# Chapter 6 ELECTRO-OPTICS

## Presentation on theme: "Chapter 6 ELECTRO-OPTICS"— Presentation transcript:

Chapter 6 ELECTRO-OPTICS
Fundamentals of Photonics 2017/4/16

(1) Electro-optic Effect
refractive index( anisotropic crystal ) change with electric field Phase or Polarization change with refractive index Electro-optic material Light Electric field Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Possible application controllable focal length. Optical scanning device U Phase modulator U polarizer analyzer Light intensity modulator U Polarization modulation Fundamentals of Photonics 2017/4/16

Pockels and Kerr Effects
The refractive index of an electro-optic medium is a function n(E) of the applied electric field E. Terms higher than the third can be neglected. Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Pockels Effect the third term is negligible n(E) r : Pockels coefficient or the linear electro-optic coefficient range: to m/V n Pockels medium or Pockels cell E (a) Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Kerr Effects the second term is negligible n(E) : Kerr coefficient or the quadratic electro-optic coefficient. n Range: to m2/V2 (for crystal) 10-22 to m2/V2 (for liquid) Kerr medium or a Kerr cell E (b) Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
(2) Electro-Optics of Anisotropic Media Crystal Optics k n2 n1 x y z nb na n3 The index ellipsoid Fundamentals of Photonics 2017/4/16 7

Fundamentals of Photonics
Pockels and Kerr Effects E = (El, E2, E3) {rijk} : linear electro-optic (Pockels) coefficients. E {ijkl} : quadratic electro-optic (Kerr) coefficients. Fundamentals of Photonics 2017/4/16 8

Fundamentals of Photonics
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Fundamentals of Photonics
index ellipsoid equation where ij(0) is a diagonal matrix with elements l/n12, l/n22, and l/n32 principal refractive indices n1(E), n2(E), and n3(E). Fundamentals of Photonics 2017/4/16 10

Fundamentals of Photonics
Trigonal 3m Crystals (LiNbO, LiTaO,…) E x y z Optic axis Uniaxial crystal n1= n2 = no, n3 = ne Assuming : E = (0,0, E), z x y no ne Fundamentals of Photonics 2017/4/16 11

Fundamentals of Photonics
Tetragonal 42m Crystal (e.g., KDP and ADP) E x y z Optic axis x1 x2 x’1 x’2 Fundamentals of Photonics 2017/4/16 12

Electra-Optic Modulators and Switches
Phase Modulators V L define V: half-wave voltage Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
V d V L V V Longitudinal modulator Traveling-wave transverse modulator Transverse modulator d=L several GHz Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
V Input light Modulated light Electrodes Cross scction E Waveguide integrated-optical phase modulator Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
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Fundamentals of Photonics
Dynamic Wave Retarders phase retardation Polarization light Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Intensity Modulators: Use of a Phase Modulator in an interferometer V Ii Io Branch 2 Branch 1 Vn A B C F(V) 0.5 1 Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Input light Ii V Modulated light I0 An integrated-optical intensity modulator (or optical switch). A Mach-Zehnder interferometer and an electro-optic phase modulator are implemented using optical waveguides fabricated from a material such as LiNbO3 Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Intensity Modulators: Use of a Retarder Between Crossed Polarizers Vn V B F(V) 0.5 1 t Polarizer s Ii Io if linear modulation Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Scanners +V - q D d L a scan resolution N Beam angular divergence: -V q D d L a Large V Fundamentals of Photonics 2017/4/16

Electro-optic polarization retator
Birefringent crystal position switch based on electro-optic phase retardation and double refraction. Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Directional Couplers Waveguide 1 PI(0) P1(0) P2(L0) Fibers Waveguide 2 V PI(0) L0 PI(z) d P2(z) P2(L) L0 z (a) power-transfer ratio Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
2017/4/16

Fundamentals of Photonics
=2n/0 : mismatch of the propagation constants F V0: switching voltage. C : coupling coefficient. Lo = /2C Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
V0: switching voltage. Lo = /2C C : coupling coefficient. F 1 Fundamentals of Photonics 2017/4/16

Electro-optic material Transparent electrodes Photoconductive material
Spatial Light Modulators x y Incident light Modulated light Transmittance T(x,y) + - Electro-optic material x y Write iamge IW(x,y) Incident light Modulated light Transparent electrodes Mirror Photoconductive material Electrically addressed spatial light modulator Photo-addressed spatial light modulator Fundamentals of Photonics 2017/4/16

BSO Transparent electrodes Dichroic reflector of red light White light (blue) Incident read light (red) Modulated light Polarizing beamsplitter Pockels readout optical modulator (PROM). Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Electro-optics of Liquid Crystal Electrical Properties of Nematic Liquid Crystals Anisotropic Uniaxial symmetry Optics axis rotate || (n||, ne ) E z  (n, no ) Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Liquid crystal cell x y z d x y z E q Phase modulator Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
(V-Vc)/Vo q Dependence of the tilt angle q on the normalized rms voltage Dependence of the normalized retardation T/Tmax=[n(q) – n0]/(ne-no) on the normalized rms voltage when n0=1.5, for the values of △n=ne-no indicated. Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Nematic Liquid-Crystal Retarders and Modulators Phase modulator Polarization modulator Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Liquid- crystal cell s y x Mirror Polarizer Incident light Reflected light Reflective light intensity modulator =/2 (off state) = (on state) Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Twisted Nematic Liquid-Crystal Modulators Linear polarization direction rotate with liquid crystal twist direction Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
x y Bright s Dark (a) (b) Polarizer Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Liquid- crystal cell s Mirror Polarizer Reflective twist nematic liquid crystal modulator, normally 45degree twisted Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Ferroelectric Liquid Crystals Faster response (us, nematic: ms) smectic-C phase q y x z Smectic layers 90° Surface stable Ferroelectric liquid crystal (SSFLC), only on-off state Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Liquid Crystals spatial light modulator Liquid-Crystal Displays passive devices relatively slow optical efficiency is limited because of polarization the angle of view is limited seven-bar-segment LCD Fundamentals of Photonics 2017/4/16

Transparent electrodes White light Incident read light (red) Modulated light Polarizing beamsplitter Light-locking layer Dielectric mirror Photoconductor Liquid crystal Hughes liquid-crystal light valve Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Photorefractive materials light free charge carriers space-charge distribution refractive index distribution Electric field (a) (b) (c) (d) Conduction band Valence band x Fe3+ Fe2+ LiNbO3 Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Simplified theory of photorefractivity rate of photoionization ND : the number density of donors ND+: the number density of ionized donors S : the photoionization cross section. electrons recombination rate n(x): electrons density , R is a constant In equilibrium, R(x) = G(x), Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Electric Field e : electron mobility K: Boltzmann’s constant T : temperature. Refractive Index Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
EXAMPLE Incident light If m is small Fundamentals of Photonics 2017/4/16

Recombination at traps Refractive index grating
Fixed-charge density E(x) △n(x) Free-carrier density I(x) + - Nonuniform light Photoionization Diffusion Recombination at traps Electric field Refractive index grating Response of a photorefractive material to a sinusoidal spatial light pattern Fundamentals of Photonics 2017/4/16

Fundamentals of Photonics
Applications of the Photorefractive Effect Wave 1 (reference) Wave 2 (object) Grating Two-wave mixing: dynamic holography Fundamentals of Photonics 2017/4/16