380A OPTI Intermediate Optics Lab 5: Linear Polarization
Tom Milster Professor, College of Optical Sciences, University of Arizona [e-mail]
Linearly Polarized EM Wave
9/24/2010
OPTI380A - Lab 5: Linear Polarization
2
1
Polarizers
! A polarizer transmits only one orientation of polarization. That is, only one direction of electric field vibration is allowed to pass through the polarizer material.
Unpolarized Light
Polarizer Polarized Light
(Figure credit: http://en.wikipedia.org/wiki/File:Wire-grid-polarizer.svg)
9/24/2010
OPTI380A - Lab 5: Linear Polarization
3
Absorptive Polarizers
! Wire-grid: parallel metallic wires
! Crystals: dichroism (two colored), dichroism (two colored), preferential absorption of light polarized in one direction
! Polaroid film: polyvinyl alcohol (PVA) plastic with iodine doping, align PVA by stretching (common in sunglasses, camera filters, LC displays) LC di ! Corning Polarcor glass: elongated silver particles
9/24/2010
OPTI380A - Lab 5: Linear Polarization
4
2
Polarizer Extinction Ratio
! A polarizers extinction ratio is the ratio of the power transmitted when the incident polarization is aligned with the transmission axis of the polarizer to the power transmitted when the incident polarization is orthogonal to the transmission axis.
Polarizer (y transmission axis) Polarizer (y transmission axis)
U0
Incident Electric Field y
U ty
Transmitted Electric Field y
Incident Electric Field x
Transmitted Electric Field x
U0
U ty U tx
2
U tx
Extinction Ratio !
9/24/2010
OPTI380A - Lab 5: Linear Polarization
5
Polarizer Specifications
-10dB = 10%, -20dB = 1% etc
9/24/2010
OPTI380A - Lab 5: Linear Polarization
6
3
Rotated Polarizer
If a polarizer is rotated by angle ", the effect on the transmitted light is to project x and y components of the incident polarization onto the rotated axis. In the example below, the transmission of the polarizer is in the y' direction.
Vector Diagram:
y'
Polarizer Transmission Axis
y
U # ! $U x sin " % U y cos " y
Uy
"
U y cos "
x'
"
$U x sin "
9/24/2010
Ux
x
OPTI380A - Lab 5: Linear Polarization
7
Law of Malus
! Let the incident polarization be in the y direction, then
y'
Polarizer Transmission Axis
y
Uy "
U # ! U y cos " y
Etienne-Louis Malus
U y cos "
x'
"
x
! Transmitted power is:
9/24/2010
Ptransmitted & Pincident cos 2 "
8
OPTI380A - Lab 5: Linear Polarization
4
Law of Malus
! Experimentally, we can use one polarizer to set the incident polarization ! A second polarizer (called an analyzer) can be rotated to observe Maluss law.
9/24/2010
OPTI380A - Lab 5: Linear Polarization
9
Plane of Incidence
! When polarized light reflects from and transmits through surfaces, the amount of reflection and transmission is defined relative to the plane of incidence.
9/24/2010
OPTI380A Lab - 5: Linear Polarization
10
5
Polarization Fresnels Equations
! The s polarization state (' plane of incidence) and p polarization state (in the plane of incidence) define Fresnels Equations of reflection and transmission.
Polarization Convention Convention
U pi
U si
"i
Fresnels Equations Equations
rs ! ts ! N i cos "i $ N t cos "t N i cos "i % N t cos "t 2 N i cos "i N i cos "i % Nt cos "t rp ! tp ! N t cos "i $ Ni cos "t N t cos "i % Ni cos "t 2 N i cos "i N t cos "i % N i cos "t
n
"r
U pr
kr
U sr
ki
Ni Nt
Surface
"t
Plane of Incidence
U pt
kt
For example, the reflected field amplitude for p polarization is:
U st
U pr ! rpU pi
The reflected power for p polarization is: 2
Ppr ! rp Ppi
9/24/2010
OPTI380A - Lab 5: Linear Polarization
11
Air-to-Glass (s Polarization)
mirror-like reflection at glancing incidence
9/24/2010 OPTI380A - Lab 5: Linear Polarization 12
6
Air-to-Glass (p Polarization)
mirror-like reflection at glancing incidence
9/24/2010 OPTI380A - Lab 5: Linear Polarization 13
Air-to-Glass Reflection
Transmission
! nair ~ 1 and nglass ~ 1.5 ! Total reflection at "=90 for both polarizations (glancing angle reflection, useful for x-rays) ! Zero reflection for parallel polarization at Brewsters angle ("B=56.5)
p s
p Reflection s
9/24/2010
OPTI380A - Lab 5: Linear Polarization
14
7
Brewsters Angle
! Sir David Brewster (1781-1868) published about diffraction of light in Philosophical Transactions of London in 1799 at an age of 18. ! When light moves between 2 media, p-polarized light will not be reflected at one incident angle called the Brewster angle the Brewsters angle.
" B ! tan $1
nt ni
9/24/2010
OPTI380A - Lab 5: Linear Polarization
R! r
2
15
Glass to Air Reflection
! nair ~ 1 and nglass ~ 1.5 ! Total internal reflection above a critical angle " crit ! arcsin(nt / ni )
s p
optical fiber
9/24/2010 OPTI380A - Lab 5: Linear Polarization 16
8
Glass-to-Air (s Polarization)
critical angle for total internal reflection
9/24/2010 OPTI380A - Lab 5: Linear Polarization 17
Glass-to-Air (p Polarization)
critical angle for total internal reflection
9/24/2010 OPTI380A - Lab 5: Linear Polarization 18
9
Beam-Splitting Polarizers
! Polarization by reflection, direct beam at Brewsters angle to separate s-wave and p-wave
For a stack of 10 plates, 20 reflections, about 3% of spolarized light is transmitted.
! Birefringent (double refraction) polarizer " Refractive index is different for different axis or polarization " Quartz and calcite: ordinary (o-ray) or extraordinary (eray) Total internal reflection of o-ray, n=1.658
Rhombohedral crystal of calcite
9/24/2010
OPTI380A - Lab 5: Linear Polarization
e-ray is transmitted, n=1.486
19
10