How Does the Jones Matrix Explain Light Polarization with Quarter Wave Plates?

[yklin_tux]

Hello, I am wondering a little about Jones matrix...

For example, If I have a Quarter Wave Plate with fast axis Horizontal, given by matrix

1 0
0 -i

and a vertically polarized light

0
1

the resultant light polarization is

0
-i

With QWP, it makes sense that if the direction of light polarization is the same as the direction of the fast, or the slow axis, then it does not make sense that the transmitted light is polarized at all, because there aren't electric field components changing phase.

So - is it ok to interpret that

0
-i

which is the resultant polarization of horizontally polarized light going through a QWP which has
fast axis also horizontal

is the same as

0
1

that is the only reasonable explanation to me thus far because nothing should happen to the polarization of light, yet the intuitive answer is different from the jones matrix one

 

[Andy Resnick]

I think you made an error- I got the resultant polarization for horizontally polarized light through a QWP (fast axis horizontal) as (1,0).

Thus, the vertical polarization is retarded by a quarter wave with respect to the horizontal- in order to convert linear polarization to circular, orient the fast axis at 45 degrees to the incident polarization state.

 

[Claude Bile]

For a QWP, if the incident polarisation is oriented along the fast or slow axis, then there will be no change in the polarisation state.

The change from (0 1)' to (0 -i)' is not regarded as a change in the polarisation state, as you can multiply through by an arbitrary phase factor to retrieve the original (0 1)' state.

Claude.

 

[yklin_tux]

Claude, I agree.
If I have a phase factor of e^i(pi/2) then I will just get

E = 0 ihat + E0 * -i*e^i(pi/2) jhat
= 0 ihat + E0 * 1 jhat which is what I began with

Correct me if I am wrong! but it makes sense to me as of now!