Electro-Optics:
Yoonchan Jeong School of Electrical Engineering, Seoul National University
Tel: +82 (0)2 880 1623, Fax: +82 (0)2 873 9953 Email: [email protected]
Electro-Optics (2)
Quadratic Electro-Optic Effect Permutation symmetries:
2
)21()12(6),31()13(5),32()23(4),33(3),22(2),11(1
=========→
Index ellipsoid:
++++++→ yxxzzyzyx
x
EEsEEsEEsEsEsEsn
x 1615142
132
122
1122 2221
jiklijkl ss =→
ijlkijkl ss =→
+++++++ yxxzzyzyx
y
EEsEEsEEsEsEsEsn
y 2625242
232
222
2122 2221
+++++++ yxxzzyzyx
z
EEsEEsEEsEsEsEsn
z 3635342
332
322
3122 2221
( )yxxzzyzyx EEsEEsEEsEsEsEsyz 464544243242241 2222 ++++++( )yxxzzyzyx EEsEEsEEsEsEsEszx 565554253252251 2222 ++++++( )2 2 261 62 63 64 65 662 2 2 2 1x y z y z z x x yxy s E s E s E s E E s E E s E E+ + + + + + =
=→
666564532261
565554532251
464544432241
363534332231
262524232221
161514131211
ssssssssssssssssssssssssssssssssssss
sij
lkijklkijkijij EEsEr ++=→ )0()( ηη E
Electro-Optic Light Modulators Longitudinal electro-optic modulation:
3
Transverse electro-optic modulation:
A. Yariv and P. Yeh, Optical Waves in Crystals, John Wiley & Sons, 1984.
A. Yariv and P. Yeh, Optical Waves in Crystals, John Wiley & Sons, 1984.
→ Large acceptance area with a thin EO crystal plate
→ Long interaction length at a given field strength
4
Electro-Optic Fabry-Perot Modulators Electro-optic amplitude modulator:
Charles Fabry (1867-1945 )
Alfred Perot (1863-1925)
A. Yariv and P. Yeh, Optical Waves in Crystals, John Wiley & Sons, 1984.
Transmission as a function of applied voltage: A. Yariv and P. Yeh, Optical Waves in Crystals, John Wiley & Sons, 1984.
A. Yariv and P. Yeh, Optical Waves in Crystals, John Wiley & Sons, 1984.
→ Gires-Tournois eltalon “Phase modulation only”
Electro-Optic Beam Deflectors Double-prism KDP beam deflectors:
A. Yariv and P. Yeh, Optical Waves in Crystals, John Wiley & Sons, 1984.
5
Electro-Optic Property of Liquid Crystal Liquid crystals:
Liquid crystal phases: smectic, nematic, and cholesteric Nematic LC: uniaxial dipole moment → Dynamic director alignment along the applied electric field → Switching time: ~msec
Twisted nematic LC in liquid crystal displays (LCDs):
VLC = 0V (off) VLC = 5V (on)
Applicable to fiber-optic devices?
6
LC-Filled Hollow Optical Fiber (1) Director alignment of nematic LC:
Highly dependent on the liquid crystals-capillary interface interaction Silica: longitudinal direction borosilicate capillaries: radial direction
Voltage off: Voltage on:
+
−
Off
V
+
−
On
V
7
LC-Filled Hollow Optical Fiber (2)
Periodical modulation of director alignment
+
−
On
V
Director Alignment
z
Comb electrode:
Electrically controllable director alignment:
→ Controllable long-period gratings
8
Properties of MLC-6295: Smectic/Nematic turning point: −30 oC, clearing point +101 oC no: 1.4772, ne: 1.5472 @20 oC, 589 nm
Director check:
LC-Filled Hollow Optical Fiber (3) Fiber image: Far-field image:
Director alignment check: Visibility detection under a microscope between crossed polarizers Uniform director alignment to the direction of the fiber axis
9
−⋅
⋅
−=
θθθθ
θθθθεθε
cossin0sincos0
001
000000
cossin0sincos0001
)(2
2
2
e
o
o
oxyz
nn
n
−⋅⋅
−=
1000cossin0sincos
)(1000cossin0sincos
),( φφφφ
θεφφφφ
εφθε φ xyzozr
)0,0(),(),( zrzrzr φφφ εφθεφθε −=∆
x
y
z
φ
θ
Mode couplings: Long-period regime: a fundamental core mode (HE11) ↔ cladding modes Cladding modes to be coupled:
),( φθε φzr∆←clmclm
clm
clm
clm HEHEHETETM 32100 ,,,,
Anisotropic Mode Couplings in the LC Core Permittivity tensor dependent on the director alignment:
Permittivity perturbation:
10
Broadband source
Spectrum analyzer
Coupling unit
LC-filled hollow fiber
V
Experimental setup: Broadband source: EDFA ASE Comb electrode: Period of 483 µm, length of 15.5 mm Applied voltage: 0 ~ 250 V
Experimental Arrangement
11
0 V
250 V 200 V
150 V
Long-Period LC Fiber Grating (1) Spectral responses with respect to applied voltages:
12
Experiments:
1500 1520 1540 1560 1580 1600
250200
150100
50
20
-2
-4
-6
-8
Wavelength [nm]Ap
plied V
oltage
[V]
(inverted)Transm
ission [dB]
Wavelength [nm]1500 1520 1540 1560 1580 1600
250200
150100
50
20
-2
-4
-6
-8
Wavelength [nm]Ap
plied V
oltage
[V]
(inverted)Transm
ission [dB]
Wavelength [nm]
1500 1520 1540 1560 1580 1600
54
32
1
20
-2
-4
-6
-8
Wavelength [nm]
Angle
θ [de
g]
(inverted)Transm
ission [dB]
Wavelength [nm]1500 1520 1540 1560 1580 1600
54
32
1
20
-2
-4
-6
-8
Wavelength [nm]
Angle
θ [de
g]
(inverted)Transm
ission [dB]
Wavelength [nm]
Simulations:
Simulations: Based on the coupled-mode theory in anisotropic media Resonant couplings to the 3rd and 4th TM cladding modes
Long-Period LC Fiber Grating (2) Normalized spectral responses:
13
...),2,1(,)()( *** =′∆+∆⋅−=′×+×′⋅∇ pEEiHEHE NLLppp εεω
≠=
=⋅=∆ ∑ ).(2),(1
,ˆ),(),,(43
),(22
),()3(
)( sqsq
eztEzr sqs
sssqoqNL ααφχεε
g
effeffs
nIn
∆≈
∆→ ,2
λλ
Tran
smis
sion
Wavelength
NonlinearShift
SpectralBandwidth
Tran
smis
sion
Wavelength
NonlinearShift
SpectralBandwidth
Nonlinear Response of Fiber Gratings (1) Coupled-mode theory with nonlinear perturbation:
Nonlinear spectral shift:
14
1564.50 1564.75 1565.00 1565.25 1565.50-25
-20
-15
-10
-5
0
Wavelength [nm]
Tran
smiss
ion
[dB]
λs (Case I)
λs (Case II)
Nonlinear Shift
Wavelength [nm]
Nd:YAG Laser
Tunable LD
LPFG I LPFG II
Oscilloscope PD 1
PD 2
Collimator
Prism λp λs
PC
PD 3
3 dB Coupler λp
λs
Experimental setup: Signal wave: Tunable LD @1565.2 nm (Case I), @1564.8 nm (Case II) Pump wave: Q-switched Nd:YAG laser (1 kHz)
Initial transmission spectra:
Nonlinear Response of Fiber Gratings (2)
15
0.0 0.2 0.4 0.6 0.8 1.0
0.50
0.55
0.60
0.65
0.70
0.75
Pump Intensity [GW/cm2]
Sign
al T
rans
mitt
ivity
(Cas
e I)
0.00
0.05
0.10
0.15
0.20
(Theoretical) Case I Case II
Case I Case II
Signal Transmittivity (Case II)
Pump Intensity [GW/cm2]
Pump:
→ ∆λs ~ 0.12 nm/(GW/cm2)
Nonlinear Response of Fiber Gratings (3) Signal (Case I):
Sign
al O
utp
ut [a
. u.]
0 1 2 3 4 5
0.55
0.60
0.65
0.70
0.75
a2
a1
a1 0.30 GW/cm2
a2 0.93 GW/cm2
Time [µsec]
Pum
p In
put
[a. u
.]
0 1 2 3 4 5
0.00
0.25
0.50
0.75
1.00
Time [µsec]
Sign
al O
utp
ut [a
. u.]
0 1 2 3 4 5
0.00
0.05
0.10
0.15
0.20b2
b1
b1 0.42 GW/cm2
b2 0.98 GW/cm2
Signal (Case II):
Time [µsec]
16
Electro-Optics:Quadratic Electro-Optic EffectElectro-Optic Light ModulatorsSlide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16
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