Ay105: lab 2, polarization!

Light is a transverse electromagnetic wave

• Solution to the Maxwell equations • Propagation in the z direction • Direction of electric field = direction of polarization

y)t-kzcos(E)tz,(E

xt)-kzcos(E)tz,(E

0yy

0xx!!

!!

εω

ω

+=

=

Linearly polarized light

• E0x = 0 => vertically polarized light

Natural light = unpolarized light

Natural light =

incoherent superposition of equally probable polarization states

Natural light (unpolarized) Linear polarizer

Absorb 1 polarization direction let the other one through

(

Malus’law

• I = I0 cos2 θ

Elliptical polarization

• Trigonometric identities, square, sum

• Equation of an ellipse

y)t-kzcos(E)tz,(E

xt)-kzcos(E)tz,(E

0yy

0xx!!

!!

εω

ω

+=

=

εε 20y

y

0x

x

2

0y

y2

0x

x sincosEE

EE

2EE

EE

= −⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛

ε = π/2 (quarter wave) => circular polarization

• Equation of a circle

1sin cosEE

EE 22

2

0y

y2

0x

x =Θ+Θ=⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛

Birefringence

Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefringence is often quantified as the maximum difference between refractive indices exhibited by the material. Crystals with asymmetric crystal structures are often birefringent, as are plastics under mechanical stress.

Halfwave plate

Halfwave vs Quarterwave plate

Stokes vector and Mueller matrices

Stokes vector intuitive view

Stokes vector e-field relationship

Mueller matrix

Jones calculus

• Traditional Stokes vectors and Mueller matrices cannot describe interference effects. The phase information does matter => Jones calculus

• Drawback: Jones calculus cannot describe depolarization, or partial polarization phenomenon, assumes light is 100% polarized

Jones vectors

Jones Matrix

Polarization in astronomy: identify asymmetries

Stars, brown dwarfs, planets SuperNovae

Off to the lab!