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

P3 LAS 2010 Femtosekundové lasery Slajdy : Prof Rick TREBINO, Kurz Utrafast optics, Georgia Tech, USA

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 2000 SHORTEST PULSE DURATION 10ps 1ps 100fs 10fs 2005 Nd:fiber The shortest pulse vs. year (for different media) Erich Ippen, MIT

Continuous vs. ultrashort pulses of light A constant and a delta-function are a Fourier-Transform pair. Irradiance vs. time Spectrum Continuous beam: Ultrashort pulse: time frequency time 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. Irradiance vs. time Spectrum Long pulse time frequency Short pulse time 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. Laser power

Light bulbs, lasers, and ultrashort pulses 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?

Generating short pulses = mode-locking Locking the phases of the laser modes yields an ultrashort pulse.

Locked modes Intensities Didomenico, J. Appl. Phys. 35, 2870 (1964). Hargrove, et al., Appl. Phys. Lett., 5, 4 (1964).

Numerical simulation of mode-locking Ultrafast lasers often have thousands of modes.

A generic ultrashort-pulse laser A generic ultrafast laser has a broadband gain medium, a pulse-shortening device, and two or more mirrors: Mode-locker Many pulse-shortening devices have been proposed and used.

Passive mode-locking: the saturable absorber For a two-level system Like a sponge, an absorbing medium can only absorb so much. High-intensity spikes burn through; low-intensity light is absorbed.

The effect of a saturable absorber First, imagine raster-scanning the pulse vs. time like this: k = 7 Intensity Short time (fs) k = 3 k = 2 k = 1 Round trips (k) Notice that the weak pulses are suppressed, and the strong pulse shortens and is amplified. After many round trips, even a slightly saturable absorber can yield a very short pulse.

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.

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. 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 Lasers lase when the gain exceeds the loss. The combination of saturable absorption and saturable gain yields short pulses even when the absorber is slower than the pulse.

The Passively Mode-locked Dye Laser Pump beam Gain medium Saturable absorber Passively mode-locked dye lasers yield pulses as short as a few hundred fs. They’re limited by our ability to saturate the absorber.

Some common dyes and their corresponding saturable absorbers

Colliding pulses have a higher peak intensity. Longitudinal position, z Intensity Single pulse Two pulses colliding And higher intensity in the saturable absorber is what CPM lasers require.

The colliding-pulse mode-locked (CPM) laser A Sagnac interferometer is ideal for creating colliding pulses. Beam- splitter Gain medium Saturable absorber CPM dye lasers produce even shorter pulses: ~30 fs.

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) In both cases, a quadratic variation of the phase with x yields a lens. x Now what if L is constant, but n varies with x: f(x) = n(x) k L n(x)

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. Losses are too high for a low-intensity cw mode to lase, but not for high-intensity fs pulse. Kerr-lensing is the mode-locking mechanism of the Ti:Sapphire laser.

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 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! Ti:Sapph Low-intensity pulse This is a type of saturable absorption.

Modeling Kerr-lens mode-locking

Titanium Sapphire (Ti:Sapphire) oxygen aluminum Al2O3 lattice 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. Slide used with permission from Dan Mittleman

Absorption and emission spectra of Ti:Sapphire Titanium Sapphire Absorption and emission spectra of Ti:Sapphire (nm) 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.

Mechanisms that limit pulse shortening The universe conspires to lengthen pulses. 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 Ti:Sapphire laser including dispersion compensation Adding two prisms compensates for dispersion in the Ti:Sapphire crystal and mirrors. cw pump beam Ti:Sapphire gain medium Prism dispersion compensator Slit for tuning This is currently the workhorse laser of the ultrafast optics community.

Commercial fs lasers Ti: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, ~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 (cont’d)

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 other attractive properties, such as a very high thermal efficiency and high average power. Amplitude Systemes The result is a family of compact and reliable lasers, with high average power, exceptional energy per pulse and excellent pulse-to-pulse stability. The latest model in the t-Pulse series delivers an unprecedented 200 nJ of energy, the highest value ever offered from a commercial femtosecond oscillator. Model t-Pulse 20 t-Pulse 100 t-Pulse 200 Pulse energy (nJ) 20 100 200 Average power (W) 1 2 Repetition rate (MHz) 50 10

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.

Gain switching Modulating the gain rapidly is essentially the same as active mode-locking. This method is a common one for mode-locking semiconductor lasers.

Synchronous pumping Pumping the gain medium with a train of already short pulses yields a train of even shorter pulses. Pump beam Gain medium Saturable absorber Short pulses (ps) The laser round-trip time must precisely match that of the train of pump pulses! Trains of 60 ps pulses from a Nd:YAG laser can yield <1 ps pulses from a sync-pumped dye laser.

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.

Diode lasers use hybrid mode-locking Autocorrelation Spectrum Autocorrelation Spectrum Kentaro Haneda†, Hiroyuki Yokoyama††, Yo Ogawa†††, and Masataka Nakazawa† †Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai-shi, Miyagi-ken 980-8577, Japan Tel: +81-22-217-5525, Fax: +81-22-217-5524, E-mail: kenbz@riec.tohoku.ac.jp ††New Industry Creation Hatchery Center, Tohoku University, Aoba, Aramakiaza, Aoba-ku, Sendai-shi, Miyagi-ken 980-8577, Japan †††Oki Electric Industry Co., Ltd., 550-1 Higashiasakawa-machi, Hachioji-shi, Tokyo, 193-8550, Japan The 10 GHz external-cavity MLLD has an active layer with an InGaAs/InGaAsP strained MQW structure, and has a saturable absorber (SA) as a mode-locker. Hybrid mode locking is achieved with RF modulation in the SA section [2]. A laser cavity is formed by the facet at the SA section with an HR coating and an external-mirror (R = 80 %). The 40 GHz monolithic MLLD [3] has an actively mode-locked laser that uses an electro-absorption (EA) modulator. Haneda, et al, UP 2004

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.

The soliton laser Nonlinear-optical effects can compensate for dispersion, yielding a soliton, which can be very short and remain very short, despite dispersion and nonlinear-optical effects.

Commercial fs fiber lasers Erbium Menlo Systems 150 fs; 150 mW IMRA America Frequency-doubled

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.