6.976 Flat Panel Display Devices - Spring 2001 Lecture 11 1

Lecture 116.976 Flat Panel Display Devices

Physics of Liquid Crystals I

• Polarization Devices

• Jones Matrix Method

• Liquid Crystals

Outline

6.976 Flat Panel Display Devices - Spring 2001 Lecture 11 2

References• Jin Au Kong, Electromagnetic Wave Theory, EMW

Publishing, Cambridge, MA, USA• B. E. A. Saleh and M. C. Teich, Fundamentals of

Photonics, John Wiley & Sons, New York• E. Hecht, Optics, Addison-Wesley Publishing• Peter J. Collings and Michael Hird, Introduction to Liquid

Crystals-Chemistry and Physics, Taylor and Francis, 1997• D. J. Channin and A. Sussman, Liquid Crystal Displays,

LCD, Chapter 4 in Display Devices, Ed. Jacques I. Pankove, Spriger-Verlag, 1980.

• P. Yeh and C. Gu, Optics of Liquid Crystal Displays, John Wiley & Sons, New York, 1999.

6.976 Flat Panel Display Devices - Spring 2001 Lecture 11 12

Jones Vectors

== δδ

δδ

y

x

jy

jx

eA

eAJ

From this we can determine intensity

22

yx AAI ++==

Yeh & Gu

6.976 Flat Panel Display Devices - Spring 2001 Lecture 11 13

Jones Matrix Formulation

==

y

x

y

x

A

A

TT

TT

A

A

1

1

2221

1211

2

2

12 TJJ ==

Saleh & Teich

6.976 Flat Panel Display Devices - Spring 2001 Lecture 11 14

Linear Polarizer

==

00

01T

Saleh & Teich

6.976 Flat Panel Display Devices - Spring 2001 Lecture 11 15

Wave Retarder

== ΓΓ−− je

T0

01(( ))dnn fs −−

λλππ

==ΓΓ2

==

ΓΓ++

ΓΓ−−φφ−−

2

2

0

0j

jj

e

eeT

change phase relative

change phase absolute

====φφ

Ã

6.976 Flat Panel Display Devices - Spring 2001 Lecture 11 16

Half-Wave Retarder Plate

−−==

j

jT

0

0(( )) ππ==−−

λλππ==ΓΓ dnn fs

2

−−

−−==

−−==

−−1

1

1

1

0

0j

j

j

j

j

Polarization rotated by 90º

−−

−−==

−−−−

==

−−j

jj

jj

j 1

1

1

0

0

R-circularly polarized ⇒L-circularly polarized Saleh & Teich

6.976 Flat Panel Display Devices - Spring 2001 Lecture 11 18

Effect of Quarter Wave Plate

Yeh & Gu

6.976 Flat Panel Display Devices - Spring 2001 Lecture 11 19

Polarization Rotators

θθθθθθ−−θθ

==cossin

sincosT

Takes linearly polarized wave

θθ++θθ==θθ

θθθθ

θθθθ

12

2

2

1

1

toconverts

where

sin

cos

sin

cos

6.976 Flat Panel Display Devices - Spring 2001 Lecture 11 20

Coordinate Transformation

(( ))

ψψψψ−−ψψψψ

==ψψ

ψψψψ−−ψψψψ

==

cossin

sincosR

J

J

cossin

sincos

J

J

y

x

f

s

(( )) (( ))ψψψψ−−== RTRT sfxy

If ψ=45°

(( ))

−−

−−==

−−

−−

−−==

−−

==°°

0

0

11

11

2

10

0

11

11

2

1

plate wave-halfFor

11

11

2

145

j

j

j

jT

R

xy

Yeh & Gu

6.976 Flat Panel Display Devices - Spring 2001 Lecture 11 21

Jones Matrices(Polarizers)

Yeh & Gu

6.976 Flat Panel Display Devices - Spring 2001 Lecture 11 22

Jones Matrices(Wave Plates)

Yeh & Gu