Electro-Optics:

Yoonchan Jeong School of Electrical Engineering, Seoul National University

Tel: +82 (0)2 880 1623, Fax: +82 (0)2 873 9953 Email: yoonchan@snu.ac.kr

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