mit非线性光学讲义iiinew

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1、NonlinearOptics§BandwidthandPulsePropagationEffectTypeIphasematchingforSHG(Assumeno>ne)nnone(q)nell'/2l/2l'lPhasematchingangleq90Þqll'lAngularToleranceofPhaseMatching(forSHG)Dk=k2-k1-k1,w2=2w1ForGaussianbeamdq®kdkduetodq:¶dk=Dk+Dkdqqq¶q70NonlinearOpticsAssumeqatphas

2、ematchingangle,Dk=0.q¶dk@{k2-k1-k1}qdq¶q¶ì2p2p2pü@ín(w)-n(w)-n(w)ýdq.211¶qîïl2l1l1þïqConsiderTypeIphasematching,4p춶üdk@íne(q,w2)-no(w1)ýdq.l1î¶q¶qþqWith-1/2éæö2æö2ùêççsinq÷÷ççcosq÷÷úne(q,w2)=+.êëène(w2)øèno(w2)øúûno(w1)hasnoqdependence.¶n(q,w)e2¶q.13é11ù=ne(q,w2)ê

3、2-2úsin2q2êëno(w2)ne(w2)úûRecallthatatphasematching,ne(q,w2)=no(w1).Weget2p3é11ùdk@no(w1)ê2-2úsin2qdq.l1êëno(w2)ne(w2)úûWhendk(dq)important?71NonlinearOpticséDklù2êsinú1.0ê2úêDklúæöêë2úûdkl1sincç÷=è2ø2-2p-p0p2pdklpdkl@2.82or@.22pdk@léù-1l111dq@ê-ú.3ê22ú2l×no(w1)sin2

4、qëno(w2)ne(w2)ûAcceptanceangleAcceptanceangle=2dqéù-1l111@ê-ú3ê22úl×no(w1)sin2qëno(w2)ne(w2)ûAssumesmallbirefringence,no(w2)@ne(w2)@no(w1).Acceptanceanglel@1l×n3(w)sin2qo1n2(w)n2(w)×o2e2[n(w)+n(w)][n(w)-n(w)]o2e2o2e2l1@2lsin2q[n(w)-n(w)]o2e272NonlinearOpticsPhaseMat

5、chingBandwidthForshortpulses(highintensity,strongnonlinearity)tpdw@1/tptwwoDk=k2-k1-k1¶dk=Dk+Dkdll1¶ll1Assumephasematchingatl,Dk=0.1l1ForTypeIphasematching,¶dk@{k2-2k1}ldl1¶l11¶ì2p2pü@ín(w2,q)-2n(w1)ýdl1¶l1îïl2l1þïl1ì¶n(w2,q)¶n(w1)ü@4pí-ýdl1îï¶l1l1¶l1l1þïl1ìn(w2,q)n

6、(w1)ü@4pí-2+2ýdl1îïl1l1þïl14pì1¶¶ü+ín(w2,q)-n(w1)ýdl1l1îï2¶l1/2¶l1þïl14pì1¶¶ü@ín(w2,q)l-n(w1)lýdl1l1î2¶l2¶l1þ73NonlinearOpticsdklpPhasematchingbandwidth@´222ìü-1l1ï1¶n¶nïdl@í-ý2lîï2¶ll2¶ll1þïNote:dlÝ,lßMaximumlengthfordlis:ìü-1l1ï1¶n¶nïl=í-ý(*)2dlîï2¶ll2¶ll1þïAltern

7、ativeapproachPulsepropagatewithgroupvelocityvg,vg(w1)¹vg(w2).Where-1dwcìldnüvg==í1-ý.dknîndlþ1Askthelengthlforpulsetoreduceoverlapbytp:21ttpp2E(w1)E(w1)E(w2)E(w2)lìüï11ï1lí-ý@tp.ïvgvgï2îw1w2þ74NonlinearOpticsìü-11ï11ïl@tpí-ý2ïvgvgïîw1w2þìü-11cï1dndnï@tpí-ý.2l1îï2dlw

8、2dlw1þïIfwelet1l2t==,pdfcdlwegetequation(*)inpage71.TimeDependentWavePropagationFors=0,weget¶2®¶2®2NL(Ñ-mo2e)E=mo2P(1)¶t¶tWithEnvelopeappr