# Polarization of Electromagnetic Waves

```Polarization of Electromagnetic Waves
• Polarization is the phenomenon in which electromagnetic waves are
restricted in direction of vibration
• Polarization is a property of waves that describes the orientation of
their oscillations
Polarization of Electromagnetic Waves
• Two beams, otherwise identical, may interact differently with matter if
their polarization states are different.
• Interference only occurs when EM waves have the same frequency and
polarization (i.e., they are coherent)
Polarization Types
• Linear
• Circular
• Elliptical
• ‘Random’ or unpolarized
Linear Polarization
• Plane EM wave – linearly polarized
• Trace of electric field vector is linear
• Also called plane-polarized light
• Convention is to refer to the electric field vector
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polclas.html
http://www.univie.ac.at/mikroskopie/1_grundlagen/optik/wellenoptik/6_polarisation.htm
Linear Polarization (Animation)
Linear Polarization (Horizontal)
https://userscontent2.emaze.com/images/cac94365-b9dc-4762-9121-96c69882485b/458fc46bb8bd-43e1-b3db-f7ae1667d4e0image20.gif
Linear Polarization (45 degrees)
http://bestanimations.com/Science/Physics/45degree-polarized-light-wave.gif
Circular Polarization
• Two perpendicular electric field components of equal amplitude with 90&deg;
difference in phase
• Electric vector rotates counterclockwise  right-hand circular polarization
• Electric vector rotates clockwise  left-hand circular polarization
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polclas.html
http://www.univie.ac.at/mikroskopie/1_grundlagen/optik/wellenoptik/6_polarisation.htm
Circular Polarization (Animation)
Left Handed Circular Polarization (LHC)
http://i.imgur.com/3bjXjMd.gif
Elliptical Polarization
• Two perpendicular eletric field components not in phase, either with different
amplitudes and/or not 90&ordm; out of phase
• Electric vector rotates counterclockwise  right-hand elliptical polarization
• Electric vector rotates clockwise  left-hand elliptical polarization
• The most general state of complete polarization is elliptical
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polclas.html
http://www.univie.ac.at/mikroskopie/1_grundlagen/optik/wellenoptik/6_polarisation.htm
Polarization Animation
Animation showing four different
polarization states and two orthogonal
projections.
By Davidjessop - Own work, CC BY-SA 4.0,
https://commons.wikimedia.org/w/index.php?curid=48021939
A circularly polarized wave as a sum of two
linearly polarized components 90&deg; out of
phase
By de:Benutzer:Averse - http://www.radartutorial.eu/06.antennas/pic/zirkulanim.gif via
de.wikipedia.org, CC BY-SA 2.0,
https://commons.wikimedia.org/w/index.php?curid=4849061
Fresnel Equations
TE polarization
x
TM polarization
Er
Et
θ1
Ei
θ2
z
ε1, μ0 ε2, μ0
Power Conservation
Example of Fresnel Equations
n1 = 1, n2 =1.5
Example of Fresnel Equations
n1 = 1, n2 =1.5
Example of Fresnel Equations
n1 = 1, n2 =1.5
Example of Fresnel Equations
n1 = 1.5, n2 =1
Example of Fresnel Equations
n1 = 1.5, n2 =1
Example of Fresnel Equations
n1 = 1.5, n2 =1
Example of Fresnel Equations
n1 = 1.0, n2 = 0.855 - j1.8955 (Gold at λ0 =0.5μm)
Example of Fresnel Equations
n1 = 1.0, n2 = 0.855 - j1.8955 (Gold at λ0 =0.5μm)
Example of Fresnel Equations
n1 = 1.0, n2 = 0.855 - j1.8955 (Gold at λ0 =0.5μm)
Wave Interference
+
=
Constructive interference
(In phase)
+
=
(Waves cancel)
( π out of phase)
Destructive interference
Wave Interference
When light waves travel different paths,
and are then recombined, they interfere.
1
*
2
Mirror
+
=
Constructive interference results when light paths differ
by an integer multiple of the wavelength: ∆r = m λ
Wave Interference
When light waves travel different paths,
and are then recombined, they interfere.
1
*
2
Mirror
+
=
Destructive interference results when light paths differ
by an odd multiple of the half wavelength: ∆r = (2m+1) λ/2
Double-Slit Experiment (Young’s Experiment)
Double-Slit Experiment (Young’s Experiment)
Fabry-Perot Interferometer
Thin Film Interference Examples
Soap Bubbles
Oil Thin Films
R. A. Serway and J. W. Jewett, “Physics for Scientists and Engineers”,
Thomson Brooks/Cole, 6th Ed. 2004
Multiple Colors
Incident Sunlight
Blue
Green
Orange
Red
External
Reflection
Oil film
Internal Reflection
http://www.explainthatstuff.com/thin-film-interference.html
Thin Film Interference Examples
Morpho butterflies
Peacock Feathers
http://en.wikipedia.org/wiki/Morpho
http://www.microscopyu.com/articles/polarized/interferenceintro.html
http://www.rowland.harvard.edu/organization/past_research/optics/default.html
Michelson Interferometer
http://www.britannica.com/EBchecked/topic/380060/Michelson-interferometer
http://skullsinthestars.com/2008/10/16/fabry-perot-and-their-wonderful-interferometer-1897-1899/
Michelson Interferometer Sample Patterns
Antireflection Layer
x
n1
θ1
nc
n2
z
antirelection
layer
Comparison of surface reflection from
a silicon solar cell, with and without a
typical anti-reflection coating.
dc
http://www.pveducation.org/pvcdrom/design/anti-reflection-coatings
```