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Polarization and Poincare circle. 
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#1
Feb713, 04:28 AM

P: 3,898

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 


#2
Feb713, 10:35 AM

Sci Advisor
P: 5,523

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 leftcircularly polarized light, χ=∞ is rightcircularly 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. 


#3
Feb813, 01:55 PM

P: 3,898

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 


#4
Feb813, 02:03 PM

Sci Advisor
P: 5,523

Polarization and Poincare circle.
If I understand your question, it's a sign convention.



#5
Feb813, 04:00 PM

P: 3,898

[tex]\epsilon=\frac {E_{max}}{E_{min}}[/tex] How do you justify +ve or ve of [itex]E_{max},E_{min}[/itex]? Thanks 


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