Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2,...

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Ay105: lab 2, polarization!

Transcript of Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2,...

Page 1: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

Ay105: lab 2, polarization!

Page 2: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

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

+=

=

Page 3: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

Linearly polarized light

• E0x = 0 => vertically polarized light

Page 4: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

Natural light = unpolarized light

Natural light =

incoherent superposition of equally probable polarization states

Page 5: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

Natural light (unpolarized) Linear polarizer

Absorb 1 polarization direction let the other one through

(<50% transmission for Natural light)

Page 6: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

Malus’law

• I = I0 cos2 θ

Page 7: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

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

= −⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎞⎜⎜⎝

Page 8: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

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

• Equation of a circle

1sin cosEE

EE 22

2

0y

y2

0x

x =Θ+Θ=⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎞⎜⎜⎝

Page 9: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

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.

Page 10: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

Halfwave plate

Page 11: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

Halfwave vs Quarterwave plate

Page 12: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

Stokes vector and Mueller matrices

Stokes vector intuitive view

Stokes vector e-field relationship

Mueller matrix

Page 13: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

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

Page 14: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

Jones vectors

Page 15: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

Jones Matrix

Page 16: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

Polarization in astronomy: identify asymmetries

Stars, brown dwarfs, planets SuperNovae

Page 17: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x

Off to the lab!

Page 18: Ay105: lab 2, polarization! - Department of Astronomy · 2019. 4. 8. · Ay105: lab 2, polarization! Light is a transverse electromagnetic wave ... ε 2 ε 0y y 0x x 2 0y y 2 0x x