Short pulse oscillator The Amplification of Ultra- short Laser pulses Pulse compressor t Solid state amplifiers Dispersive delay line Short pulse oscillator

Pulse energy vs. Repetition rate “Table-Top Systems” Regen + multipass 10-9 10-6 100 10-3 Regen 1 W average power Pulse energy (J) Regen + multi-multi-pass RegA Cavity-dumped oscillator Oscillator 109 106 103 100 10-3 Rep rate (pulses per second)

E Ipeak = A t Pave = E r Maximum intensity on target Pulse energy E Ipeak = Increase the energy (E), Decrease the duration (t), Decrease the area of the focus (A). A t Beam area Pulse length Average power Signal is proportional to the number of photons on the detector per integration time. Pave = E r Pulse energy Rep rate

Transmission of output coupler: ~2% Cavity Dumping Before we consider amplification, recall that the intracavity pulse energy is ~50 times the output pulse energy. R=100% R=98% Eintracavity E E = Toutput Eintracavity Transmission of output coupler: ~2% What if we instead used two high reflectors, let the pulse energy build up, and then switch out the pulse. This is the opposite of Q-switching: it involves switching from minimum to maximum loss, and it’s called “Cavity Dumping.”

Cavity dumping: the Pockels cell A voltage (a few kV) turn the crystal into a half- or quarter-wave plate. V Pockels cell Polarizer If V = 0, the pulse polarization doesn’t change. If V = Vo, the pulse polarization switches to its orthogonal state. Abruptly switching a Pockels cell allows us to extract a pulse from a cavity. This allows us to achieve ~100 times the pulse energy at 1/100 the repetition rate (i.e., 100 nJ at 1 MHz).

Amplification of Laser Pulses, in General Very simply: a powerful laser pulse at one color pumps an amplifier medium, creating an inversion, which amplifies another pulse. Laser oscillator Amplifier medium Pump (ns or ms pulse) Energy levels

So should the ultrashort pulse arrive early or late? For femtosecond pulses - the ultrashort pulse is so much shorter than the (ns or ms) pump pulse that supplies the energy for amplification. So should the ultrashort pulse arrive early or late? Energy decays and is wasted. Pump energy arrives too late and is wasted. Early: Late: pump pump time time In both cases, pump pulse energy is wasted, and amplification is poor.

So we need many passes. All ultrashort-pulse amplifiers are multi-pass. The ultrashort pulse returns many times to eventually extract most of the energy. time pump This approach achieves much greater efficiency.

Two Main Amplification Methods Multi-pass amplifier Regenerative amplifier pump input output gain Pockels cell polarizer gain pump input/output

Regenerative Amp. – kHz rep.rate design Faraday rotator Thin Film Polarizer thin-film polarizer

after injection pulse of the PC: 90o - on the way in: 0o after injection pulse of the PC: 90o during amplification rounds (PC off): stay 90o after ejection pulse of the PC: 0o 90o 0o 45o 0o Pulse polarization add 45o independent of the propagation direction: (0o to 45o) (45o to 90o) set such that: - on the way in: subtract 45o - on the way out: add 45o thin-film polarizer

A Multi-Pass Amplifier A Pockels cell (PC) and a pair of polarizers are used to inject a single pulse into the amplifier

A PROBLEM: Pulse intensities inside an amplifier can become so high that damage, self focusing, SPM occurs at the crystal, PC, TFP. Solution: Expand the beam and use large amplifier media. Usually, that’s still not enough. Expand the pulse in time, too.

Chirped-Pulse Amplification Short pulse oscillator CPA is THE big development. G. Mourou and coworkers 1983 t Dispersive delay line t Solid state amplifier(s) Chirped-pulse amplification involves stretching the pulse before amplifying it, and then compressing it later. t Pulse compressor We can stretch the pulse by a factor of 10,000, amplify it, and then recompress it! t

Stretching and Compressing Ultrashort Pulses – introduce dispersion of opposite signs ! Pulse stretcher d f 2f grating This looks just like a “zero-dispersion stretcher” we mentioned in pulse shaping. But when d ≠ f, it’s a dispersive stretcher and can stretch fs pulses by a factor of 10,000! With the opposite sign of d-f (or with two grating-pair set-up), we can compress the pulse. Usually, one uses mirrors instead of lenses.

CPA vs. Direct Amplification 0,0001 0,001 0,01 0,1 1 10 100 Nd:Glass Ti:sapphire Fluence (J/cm2) Direct Amplification Excimers Dyes 1 10 100 1000 4 5 6 (1 ns) Pulse Duration (fs) CPA achieves the fluence of long pulses but at a shorter pulse length!

Regenerative Chirped-Pulse Amplification with a kHz pulsed pump.   Wavelength: 800 nm (Repetition rates of 1 to 50 kHz) High Energy: <130 fs, >2 mJ at 1 kHz Short Pulse: <50 fs, >0.7 mJ at 1 kHz

CPA works ! Still, there are some issues (especially if you try to push for really high energies): Gain saturation Gain narrowing Thermal aberrations Contrast ratio

Single-pass Amplification Math Assume a saturable gain medium and J is the fluence (energy/area). Assume all the pump energy is stored in the amplifier, but it will only have so much energy. Amplifier medium pump Jin Jpump Jout Jsat lL lpump Jsto Jsto= stored pump fluence = Jpump*(lpump/lL) Jsat= saturation fluence (material dependent) At low intensity, the gain is linear: (small fraction of stored energy is used over dz) At high intensity, the gain “saturates” and hence is constant: (all the excited molecules are stimulated down) (all the stored energy is used over dz) Intermediate case interpolates between the two:

Single-pass Amplification Math This differential equation can be integrated to yield the Frantz-Nodvick equation for the output of a saturated amplifier: where the small signal gain per pass is given by: (Jin – before the gain medium; Jout – after the gain medium)

Frantz-Nodvick equation J G  exp( g L)  exp( sto L) J sat 1 1,2 1,4 1,6 1,8 2 2,2 2,4 2,6 Jout/Jin Gain 1 2 3 4 5 Losses ~ 10% (prop. to Jin !!!) J /J Without considering losses: in sat 30 passes ~ 105 gain 35 passes ~ 106 gain 40 passes ~ 107 gain (1 nJ to 0.1 mJ) (1 nJ to 1 mJ) (1 nJ to 1 mJ)

Gain Narrowing If G(w) = exp(-aw2), On each pass through an amplifier, the pulse spectrum gets multiplied by the gain spectrum, which narrows the output spectrum—and lengthens the pulse! If G(w) = exp(-aw2), then after N passes, the effective gain spectrum will become GN(w) = exp(-Naw2), which is narrower by N1/2 Different spectral components of the pulse experience different gain.

Gain Narrowing Example Ti:sapphire gain cross section (effective gain gets narrower according to number of passes) ~15-fs pulse in 0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 2.5 3 Normalized spectral intensity 65-nm FWHM Cross section (*10^-19 cm^2) 32-nm FWHM (longer pulse out) 650 700 750 800 850 900 950 1000 Wavelength (nm) Factor of 2 loss in pulse bandwidth for 107 gain

Beating gain narrowing Birefringent plate Polarizer E Introduce some loss at the gain peak to reduce the high gain there. Gain and loss Spectrum: before and after Gain & modulation 650 850 900 Wavelength (nanometers) 700 750 800 1 1.5 2 2.5 950 20% Gain modulation Before After with filter without filter Spectrum Wavelength (nm) We can use up to half of the gain bandwidth. ~10 fs in Ti:sapphire

Thermal Effects (aberrations) in Amplifiers The pump pulse deposits significant energy into the gain medium. At best - the energy extracted by light is ~40% for Ti:Sapphire (500nm/800nm~0.6). The reminder goes into heat ! The heat deposition causes thermal gradients and resulting changes of the index of refraction and, thus, lensing, small-scale self-focusing, thermally-induced birefringence, and distortions to the beam mode. These thermal aberrations increase the beam size and reduce the available intensity (needed for the further amplification). Ipeak = E A t

Thermal Effects (aberrations) in Amplifiers For proper operation – the Ti:Sapphire crystal needs to be cooled. For a given feasible pulse energy - the cooling time limits the rep. rate. Low temperatures enhance the thermal conductivity and, thus, allow a more efficient cooling and higher repetition rates. (need < -140oC : cryogenic cooling) The heating - limit the power (pulse energy * rep.rate) that can be extracted from the laser system !

Static Wave-front Correction (properly designed optics) 2.5 times improvement in peak intensity has been achieved CUOS

Dynamic Correction of Spatial Distortion (after the laser system) 50 mm diameter 37 actuators

Contrast ratio The pulse has leading and following satellite pulses. - pre/post-pulses from oscillator - pre/post-pulses from amplifier - ASE from amplifier

Amplification reduces the contrast by a factor of up to 10. Amplified Spontaneous Emission (ASE) Fluorescence from the gain medium is amplified before the ultrashort pulse arrives. This yields a 10-30 ns background with low peak power but large energy. Depends on the noise present in the amplifier at t = 0 ASE shares the gain and the excited population with the pulse. Amplification reduces the contrast by a factor of up to 10.

A Pockels cell “Pulse Picker” A Pockels cell can pick a pulse from a train and suppress satellites. To do so, we must switch the voltage from 0 to kV and back to 0, typically in a few ns. few ns V Voltage Time (Switching high voltage twice in a few ns is quite difficult, requiring avalanche transistors, microwave triodes, or other high-speed electronics.)

Pockels cells suppress pre- and post-pulses. 10 ns oscillator Pockels cells stretcher 10-2-10-3 Unfortunately, Pockels cells aren’t perfect. They leak ~1%. amplifier compressor

Issues in Ultrafast Amplification and Their Solutions Pulse length discrepancies: Multi-pass amplifiers and regenerative amplifiers (“Regens”). Damage: Chirped-Pulse Amplification (CPA) Gain saturation: Frantz-Nodvick Equation Gain narrowing: birefringent filters Thermal effects: cold and wavefront correction Satellite pulses, Contrast, and Amplified Spontaneous Emission: Pockels’ cells Commercial systems: lots of money! Pockels cell polarizer gain pump input/output