Ultrashort Pulse Lasers: Principles and Applications, Slides of Electronics engineering

Download Ultrashort Pulse Lasers: Principles and Applications and more Slides Electronics engineering in PDF only on Docsity! 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 and Ti:Sapphire Active mode-locking Other mode-locking techniques Limiting factors Commercial lasers Docsity.com But first: the progress has been amazing! YEAR Nd:glass S-P Dye Dye CW Dye Nd:YAG Diode Nd:YLF Cr:YAG Cr:LiS(C)AF Er:fiber Cr:forsterite Ti:sapphire CP M w/Compression Color Center 1965 1970 1975 1980 1985 1990 1995 Dye 2000 S H O R T E S T P U L S E D U R A T IO N 10ps 1ps 100fs 10fs 2005 Nd:fiber The shortest pulse vs. year (for different media) Docsity.com For many years, dyes have been the broadband media that have generated ultrashort laser pulses. Docsity.com Ultrafast solid-state laser media have recently replaced dyes in most labs. • Solid-state laser media have broad bandwidths and are convenient. L a s e r p o w e r Docsity.com But a light bulb is also broadband. What exactly is required to make an ultrashort pulse? Answer: A Mode-locked Laser Okay, what’s a laser, what are modes, and what does it mean to lock them? Light bulbs, lasers, and ultrashort pulses Docsity.com Usually, additional losses in intensity occur, such as absorption, scat- tering, and reflections. In general, the laser will lase if, in a round trip: Gain > Loss This called achieving Threshold. The laser A laser is a medium that stores energy, surrounded by two mirrors. A partially reflecting output mirror lets some light out. A laser will lase if the beam increases in intensity during a round trip: that is, if 3 0I I R = 100% R < 100% I0 I1 I2 I3 Laser medium with gain, G Docsity.com Calculating the gain: Einstein A and B coefficients • In 1916, Einstein considered the various transition rates between molecular states (say, 1 and 2) involving light of irradiance, I: • Absorption rate = B N1 I • Spontaneous emission rate = A N2 • Stimulated emission rate = B N2 I 2 1 Docsity.com Laser gain • Neglecting spontaneous emission: • • The solution is: • • • There can be exponential gain or loss in irradiance. Normally, N2 < N1, and there is loss (absorption). But if N2 > N1, there’s gain, and we define the gain, G:   2 1 2 1 dI dI c BN I - BN I dt dz B N - N I      2 1( ) (0)expI z I N N z    2 1expG N N z  [Stimulated emission minus absorption] Proportionality constant is the absorption/gain cross-section,   2 1g N N    1 2N N   If N2 > N1: If N2 < N1 : Docsity.com Why inversion is impossible in a two-level system (cont’d) 0 2BI N AN A N      1 / sat N N I I    / 2satI A B In steady-state: ( 2 )A BI N AN    where: N is always positive, no matter how high I is! It’s impossible to achieve an inversion in a two-level system!  2 d N BI N AN A N dt        /( 2 )N AN A BI    /(1 2 / )N N BI A    Isat is the saturation intensity. 2 1 N2 N1 Docsity.com Why inversion is possible in a three- level system Assume we pump to a state 3 that rapidly decays to level 2. 2 1 2 dN BIN AN dt   1 1 2 dN BIN AN dt    1 22 2 d N BIN AN dt     Absorption Spontaneous emission 1 2N N N   1 2N N N  The total number of molecules is N: 22N N N   d N BIN BI N AN A N dt         Fast decay Laser Transition Pump Transition 1 2 3 Level 3 decays fast and so is zero. 12N N N   Docsity.com Why inversion is possible in a three- level system (cont’d) 1 / 1 / sat sat I I N N I I     /satI A B In steady-state: ( ) ( )A BI N A BI N     where: Now if I > Isat, N is negative!  ( ) /( )N N A BI A BI     Isat is the saturation intensity. d N BIN BI N AN A N dt         0 BIN BI N AN A N       Fast decay Laser Transition Pump Transition 1 2 3 Docsity.com What about the saturation intensity? A is the excited-state relaxation rate: 1/t /satI A B Laser Transition Pump Transition Fast decay Fast decay 1 2 3 0 B is the absorption cross-section, , divided by the energy per photon, ħw:  / ħw satI w t  The saturation intensity plays a key role in laser theory. Both  and t depend on the molecule, the frequency, and the various states involved. ħw ~10-19 J for visible/near IR light t ~10-12 to 10-8 s for molecules  ~10-20 to 10-16 cm2 for molecules (on resonance) 105 to 1013 W/cm2 Docsity.com Two-, three-, and four-level systems Two-level system Laser Transition Pump Transition At best, you get equal populations. No lasing. It took laser physicists a while to realize that four-level systems are best. Four-level system Lasing is easy! Laser Transition Pump Transition Fast decay Fast decay Level empties fast! Three-level system If you hit it hard, you get lasing. Laser Transition Pump Transition Fast decay Molecules accumulate in this level. Docsity.com A dye’s energy levels • Dyes are big molecules, and they have complex energy level structure. S0: Ground electronic state S1: 1 st excited electronic state S2: 2 nd excited electronic state E n e rg y 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. Pump Transition Docsity.com The Shah function and a pulse train ( ) m f t mT     ( ) III( / ) ( )E t t T f t  where f(t) is the shape of each pulse and T is the time between pulses. Set t’ /T = m or t’ = mT An infinite train of identical pulses (from a laser!) can be written: ( / ) ( ) m t T m f t t dt          Convolution Docsity.com 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) 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( / ) (2 E FT w w p w  A train of pulses results from a single pulse bouncing back and forth inside a laser cavity of round-trip time T. The spacing between frequencies—called laser modes—is then w = p/T or n = 1/T. Docsity.com Mode-locked vs. non-mode-locked light Mode-locked pulse train: Non-mode-locked pulse train: ( ) ( ) ( 2 / ) m E F m Tw w  w p     exp( )( ) ( ) ( 2 / )m m iE F m Tw w   w p     Random phase for each mode A train of short pulses A mess… ( ) ( 2 / ) ( III( / 2 ) m F m T F Tw  w p w w p       ( ) () /exp( 2 )m m F m Tiw  w p     Docsity.com Numerical simulation of mode- locking Ultrafast lasers often have thousands of modes. Docsity.com A generic ultrashort-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 Docsity.com Pulsed Pumping Long and potentially complex pulse Pumping a laser medium with a short-pulse flash lamp yields a short pulse. Flash lamp pulses as short as ~1 µs 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. Docsity.com Passive mode- locking: the saturable absorber • Like a sponge, an absorbing medium can only absorb so much. High-intensity spikes burn through; low-intensity light is absorbed.  (I)   0 1  I Isat  0 1 1 / sat N N N I I        0 N  For a two- level system Docsity.com The effect of a saturable absorber First, 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) In te n s it y k = 1 k = 7 Notice that the weak pulses are suppressed, and the strong pulse shortens and is amplified. k = 2 k = 3 Docsity.com Passive mode- locking: the saturable absorber • High-intensity spikes (i.e., short pulses) see less loss and hence can lase while low-intensity backgrounds (i.e., long pulses) won’t. Docsity.com Saturabl e gain and loss The 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. Docsity.com The Passively Mode-locked Dye Laser Passively mode-locked dye lasers yield pulses as short as a few hundred fs. They’re limited by our ability to saturate the absorber. Pump beam Gain medium Saturable absorber Docsity.com Some common ayes anda their corresponding saturable absorbers Saturable Wavelength Gain dye absorber in nm Rh6G DODCI, DDI 575-620 Kiton Red DQOCI 600-655 DCM DODCI, DTDCI 620-660 Pyridine 1 DTDCI, DDI 670-740 LD 700 DTDCI, DDI, IR 140 700-800 Pyridine 2 IR 140, HITC 690-770 Styryl 9M DDI, IR 140 780-860 Docsity.com A lens and a lens x A 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 constant, but n varies with x: f(x) = n(x) k L n(x) x In both cases, a quadratic variation of the phase with x yields a lens. Docsity.com Kerr-lens mode- locking • A medium’s refractive index depends on the intensity. • n(I) = n0 + n2I • If the pulse is 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. Docsity.com Kerr-lensing is a type of saturable 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 Mirror Additional focusing optics can arrange for perfect overlap of the high-intensity beam back in the Ti:Sapphire crystal. But not the low- intensity beam! This is a type of saturable absorption. Docsity.com Titanium Sapphire It can be pumped with a (continuous) Argon 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. Absorption and emission spectra of Ti:Sapphire (nm) Docsity.com 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-velocity dispersion: • GVD spreads the pulse in time. And everything has GVD… • All fs lasers incorporate dispersion-compensating components. • We’ll spend several lectures discussing GVD!! • Etalon effects: • This yields multiple pulses, spreading the energy over time, weakening the pulses. The universe conspires to lengthen pulses. Docsity.com 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. cw pump beam Ti:Sapphire gain medium Prism dispersion compensator Slit for tuning Docsity.com Commercial fs lasers Cutput Power (Wi aH rel Le | rel a | —— oe versie | i ———- Wael game if 4 SW Wadigump _| | J 27a i cv | x __ aT | 38 pe m™ |S 4 f m4 _ _ TT <1 L bof to uf ome] Io oto to “S| aa l Lo Lo — Lo l l fou id Boa bio goa qq mon Wavelength (ami) Typical 2-VWawe Power Tuning Curves for Verdi-purnped Mira Optima gao-F Docsity.com Ytterbium Tungstate (Yb:KGW) Model t-Pulse 20 t-Pulse 100 t-Pulse 200 Pulse 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 other attractive properties, such as a very high thermal efficiency and high average power. Amplitude Systemes Docsity.com Active mode- locking • Any 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:Sapphire laser mode-locking. Docsity.com Hybrid mode- locking • Hybrid mode-locking is any type of mode-locking incorporating two or more techniques simultaneously. • Sync-pumping and passive mode- locking • Active and passive mode-locking • • However, using two lousy methods together doesn’t really work all that much better than one good method. Docsity.com Diode lasers use hybrid mode- locking Haneda, et al, UP 2004 Autocorrelation Spectrum Autocorrelation Spectrum Docsity.com Additive-pulse mode- locking • Nonlinear effects in an external cavity can yield a phase-distorted pulse, which can be combined in phase with the pulse in the main cavity, yielding cancellation in the wings, and hence pulse-shortening. Early fiber lasers used this mechanism. Docsity.com Ultrafast Q-switching using distributed feedback When two beams cross at an angle, their intensity is sinusoidal. When energy is deposited sinusoidally in space, the actual gain (g) goes quadratically with the energy deposited, yielding a type of very fast Q- switching. Using several stages, fs pulses have been created this way. Intensity fringes Docsity.com dye cell pump pulse Docsity.com Pump lasers for ultrafast lasers Previously, only the Argon Ion laser was available, but much more stable intracavity-frequency-doubled solid-state lasers are now available. Docsity.com