超快光学-第09章-非线性三阶效应ppt课件.ppt

中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Third-order nonlinearities:Four-wave mixingThird-harmonic generationInduced gratingsPhase conjugationNonlinear refractive indexSelf-focusingSelf-phase modulationContinuum generation中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Third-harmonic generation3wwTHG MediumWe must now cube the input field:Third-harmonic generation is weaker than second-harmonic and sum-frequency generation,so the third harmonic is usually generated using SHG followed by SFG,rather than by direct THG.中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Noncollinear third-harmonic generationWe can also allow two different input beams,whose frequencies can be different.So in addition to generating the third harmonic of each input beam,the medium will generate interesting sum frequencies.THGmediumSignal#1Signal#2w ww www中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Third-order difference-frequency generation:Self-diffractionConsider some of the difference-frequency terms:NonlinearmediumSignal#1Signal#2www ww w中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识SamplemediumSignalwwwThe excite-probe geometryOne field can contribute two factors,one E and the other E*.This will involve both adding and subtracting the frequency and its k-vector.This effect is automatically phase-matched!The excite-probe beam geometry has many applications,especially to ultrafast spectroscopy.The signal beam can be difficult to separate from the input beam,E1,however.中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识NonlinearmediumWave plateyielding 45polarizationSignalwwwPolarization gatingHere field#2 contributes two factors,one E and the other E*.But one is vertically polarized,while the other is horizontally polarized.This yields a signal beam thats orthogonally polarized to the input beam E1.If E1 is horizontally polarized,the signal will be vertically polarized:This arrangement is also automatically phase-matched.Its also referred to as polarization spectroscopy due to its many uses in both ultrafast and frequency-domain spectroscopy.The input beam in the signal beam direction is rejected by polarizer!中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识xThe irradiance of two crossed beams is sinusoidal,inducing a sinusoidal absorption or refractive index in the mediuma diffraction grating!An induced grating results from the cross term in the irradiance:Many nonlinear-optical effects can beconsidered as induced gratings.xxx xTime-independent fringes中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Diffraction off an induced gratingA third beam will then diffract into a different direction.This results in a beam thats the product of E1,E2*,and E3:This is just a generic four-wave-mixing effect.x中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Induced gratingsPhase-matching condition:Assume:The diffracted beam has the same frequency and k-vector magnitude as the probe beam,but its direction will be different.butDiffractedsignalwex1wex2wsig=wprwprqexzqprqsigx中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Phase-matching induced gratingsPhase-matching:z-component:x-component:wexwexwprqexzqprqsigxThe minus sign is just the excite-probe effect.The“Bragg Condition”中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Induced gratingswith different frequenciesNonlinearmediumDiffractedsignalwww w w3w3Phase-matching condition:This effect is called non-degenerate four-wave mixing.In this case,the intensity fringes sweep through the medium:a moving grating.The set of possible beam geometries is complex.I wrote a thesis on this!中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Acousto-optics involves diffracting light off a grating induced by an acoustic wave.Acousto-optics works because acoustic waves have about the same wavelengths as(visible)light waves.Such diffraction can be quite strong:70%.Acousto-optics is the basis of useful devices.QuartzDiffractedbeamw wacousticwAcoustic transducerPressure,density,and refractive-index variations due to acoustic waveInputbeamAn acoustic wave induces sinusoidal density,and hence sinusoidal refractive-index,variations in a medium.中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Induced gratings with plane waves and more complex beams(of the same frequency)All such induced gratings will diffract a plane wave,reproducingthe distorted wave:A plane wave and avery distorted waveA plane wave and a slightly distorted wave Two plane wavesA plane wave and aslightly distorted waveE2 and E3 are plane waves.Holography is an induced-grating process.One of the write beams has a complex spatial patternthe image.Different incidence angles correspond to different fringe spacings.Different object views are stored as different fringe spacings.A third beam(a plane wave)diffracts off the grating,acquiring the image infor-mation.Different fringe spacings yield different diffraction angleshence 3D!The light phase stores the angular info.中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Phase conjugationWhen a nonlinear-optical effect produces a light wave proportional to E*,the process is called a phase-conjugation process.Phase conjugators can cancel out aberrations.The second traversal through the medium cancels out the phase distortion caused by the first pass!Distorting mediumA phase-conjugate mirror reverses the sign of the phase A normal mirror leaves the sign of the phase unchanged中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Phase conjugation=Time reversalA light wave is given by:If we can phase-conjugate the spatial part,we have:Thus phase conjugation produces a time-reversed beam!中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Degenerate four-wave mixingConsider only processes with three input frequenciesand an output frequency that are identical.Identical frequencies=degenerate.Degenerate four-wave mixing gives rise to an amazing variety of interesting effects.Some are desirable.Some are not.Some are desirable some of the time and not the rest of the time.Because the k-vectors can have different directions,well distinguish between them(as well as the fields):中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Single-field degenerate four-wave mixingSingle-field degenerate four-wave mixing gives rise to“self”effects.These include:Self-phase modulationSelf-focusing(whole-beam and small-scale)Both of these effects participate in the generation of ultrashort pulses!If just one beam is involved,all the k-vectors will be the same,as will the fields:So the polarization becomes:中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Degenerate 4WM means a nonlinearrefractive index.So the refractive index is:Recall the inhomogeneous wave equation:and the polarization envelope(the linear and nonlinear terms):Substituting the polarization into the wave equation(assuming slow variation in the envelope of E compared to 1/w):since中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Nonlinear refractive index(contd)Usually we define a nonlinear refractive index,n2:The refractive index in the presence of linear and nonlinear polarizations:Assume that the nonlinear term n0:Now,the usual refractive index(which well call n0)is:So:So:since:中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识The nonlinear refractive index magnitude and response timeA variety of effects give rise to a nonlinear refractive index.Those that yield a large n2 typically have a slow response.Thermal effects yield a huge nonlinear refractive index through thermal expansion due to energy deposition,but they are very very slow.As a result,most media,including even Chinese tea,have nonlinear refractive indices!vibrational中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Whole-beam self-focusingThis is precisely the behavior of a lens!But one whose focal power scales with the intensity.If the beam has a spatial Gaussian intensity profile,then any nonlinear medium will have a spatial refractive index profile that is also Gaussian:Near beam center:The nonlinear refractive index,causes beams to self-focus.The phase delay vs.radial co-ordinate will be:中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Small-scale self-focusingSuch filaments grow exponentially with distance.And they grow from quantum noise in the beam,which is always there.As a result,an intense ultrashort pulse cannot propagate through any medium without degenerating into a mass of tiny highly intense filaments,which,even worse,badly damage the medium.If the beam has variations in intensity across its profile,it undergoessmall-scale self-focusing.Each tiny bump in the beam undergoes its own separate self-focusing,yielding a tightly focused spot inside the beam,called a“filament.”IntensityPosition中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Small-scale self-focusing vs.distance:SimulationA somewhat noisy beam becomes a very noisy one.中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Real examples of beam filamentationAll peak powers are in the 15 to 35GW/cm2 range.All beams began life smooth!中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识The self-phase-modulated pulse develops a phase vs.time proportional to the input pulse intensity vs.time.Self-phase modulation&continuum generationThe further the pulsetravels,the moremodulation occurs.A flat phase vs.time yields the narrowest spectrum.If we assume thepulse starts with a flat phase,then SPM broadens the spectrum.This is not a small effect!A total phase variation of hundreds can occur!A broad spectrum generated in this manner is called Continuum.That is:Pulse intensity vs.time中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识The instantaneous frequency vs.time in SPMA 10-fs,800-nm pulse thats experienced self-phase modulation with a peak magnitude of 1 radian.中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Self-phase-modulated pulse in the frequency domain The same 10-fs,800-nm pulse thats experienced self-phase modulation with a peak magnitude of 1 radian.Its easy to achieve many radians for phase delay,however.中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识A highly self-phase-modulated pulseA 10-fs,800-nm pulse thats experienced self-phase modulation with a peak magnitude of 10 radians Note that the spectrum has broadened significantly.When SPM is very strong,it broadens the spectrum a lot.We call this effect continuum generation.中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Continua created by propagating 500-fs 625nm pulses through 30 cm of single-mode fiber.The Supercontinuum Laser Source,Alfano,ed.Broadest spectrum occurs for highest energy.LowEnergyMediumEnergyHighEnergyExperimental continuum spectrum in a fiber中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Continuum generation simulationsInput Intensity vs.time(and hence output phase vs.time)Output spectrum:Instantaneously responding n2;maximum SPM phase=72p radiansThe Super-continuumLaser Source,Alfano,ed.Original spectrum is negligible in width compared to the output spectrum.Oscillations occur in spectrum because all frequencies occur twice and interfere,except for inflection points,which yield maximum and minimum frequencies.Dw中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Continuum generation simulationOutput phase vs.time(input intensity vs.time,due to slow response)Output spectrum:Noninstantaneously responding n2;maximum SPM phase=72p radiansThe SupercontinuumLaser Source,Alfano,ed.Asymmetry in phase vs.timeyields asymmetry in spectrum.中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Experimental continuum spectraInputwavelength625-nm(70 fs and 2 ps)pulses in Xe gasL=90 cmThe SupercontinuumLaser Source,Alfano,ed.Data taken by Corkum,et al.p=15&40 atm中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Ultraviolet continuum4-mJ 160-fs 308-nm pulses in 40 atm of Ar;60-cm long cell.Lens focal length=50 cm.Good quality output mode.The SupercontinuumLaser Source,Alfano,ed.中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识308 nm input pulse;weak focusing with a 1m-focal-length lens.The Super-continuumLaser Source,Alfano,ed.UV Continuum in Air!Continuum is limited when GVD causes the pulse to spread,reducing the intensity.中国中国历历史上吸烟的史上吸烟的历历史和史和现现状、所采取的措施以及由此状、所采取的措施以及由此带带来的痛苦和灾来的痛苦和灾难难，可以，可以进进一步了解吸烟一步了解吸烟对对人民健康的危害，提高人民健康的危害，提高师师生的控烟意生的控烟意识识Continuum in airBeam profile of a high-power beam(1000Pcr)after 15m.Note the multiple filamentation.Use a negatively chirped pulse to pre-compensate for the dispersion of air.Then“temporal focusing”occurs.The self-focusing can compensate diffraction:light bullets!Usually this only happens for pieces of the beam:filamentation,and its messy.Conical emission from a fs beam in air,near the crit