超快光学 第24章 阿秒脉冲

1、Single-cycle and attosecond light pulsesBandwidth, bandwidth, bandwidthUV wavelengthPossible routes: Raman scattering High-harmonic generationMeasurement of attosecond pulsesSources:The physics of attosecond light pulses, Pierre Agostini and Louis F DiMauro Rep. Prog. Phys. 67 (2004) 813.Chang Hee N

2、AM and Kyung Taec Kim Reinhard Kienberger1, M. Hentschel1, M. Drescher1,2, G. Reider1, Ch. Spielmann1, Ferenc Krausz11Institut fr Photonik, Technische Universitt Wien, AUSTRIA2Fakultt fr Physik, Universitt Bielefeld, GERMANYWhy try to make attosecond pulses?Bohr-orbit time in hydrogen: 152 attosecon

3、dsH2 vibrational oscillation period: 7 fsMolecular vibrations can also be very fast.t=0t0Sub-fsX-ray pumpSub-fsX-ray probeX-Ray Pump / X-Ray Probe SpectroscopyX-ray Excite-Probe SpectroscopyWith sub-fs x-ray pulses, we could trace inner shell relaxation processes.BandwidthSo for a sub-fs pulse, Dn D

4、n 1015 Hz. This is a lot!Long pulseShort pulseIrradiance vs. timeSpectrumtimetimefrequencyfrequencyThe uncertainty principle requires that Dt Dn 1.Single-cycle pulsesThe shortest possible pulse of a given wavelength is one cycle long.Such a pulse immediately evolves into a single-cycle pulse:Imagine

5、 a half-cycle pulse. Its electric field looks like this:Because this pulse field has nonzero area, it has an w w = 0 componentwhich has infinite wavelength! And this wavelength diffracts away immediately:TimeElectric field0TimeElectric field02/0RzwAttosecond pulses are short-wavelength pulses.If you

6、 compress a single-cycle pulse of one wavelength, you necessarily reduce its wavelength!A single-cycle red pulse:Compressing a single-cycle red pulse:A single-cycle 800-nm pulse has a period of 2.7 fs. t (and z)To achieve a period of 1 fs requires a wavelength of 300 nm.An infinite train of identica

7、l pulses can be written:The Fourier transform of an infinite train of pulses( )III(/) (2EFTwww%where f(t) represents a single pulse and T is the time between pulses. The Convolution Theorem states that the Fourier Transform of a convolution is the product of the Fourier Transforms. So:E(t) = III(t/T

8、) * f(t)t-3T-2T0T2T3T-TE(t)wT/2-4-2024F E(t)F f(t)A series of modes, and the shorter the pulse the broader the spectrum.Generating short pulses = Mode-lockingLocking vs. not locking the phases of the laser modes (frequencies)Random phasesLight bulbIntensity vs. timeUltrashort pulse!Locked phasesTime

9、TimeIntensity vs. timeMethods for generating many equally spaced modes with 1015 Hz bandwidthCascaded Raman scatteringHigh-harmonic generationBut do they lock the modes?FrequencyRaman scattering and attosecond pulsesS. E. Harris and A. V. Sokolov PRL 81, 2894frequencyRaman processes can cascade many

10、 times, yielding a series of equally spaced modes!Input two frequencies nearly resonant with a Raman resonance.At high intensity, the process cascades many times.Input pulsesOutput pulse as input to a second processOutput pulse of second process as input to a third processOutput pulse of third proce

11、ss as input to a fourthprocessEtc.Cascaded Raman generationDwba = 2994 cm-1A. V. Sokolov et al. PRL 85, 85 562This can be done with nanosecond laser pulses!A. V. Sokolov et al. PRL 85, 562Experimental demonstration of cascaded Raman scattering- 400MHz+ 100MHz+ 700MHz2994 cm-1Detuning from 2-photon r

12、esonance75,000 cm-1 (2.3 x 1015 Hz) of bandwidth has been created!Numerical simulation of Raman scattering in D2Harris and Sokolov. PRL 81, 2894z (cm)01.83.6Propagation distanceIs the light produced using cascaded Raman scattering an attosecond pulse?Unfortunately, no one has reliably measured the s

13、pectral phase of this light, so we dont know its pulse lengthAnd if you havent measured it, you havent made it!As a footnote, they did a complex set of four-wave-mixing cross-correlations, which implied that it was a single cycle, but we cant be sure. High Harmonic Generation in a gasgratingdetector

14、Laser dump800 nm 1015 Hz).Spatial coherence.Reasonable stability.The physics seems to imply that the XUV pulse should be really shortMaybe HHG just naturally produces attosecond pulses without even tryingAre the high harmonics actually in phase?P. Antoine et al., PRL 77, 1234cutoffplateauMeasuring t

15、he relative phases of adjacent harmonics:The resulting intensity vs. time:Using a 100 fs input pulse, the answer is NO!The highest and most intense harmonics are generated by the shortest pulses.Measured XUV spectral intensity from neonM. Schnrer et al., PRL 83, 722 (1999)Ch. Spielmann et al., Scien

16、ce 278, 661 (1997)Z. Chang et al., PRL 79, 2967 (1997) Wavelength (nm)Note the broader harmonics from the 7-fs pulse due to the spectrally broader excitation pulse.Theory says many-fs input pulses yield many-fs XUV pulses, but few-fs input pulses could yield attosecond XUV pulsesA 5-fs input pulse i

17、n theory yields an attosecond XUV pulse302520151050Time(fs)tIR = 100 fsIR E-fieldHarmonic emissionIonization tIR = 25 fstIR = 5 fsI. P. Christov, M. M. Murnane, and H. C. Kapteyn, PRL 78, 1251, (1997)Theory predicts that few-cycle-driven XUV/HHG emission consists of attosecond pulses.Simulation3D co

18、de: N. Milosevic & T. Brabec, 2001I. Christov et al., PRL 78, 1251 (1997)C. Kann et al., PRL 79, 2971 (1997)Isolated sub-femtosecond XUV pulse!Time (fs)-6-4-20246X-ray intensityEnergy (eV)869094t tx = 530 asLaser electric field“Observation of attosecond light localization in HHG”N. A. Papadogiannis

19、et al. PRL 83, 4289MCPAl-SiDigital scopeTi:StArHHGAs with any long-sought milestone, false claims abound.These guys basically performed an interferometric autocorrelation measurement, but with HHG as the nonlinear process instead of SHG.“Observation of attosecond light localization in HHG” N. A. Pap

20、adogiannis, et al. PRL 83, 4289Harmonic autocorrelationA false claimThese authors saw peaks, more indicative of the broad spectrum than a short pulse. They also saw unphysical asymmetries, without question due to noise.Dont believe everything you read, even if its in a peer-reviewed scientific journ

21、al!Zeroth-order phase: the absolute phaseThe absolute phase is the same in both the time and frequency domains.An absolute phase of /2 will turn a cosine carrier wave into a sine.Its usually irrelevant, unless the pulse is only a cycle or so long.Different absolute phases for a single-cycle pulseNot

22、ice that the two four-cycle pulses look alike, but the three single-cycle pulses are all quite different.f(t)exp(i0) F(w)exp(i0)Different absolute phases for a four-cycle pulse- 505- 505- 10010- 10010HHG and the absolute phase (carrier-offset phase)FewcyclepulseMulticyclepulseE (t) = E(t) cos(wLt)E

23、(t) = E(t) sin(wLt)Input pulse instantaneous intensityt (fs)HHG is very sensitive to the peak intensity, which is higher for a 0-absolute phase (cos) than for 90-absolute phase (sin).Threshold for HHGTheory predicts much more intense XUV for a zero (or ) absolute phase.A. Apolonski et al. PRL 85, 74

24、0Laser electric fieldIntensity of the XUV harmonic radiationThe absolute phase varies! “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” D. J. Jones, et al., Science 288, 635.Pulse field vs. timeThe intensity profile has a round-trip time of L

25、/vg,while the carrier wave has a round-trip time of L/v.If these times differ, the absolute phase (also called the carrier-envelope offset phase) will vary from pulse to pulse.2/wL = TwL = mode spacingT = pulse spacingVariable absolute phase in the frequency domainCarrier-envelope phase control of f

26、emtosecond mode-locked lasers and direct optical frequency synthesis, D. J. Jones et al. Science 288, 635The frequency of absolute-phase variation is related to d, the extra residual frequency.2/wL = TwLwn = nwL+ d d = D/T( )Ew%( )E ttwwn = nwL+ d d 0The nth laser mode:Proof that:0( )( )()exp()(2 )e

27、xp(2).()exp()mE tf tf tTif tTif tmTimDDD0( )( )exp()exp()mEFim TimwwwD%0( )exp()mFimTwwDA repetitive pulse train with drifting absolute phase:Its Fourier transform via the Shift Theorem:where D 2( )0nnifEifwwwww%2/nLnnTTwwdDwhere:0,1,2,n KProof (continued)0( )( )exp()mEFimTwwwD%If w = wn = (2n +D)/T

28、:If w = (2n +D)/T + e wn:0022exp)exp2mmnnFimTinmTTDDD 1ReImQED0022exp)exp0mmnnFimTTTim TeeeDDD( )Ew%( )Ew%If a pulse has more than one octave, it has both f and 2 f for some frequency, f. Interfering them in a SHG crystal yields two contributions at 2 f : that from the original beam and the SH of f.

29、Simply measuring the spectrum of the pulse plus it SH is performing spectral interferometry and yields a fringe phase:Apolonski et al.PRL 85 7400002Stabilizing the absolute phaseStabilizing the SH spectrum near 2 f stabilizes the abs phase.Chirped mirrorsTelescopeWedgesHow to measure an attosecond p

30、ulse? Attosecond autocorrelation is too difficult.Using the relatively narrowband 800-nm pump pulse as the gate yields an output electron energy width about half as broad.The 800-nm beam is easier to work with.Theres a wider choice of nonlinear effects.But the 800-nm pulse is a lot longer!Fortunately, femt