Lecture 11: Introduction to nonlinear optics I.

Transcription

1 Lectue : Itoducto to olea optcs I. Pet Kužel Fomulato of the olea optcs: olea polazato Classfcato of the olea pheomea Popagato of wea optc sgals stog quas-statc felds (descpto usg eomalzed lea paametes)! Lea electo-optc (Pocels) effect! Quadatc electo-optc (Ke) effect! Lea mageto-optc (Faada) effect! Quadatc mageto-optc (Cotto-Mouto) effect Popagato of stog optc sgals (pope olea effects) et lectue

2 Nolea optcs pemetal effects le Wavelegth tasfomato Iduced befgece stog felds Depedece of the efactve de o the feld test etc. lead to the cocept of the olea optcs The pcple of supeposto s o moe vald The spectal compoets of the electomagetc feld teact wth each othe though the olea teacto wth the matte

3 Nolea polazato Talo epaso of the polazato stog felds: P () (3) l χ χ χ l! P () t χ~ ( t t ) ( t )! χ () χ (3) l dt ( t t, t t ) ( t ) ( t ) dt dt ( t t, t t, t t ) ( t ) ( t ) ( t ) l dt dt P () ( ω) χ ( ω) ( ω) dω χ ( ω; ω, ω ) ( ω ) ( ω ) dω dω (3) %""" "" $ """"" # ωω ω ( ω; ω, ω, ω ) ( ω ) ( ω ) ( ω )! χl 3 l 3 %""""""" $ """"""" # ωω ω ω3

4 Lea electo-optc effect (Pocels effect) Stog low-fequec feld s (eomalzato of optcal costats due to secod-ode susceptblt) Popagato of a wea hgh-fequec optcal feld such a dstubed leazed medum () S S ( ) P χ χ New effectve pemttvt teso: () S L () S ( χ ) χ χ Wave equato (asotopc meda): ( ) ω µ

5 Pocels effect: cotued Descpto usg defomatos of the dcat We defe the ecpocal delectc teso: K ( ) Idcat the sstem of the pcpal delectc aes: z z Idcat a geeal sstem of aes: K Now the eteal stog electc feld s swtched o

6 Idcat electo-optcs Recpocal delectc teso s eomalzed due to eteal feld: Pocels electo-optc teso K K S Defomed dcat: K K K K33 z K K3 z K3 z Legth of pcpal aes s modfed Oetato of the ellpsod s modfed The Pocels teso ad the secod ode susceptblt teso ae elated b the followg equato: χ ()

7 Pocels teso Itsc smmet: elated to the fact that s a hemtc teso: Fo smmetc tesos Vogt otato ca be toduced: dces () 33 3 o 3 3 o 3 o cotacto (l) A 6 3 mat l s toduced, whee l 6 s a cotacted de, ad 3. l

8 Pocels effect: cubc meda I cubc o-cetosmmetc meda (GaAs, IP, GaP, CdTe, ZTe ): l Fo a appled electc feld (,, z ): z z z z

9 ample: //c 4 z Rotato b 45 the plae wll dagoalze the equato: ( ) ( ) ( ) ( ) ξ η ξ η η ξ Oe gets: z η ξ

10 ample: //c, cotued Tasvese geomet: ξ η z Logtudal geomet: () () () () Optcal beam () Optcal beam ()

11 ample: // (,,) z 4 z 4 z ) Rotato b 45 the plae (as pevousl); ew vaables ξ, η ξ η z 4 ηz ) Rotato b 45 the ηz plae; ew vaables η, z z η ξ Optcal beam () ()

12 lecto-optc modulato polaze It was show pevousl quate-wave plate π/4 π/ π/4, δ lecto-optc dephasg: I δ O modulato δ ( cos( δ δ) ) ( s δ) aalze Tasvese setup: δ π λ 3 4 L U d Logtudal setup: δ π λ 3 4 U

13 Quadatc electo-optc effect NL (3) 3χl S (3) l S l (Ke effect) Ke effect ca be of a geat mpotace the meda whee the Pocels effect vashes (cetosmmetc meda): S S S S S S ( ) P χ χ l l l The same teatmet ca be used as fo the lea Pocels effect; the followg dffeeces should be emphaszed: t s a 3 d ode olea effect (the electc feld should be ve stog) t s a quadatc effect, so the duced befgece s popotoal to ( S ) the effect depeds o a 4 th a teso, so the smmet popetes ae dffeet compag to the lea O effect

14 Mageto-optc effects (Faada, Cotto-Mouto) The polazato, ad cosequetl, the pemttvt ca deped o the magetc feld: P () (3) () χ χ χl l h B h (3) l B B l! Faada effect Cotto-Mouto effect () (3) ( B) h B h B B! l l Itsc smmet popetes the magetc feld (Osage theoem): ( B) ( B) ( B) ( B) Fom ths elato we fd codtos fo h ad h l

15 Faada effect ( B) h () B ( B) ( B) ( B) ( B) These codtos ae smla as fo the spatal dspeso ad the optcal actvt The teso h s puel maga atsmmetc fst two dces Smlal as fo the optcal actvt, we ca defe the effectve pemttvt teso: g g 3 g g 3 g g 3 3 zz

16 ffect of a logtudal feld Cubc o-cetosmmetc medum Wave equato: z B B gevalues (effectve efactve dces), B II I ± gevectos (Polazato decto), Cumulatve chaacte of the Faada effect

17 ffect of a tasvese feld Wave equato: z B B gevalues: 4 B II I Cotto-Mouto effect: ve small coecto to a lea befgece