Lcur : Iroduco o olar opcs II r Kužl ropagao of srog opc sgals propr olar ffcs Scod ordr ffcs! Thr-wav mxg has machg codo! Scod harmoc grao! Sum frqucy grao! aramrc grao Thrd ordr ffcs! Four-wav mxg! Opcal Krr ffc
Nolar polarao ε d! ;, %""" "" $ """"" # ε! Irsc symmry: For symmrc sors Vog oao ca b roducd: dcs 33 3 or 3 3 or 3 or coraco l 3 4 5 6 A 3 6 marx l s roducd, whr l 6 s a coracd dx, ad 3 l 3 3 3 3 33 4 4 34 5 5 35 6 6 36
Thr-wav mxg Couplg bw wo opcal wavs ad : { } { } R R Th oal fld: c c Lar par of h polarao L : L ε Nolar par of h polarao NL : 4 NL
Nolar polarao for hr wav mxg NL 4 c c If w a o accou h dsprso, h suscpbly s wghd:, Th polarao NL, wh roducd o h Maxwll quaos, bcoms h sourc of h radao a frqucs,, I causs a rgy rasfr bw h fudamal ad h mxd spcral compos Thr wav mxg: wo al compos ad gv ras o a hrd o 3 A phas machg codo has o b fulflld : a mos o ffc rgy rasfr chal s gral possbl
Scod harmoc grao SHG Couplg bw ad ohr spcral compos ar omd: c c c c, NL c, NL c 4 Th wav quao h m doma h rads: µ ε µ NL Absorpo ca b a o accou ε; howvr, w glc hr Th wavs ar supposd o propaga alog ; hr ampluds do o dpd o x ad y
SHG: coud,, Th rgy rasfr bw h wo wavs s assumd o b vry small h scal of h wavlgh: d d d d > > d d d d >> Coupld wav quaos:,, d d c d d c NL NL µ µ
Coupld-wav quaos Th wav quaos whou couplg df h wav vcors ad : c c W fally oba:,, d d c d d c NL NL µ µ l l l l d d d d η η
Cosa fld approxmao Th fudamal wav s supposd o o b dpld: d Soluo: d η l l B A wh η A l l B drmd from h boudary codo:
SHG soluo L η L l l 3 L ff L η I η I s L L Characr of h soluo dpds crcally o h valu of Boh wavs do o propaga wh h sam phas vlocy: hy ar o cosaly phas, bu bcom prodcally ou-of-phas Ths lads o a modulao of I wh h prod calld cohrc lgh: π π l c λ Typcally:, l c µm Ths s h maxmum crysal lgh ha ca ffcly parcpa o SHG
has machg codo I η 3 ff I L All h crysal lgh parcpas ffcly o h grao How o achv h phas machg codo: Compsao of h brfrgc ad h dsprso OO- raco θ,, o, θ opcal axs o, o,, θ s θ o,, o, o,,
has machg codo: coud O- raco: opcal axs,, o, θ θ, o,, o, θ o,, Th choc of h polaraos dpds o h avalabl coffcs of g coupls oly paralll polaraos ad hus ca vr allow h phas machg,, θ,θ
Thr-wav mxg: summary Gral quaos of hr-wav mxg ± ± 3 ± ± 3 frqucy rasformao phas machg codo Sum ad dffrc frqucy grao SFD, DFD: Ipu: wo srog bams ad ± 3 Oupu: srog bam 3 ± 3 aramrc grao amplfcao of wa bams: Ipu: srog 3 wa Oupu: mdum mdum Up-covrso 3 3 Ipu: srog wa Oupu: wa 3 3 3
Four-wav mxg Thrd ordr ffc: 4 3 3 NL l l Rqurd codos for h wavlgh rasformao: 4 3 4 3 or 4 Dgrad cass ar frquly usd Tras grag xprms 3 4 3 c
ropagao Krr-l mda Dgrad cas o vry srog opcal bam: NL 3 3 Idcs ar omd h bam s larly polard ad s a gmod of h mdum Th bam propagad alog :, A Wav quao: da 3 c A 3µ A A d Lar wav quao: dfo of Nolar polarao
ropagao Krr mda: coud A A d da 3 3 ε µ Rmag rms h wav quao f 3 s ral h A A A A 3 3 xp η A, Th wav vcor s rormald: ε 3 3 A c K ε η 3 3 I Th ffcv rfracv dx dpds o h sy of h bam:
ropagao Krr mda Slf-phas modulao ulrashor pulss rfracv dx s m dpd phas of h puls s modulao crao of w frqucy compos badwdh broadg puls shorg Slf-focusao s bams Krr lsg du o spaal profl of h bam