Register to reply

Polarization and Poincare circle.

by yungman
Tags: circle, poincare, polarization
Share this thread:
yungman
#1
Feb7-13, 04:28 AM
P: 3,883
What is the theory behind mapping of the latitude and longitude of the sphere in the Poincare Circle to the polarization of the TEM wave?

That is, why:

1) Linear polarization when ε=0 deg?
2) Circular polarization when ε=+/- 45 deg?
3) Elliptical when ε is not 0 or +/- 45 deg?
4) RH rotation if ε=-ve. and LH rotation if ε=+ve.?

Where 2ε= latitude.

Thanks

Alan
Phys.Org News Partner Physics news on Phys.org
IHEP in China has ambitions for Higgs factory
The physics of lead guitar playing
The birth of topological spintronics
Andy Resnick
#2
Feb7-13, 10:35 AM
Sci Advisor
P: 5,508
The first step is to represent the polarization state by a complex number: the general elliptic state with azimuth θ and ellipticity ε is combined into χ= tan(ε +π/4)exp(-i*2θ.) This maps polarization states to the "cartesian complex plane", and recall that -π/2 ≤ θ < π/2 and -π/4 ≤ ε ≤ π/4. χ= 0 refers to left-circularly polarized light, χ=∞ is right-circularly polarized light.

To construct the Poincare sphere, perform a stereographic mapping of the plane to a unit sphere: latitudes on the sphere then correspond to circles of constant ε on the complex plane and longitude corresponds to lines of constant azimuth on the plane.

Azzam and Bashara's "Ellipsometry and Polarized Light" is an excellent resource for this material.
yungman
#3
Feb8-13, 01:55 PM
P: 3,883
Thanks for your reply.

The book is way to expensive as This is only a small part of my study in antenna theory.

Can you show me how the polarity of the ellipticity angle relate to the direction of rotation? That is, why +ve ε gives rise to Left hand rotation and -ve ε gives rise to Right hand rotation.

Thanks

Andy Resnick
#4
Feb8-13, 02:03 PM
Sci Advisor
P: 5,508
Polarization and Poincare circle.

If I understand your question, it's a sign convention.
yungman
#5
Feb8-13, 04:00 PM
P: 3,883
Quote Quote by Andy Resnick View Post
If I understand your question, it's a sign convention.
No so much about convention, but rather why ε affect the direction of rotation.

[tex]\epsilon=\frac {E_{max}}{E_{min}}[/tex]

How do you justify +ve or -ve of [itex]E_{max},E_{min}[/itex]?

Thanks


Register to reply

Related Discussions
Describing polarization of a coheret state parametrizing on poincare sphere Quantum Physics 1
Poincare disk model. Circle question. Calculus & Beyond Homework 0
Circumference of a circle in Poincare Half Plane Differential Geometry 1
Difference in polarization with birefringence substance and polarization filter Classical Physics 0
Poincare sphere and Degree of polarization Classical Physics 2