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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 )