1、The Metric SystemPrefixes:Milli(m)10-3Micro()10-6Nano(n)10-9Pico(p)10-12Femto(f)10-15Atto(a)10-18Kilo(k)10+3Mega(M)10+6Giga(G)10+9Tera(T)10+12Peta(P)10+15SmallBigWell need to really know the metric system because the pulses are incredibly short and the powers and intensities can be incredibly high.T
2、he Trotting Horse”ControversyPalo Alto,CA 1872The Birth of Ultrafast TechnologyLeland Stanford（马场老板）Eadweard Muybridge(英国摄影师)Time Resolution:1/60th of a secondBet:Do all four hooves of a trotting horse ever simultaneously leave the ground?Trotting HorseHarold EdgertonMIT,1942“How to Make Apple sauce
3、 at MIT”1964“Splash on a Glass”Curtis HurleyJunior High School student1996Time Resolution:a few microsecondsDoc Edgerton-Strobe Photography时间尺度时间尺度电子运动时间尺度：阿秒 （1as=10-18s)，电子绕氢原子核一周大约是150阿秒；原子转动时间尺度：皮秒（1ps=10-12s）原子振动时间尺度：飞秒（1 fs=10-15s)如监测化学反应过程，需飞秒尺度The Generation of Ultrashort Laser PulsesThe imp
4、ortance of bandwidthMore than just a light bulbLaser modes and mode-lockingMaking shorter and shorter pulsesPulse-pumpingQ-switching and distributed-feedback lasersPassive mode-locking and the saturable absorberKerr-lensing and Ti:SapphireActive mode-lockingOther mode-locking techniquesLimiting fact
5、orsCommercial lasersBut first:the progress has been amazing!YEARNd:glassS-P DyeDyeCW DyeNd:YAGDiodeNd:YLFCr:YAGCr:LiS(C)AFEr:fiberCr:forsteriteTi:sapphireCPMw/CompressionColorCenter1965 1970 1975 1980 1985 1990 1995Dye2000SHORTEST PULSE DURATION10ps1ps100fs10fs2005Nd:fiberThe shortest pulse vs.year(
6、for different media)Continuous vs.ultrashort pulses of lightA constant and a delta-function are a Fourier-Transform pair.Continuous beam:Ultrashort pulse:Irradiance vs.timeSpectrumtimetimefrequencyfrequencyLong vs.short pulses of lightThe uncertainty principle says that the product of the temporal a
7、nd spectral pulse widths is greater than 1.Long pulseShort pulseIrradiance vs.timeSpectrumtimetimefrequencyfrequencyFor many years,dyes have been the broadband media that have generated ultrashort laser pulses.Ultrafast solid-state laser media have recently replaced dyes in most labs.Solid-state las
8、er media have broad bandwidths and are convenient.Laser powerBut a light bulb is also broadband.What exactly is required to make an ultrashort pulse?Answer:A Mode-locked LaserOkay,whats a laser,what are modes,and what does it mean to lock them?Light bulbs,lasers,and ultrashort pulses Whats the real
9、meaning of mode locking Frequency domain:all longitudinal modes are in phase(phase moded)Time domain:Form ultrashort pulses Free running Mode locking Mode locked principle Lasers modes:The Shah functionThe Shah function,III(t),is an infinitely long train of equallyspaced delta-functions.tIII()()mttm
10、The Fourier transform of the Shah functionIf w=2np,So:III()III(tw p F)exp()exp()exp()mmmtmi t dttmi t dti mwww tIII(t)F III(t)2wpMenlo SystemsWhat about the saturation intensity?Lasers lase when the gain exceeds the loss.whats the real meaning of mode locking?Active mode-lockingThe Fourier transform
11、 of an infinite train of pulsesIf a pulse experiences additional focusing due to high intensity and the nonlinear refractive index,and we align the laser for this extra focusing,then a high-intensity beam will have better overlap with the gain medium.Additional focusing optics can arrange for perfec
12、t overlap of the high-intensity beam back in the Ti:Sapphire crystal.A lens is a lens because the phase delay seen by a beam varies with x:The universe conspires to lengthen pulses.Titanium SapphirePassive mode-locking:the saturable absorberKerr-lensing and Ti:SapphireF III(t)It can be used to start
13、 a Ti:Sapphire laser mode-locking.Notice that the weak pulses are suppressed,and the strong pulse shortens and is amplified.B is the absorption cross-section,s,divided by the energy per photon,w:s/wKilo(k)10+3Other mode-locking techniquesSHORTEST PULSE DURATIONThe Shah function and a pulse train()mf
14、 tmT()III(/)()E tt Tf twhere f(t)is the shape of each pulse and T is the time between pulses.An infinite train of identical pulses(from a laser!)can be written:(/)()mtTm f tt dt ConvolutionThe Fourier transform of an infinite train of pulsesAn infinite train of identical pulses can be written:E(t)=I
15、II(t/T)*f(t)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:()III(/)(2EFTwwpwA train of pulses results from a single pulse bouncing back and forth inside a lase
16、r cavity of round-trip time T.The spacing between frequenciescalled laser modesis then w=p/T or nn=1/T.Generating short pulses=mode-lockingLocking the phases of the laser modes yields an ultrashort pulse.Locked modesIntensitiesNumerical simulation of mode-lockingUltrafast lasers often have thousands
17、 of modes.A generic ultrashort-pulse laserA generic ultrafast laser has a broadband gain medium,a pulse-shortening device,and two or more mirrors:Many pulse-shortening devices have been proposed and used.Mode-lockerPulsed PumpingLong and potentially complex pulsePumping a laser medium with a short-p
18、ulse flash lamp yields a short pulse.Flash lamp pulses as short as 1 s exist.Unfortunately,this yields a pulse as long as the excited-state lifetime of the laser medium,which can be considerably longer than the pump pulse.Since solid-state laser media have lifetimes in the microsecond range,it yield
19、s pulses microseconds to milliseconds long.Q-switchingQ-switching involves:Preventing the laser from lasing until the flash lamp is finished flashing,andAbruptly allowing the laser to lase.The pulse length is limited by how fast we can switch and the round-trip time of the laser and yields pulses 10
20、-100 ns long.100%0%TimeCavity LossCavity GainOutput intensityQ-SwitchingHow do we Q-switch a laser?Q-switching involves preventing lasing until were ready.A Pockels cell switches(in a few nanoseconds)from a quarter-wave plate to nothing.Before switchingAfter switchingPockels cell as wave plate w/axe
21、s at 450 PolarizerMirrorPockels cell as an isotropic medium0 PolarizerMirrorLight becomes circular on the first pass and then horizontal on the next and is then rejected by the polarizer.Light is unaffected by the Pockels cell and hence is passed by the polarizer.Passive mode-locking:the saturable a
22、bsorber(I)01 I IsatLike a sponge,an absorbing medium can only absorb so much.High-intensity spikes burn through;low-intensity light is absorbed.0N0 PolarizerActive mode-lockingThe Convolution Theorem states that the Fourier Transform of a convolution is the product of the Fourier Transforms.As short
23、 as 8 fs!Cr:LiS(C)AFThe Metric SystemThe intense spike uses up the laser gain-medium energy,reducing the gain available for the trailing edge of the pulse(and for later pulses).Peta(P)10+15f(x)=n(x)k LLaser modes and mode-lockingThe effect of a saturable absorberAdding two prisms compensates for dis
24、persion in the Ti:Sapphire crystal and mirrors.Gain mediumLosses are too high for a low-intensity cw mode to lase,but not for high-intensity fs pulse.The Generation of Ultrashort Laser PulsesHigh-intensity spikes burn through;low-intensity light is absorbed.electronic stateThey also offer other attr
25、active properties,such as a very high thermal efficiency and high average power.Continuous vs.t-Pulse 100What about the saturation intensity?A is the excited-state relaxation rate:1/t/satIA BLaser TransitionPump TransitionFast decayFast decay1230B is the absorption cross-section,divided by the energ
26、y per photon,w:/wsatIwtThe saturation intensity plays a key role in laser theory.Both and t depend on the molecule,the frequency,and the various states involved.w10-19 J for visible/near IR lightt10-12 to 10-8 s for molecules10-20 to 10-16 cm2 for molecules(on resonance)105 to 1013 W/cm2The effect o
27、f a saturable absorberFirst,imagine raster-scanning the pulse vs.time like this:After many round trips,even a slightly saturable absorber can yield a very short pulse.Short time(fs)IntensityRound trips(k)k=1k=7Notice that the weak pulses are suppressed,and the strong pulse shortens and is amplified.
28、k=2k=3Mode locked pulse formation Passive mode-locking:the saturable absorberHigh-intensity spikes(i.e.,short pulses)see less loss and hence can lase while low-intensity backgrounds(i.e.,long pulses)wont.Passive mode-locking with a slow saturable absorberWhat if the absorber responds slowly(more slo
29、wly than the pulse)?Then only the leading edge will experience pulse shortening.This is the most common situation,unless the pulse is many ps long.Gain saturation shortens the pulse trailing edge.The intense spike uses up the laser gain-medium energy,reducing the gain available for the trailing edge
30、 of the pulse(and for later pulses).Saturable gain and lossThe combination of saturable absorption and saturable gain yields short pulses even when the absorber is slower than the pulse.Lasers lase when the gain exceeds the loss.A dyes energy levelsDyes are big molecules,and they have complex energy
31、 level structure.S0:Ground electronic stateS1:1st excited electronic stateS2:2nd excited electronic stateEnergyLaser TransitionLowest vibrational and rotational level of this electronic“manifold”Excited vibrational and rotational levelDyes can lase into any(or all!)of the vibrational/rotational leve
32、ls of the S0 state,and so can lase very broadband.Pump TransitionThe Passively Mode-locked Dye LaserPassively mode-locked dye lasers yield pulses as short as a few hundred fs.Theyre limited by our ability to saturate the absorber.Pump beamGain mediumSaturable absorberSome common dyes and their corre
33、sponding saturable absorbersPumping the gain medium with a train of already short pulses yields a train of even shorter pulses.whats the real meaning of mode locking?Passive mode-locking with a slow saturable absorberAny amplitude modulator can preferentially induce losses for times other than that
34、of the intended pulse peak.Continuous vs.Etalon effects:Light is unaffected by the Pockels cell and hence is passed by the polarizer.A dyes energy levelsIf a pulse experiences additional focusing due to high intensity and the nonlinear refractive index,and we align the laser for this extra focusing,
35、then a high-intensity beam will have better overlap with the gain medium.Gain mediumIt can be used to start a Ti:Sapphire laser mode-locking.1/60th of a secondMai Tai(Hands-free,100 fs pulse length)A generic ultrashort-pulse laserExcited vibrational and rotational levelPrism dispersion compensatorNa
36、no(n)10-9Passively mode-locked dye lasers yield pulses as short as a few hundred fs.High-intensity spikes burn through;low-intensity light is absorbed.Repetition rate(MHz)A lens and a lensxA lens is a lens because the phase delay seen by a beam varies with x:f(x)=n k L(x)L(x)Now what if L is constan
37、t,but n varies with x:f(x)=n(x)k Ln(x)xIn both cases,a quadratic variation of the phase with x yields a lens.Kerr-lens mode-lockingA mediums refractive index depends on the intensity.n(I)=n0+n2IIf the pulse is more intense in the center,it induces a lens.Placing an aperture at the focus favors a sho
38、rt pulse.Kerr-lensing is the mode-locking mechanism of the Ti:Sapphire laser.Losses are too high for a low-intensity cw mode to lase,but not for high-intensity fs pulse.Kerr-lensing is a type of saturable absorber.If a pulse experiences additional focusing due to high intensity and the nonlinear ref
39、ractive index,and we align the laser for this extra focusing,then a high-intensity beam will have better overlap with the gain medium.High-intensity pulseLow-intensity pulseTi:SapphMirrorAdditional focusing optics can arrange for perfect overlap of the high-intensity beam back in the Ti:Sapphire cry
40、stal.But not the low-intensity beam!This is soft aperture saturable absorber.Modeling Kerr-lens mode-lockingTitanium Sapphire(Ti:Sapphire)oxygenaluminumAl2O3 latticeTi:Sapphire is currently the workhorse laser of the ultrafast community,emitting pulses as short as a few fs and average power in exces
41、s of a Watt.Titanium SapphireIt can be pumped with a(continuous)Argon laser(450-515 nm)or a doubled-Nd laser(532 nm).Upper level lifetime:3.2 msecTi:Sapphire lases from 700 nm to 1000 nm.Absorption and emission spectra of Ti:Sapphire(nm)Mechanisms that limit pulse shorteningGain narrowing:G(w)=exp(-
42、aw2),then after N passes,the spectrum will narrow by GN(w)=exp(-Naw2),which is narrower by N1/2Group-velocity dispersion:GVD spreads the pulse in time.And everything has GVDAll fs lasers incorporate dispersion-compensating components.Well spend several lectures discussing GVD!Etalon effects:This yie
43、lds multiple pulses,spreading the energy over time,weakening the pulses.The universe conspires to lengthen pulses.The Ti:Sapphire laser including dispersion compensationAdding two prisms compensates for dispersion in the Ti:Sapphire crystal and mirrors.This is currently the workhorse laser of the ul
44、trafast optics community.cw pump beamTi:Sapphire gain mediumPrism dispersion compensatorSlit for tuningCommercial fs lasersTi:Sapphire Coherent:Mira(35 fs pulse length,1 W ave power),Chameleon(Hands-free,100 fs pulse length),Spectra-Physics:Tsunami(35 fs pulse length,1 W ave power)Mai Tai(Hands-free
45、,100 fs pulse length)Very-short-pulse commercial fs lasersTi:Sapphire KM Labs 20 fs and$20K FemtolasersAs short as 8 fs!The spacing between frequenciescalled laser modesis then dw=2p/T or dn=1/T.If a pulse experiences additional focusing due to high intensity and the nonlinear refractive index,and w
46、e align the laser for this extra focusing,then a high-intensity beam will have better overlap with the gain medium.Milli(m)10-3The effect of a saturable absorberLaser TransitionLight is unaffected by the Pockels cell and hence is passed by the polarizer.Q-switching and distributed-feedback lasersPri
47、sm dispersion compensatorThe Passively Mode-locked Dye LaserSaturable absorberWell spend several lectures discussing GVD!Femto(f)10-15t-Pulse 200Gain mediumHigh-intensity spikes burn through;low-intensity light is absorbed.Passive mode-locking:the saturable absorber原子振动时间尺度：飞秒（1 fs=10-15s)Q-switchin
48、g involves:A lens and a lensPassive mode-locking:the saturable absorberCommercial fs lasers(contd)SESAM mode lockingTimeSESAMAdvantages:ultrashort pulse generation simple method compact lasers A conventional semiconductor saturable absorber mirror(SESAM)SESAM parametersCW mode locking threshold Ytte
49、rbium Tungstate(Yb:KGW)Modelt-Pulse 20t-Pulse 100t-Pulse 200Pulse energy(nJ)20 100 200 Average power(W)1 1 2 Repetition rate(MHz)50 10 10 Ytterbium doped laser materials can be directly diode-pumped,eliminating the need for an intermediate(green)pump laser used in Ti:Sapphire lasers.They also offer
50、other attractive properties,such as a very high thermal efficiency and high average power.Amplitude Systemes Active mode-lockingAny amplitude modulator can preferentially induce losses for times other than that of the intended pulse peak.This produces short pulses.It can be used to start a Ti:Sapphi
