the azimuthal angle of the fast axis and δ the phase retardation.

For a circular rotator (say, the cholesteric liquid crystal phase), the cartesian Jones matrix is [[cos(δ/2) +/-sin(δ/2)], [-/+sin(δ/2) cos(δ/2)]] and for circular basis states [[exp(-/+ iδ/2) 0],[0 exp(-/+iδ/2)]].

7. ### galvin452

15
Hi Andy, not sure whar you mean by a linear rotator vs a circular rotator. I know you can rotate the angle of linear polarized light which I assume is what you mean by a linear rotator. What is a circular rotator?
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