Post on 23-Jan-2021
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
(<50% transmission for Natural light)
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 2
0y
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!