Understanding Poincare-sphere?

[Schulerbible]

Understanding Poincare-sphere!?

Dear physicists,

I have a huge problem understanding the working principle of Poincare-sphere. I know that the Poincare-sphere descibes a four-component Stokes vector and I know where I can find all forms of polarization (linear, circular, elliptical, ...).

The problem I have is to show via the Poincare sphere what happens when we have +45° linear polarized light onto a quater waveplate (Quater waveplate: we have fast axis vertical and slow axis horzonal oriented). The output must be something left or right handed polarized. But I don't know how to read the result out of the sphere! I read several books and descriptions but I couldn't find a proper answer.

Another point, does anybody knows how one can find the principal states of polarization on the Poincare-sphere?

Many thanks

Cheers
Tobias

 

[eljose79]

Dear Tobias,

Thank you for reaching out for help with understanding the Poincare-sphere. It can definitely be a complex concept to grasp, but I will do my best to explain it to you in a simple way.

Firstly, the Poincare-sphere is a geometric representation of the polarization states of light. It is a three-dimensional sphere, with the surface representing all possible polarization states and the center representing unpolarized light. The four components of the Stokes vector (S0, S1, S2, S3) are represented by the x, y, z, and w axes respectively.

Now, in order to understand what happens when +45° linear polarized light is incident on a quarter waveplate, we need to understand how the quarter waveplate works. A quarter waveplate is an optical device that can change the polarization state of light. It has a fast axis and a slow axis, which are perpendicular to each other.

When linearly polarized light is incident on the quarter waveplate, it gets split into two components, one parallel and one perpendicular to the fast axis. The parallel component travels faster than the perpendicular one, resulting in a phase difference of 90° between the two components. This phase difference changes the polarization state of the light, resulting in circularly polarized light.

Now, let's look at the Poincare-sphere. If we start with +45° linear polarized light, it will be represented on the Poincare-sphere as a point on the equator, with S1 and S2 components equal to each other and S3 component equal to 0. When this light is incident on the quarter waveplate, it will move towards the north pole of the Poincare-sphere, representing circularly polarized light. The direction of rotation (left or right-handed) will depend on the orientation of the fast axis of the quarter waveplate.

To find the principal states of polarization on the Poincare-sphere, you can use the fact that the principal states are represented by the two points on the equator that are furthest apart from each other. These points are called the principal points and are located at the intersection of the equator and the S3 axis.

I hope this explanation helps you understand the Poincare-sphere better. If you need further clarification or have any other questions, please don't hesitate to ask.