Linear electro-optic effect:

EE6.4686.568 Elcto-optcs Elcto-optc optc ffct: D ρ, B E, t B, D H j, t D ε E P εe K ffct 3 P ε χ E χ E χ E 3..., La lcto-optc ffct: ε ε χ χ E ε E jk, j j jk k k Pockls ffct Wh o E appld, ε ε ε ε x ε 33 y Rfactv dcs o pcpl axs

EE6.4686.568 Elcto-optcs Rfactv dx llpsod: p D D D E U v v v v ε Wh o lctc fld appld,, 33 y x y x y x D D D D U ε ε ε ε, y x y x Rfactv dx llpsod x y x

EE6.4686.568 Elcto-optcs Rfactv dx llpsod: U v v E D v D v D ε Gally, ηj x x j, η s a 3x3 tso, η ε - o ε η -, j Wh lctc fld appld, η j η E jk k, jk : 3x3x3 tso, 7 compots jk jk, Why? y x x y No EO ffct fo cystal wth ctal symmty, why? y y x - j E j E x,

EE6.4686.568 Elcto-optcs v ε ε ε E,, jk k jk jk j 3 3 6 5 E 3 3 33 η η E 6 4 4 4 43 E3 5 5 53 6 6 63 3 5 4 3 3

EE6.4686.568 Elcto-optcs Wh E oly, η η 3 3 E 3 3 33 4 4 43 3 5 5 53 6 6 63

EE6.4686.568 Elcto-optcs Tak LNbO 3 as a xampl : Tak LNbO 3 as a xampl : 3 3 3 33 3 5 33 3 E E η η η 5, 33 3 3 E y E x E, 33 E 3 E, 3 3 E, ' 3 E, 33 3 E, 33 3 E

EE6.4686.568 Elcto-optcs Tak LNbO 3 as a xampl: Zcut E 3 33 TM polaato 3 3E TE polaato,,

EE6.4686.568 Elcto-optcs o 3 33E, 3 33E, 3 o 3E, 3 3E, Dfft dx chags of TE ad TM wavs

EE6.4686.568 Elcto-optcs Tak LNbO 3 Itsty modulato Zcut TM polaato L L out,,, out L L, I out out L I cos I 4 L, I out π π 3 V I cos L I cos γ 33 L, λ λ d π V 3 γ π 33 L λ d π, V π λd 3 γ 33 L

EE6.4686.568 Elcto-optcs Tak LNbO 3 Itsty modulato Zcut TM polaato I out π π 3 V I cos L I cos γ 33 L, λ λ d La go Fqucy doubl go

EE6.4686.568 Elcto-optcs Opatg chaactstcs Modulato dpth η I max I I max m, η %, I m Badwdth: th hghst fqucy th modulato ca opat, R ad C Isto loss db: Iout IL db log I I,

EE6.4686.568 Elcto-optcs Pow cosumpto: Pf, f: badwdth P fw f εe ω dv, fo a chal wavgud, assumg th E fld s ufom, C Wd L ε ε d d C ~.4pF W εe ω dv LdW d εe ω, Tak LNbO 3 as a xampl: E Vπ d dwd λ W ε ω ε, 3 E dv Pf ~ µwmh L γ 33 λ γ 3 33 L

EE6.4686.568 Elcto-optcs Pow cosumpto: Pf, f: badwdth P fw f εe ω dv, fo a bulk EO modulatos, assumg th E fld s ufom, 3 33E, C Wd L ε ε d d C ~ 3pF W εe ω dv LdW d εe ω, Tak LNbO 3 as a xampl: E Vπ d λ γ 3 33 L W dwd λ ε ω ε, 3 E dv Pf ~ WMH L γ 33

EE6.4686.568 Elcto-optcs Phas modulato: E 3 33, Phas shft du to th appld voltag: 3 π d ϕ 33E L, V E, 3 λ λ π L Exampls: 33

EE6.4686.568 Elcto-optcs - E 3 3, 3 33E,

EE6.4686.568 Elcto-optcs Polaato modulato: 3 3 33 η η 5 5 E x y E 3 y E 3 y,, x y V π d E L λ 3 33, Phas shft du to th appld voltag:

EE6.4686.568 Elcto-optcs Polaato modulato: x W θ y π, sθ, y, cosθ, x y x E 3 y, 3 y E y, 3 π out sθ xp xl sθ xp L E 3 y out cosθ xp yl cosθ xp L E, y, y,, Phas dffc du to th appld voltag: 3 3 φ LE y LV y W,

EE6.4686.568 Elcto-optcs Polaato modulato: W x Phas dffc du to th appld voltag: y 3 3 φ LE y LV y W, x x θ Wh φ π, θ y y x θ Wh φ π, θ x θ y y

EE6.4686.568 Elcto-optcs TE-TM TM covt: 3 V, d hft dg Phas S 4 8 5 9 6 3 L mm L 5mm 3 4 Bas V

EE6.4686.568 Elcto-optcs Quatum Ky Dstbuto b QKD Btt ad Bassad 984 potocol Poc. IEEE It. Cof. Computs, Systms ad Sgal Pocssg, 984, pp. 75 79. Sgl photo JUSTIN MULLINS, IEEE SPECTRUM, p. 4, May

EE6.4686.568 Elcto-optcs Quatum Ky Dstbuto QKD Btt ad Bassad 984 potocol Poc. IEEE It. Cof. Computs, Systms ad Sgal Pocssg, 984, pp. 75 79. JUSTIN MULLINS, IEEE SPECTRUM, p. 4, May

EE6.4686.568 Elcto-optcs Quatum Ky Dstbuto b QKD W. T. Buttl, tal. Physcal Rvw, Vol 57, 998, pp. 379-38

EE6.4686.568 Elcto-optcs Itgatd QKD Rcv Rcv: Bob QKD Lks Tasmtt: lc QKD Lks Iput photo polaato stats Dtcto polaato bass Fal polaato stats S sgl photo dtcto sgal TE La TE TE Ccula TE & TM x TM La TM TM Ccula TE & TM x Ccula lft- La TE & TM x had Ccula lfthad Ccula TE Ccula ght- had La TE & TM x Ccula ghthad Ccula TM Rcv: Bob

EE6.4686.568 Elcto-optcs 3 V d, Phas Sh hft dg 4 8 5 9 6 3 L mm L 5mm 3 4 Bas V

EE6.4686.568 Elcto-optcs Iput photo polaato stats ppld voltag Dtcto polaato bass Fal polaato stats dtctd sgal TE La TE TE V Ccula Ccula x TM La TM TM V Ccula Ccula x Ccula lft-had La Ccula x Ccula lft-had V Ccula TE Ccula ght-had La Ccula x Ccula ght-had V Ccula TM

EE6.4686.568 Elcto-optcs EO Polym polg Polg of polym matals, cotact polg ad cooa polg:

EE6.4686.568 Elcto-optcs Ndl Elctod V V Polg Elctod EO polym Buff Lay HatgCoolg block Flm Buff Lay HatgCoolg block dvatags: Low voltag ~ 8V Good flm qualty Ufom polg voltag Easy cotol of polg voltag Slct polg aa

EE6.4686.568 Elcto-optcs I-V cuv dug polg: Polg voltag : 9V EO coffct ~ pmv

EE6.4686.568 Elcto-optcs TM-pass wavgud Pola Bfo polg TE.594.59 TM.594.598 ft polg TM put TE put

EE6.4686.568 Elcto-optcs Dctoal coupl: Dctoal coupl: 3 Fo, U-coctd pot 4 d d d d d d d d d d d d d d d d d d

EE6.4686.568 Elcto-optcs Dctoal coupl: 3 Fo, U-coctd pot 4 d d d d cos B s d d d d C cos D s

EE6.4686.568 Elcto-optcs 3 U-coctd pot 4 s cos B Fo, s cos D C s D Fo, s cos D D d d s cos B 4 D 4 B

EE6.4686.568 Elcto-optcs Dctoal coupl: U-coctd pot 3 4 Fo, cos s s P P s L π π 3 33E, λ λ

EE6.4686.568 Elcto-optcs s cos B Fo ½ s cos D C Fo ½, s cos B s cos D

EE6.4686.568 Elcto-optcs s cos B cos s B d s cos cos s B B d s cos D d d B B

EE6.4686.568 Elcto-optcs s cos cos s B B d d s cos B s cos D d d d s cos B s cos B s cos D D B

EE6.4686.568 Elcto-optcs s cos B s cos B s cos D D B

EE6.4686.568 Elcto-optcs Wh, cos s cos s cos B s cos D s B D

EE6.4686.568 Elcto-optcs Wh, s cos P P s cos P P

EE6.4686.568 Elcto-optcs Tavlg-wav lctods: U-coctd pot 3 Fo hgh-spd lctod usg tasmsso ls: 4 Fo, cos s B Vgt V Z VL ZL Γ - V - ZL Z V ZL Z -l l

EE6.4686.568 Elcto-optcs Stadg wavs fo mpdac msmatchg: Vgt B - V ZL - Z Z VL Γ V ZL V ZL Z - l l -λ -3λ4 -λ -λ4 V V Stadg wavs Caclld E 3 33,

EE6.4686.568 Elcto-optcs Tavlg wavs fo mpdac matchg: Vgt B - V ZL - Z Z VL Γ V ZL V ZL Z - l l V V tavlg wavs E 3 33, -λ -3λ4 -λ -λ4

EE6.4686.568 Elcto-optcs K ffct :

EE6.4686.568 Elcto-optcs pplcatos of K ffct : λke I I, Slf-phas modulato Slf-Focusg

EE6.4686.568 Elcto-optcs coustc-optc optc Modulatos Bagg codto: π s θ π, λ Λ x I s cos Ωt π Λ x,, R I s,

EE6.4686.568 Elcto-optcs Doppl shft gl msmatch

EE6.4686.568 Elcto-optcs coustc optcs dvcs Modulato Badwdth: s θ θ f, Bam Sca λ λ λ λ δθ B, Λ D v s v s Numb of solvabl spots:

EE6.4686.568 Elcto-optcs coustc optcs dvcs F spac t-cocto Isolato

EE6.4686.568 Elcto-optcs Lght popagato asotopc cystals Optcal axss o lght o

EE6.4686.568 Elcto-optcs Lght popagato asotopc cystals Optcal axs o lght o

EE6.4686.568 Elcto-optcs Lght popagato asotopc cystals Optcal axs Polaato bam spltt o

EE6.4686.568 Elcto-optcs Lght popagato asotopc cystals

EE6.4686.568 Elcto-optcs Lght popagato asotopc cystals > o

EE6.4686.568 Elcto-optcs Faaday otato

EE6.4686.568 Elcto-optcs Fb optcs dvcs Coupl FCPC FCPC SCPC SCPC

EE6.4686.568 Elcto-optcs Cculato