Understanding Jones Matrix: Exploring Light Polarization and 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!

 

[pmacias]

The Jones matrix is a mathematical tool used to describe the polarization of light. It takes into account the direction and phase of the electric field components of the light waves. In this case, the Quarter Wave Plate (QWP) is a device that changes the polarization of light by a quarter of a wavelength.

In your example, the QWP has a fast axis that is horizontal, meaning that it changes the polarization of light that is polarized in the horizontal direction. The Jones matrix for this QWP reflects this change by having a nonzero element in the (2,2) position, indicating that the electric field component in the horizontal direction will be changed.

When vertically polarized light is incident on the QWP, the Jones matrix calculation shows that the resultant polarization will be in the (-i) vertical direction. This means that the electric field component in the vertical direction will be shifted in phase by a quarter of a wavelength.

Your interpretation is correct in that the resultant polarization is the same as the incident polarization. This is because the QWP only affects light that is polarized in the direction of its fast or slow axis. In this case, the vertical polarization is not affected by the QWP because it is perpendicular to the fast axis.

It is important to remember that the Jones matrix is a mathematical representation of the physical phenomenon of light polarization. It may seem counterintuitive, but the mathematical calculations accurately describe the behavior of light in this scenario.