cos = sin x y ϕ ϕ ϕ

8. Polarization 8. Polarization

( )

⎩⎨

⎧ ⎥⎦⎤

⎢⎣⎡

⎟⎠

⎜ ⎞

⎝⎛ −

= c

t z j

z,t Re Aexp 2πν

Ε

y x ˆ ˆ Α = A

+ A

( )

( )

x

x a j , A a j

A = exp ϕ = exp ϕ

x

축,

축 두개의 직교 편광 성분으로 모든 파동방정 식의 해를 기술할 수 있다.

Polarization (I) Polarization (I)

( )

⎩⎨

⎧ ⎥⎦⎤

⎢⎣⎡

⎟⎠

⎜ ⎞

⎝⎛ −

−

= c

t z j

z,t Re Aexp 2πν

Ε

(

)

(

)

x

x a j , A a j

A = exp − ϕ = exp − ϕ

Different notation

Polarization (II) Polarization (II)

( )

Ε x y

cos 2

x x x

E a t z

πν c ϕ

⎡ ⎛ ⎞ ⎤

= ⎢⎣ ⎜⎝ − ⎟⎠ + ⎥⎦

cos 2

y y y

E a t z

πν c ϕ

⎡ ⎛ ⎞ ⎤

= ⎢⎣ ⎜⎝ − ⎟⎠ + ⎥⎦

Polarization (III) Polarization (III)

Ε ϕ ϕ Ε

Ε Ε ₂

y x

y x 2

y 2 y 2

x 2 x

a 2 a

a

a

+ − cos = sin

x

y ϕ

ϕ ϕ = −

Polarization Ellipsoid Polarization Ellipsoid

π ϕ = 0 or

Linear Polarization Linear Polarization

2 ϕ = π : Polarized Circularly

Right

2 ϕ = −π :

Polarized Circularly

Left

Circular Polarization Circular Polarization

다른 표기 a_x → a₁, a_y → a₂ , ϕ = ϕ_y −ϕ_x → δ = δ₂ −δ₁

a b a

a = ∓

= χ

α , tan tan

1 2

( 2 : 장축의 길이, 2 : 단축의 길이 )a b

Elliptical Polarization Elliptical Polarization

x y x y x y

Comparison of Three Polarization Types Comparison of Three Polarization Types

Types of Polarization Types of Polarization

• 빛이 액정을 통과하면서 복굴절 현상으로 인해 빛의 진동축이 회전됨

• LCD는 이러한 빛의 편광 변화를 통해 빛의 세기를

polarizer

Liquid Crystal Display Liquid Crystal Display

ON OFF

LCD Cell LCD Cell

Polarization Filter Polarization Filter

( )x y y

( )

x a j , A a j

A = exp ϕ = exp ϕ

⎟⎟⎠

⎜⎜ ⎞

⎝

= ⎛

y x

A J A

R. Clark Jones (1916-2004)

Jones Vector Jones Vector

Jones Vectors Jones Vectors

⎟⎟ ⎠

⎞

⎜⎜ ⎝

⎟⎟ ⎛

⎠

⎜⎜ ⎞

⎝

= ⎛

⎟⎟ ⎠

⎞

⎜⎜ ⎝

⎛

y 1

x 1 22

21

12 11

y 2

x 2

A A T

T

T T

A A

1

2 TJ

J =

Jones Calculus Jones Calculus

⎟⎟

⎠

⎜⎜ ⎞

⎝

= ⎛

0 0

0 T 1

Jones Matrix for Linear Polarizer Jones Matrix for Linear Polarizer

( )

exp ⎟⎟

⎠

⎜⎜ ⎞

⎝

⎛

= −

Γ j 0

0 T 1

retarder wave

- Quarter

: 2 Γ ₌

retarder wave

- Half

: Γ =π

Jones Matrix for Wave

Jones Matrix for Wave RetardersRetarders

cos sin

sin

cos ⎟⎟

⎠

⎜⎜ ⎞

⎝

⎛ −

= θ θ

θ T θ

⎟⎟ ⎠

⎜⎜ ⎞

⎝

⎟⎟ ⎛

⎠

⎜⎜ ⎞

⎝

⎛ −

⎟⎟ =

⎠

⎜⎜ ⎞

⎝

⎛

2 1 2

2 s

s

θ θ θ

θ

θ θ

θ θ

sin co cos

sin

sin cos

sin co

θ θ

θ₂ = ₁ +

Jones Matrix for Polarization Rotators Jones Matrix for Polarization Rotators

( )^J

R J'

=

( ) _⎟⎟

⎠

⎜⎜ ⎞

⎝

= ⎛

θ θ

θ θ θ

cos sin

-

sin R cos

( ) ( )θ

−

=

( ) ( )θ T R θ R

T

= −

Coordinate Transformation Coordinate Transformation

2 2 2

1

0 a a

s = +

δ

2cos

1

2 2a a

s =

δ

2sin

1

3 2a a

s =

2 2 2

1

1 a a

s = −

2 3 2

2 2

1 2

0 s s s

s = + +

Stokes Parameters Stokes Parameters

⎟⎟

⎟ ⎟

⎟

⎠

⎞

⎜⎜

⎜ ⎜

⎜

⎝

⎛

3 2 1 0

S S S

S ^S₀ = Total power(polarized + unpolarized)

S₁ = Power through LH polarizer – power through LV polarizer S₂ = Power through L+45 polarizer – power through L-45 polarizer S₃ = Power through RC polarizer – power through LC polarizer

2 3 2

2 2

1 S S

S

P_polarized

= + +

Stokes Parameters Stokes Parameters (Polarized +

(Polarized + UnpolarizedUnpolarized) (I)) (I)

Stokes Parameters Stokes Parameters (Polarized +

(Polarized + UnpolarizedUnpolarized) (II)) (II)

DOP

d unpolarize polarized

polarized

P P

P

= +

0

2 3 2

2 2

1

S

S S

S + +

= DOP

2 2 2

DOP = s + s + s

Degree of Polarization Degree of Polarization

Poincar

Poincaréé Sphere (I)Sphere (I)

ψ χ 2 2

s

s₁ = ₀ cos cos

ψ χ 2 2

s

s₂ = ₀ cos sin

χ

2 s

s₃ = ₀ sin

Poincar

Poincaréé Sphere (II)Sphere (II)