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: 10-12 to 10-10 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: 10-18 to 10-14 m2/V2 (for crystal) 10-22 to 10-19 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 2017/4/16 9

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 2017/4/16

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

Pockels readout optical modulator (PROM). 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) = 0 (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

Optically Addressed Spatial Light Modulators 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