Liquid Crystal Optics in the Far Infrared (THz)

Ci-Ling PanDepartment of Photonics and

Institute of Electro-Optical Engineering (IEO)National Chiao Tung University (NCTU)

Hsinchu City 30010Taiwan ROC

Acknowledgements

• Ru-Pin Chao Pan, Chao-Yuan Chen, Cho-Fan Hsieh, H. L. Chen , T. A. Liu, T. R. Tsai (NCTU)• M. Hangyo, M. Tani (Osaka U.)• X. –C. Zhang (RPI)

Outline

• Motivation and Objectives• Liquid Crystals (LC) and THz

Techniques: Basics• THz Optical Constants of LC• Examples of LC THz devices:

phase shifter, quarter-wave compensator, filters

• Motivations:

• Increasing demands for THz quasi-optic components.

• LC has played an important role in the visible optics as

well as electro-optics and could be as eminent in THz

optics.

Motivation and Objectives

• Objectives:

• Characterization of LCs in the THz regime

• To develop THz photonic devices with LC-enabled

functionality

Liquid Crystal: A Unique State of Matter

Orientationalorderedsolid

Orientationaldisorderedsolid

Liquid

Liquid crystal(nematic phase)

Liquid

(Isotropic phase)

The first Liquid Crystal

Otto Lehmann's polarizing microscope

(From his book, 1900)

cholesteryl benzoate: related to cholesterol

F. Reinitzer, Z. Phys. Chem. 9, 241 (1988)

O. Lehmann, ibid., 4, 262 (1989)

Friedrich Reinitzer, 1857-1927

(image from www-ub.kfunigraz.ac.at)

Properties of LC Materials

Yeh & Gu

• LC is state of matter intermediate between solid and amorphous liquid– Liquid with

ordered arrangement of molecules– Molecules with

orientation order (like crystals) but lack positional order (like liquids)

• Organic substances with anisotropic molecules that are highly enlongated or flat

• Ordering leads to anisotropy of– Mechanical properties– Electrical properties– Magnetic properties– Optical properties

Building Blocks of Liquid Crystals

CNChemist’s

View

Physicist’sEngineer’s

View

• Shape Anisotropy• Length > Width

The molecule above (5CB) is ~2 nm × 0.5 nm

Different Points of View

CH3 - (CH2)4 C N

LongMolecular

Axis

θ

H H

H H

H H

H H

C NCC C

H HHH

C CH H

HH

H

n

The local average axis

of the long molecular axis

director

The Nematic Director n

HH

Orientational Order of LCs

• Director n at any point is the preferred orientation in the immediate neighborhood

• In homogeneous LC, it is constant throughout medium

• In inhomogeneous medium,n=n(x,y,z)

• Order parameter of an LC isgiven by

θ is the angle between the long axis and director n

)1cos3(21)(cos 22 −== θθPS

θn

n

More on the Order Parameter

θn

n

no order

perfect order

perfect crystal

isotropic fluid

)1cos3(21)(cos 22 −== θθPS

31

coscos

2

2 =Ω

Ω=

∫

∫

Ω

Ω

d

dθθ

1)0(cos2 == oθ

1)(cos2 == θPS

0)(cos2 == θPS

Effects of Order ParameterCompoundThe order parameter, S, is proportional to a number of important

parameters which dictate LC device performance.

Sn ∝∆S∝∆ε

S∝∆χS∝∆ηViscosity Anisotrophy

Magnetic AnisotrophyBirefringenceDielectric AnisotrophyElastic Constants: 2Skii ∝

SSSKVth =∝∆

∝2

ε

Dielectric Constants• Nematic and smectic LCs are uniaxially symmetric

with axis of symmetry parallel to the director n– Dielectric constants differ in value along the preferred

axis (ε//) and perpendicular to the preferred axis (ε⊥ )– Dielectric anisotropy is ∆ε = ε// - ε⊥, -2εo≤ ∆ε ≤ 15 εo

• The macroscopic energy is: • If θ is the angle between the director and z-axis

EDWemrr

.21

=

θεθε

θεθε

22

2

22

sincos21

)sincos(

⊥//

⊥//

+=

+=

zem

z

DW

ED

Anisotropy: Dielectric Constant+++++

- -- --

E

ε

ε

∆ε = ε − ε > 0

E

∆ε = ε − ε < 0

++++

----

positive

negativeall angles inthe plane ⊥to E arepossible for the-∆ε materials

E

Dielectric Constants: Temperature Dependence

4’-pentyl-4-cyanobiphenyl

3 2)4 C N

Temperature Dependence

Average Dielectric Anistropy

T-TNI (°C)

43 2)4 C NCH3-(CH2) C N

Δε ∝ S(T)

〈Δε〉= 31

(2ε⊥+ε//)

16

14

12

10

8

625 30 35

Die

lect

ricC

onst

ant

εis

ε//

Extrapolated from isotropic phase

Δε ∝ S(T)

〈Δε〉= 31

(2ε⊥+ε//)

ε⊥

ne and no: Temperature Dependence

NI

Average Index

TemperatureDependence

∆n ∝ S(T)

1.8

1.7

1.6

1.5

1.450 40 30 0

T-T (°C)

Inde

x of

Ref

ract

ion

20 10

ne

no

nisoExtrapolated from isotropic phase

( )222 231

oe nnn += ( )222 231

oe nnn +=

•5CB (K15): 4’-n-pentyl-4-cyanobiphenyl

CNC5H11

Nematic phaseT = 22.4 0C ---- 34.5 0C

In the visible, ∆n (λ,T)=ne-no=0.14~0.19

n

5CB: a typical NLC

0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.801.40

1.45

1.50

1.55

1.60

1.65

1.70

1.75

1.80

1.85

1.90

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

Ref

ract

ive

inde

x

Wavelength(um)

ne (25.1oC)

no (25.1oC)

Bire

frin

genc

e (∆

n)

T-Ray: Next frontier in Science and Technology

103 106 109 1012 1015 1018 1021 1024100

MF, HF, VHF, UHF, SHF, EHF

microwaves visible

kilo mega giga tera peta exa zetta yotta

x-ray γ -ray

THz Gapelectronics photonics

Hz

Frequency (Hz)

1 THz ~ 1 ps ~ 300 µm ~ 33 cm-1 ~ 4.1 meV ~ 47.6 oK

dc

Terahertz wave (or T-ray), which is electromagnetic radiation in a frequency interval from 0.1 to 10 THz, lies a frequency range with rich science but limited technology.

Courtesy of X.-C. Zhang

Frequency (THz)

.01 .1 1 10 100 1000

T=30K

3000K

300K

10-8

10-10

10-12

10-14

10-16

10-18

Em

issi

vity

(J/m

2 )

Blackbody Radiation:Natural Source of THz Radiation

Natural sources of THz are very weak.

Peter Siegel, JPL

“Traditional” electronic approaches to“THz light”

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

0.1 1 10

Frequency (THz)

CW

Pow

er (µ

W)

Impact AvalancheTransit Time (IMPATT) diodes

FrequencyMultipliers

Resonanttunnelingdiodes

Quantumcascade

laser(May 2002)

Courtesy: R. Trebino

THz and Optical Parametric Generators

Gavin D. Reid, University of Leeds, and Klaas Wynne, University of Strathclyde

THz picks up where OPG’s leave off.

Generation of THz Wave:current surge effect

• Hertzian dipole antenna in free space.

ttJ

rtrE

∂∂

∝)(1),(

bEetntJ µ)()( =

Pulsed laser

Biased Dipole

THz radiation

0 1 2

-2

0

2

~10-12 sec

J'(t)

J(t)

Am

plitu

de (

a.u.

)

Time dealy(ps)

Detection of THz Wave: Photoconductive Antenna

∫ −=2

1

)()()(t

tcdttntEmeI τµττ

I(τ): detected signal current, e: electron charge, µ: carrier mobility, τc: carrier life time, m: repetition rate, τ: relative time delay between THz pulse and gating laser pulse, n(t): photo-induced transient carrier density, E(t): THz field.Substrate with • Shorter carrier life time: n(t)~delta function =>E(t)∝I(t)• Long carrier life time: n(t)~step function=>E(t)∝dI(t)/dt

A

Optical pulse

THz pulse

Substrate

Generation of THz Wave:Optical rectification

• Transient polarization generated after pulse laser (wide band width) excited optical nonlinear materials

• Transient polarization:

• Radiated THz field: 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0-0.7

0.0

0.7

~10-12 sec

P''(t)

P(t)

Am

plitu

de (

a.u.

)

Time delay (ps)

)()(),,()( *)2( ωωωωχ EEP Ω+−Ω+Ω=Ω

)()( 22

tPt

tJt

Errrr

∂∂

∝∂∂

∝

)0()()()0,,,()( *)3( dcEEEP ωωωωχ Ω+−Ω+Ω=Ω

Detection of THz Wave: Electro-Optic Sampling

∆I(t)=I0sin(∆Γ)

)(3

041 tEdr

THzn

λπ

=∆Γ

ZnTe

Wollastonpolarizer

[1,-1,0]

[1,1,0

]

λ/4 plate

pellicle

probe beam

THz b

eam

sp

polarizer r E

r E

detector

∆I

0 20 40 60 80 100 120 140

-0.00010

-0.00005

0.00000

0.00005

0.00010

0.00015

0.00020

elec

tric

field

(a.u

.)

time delay (psec)

Reference

0.0 0.5 1.0 1.5 2.0 2.5 3.01E-23

1E-22

1E-21

1E-20

1E-19

1E-18

1E-17

1E-16

1E-15

1E-14

pow

er (a

.u.)

frequency (THz)

Reference

Free space THz time domain waveform

THz frequency domain spectrum

Terahertz Time-Domain Spectroscopy (THz-TDS)

Emitter

Detector

THz Emitter

Detector

THz

•The emitter and detector using small gap LT-GaAs photoconductive antenna•The signal to noise ratio is up to million•The bandwidth is between 0.1 to 1.5 THz

(1)

(2) (3) (4) (5)

(6)(7)

(8)

(10)

(1)Ti:Sapphire (2)Neutral Density Filter(3)Quarter Wave plate(4)Beam Splitter(5)Mirror coated with Ag(6)Object Lens(7)Emitter:LT-GaAs Photoconductive

Antenna with Silicon Lens(8)Parabolic Mirror coated with Au(9)Detector:LT-GaAs Photoconductor

Antenna with Silicon Lens(10)Optical Delay Stage

(9)

(1)

(2) (3) (4) (5)

(6)(7)

(8)

(10)

(1)Ti:Sapphire fs Laser(2)Neutral Density Filter(3)Quarter Wave plate(4)Beam Splitter(5)Mirror coated with Ag(6)Object Lens(7)Emitter:LT-GaAs Photoconductive

Antenna with Silicon Lens(8)Parabolic Mirror coated with Au(9)Detector:LT-GaAs Photoconductor

Antenna with Silicon Lens(10)Optical Delay Stage

(9)

incoming THz wave

ammeter

photoconductive antennafemtosecond optical beam

A

Measuring THz pulses using

photoconductive sampling

train of THz pulses

train of fsecoptical pulsestime

femtosecondlaser pulse

antenna impedance

Antenna impedance vs. time

Scanning the delay is performed as in cross-correlation.

Because the fs optical pulse is shorter than the THz pulse, this works.

1. 兆赫輻射可以清楚

的看到鈔票上的浮水印

2. 兆赫輻射可以檢測出信封裡面的粉末分布未來有可能應用於生物戰劑如碳疽桿菌之檢測）

THz Imaging: Examples

優點及應用:

• 對人體安全

• 非接觸性

• 極佳的訊噪比

• 可應用於反恐、醫學組織診斷、 食物檢測、化學成分分析、材料特性分析

THz Movie of a Match Box

Sample

ZnTe

compensator

PC Antenna

Wollastonprism

Balanceddetector

BS

Femtosecond laserX-Z Stage

time domain (amplitude) frequency domain (amplitude) phase

THz Biomedical Sensing:Refractive index and absorption coefficient of deoxyhemoglobin

0.2 0.4 0.6 0.8 1.0 1.2 1.41.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

Hemoglobin (powder-320µm) Hemoglobin (Thin film-350µm) Hemoglobin (powder-960µm)

Ref

ract

ive

inde

x (n

)

Frequency (THz) 0.2 0.4 0.6 0.8 1.0 1.2 1.4020

40

60

80

100

120

140

160 Hemoglobin (powder-320µm) Hemoglobin (Thin film-350µm) Hemoglobin (powder-960µm)

Abso

rptio

n co

effe

cien

t (cm

-1)

Frequency (THz)

14 528 46120 240150 250Absorption coefficient (cm-1)

~1.61 (0.03)~1.87 (0.02)~2.01 (0.03)

~2.04 (0.07)Refractive index-mean value (with standard deviation)

Hemoglobin(Thin film)

Hemoglobin(powder)

BloodWater

Burn-depth detection of pork with T-ray technology (I)

0.533mm

1. Heated with 150°C for 10 min2.Dehydrated

Burnt Pork

1. Heated with 150°C for 10 min (burnt part)2.Dehydrated

DehydratedPreparation process

~1mm0.27mmThickness

Staked PorkNormal PorkType

0.533mm

1. Heated with 150°C for 10 min2.Dehydrated

Burnt Pork

1. Heated with 150°C for 10 min (burnt part)2.Dehydrated

DehydratedPreparation process

~1mm0.27mmThickness

Staked PorkNormal PorkType

-4 -2 0 2 4 6 8 10 12 14 16 18-2

-1

0

1

2

3

Reference Burnt pork Normal pork

Nor

mal

ized

Am

plitu

de (a

.u.)

Time delay (ps)

porcine skin

measured waveform

Incident THz wave

Second reflected wave

First reflected wave

1.746.18Burn

1.67Normal

0.533Burnt

3.010.27Normal

n (refractive index)

T (time of flight, ps)d (thickness, mm)

1.746.18Burn

1.67Normal

0.533Burnt

3.010.27Normal

n (refractive index)

T (time of flight, ps)d (thickness, mm)

Refractive index of burnt and normal porcine is determined via THz time of flight

Burnt depth of 0.53mm is resolved via THz imaging

Norm

al porcine skin

Burned porcine skin

Incident THz wave

First reflected wave

Second reflected wave

Third reflected wave

Norm

al porcine skin

Burned porcine skin

Incident THz wave

First reflected wave

Second reflected wave

Third reflected wave

Z·

Z (depth)

X

Y1 (0.0 mm)

2 (0.53 mm)3 (0.90 mm)

(1cm)

1.5mm

0.0mm

(0 cm)

-3 0 3 6 9 12 15 18 21-4

-3

-2

-1

0

1

2

4.21 ps6.16 ps

1

32

Incident THz wave Stacked (Burnt + normal) pork

Nor

mal

ized

am

plitu

de (a

.u.)

Time delay (ps)

x y

Burn-depth detection of pork with T-ray technology (II)

Homeland Security

Towards THz Communication LinkAnalog THz wave

0 5 10 15 20 25 30 35 40 45 50 55-1.0

-0.5

0.0

0.5

1.0

Nor

mal

ized

am

plitu

de (a

.u.)

Time (sec)

0 5 10 15 20-100

-90-80-70-60-50-40-30-20-10

0

Mag

nitu

de (d

B)

Frequency (kHz)

0 5 10 15 20 25 30 35 40 45 50 55-1.0

-0.5

0.0

0.5

1.0

Nor

mal

ized

am

plitu

de (a

.u.)

Time (sec)

0 5 10 15 20-100

-90-80-70-60-50-40-30-20-10

0

Mag

nitu

de (d

B)

Frequency (kHz)

Original music time sequence and a portion of spectrum

Received music time sequence and a portion of spectrum

Opt. Exp.,Dec’05

The 1st directly modulated THz Link

~ 100 Cm

THz-TDS: Extraction of Far IR Optical Constants of Materials

∆ttime delay

sample

I(ω)

ω

I(ω)

ω

Power Spectrum

ϕ(ω)

ω

ω

ϕ(ω)

Phase

Imaginary index κ

Real index n+Spectral Absorption

time-domain waveforms

frequency-domain data

Transmission function

Numerical method, (L. Duvillaret et al. IEEE J. Sel Top quantum Electron. 2, 739 (1996) )

)()()(

ωωω

REF

SAMPLE

EET =

n, k

FFT

How to derive n and k from THz-TDS (I)

How to derive n and k from THz-TDS (II)

1: air2: fused silica3’:sample3: air4: fused silica5: air

31 5

E reference

2 4

E sample1 2 3’ 4 5

L

Terms considered:1. transmission and reflection coefficients at a-b interface;2. propagation coefficient in medium a;3. Fabry-Perot effect between layers 2 and 4;

a, b: 1-4

How to derive n and k from THz-TDS (III)

[ ] )( )(),()( )(),()(),()(),()()(

0k )(

322

334

45434323212

3

ωωωω

ωωωωωωωω

ω

ERLPR

TLPTLPTLPTE

FP

k

reference

•

•=

∑∞+

=4444 34444 21

[ ] )( )(),()( )(),()(),()(),()()(

0k)(

232

343

45443323212

'3

'''

'''

ωωωω

ωωωωωωωω

ω

ERLPR

TLPTLPTLPTE

FP

k

sample

•

•=

∑∞+

= 4444 34444 21

( )

)()~~(exp)~~()1~(~

)()(

'

'

''''

3232

223

3

3

3423

4323 ωω

ωω

ω

FPnncdi

nnnn

PP

TTTT

EE

T

air

reference

sample

×⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −−×

+

+==

= Transmission coefficient

The Complex refractive indices of 5CB

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.9

0.000.010.020.030.040.050.060.070.080.090.100.110.120.130.140.15

kn

Frequency (THz)

ne and ke at 25oC

no and ko at 25oC

n at 36oC

Sample cell:

Filled with 5CB (Merck)Homogeneous alignmentCell Gap: 250±2μmSubstrates: fused silica

(3.120 mm)

Reference cell:

d

dup

ddown

d = dup + ddown

Temperature Dependence results

-10 -8 -6 -4 -2 00.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Bire

fring

ence

∆n

T-Tc

0.500 THz

Measured Tc: 34.5℃Δn of 5CB: 0.15 ~0.2

-10 -8 -6 -4 -2 0 2 4 61.50

1.52

1.54

1.56

1.58

1.60

1.62

1.64

1.66

1.68

1.70

1.72

1.74

1.76

1.78

n

T-TC

0.500THzne

no

nave niso

32 eo

avennn +=

Comparison of THz and visible Data

24 26 28 30 32 34 36 38 40 421.40

1.45

1.50

1.55

1.60

1.65

1.70

1.75

1.80

1.85

1.90

1.95

Ref

ract

ive

inde

x

Temperature (oC)

ne 0.717 THz no 0.717 THz ne 632.8 nm no 632.8 nm

Optical Constant of E7 in the THz range

ne

no

ke

ko0.2 0.4 0.6 0.8 1.0 1.2

-0.2

-0.1

0.0

0.1

-0.2

-0.1

0.0

0.1

0.0

0.1

0.2

0.3

0.0

0.1

0.2

0.3

Imag

inar

y In

dex

Frequency (THz)

(a)

(c)

∆ n

1.2

1.5

1.8

2.1

1.2

1.5

1.8

2.1

(b)

Rea

l Ind

ex

Rotation axis

Polarization

LC cell

Propagation direction

THz wave

Magnet(~ 5000Gauss at cell position)

Magnetically controlled LC-based THz phase shifter

APL, Dec’03, Opt. Exp., June’04, selected by the Virtual Journal on Ultrafast Sciences, Taiwan patent’04, US patents filed

Sandwiched LC Cell Structure

• The fuse silica substrates have been coated DMOAP toobtain the homeotropic alignment.

• The thickness of substrates are about 1.57 mm.

Teflon Spacer(1.32 mm)

10 mm

Teflon Spacer(0.93 mm)

Teflon Spacer(3.00 mm)

Cell Ⅰ Cell Ⅱ Cell Ⅲ

How does the Phase Shifter work?

N

N

S

S

P

N

N

S

S

P

Δt

Theoretical Analysis

∫ ∆=L

eff dzzncf

0

),(2)( θπθδ

Phase shift, δ(θ), can be written as

where L is the thickness of LC layerΔneff is the change of effective birefringencef is the frequency of the THz waves

c is the speed of light in vacuum

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−⎥⎦

⎤⎢⎣

⎡+=

−

oeo

nnnc

fL21

2

2

2

2 )(sin)(cos2)( θθπθδ

We can assume that the LC molecules are reoriented parallel to the magnetic field direction, the phase shift can then be rewritten as:

Threshold magnetic field ≈ 100 GaussMagnetic field of magnet ≈ 5000Gauss

where L is the thickness of LC layerno is ordinary refractive index of LCne is the extra-ordinary refractive index of LCf is the frequency of the THz wavesc is the speed of light in vacuum

Transmitted Waveform through the E7 LC Phase Shifter

2 4 6 8

-0.6

0.0

0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0

1E-5

1E-4

1E-3

0.01

0.1

1

Am

plitu

de (a

.u.)

Frequency (THz)

Tran

smitt

ed T

Hz

Fiel

d (a

.u.)

Time Delay (ps)

0o

30o

50o

Phase Shift vs Magnetic Field Orientation

0 10 20 30 40 50 600

50

100

150

200

250

300

350

400

Phas

e Sh

ift (d

egre

es)

θ (degrees)

1.025 THz 0.49 THz theoretical

368o

524um

12mm

DMOAP

E7 (MERCK)

Electrically tunable LC THz phase shifter

Electrically tunable LC THz phase shifter

Fused silica substrate (0.858mm)Homeotropic alignment

E7(524um)

Copper spacer

THz wave

Polarization

z

y

x

IEEE MWCL, Feb.,2004

OL, April 15, 2006

Transmitted Waveform through the E7 LC Electrically-tuned Phase Shifter

10 20 30 40

-15

0

15

30

45

0v 15v 30v 35v 40v 125v

THz

Fiel

d am

plitu

de (a

.u.)

Delay time (ps)

14 15 16

-15

0

15

30

45

10 20 30 40

-15

0

15

30

45

0v 15v 30v 35v 40v 125v

THz

Fiel

d am

plitu

de (a

.u.)

Delay time (ps)

14 15 16

-15

0

15

30

45

Theoretical Analysis

oeo

eff nnnn −⎥

⎦

⎤⎢⎣

⎡+=∆

− 21

2

2

2

2 )(sin)(cos θθ

θθθ

θπ

θdq

VV

dz

m

th ∫ ⎟⎟⎠

⎞⎜⎜⎝

⎛

−+

=0

2/1

22

2

sinsinsin1

331 )( kkkq −=

voltkdlV

oath 9.26

21

3 =⎟⎟⎠

⎞⎜⎜⎝

⎛=

εεπde Gennes, Phys. Liq. Cryst., 1983

Kane, APL 20(1972)199, 22, 386 (1973).

θ

n( )dzzVn

cfV

d

eff∫ ∆= 0 ,2)( πδ

, V> Vth

Phase Shift vs applied Voltage

0 25 50 75 100 1250

15

30

45

60

75

90

Ph

ase

shift

(deg

ree)

Applied voltage (Vrms)

0.31THz 0.60THz 0.81THz 1.00THz

Device Response : Switch-off time

0 150 300 450 6000.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ized

tran

smitt

ance

(a.u

.)

Time (sec)

fall time

ms 165 0

2off ==acE εε

γτ

191 secoff

t

eII τ−

= 0

Phase Shift: E vs B tuned

0.2 0.4 0.6 0.8 1.00

20

40

60

80

100

Phas

e Sh

ift (D

egre

e)

Frequency (THz)

15v 30v 35v 40v 45v 125v

0.2 0.4 0.6 0.8 1.00

50

100

150

200

250

300

Phas

e Sh

ift (D

egre

e)Frequency (THz)

10o

20o

27.5o

30o

35o

40o

E-field tuned LC THz Phase Shifter B-field tuned LC THz Phase Shifter

Quarter wave plate/Compensator

0 15 30 45 60 75 90 105 120 135 150 165 180

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Nor

mal

ized

Pow

erRotating angle (degree)

Theoretical curve Experimental data

rotated axis is the propagation of THz beam

Lyot-type LC Tunable THz Filter

Principle of the Lyot Filter

)(

)cos()2

cos(

222

22

0

fcfdndn

fIIT

⋅∆⋅=⋅⋅∆⋅

=⋅∆⋅

=Γ

∆⋅⋅=Γ

=≡

τππ

λπ

τπ

Polarizer ∥ Analyzer

R: Retarder with retardation of Γ

P R A

I0 I

T is function of frequency (f) Filter

Sketch of LC THz wavelength selector

FR1 TR1 FR2 TR2

P

Liquid crystal cell

N S N S

Magnet

FR1 and FR2 are fixed retarder with 4.5-mm and 9-mm homogeneous LC cells

N S

Polarization

N S

LC cell

Propagation axis

Rotation axis

THz wave

MagnetLC cell

TR1 and TR2 are tunable retarder with 2-mm and 4-mm homeotropic LC cell

FR1 TR1 FR2 TR2

P

Unit A : Unit B = 1 : 2 (retardation)

0 .0 0 .2 0 .4 0 .6 0 .8 1 .0

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

T

F re q u e n c y (T H z )

T o ta l U n it A U n it B

Lyot-type LC THz filter: Results

2.6 2.5 2.4 2.3 2.2 2.1 2.0 1.9 1.8

5.2 5.0 4.8 4.6 4.4 4.2 4.0 3.8 3.6

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

∆t of TR2 (ps)

Cen

ter f

requ

ency

(TH

z)

∆t of TR1 (ps)

measured points theoretical curve

Tunable range : 0.388 ~ 0.564 THz (~ 40 % of fcenter) !

0.0 0.2 0.4 0.60.0

0.2

0.4

0.6

0.8

1.0

20 30 40

-0.9

0.0

0.9

Fiel

d (a

.u.)

Time Delay (ps)

T/T M

AX

Frequency (THz)

measured theoretical

Tunable THz Photonic Crystal Filter Using Nematic Liquid Crystal

THz wave

Polarization

N

Magnets

N

x

yz

Mylar

2D-MHA

NLC

θ

SS

THz wave

Polarization

N

Magnets

N

x

yz

x

yz

Mylar

2D-MHA

NLC Mylar

2D-MHA

NLC

θ

SSSS

The 2D-MPC sample was made from 0.5 mm-thick Al plateThe triangular lattice constant: s = 0.99 mm, The diameter of each hole: d = 0.56 mm.

d

diff

dm

dminspp n

cGkν

εεεε

πν ≈++=

20

rv

cutoff 1.841cd

νπ

=

The transmission spectrum of the 2D-MHA is characterized by three frequencies.

The band-pass peak frequency is above the cutoff frequency.The transmittance is several times larger than the porosity of

the holes.

d

diffsppR n

ννν ≅=

scdiff 3/2'=ν

Transmission of the 2D-MPC w/w.o. LC

0.1 0.2 0.3 0.4 0.50.0

0.2

0.4

0.6

0.8

1.0d=0.56 mms=0.99 mm

t=0.5 mm t=0.35 mm t=0.35 mm with Mylar e ray with LC o ray with LC

Tr

ansm

ittan

ce

Frequency (THz)

Frequency shifter and Peak Transmittance of the LC Tunable THz Photonic Crystal

0.56 0.58 0.60 0.62 0.640.10

0.11

0.12

0.13

0.14

0.15

0.16

theory experiment

Shift

of p

eak

freq

uenc

y (T

Hz)

1/neff

1.56 1.60 1.64 1.68 1.72 1.760.56

0.60

0.64

0.68

0.72

0.76

Peak

tran

smitt

ance

neff

Frequency Shift Peak Transmittance

• Optical constants of several LCs measured in the THz range. Birefringence of 5CB and E7 comparable to those in the visible. Attenuation negligible.

• Several LC-based THz devices demonstrated.

1. Room-temperature 2π magnetically tunable THz phase shifter

2. LC-based THz quarter-wave plate w/fine electrical tuning.

3. LC-type tunable Lyot-type THz filter.

4. LC-type tunable photonic crystal THz filter.

Summary

1. Tsong-Ru Tsai, Chao-Yuan Chen, Ci-Ling Pan, Ru-Pin Pan, and X.-C. Zhang, “THz Time-Domain Spectroscopy Studies of the Optical Constants of the Nematic Liquid Crystal 5CB”, Appl. Optics, Vol. 42, No. 13, pp 2372-2376 (May 1, 2003) .

2. Ru-Pin Pan, Tsong-Ru Tsai, Chao-Yuan Chen, and Ci-Ling Pan, “Optical Constants of Two Typical Liquid Crystals 5CB and PCH5 in the THz Frequency Range”, J. of Biological Physics, V. 29, No.2-3, pp.335-338, July, 2003.

3. Ru-Pin Pan, Tsong-Ru Tsai, Chiunghan Wang, Chao-Yuan Chen, And Ci-Ling Pan, “The Refractive Indices of Nematic Liquid Crystal 4, 4’-n-pentylcyanobiphenyl in the THz Frequency Range,” Mol. Cryst. Liq. Crystl., Vol. 409, pp. 137-144, 2004.

4. Tsong-Ru Tsai, Chao-Yuan Chen, Ci-Ling Pan, Ru-Pin Pan, and X.-C. Zhang, “Room Temperature Electrically Controlled Terahertz Phase Shifter,” IEEE Microwave and Wireless Components Lett., Vol. 14, No. 2, pp. 77-79, February 2004.

5. Chau-Yuan Chen, Tsong-Ru Tsai, Ci-Ling Pan, and Ru-Pin Pan“Terahertz Phase Shifter with Nematic Liquid Crystal in a Magnetic Field”, Appl. Phy. Letts, Vol.83, no.22, pp4497-4499, December 1, 2003.

6. Chao-Yuan Chen, Cho-Fan Hsieh, Yea-Feng Lin, Ru-Pin Pan, and Ci-Ling Pan, “Magnetically Tunable Room-Temperature 2π Liquid Crystal Terahertz Phase Shifter,” Opt. Express, Vol. 12, No. 12, pp. 2625-2630 June 14, 2004.

7. Ci-Ling Pan, Cho-Fan Hsieh, and Ru-Pin Pan, Masaki Tanaka, Fumiaki Miyamaru, Masahiko Tani, and Masanori Hangyo, “Control of enhanced THz transmission through metallic hole arrays using nematic liquid crystal,” Optics Express, Vol. 13, No. 11, pp. 3921 -3930, May 30, 2005.

References (LC THz Optics )