第三讲 超短脉冲的产生

1、Lecture 3 Generation of ultrashort pulses,The Metric System,Prefixes:,Milli (m)10-3,Micro ()10-6,Nano (n)10-9,Pico (p)10-12,Femto (f)10-15,Atto (a)10-18,Kilo (k)10+3,Mega (M)10+6,Giga (G)10+9,Tera (T)10+12,Peta (P)10+15,Small,Big,Well need to really know the metric system because the pulses are incr

2、edibly short and the powers and intensities can be incredibly high.,The Trotting Horse” Controversy Palo Alto, CA 1872,The Birth of Ultrafast Technology,Leland Stanford （马场老板）,Eadweard Muybridge (英国摄影师),Bet: Do all four hooves of a trotting horse ever simultaneously leave the ground?,Trotting Horse,

3、Harold Edgerton MIT, 1942,“How to Make Apple sauce at MIT” 1964,“Splash on a Glass” Curtis Hurley Junior High School student 1996,Time Resolution: a few microseconds,Doc Edgerton - Strobe Photography,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

4、),如监测化学反应过程，需飞秒尺度,The Generation of Ultrashort Laser Pulses,The importance of bandwidth More than just a light bulb Laser modes and mode-locking Making shorter and shorter pulses Pulse-pumping Q-switching and distributed-feedback lasers Passive mode-locking and the saturable absorber Kerr-lensing an

5、d Ti:Sapphire Active mode-locking Other mode-locking techniques Limiting factors Commercial lasers,But first: the progress has been amazing!,The shortest pulse vs. year (for different media),Continuous vs. ultrashort pulses of light,A constant and a delta-function are a Fourier-Transform pair.,Conti

6、nuous beam: Ultrashort pulse:,Irradiance vs. time,Spectrum,time,time,frequency,frequency,Long vs. short pulses of light,The uncertainty principle says that the product of the temporal and spectral pulse widths is greater than 1.,Long pulse,Short pulse,Irradiance vs. time,Spectrum,time,time,frequency

7、,frequency,For 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 laser media have broad bandwidths and are convenient.,But a light bulb is also broadband. What exactly is

8、 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 meaning of mode locking,Frequency domain: all longitudinal modes are in phase ( phase moded) Time domain

9、: Form ultrashort pulses,Free running,Mode locking,Mode locked principle,Lasers modes: The Shah function,The Shah function, III(t), is an infinitely long train of equally spaced delta-functions.,t,The Fourier transform of the Shah function,If w = 2np, So:,III(t),The Shah function and a pulse train,w

10、here 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:,Convolution,The Fourier transform of an infinite train of pulses,An infinite train of identical pulses can be written: E(t) = III(t/T) * f(t) where f(t) repres

11、ents 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:,A train of pulses results from a single pulse bouncing back and forth inside a laser cavity of round-trip time T. The spacing

12、 between frequenciescalled laser modesis then dw = 2p/T or dn = 1/T.,Generating short pulses = mode-locking,Locking the phases of the laser modes yields an ultrashort pulse.,Locked modes,Intensities,Numerical simulation of mode-locking,Ultrafast lasers often have thousands of modes.,A generic ultras

13、hort-pulse laser,A 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-locker,Pulsed Pumping,Pumping a laser medium with a short-pulse flash lamp yields a short pulse. Flash lamp puls

14、es 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 yields pulses microseconds to milliseconds long.,Q-s

15、witching,Q-switching involves: Preventing the laser from lasing until the flash lamp is finished flashing, and Abruptly 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 - 100 ns long.,Q-Switching,How do we Q-s

16、witch 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 switching,After switching,Pockels cell as wave plate w/ axes at 45,0 Polarizer,Mirror,Pockels cell as an isotropic medium,0 Polarizer,Mi

17、rror,Light 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 absorber,Like a sponge, an absorbing medium can only absorb so much.

18、High-intensity spikes burn through; low-intensity light is absorbed.,What about the saturation intensity?,A is the excited-state relaxation rate: 1/t,B is the absorption cross-section, s, divided by the energy per photon, w: s / w,The saturation intensity plays a key role in laser theory.,Both s and

19、 t depend on the molecule, the frequency, and the various states involved.,w 10-19 J for visible/near IR light,t 10-12 to 10-8 s for molecules,s 10-20 to 10-16 cm2 for molecules (on resonance),105 to 1013 W/cm2,The effect of a saturable absorber,First, imagine raster-scanning the pulse vs. time like

20、 this:,After many round trips, even a slightly saturable absorber can yield a very short pulse.,Intensity,Round trips (k),Notice that the weak pulses are suppressed, and the strong pulse shortens and is amplified.,Mode locked pulse formation,Passive mode-locking: the saturable absorber,High-intensit

21、y 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 absorber,What if the absorber responds slowly (more slowly than the pulse)? Then only the leading edge will experience pulse shortening.

22、,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 of the pulse (and for later pulses).,Saturable gain and loss,The combinati

23、on 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 levels,Dyes are big molecules, and they have complex energy level structure.,S0: Ground electronic state,S1: 1st excited electr

24、onic state,S2: 2nd excited electronic state,Energy,Laser Transition,Lowest vibrational and rotational level of this electronic “manifold”,Excited vibrational and rotational level,Dyes can lase into any (or all!) of the vibrational/rotational levels of the S0 state, and so can lase very broadband.,Pu

25、mp Transition,The Passively Mode-locked Dye Laser,Passively mode-locked dye lasers yield pulses as short as a few hundred fs. Theyre limited by our ability to saturate the absorber.,Some common dyes and their corresponding saturable absorbers,A lens and a lens,A lens is a lens because the phase dela

26、y seen by a beam varies with x: f(x) = n k L(x),L(x),Now what if L is constant, but n varies with x: f(x) = n(x) k L,n(x),In both cases, a quadratic variation of the phase with x yields a lens.,Kerr-lens mode-locking,A mediums refractive index depends on the intensity. n(I) = n0 + n2I If the pulse i

27、s more intense in the center, it induces a lens. Placing an aperture at the focus favors a short 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 saturab

28、le absorber.,If 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.,High-intensity pulse,Low-intensity pulse,Ti:Sapph,This is soft a

29、perture saturable absorber.,Modeling Kerr-lens mode-locking,Titanium Sapphire (Ti:Sapphire),Ti:Sapphire is currently the workhorse laser of the ultrafast community, emitting pulses as short as a few fs and average power in excess of a Watt.,Titanium Sapphire,It can be pumped with a (continuous) Argo

30、n laser (450-515 nm) or a doubled-Nd laser (532 nm).,Upper level lifetime: 3.2 msec,Ti:Sapphire lases from 700 nm to 1000 nm.,Mechanisms that limit pulse shortening,Gain narrowing: G(w) = exp(-aw2), then after N passes, the spectrum will narrow by GN(w) = exp(-Naw2), which is narrower by N1/2 Group-

31、velocity dispersion: GVD spreads the pulse in time. And everything has GVD All fs lasers incorporate dispersion-compensating components. Well spend several lectures discussing GVD! Etalon effects: This yields multiple pulses, spreading the energy over time, weakening the pulses.,The universe conspir

32、es to lengthen pulses.,The Ti:Sapphire laser including dispersion compensation,Adding two prisms compensates for dispersion in the Ti:Sapphire crystal and mirrors.,This is currently the workhorse laser of the ultrafast optics community.,Commercial fs lasers,Ti:Sapphire Coherent: Mira (35 fs pulse le

33、ngth, 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, 100 fs pulse length),Very-short-pulse commercial fs lasers,Ti:Sapphire KM Labs 20 fs and $20K Femtolasers,As short as 8 fs!,Commercial fs lasers (contd

34、),SESAM mode locking,Time,SESAM,Advantages: ultrashort pulse generation simple method compact lasers,A conventional semiconductor saturable absorber mirror (SESAM),SESAM parameters,CW mode locking threshold,Ytterbium Tungstate (Yb:KGW),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 o