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

2. 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)

3. 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

4. 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.”

5. 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).

6. 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

7. 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.

8. 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.

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

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

11. 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

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

13. 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.

14. 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

15. 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.

16. 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!

17. 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

18. 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

19. 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:

20. 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)

21. Frantz-Nodvick equationJ 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)

22. 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.

23. 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

24. 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

25. 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

26. 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 !

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

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

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

30. 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 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.

31. 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.)

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

33. 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