Chapter 9 Electro-Optics Gabriel Popescu University of Illinois at Urbana Champaign Beckman Institute Quantitative Light Imaging Laboratory http://light.ece.uiuc.edu Principles of Optical Imaging Electrical and Computer Engineering, UIUC
Electro Optics 1 st order effect: w 1 Pi ii jjrijkej ( ) Ek () i i i i j ijk j k ( ) 4 Dx n n r13ey EDc n ner133ez EDC 6 5 4 Dy n n r13e xedc 4 r kdp 53 Dz ne Ez D n E n n r E E DC DC 11O z Chapter 9: Electro Optics
Electro Optics 4 n n r63e Dc 4 ij n r63edc n ne ' ij W( ) W( ) cos sin n cos sin sin cos n sin cos n ij n ; 4 n e b i 4 n r63 Ez ( DC) biaxial crystal Chapter 9: Electro Optics 3
Modulators Eg KDP(tetra 4m ) r 41, r 5, r 63 only three nonzero elements n KDP 41 5 63 x n ; 1 1 n n n n n n n n x y n 1 n n 1 r 1 1 3 n n r63ez ( DC) Chapter 9: Electro Optics 4
Modulators ( n n ') d n r E ( DC ) d 3 x y 63 z n V V n r 3 63 linearize T V T sin 4 sin s Add QW V Chapter 9: Electro Optics 5
Modulators Let V V sin t m m T sin sin m m t 4 1 1 1 cos sin 1 sin sin m m t m m t 1 1T 1 sin t m m m m linear Chapter 9: Electro Optics 6
Quadratic (Kerr) ( ) 1 i ii jj ijk j k e P s E ( ) E ( DC ) E ( DC ) Chapter 9: Electro Optics 7
Applications of EO longitudinal modulators transverse For LiNiO 3 : 1 3 nx n n r 13 E 1 3 ny n n r13e 1 3 nz ne ne r33e 3 v nl n rv 13 V 3 v n r Ed 13 Phase mod(indep. of polariz.) Chapter 9: Electro Optics 8
Chapter 9 Acousto-optics Gabriel Popescu University of Illinois at Urbana Champaign Beckman Institute Quantitative Light Imaging Laboratory http://light.ece.uiuc.edu Principles of Optical Imaging Electrical and Computer Engineering, UIUC
Acousto optics optics i j i ijklsklej jkl x 1 6 ac wave: z S13 S5 13 5 3 4 P n n p S E U ( z, t) xa cos( t kz) Chapter 9: Acousto optics 1
Chapter 1: Introduction 11
Acousto optics optics K k K k 1 k k1 nk sin k / K / K sin B ; Bragg angle
Acousto optics optics small ( k k ) Doppler Shift Δk Δv Kvs Quantum mechanics k' k ' conservation of momentum conservation of energy Chapter 9: Acousto optics 13
Anisotropic media k' k k ' n-different ' - negative k'sin ' ksin ; ' n' n sin ' sin ; n sin ' sin n' n' k wavelength of sound Chapter 9: Acousto optics 14
Anisotropic Ex: C k ' k -(e) k ' - scattered in prop. Plane (o) k ' (o) n sin ' e sin n' n ' n n e ', n n e e n n n n Chapter 9: Acousto optics 15 e
Small angle Scattering I scatt I inc sin ( L L ) 3/ k ( nn 1 ) ep ijke S e 4 cos cos 1 i ke j Kin. Energy/ V = ½ W total I ac v s 1 v U U 1 1 3 s vs u vs [ U ] I ac t 1 3 vs S U S z U Chapter 9: Acousto optics 16
Small angle Scattering S 3/ ac 3 Small cos 1 1 s I I ac k ( nn 1 ) I P 3 v 4 cos cos v s M 6 n p v p 3 s table 3/ 3 k ( nn 1 ) v s M I ac 6 3 4 n vs MI ac Chapter 9: Acousto optics 17
Small angle Scattering Detuning: sin B k sin sin 1 ; B k k sin k sin 1 1 ( Bragg) k sin ( ) k 1 cos 1 1 k cos 1 ( ) k(cos 1cos ) k sin B I scat sin L 1 ; I inc 1 s 1 Chapter 9: Acousto optics 18
Finite Beams A B nw ; L ; f f size of acoustic beam 1 ; L nv cos 4v cos s s s -Full v nw w s 1 ; W or nvs cos ( ) f L! Not overlap with undiffracted order 1 Chapter 9: Acousto optics 19
N N spots f nw W f N nv s cos v s B f ; cond B nv s f f n L nv s f L Chapter 9: Acousto optics