Polarization
animation
Plane wave
E  Eo e

i k r t

Polarization determined by
Eo   Eo x xˆ  Eo y yˆ 
Linearly polarized light
Condition on phase of Ey vs Ex for linear pol:
Jones Vector
General Jones vector:
 A 
 i 
 Be 
often normalized
usually ignore overall phase and
keep relative phase of
components:
linearly pol light:
ei
Eox 2  Eoy 2
1
Eox 2  Eoy 2
 Eox 


 Eoy ei 


 Eox 


 Eoy ei 


Circularly polarized light
Condition on Ey vs Ex phase for R,L-Circ light:
Condition on amplitudes for for R,L-Circ light:
Jones vectors
Circular rotation of E
Right-circular light
Freeze wave in time. If walk along the wave
in either direction, I will see E rotating like my
fingers curl, if RH light. (E is like threads on
a common screw)
The light in the figure is a) RH b) LH
Another description:
I’m looking at a light on a screen (at the front
of the screen), E rotates CCW for R-circ light
The light in the animation is a) RH b) LH
Elliptically polarized light
Elliptically polarized light
How do you get light with an E-vector that traces
the ellipse in the diagram?
a)
b)
c)
d)
Ey < Ex
Ey > Ex
Ey = Ex
Ey = Ex
and p/2 phase shift
and p/2 phase shift
and 0 phase shift
and p/2 phase shift
How to get ellipse axes not aligned with x,y?
a) Ey ≠ Ex and 0 phase shift
b) Ey > Ex and p/2 phase shift
c) Ey = Ex and phase not 0, p/2, p, 3p/2…
d) Ex ≠ Ey and phase not 0, p/2, p, 3p/2…
e) c and d
a
Summary: conditions to get a noncircular ellipse
Whenever relative phase is ±p/2 and |Ex| ≠ |Ey|
Whenever phase is not mp/2, and |Ex|, |Ey| are arbitrary
E  4ˆ
x cos(kz  t)  4 ˆ
y sin(kz  t)
What kind of polarization is this?
a) linear
b) R-circ
c) L-circ
d) R-ellip
e) L-ellip
E  4ˆ
x cos(kz  t)  6 ˆ
y cos(kz  t)
What kind of polarization is this?
a) linear
b) R-circ
c) L-circ
d) R-ellip
e) L-ellip
p
E  4ˆ
x cos(kz  t  )  4 ˆ
y cos(kz  t)
4
What kind of polarization is this?
a) linear
b) R-circ
c) L-circ
d) R-ellip
e) L-ellip
Elliptically polarized light math
 A 
 i 
 Be 
General case
a
1
 2 AB cos  
a  tan 1  2
2
2
 A  B 
angle of ellipse axis closest to x-axis
Emin Eminor
e

Emax Emajor
Find both of these to see which ellipse axis is the major (longest) one:
Ea  Eeff
Ea p 2  Eeff
A2 cos 2 a  B 2 sin 2 a  AB cos  sin 2a
A2 sin 2 a  B 2 cos 2 a  AB cos  sin 2a
Eeff  E0 x 2  E0 y 2
Sky seen through polarizer
Bees have polarized eyes
for navigation
Why scattered sunlight is partially polarized
You stand facing the air molecules at a 90 deg scattering angle
From what we know about radiation vs acceleration line, the strongest
polarization you see is a) horizontal b)vertical c) neither
Why sunlight (scattered light) is partially polarized
To get the most polarization difference,
look at the molecules that have to
scatter light 90 degrees to get to you
Why: dipole radiation’s angular dependence!
Sunset carousel demo and polarization
LCD screen teardown
Boomerang Nebula coldest known distant region: 1K
Color indicates angle of polarization axis, polarization
caused by scattering of light off tiny dust particles