View
220
Download
2
Category
Preview:
Citation preview
Linearly Polarised Light
Ez = E0z cos(kx� �t)Ey = E0y cos(kx� �t)
tan� =E0z
E0y=
Ez
Ey
polarisation angle
Circularly Polarised Light
Ez = E0 sin(kx� �t)Ey = E0 cos(kx� �t)
Circularly Polarised Light
Ez = E0 sin(kx� �t)Ey = E0 cos(kx� �t)
Circularly Polarised Light
special caseE0z = E0y
� = +⇥/2
= E0z cos(kx� ⇥t� �)= E0y cos(kx� ⇥t)
Ez = E0 sin(kx� �t)Ey = E0 cos(kx� �t)
Circularly Polarised Light
Right circular polarization
E0z = E0y
� = +⇥/2
Ez = E0z cos(kx� ⇥t� �)Ey = E0y cos(kx� ⇥t)
observer looking at the light source: field vector rotates clockwise
Negative helicity
Circularly Polarised Light
Left circular polarization
Ez = E0z cos(kx� ⇥t� �)Ey = E0y cos(kx� ⇥t)
observer looking at the light source: field vector rotates counter-clockwise
Positive helicity
E0z = E0y
� = �⇥/2
Superposition of equalR & L Circular polarization = Plane polarized light
Superposition of unequalR & L Circular polarization = Elliptically polarized light
Superposition of Polarisation Elliptical Polarisation
Ez = E0z cos(kx� ⇥t� �)Ey = E0y cos(kx� ⇥t)
� = ±⇥/2E0z ⇥= E0y
� ⇥= ±⇥/2E0z ⇥= E0y
Polarisation States
Ez = E0z cos(kx� ⇥t� �) Ey = E0y cos(kx� ⇥t)
linear
right/left circular
right/left elliptical, axes along y,z
right/left elliptical, axes at angle θ to y
� = 0, ⇥
� = ±⇥/2
� = ±⇥/2
� ⇥= ±⇥/2
E0z = E0y
E0z �= E0y
E0z �= E0y
Polarisation States
Ez = E0z cos(kx� ⇥t� �) Ey = E0y cos(kx� ⇥t)
Polarisation
Types of polarisationlinear, circular, elliptical
Polarisation opticsuni-axial crystalspolarising prismswave plates (λ/2 and λ/4)
Interference with polarised light
Uni-Axial Crystals
nx,y �= nz
Uni-Axial Crystals
(also possible: positive anisotropy nex > no)
negative anisotropy: nex < no
EZ
EY
.nex extraordinary ray index
y
z
.no ordinary ray index
Ez and Ey components “see”different refractive index
Retardation of Polarisation
ky = 2⇥no/�vac
kz = 2⇥nex/�vac
beam in x direction
λ/2-Plate: Polarisation Rotation
Ez = E0z cos(kx� �t)Ey = E0y cos(kx� �t)
Ez = E0z cos(kx� �t)Ey = �E0y cos(kx� �t)
(ky � kz)�x = k�/2 = ⇥
λ/4-Plate: Linear ↔ Elliptical
Ez = E0z cos(kx� �t)Ey = E0y cos(kx� �t)
(ky � kz)�x = k�/4 = ⇥/2
Ez = E0z sin(kx� �t)Ey = E0y cos(kx� �t)
EZ
EY
λ/4-Plate: Elliptical ↔ Linear
Babinet-SoleilBabinet
Variable Retardation Plates
Polarising Prisms and Beam Splitter
Snell‘s law:
total internal reflection for o-ray
no sin �s = nair sin �o,air
nex sin �s = nair sin �ex,air
1no
< sin �s <1
nex
Polarisation Analysis
• rotate the λ/4 plate to get linear polarisation• check for linearity with a rotatable polariser• get the angles δ and Θ from the orientations
Polarisation
Types of polarisationlinear, circular, elliptical
Polarisation opticsuni-axial crystals - birefringencepolarising prismswave plates (λ/2 and λ/4)
Interference with polarised light
Interference with Polarised Light
The End
Recommended