光學應用講義Interacting Airy and nonlinear beams

1InteractingAiryandnonlinearbeams

Xi’anJiaotongUniversityandTAMUQ,DohaSOPO,Suzhou,August20142OutlineAcceleratinglightbeams?Quantum-mechanicalAirywave-packetsNonlinearAirybeamsinopticsInteractingacceleratingbeamsSummary3Yes,but…CourtesyofD.ChristodoulidesBut,canlightaccelerate?Yes,ofcourse!5Inquantummechanics:AirywavepacketM.V.BerryandN.L.Balazs,“Nonspreadingwavepackets,Am.J.Phys.47,264(1979)|Ψ|2xNon-spreadingAirywave-packett>0accelerationFree-particleSchr?dingerequationAirywave-packetsolutionCourtesyofAdyArie6FromQuantumMechanicstoOptics|Ψ|2xFreeparticleSchr?dingerequationBerryandBalzas,1979Infiniteenergywavepacket

NondiffractingFreelyaccelerating

BerryandBalzas,Am.J.Phys,47,264(1979)Siviloglou,Broky,Dogariu,&Christodoulides,Phys.Rev.Lett.

99,213901(2007).Scaledparaxialwaveequations|Φ|2SiviloglouandChristodulides,2007Finiteenergybeam

NearlynondiffractingFreelyaccelerating7Airybeam:Whatisacceleratingthere?Siviloglouetal.,PRL

99,213901(2007)BerryandBalazs,AmJPhys

47,264(1979)8Airybeam–amanifestationofcausticInraydescription,theraysaretangenttotheparaboliclinebutdonotcrossit.TheAirybeamisabeamwithcurvingpropagationtrajectoryKaganovskyandHeyman,Opt.Exp.18,8440(2010)Caustic:Anenvelope

of

lightraysreflectedorrefractedbyacurvedsurfaceorobjectortheprojection

ofthatenvelopeofraysonanothersurface.9CurvedcausticsineverydaylifeAirybeamspropagatinginNLmediaEquationInputbeamNotrunca-tion,a=0Truncateda=0.2

10CounterpropagatingAirybeamsLinearmedium:InterferenceofbeamsUpperrow:In-phaseLowerrow:Out-of-phase11CounterpropagatingAirybeamsKerrmedium:GenerationofsolitonsNoacceleration!Upperrow:In-phase(attraction)Lowerrow:Out-of-phase(repulsion)12CounterpropagatingAirybeamsKerrmedium:GenerationofsolitonsNoacceleration!Blacklines:Trajectoriesofthemainlobes13InteractingAirybeamandasolitonKerrmedium:NLinterferenceTop:In-phaseBottom:Out-of-phase14Summary15IntroducedinteractingAirywave-packetsandbeamsInlinearmedia:Superpositionandinterference;nosolitonsInNLoptics:NonlinearinterferenceandgenerationofsolitonsDepictedcount