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