A Pockels cell is a device that can switch a pulse (in and) out of a resonator. It’s used in Q-switches and cavity dumpers. A voltage (a few kV) can turn a crystal into a half- or quarter-wave plate. V
dJ g0 J dz dJ g 0 J sat dz dJ g 0 J sat 1 e J / J sat dz


Single-pass Amplification Math
This differential equation can be integrated to yield the FrantzNodvick equation for the output of a saturated amplifier:
Pulse energy vs. Repetition rate
100 Pulse energy (J) Regen + multipass Regen 10-3 Regen + multimulti-pass RegA Cavity-dumped oscillator Oscillator 10-3 100 103 Rep rate (pps) 106 109 1 W average power
lpump lL
Energy levels
Jpump (lpump/lL)
Laser oscillator
Amplifier medium
Nanosecond-pulse laser amplifiers pumped by other ns lasers are commonplace.
Single-pass Amplification Math
Another problem with amplifying ultrashort laser pulses…
Another issue is that 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?
pump
input/ output gain
Gain n: Frantz-Nodvick Equation
Gain narrowing: Birefringent filters
Thermal effects: cold and wavefront correction
Satellite pulses, Contrast, and Amplified Spontaneous Emission: Pockels’ cells Systems cost lots of money: Earn more money… polarizer Pockels cell
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).
Issues in Ultrafast Amplification and Their Solutions
Pulse length discrepancies: Multi-pass amplifiers and regenerative amplifiers (“Regens”).
Damage: Chirped-Pulse Amplification (CPA)
pump Jpump Jin lL Amplifier medium Jsto Jsat
lpump
Jout
Assume a saturable gain medium and J is the fluence (energy/area). Assume all the pump energy is stored in the amplifier, but saturation effects will occur.
Short pulse oscillator
The Amplification of Ultrashort Laser Pulses
t
Dispersive delay line
Most of this lecture courtesy of Francois Salin
t
Solid state amplifier
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. Pump
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. pump time
Jsto= stored pump fluence = Jpump (lpump/lL) Jsat= saturation fluence (material dependent)
At low intensity, the gain is linear: At high intensity, the gain “saturates” and hence is constant: Intermediate case interpolates between the two:
J out
J in J sat log G0 exp J sat
1 1
where the small signal gain per pass is given by:
J sto G0 exp( g0 L) exp( ) J sat
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
Frantz-Nodvick equation
J out J in J sat log G0 exp J sat
2,6
2,4 2,2 2 1,8 1,6 1,4 1,2 1 0 1 2 0,4 0,2 0
1 1
10-6
10-9
What are the goals in ultrashort pulse amplification?
Maximum intensity on target
E Ipeak = A t
Beam area
Pulse energy
Increase the energy (E), Decrease the duration (t), Decrease the area of the focus (A).
Pump energy arrives too late and is wasted. Energy decays and is wasted.
Early:
Late:
pump time
pump time
In both cases, pump pulse energy is wasted, and amplification is poor.
This approach achieves much greater efficiency.
Two main amplification methods
Multi-pass amplifier pump input Regenerative amplifier pump
Eintracavity E R=100% R=98%
Transmission of output coupler: ~2%
E = Toutput Eintracavity
What if we instead used two high reflectors, let the pulse energy build up, and then switch out the pulse?
Polarizer
Pockels cell
If V = 0, the pulse polarization doesn’t change. If V = Vp, the pulse polarization switches to its orthogonal state.
(voltage may be transverse or longitudinal)
Center for Intense Lasers and Applications (CELIA) Université Bordeaux I, France
t
Pulse compressor