1. Chirped pulse amplification
OPO OVERVIEW
Second harmonic, difference frequency, optical parametric oscillation
:Phase matching
:Phase matching with periodically poled crystals
Broadband parametric amplification
Chirped pulse amplification
Fourier plane optical parametric amplification (FOPA)

2. LOSS GAIN GAIN SF DF OPG or OPO or OPA
Second harmonic, difference frequency, optical parametric oscillation
LOSS
GAIN
GAIN SF DF
OPG
or OPO or OPA

3. What is the difference between population inversion gain
Second harmonic, difference frequency, optical parametric oscillation
What is the difference between population inversion gain
and optical parametric gain?
Population inversion OPG
Lasts after the pump Instantaneous
Energy dissipation no dissipation in matter
(relaxation mechanisms)
Analogy?

4. Analogy: population inversion gain versus optical parametric gain
TIME Ip
TIME Ip G A I N
TIME G A I N
TIME

5. TYPE I Phase matching Phase matching in second harmonic generation
Fundamental
Phase matching
Second harmonic
dE2 dz
= a E12
SHG E2
Different wavelengths
dE1 dz
= -a E2E1*
ENERGY EXCHANGE ALWAYS
FROM 1 TO 2
Distance z

6. TYPE II Phase matching Phase matching in second harmonic generation
SHG
dE2 dz
= a EoEe
Phase matching
dEo dz
= -a E2Ee* Eo
dEe dz
= -a E2Eo* Ee
THE SIGN OF ENERGY
EXCHANGE CAN CHANGE
Distance z

7. Tuning the crystal length for optimum short pulse compression
LONG CRYSTALS = HIGHER CONVERSION
LONG CRYSTALS = NARROWER BANDWIDTH
The obvious solution for short pulses: short crystals? Not always!
One can use long crystals to compress pulses down
to femtoseconds.
THE GENERATED PULSES ARE SHORTER THAN
THE FUNDAMENTAL, AND THAN THE INVERSE
BANDWIDTH OF THE SECOND HARMONIC PROCESS.
Where does one get the bandwidth?
From the amplitude modulation of the pump,
as the pump is depleted at a faster rate than
the pump risetime.

8. Compression in SHG
Motion of pulses in the frame of reference of the second harmonic
Weak pulses: the second harmonic broadens as the
overlap of the two fundamental pulses increases

9. Strong pulses Compression in SHG
Motion of pulses in the frame of reference of the second harmonic
Strong pulses
The trick: sum frequency group velocity between that of fundamental o and fundamental e

11. Phase matching with periodically poled crystals
Use the orientation for
maximum NL coefficient.
Periodically reverse the sign
of the coefficient (a),
when
SHG E2
sin Dk z = sin (k2 - 2k1z)
changes sign
Distance z
dE2 dz
= a E12
Advantage: Large nonlinearity
dE1 dz
= -a E2E1*
Disadvantage: Periodic structure
Narrow band

12. (a)
(b)
(c)

13. Find the angles? SNLO
CHIRP AMPLIFICATION

14. There are two solutions to the narrow bandwidth
of Periodically Poled crystals:
1. Pole the crystal “non-periodically”
“ENGINEERABLE COMPRESSION OF ULTRASHORT PULSES BY USE OF
SECOND HARMONIC GENERATION IN CHIRPED-PERIOD-POLED
LITHIUM NIOBATE”, Optics Letters 22, 1341 (1997)
“SIMULTANEOUS FEMTOSECOOND-PULSE COMPRESSION AND SHG
IN APERIODICALLY POLED KTiOPO4”, Optics Letters 24, 1071 (1999)
2. Convert the spectrum piece by piece x
Periodically poled
crystal of period
changing with x.

15. Other solution: use many crystals for each wavelength range
grating
Laser source y
grating
This is part of OPCPA

16. CHIRPED PULSE AMPLIFICATION
LASER DAMAGE
CHIRPED PULSE AMPLIFICATION
LINEAR
DISPERSION
(+)
LINEAR
DISPERSION
(-)
AMPLIFIED
SHORT
PULSE
SHORT
PULSE
GAIN
If the parametric gain is sufficiently broad for the short
pulse, it is also sufficiently broad for the dispersed pulse.
THE PARAMETRIC GAIN HAS NO ENERGY STORAGE:
THE DURATION OF HAVE TO BE MATCHED
PUMP
SIGNAL
PUMP DEPLETION: “DIP” IN PUMP.
TECHNICAL CHALLENGE: PUMP 100 ps OR LESS
SIGNAL STRETCHED TO > 100 ps.

17. Motivation for 5-fs (2-cycle) lasers
Relativistic HHG
5 fs cos
Generation of single attosecond light and
electron pulses in gas and plasma medium
20 fs
5 fs cos
5 fs sin
Gas harmonics
l3 regime
A. Baltuska et al., IEEE J. of Sel. Top. in Quantum Electronics 9, 972 (2003)
G. D. Tsakiris et al., New J. Phys. 8, 19 (2006)
A. Baltuska et al., IEEE J. of Sel. Top. in Quantum Electronics 9, 972 (2003)
N. M.Naumova et al., Phys. Plas. 12, (2005)
G. D. Tsakiris et al., New J. Phys. 8, 19 (2006)
A. Baltuska et al., IEEE J. of Sel. Top. in Quantum Electronics 9, 972 (2003)

18. Optical parametric chirped pulse amplification (OPCPA)
Pump
Signal
Idler
BBO
Advantages
Broad gain bandwidth,
supporting few-cycle pulses
Good contrast achievable
...
* D. Herrmann et al. Opt. Lett., 34, 2459 (2009)
F. Tavella et al. Opt. Lett. 32, 2227 (2007)
S. Witte et al. Opt. Express 14, 8168 (2006)
S. Adachi et al. Opt. Express 16, (2008)

19. Synthesizer principles
Parallel synthesis
Pro:
Shorter „beam path“
Simple narrow bandwidth mirrors
Contra:
Interferometric stability needed
Very sensitive  high rep.rate
Broad bandwidth mirrors after beam combination
Similar principle: frequency domain OPA l Il
Serial synthesis
Pro:
No special requirements on stability
Insensitive
Contra:
Longer „beam path“
Broad bandwidth mirrors
S.-W. Huang et al. Nat. Photon 5, 475 (2011)
C. Manzoni et al. Opt. Lett. 37, 1880 (2012)
B. E. Schmidt et al. Nat. Commun. 5, 3643 (2014)
D. Herrmann et al., Opt. Exp. 18, p (2010)
A. Harth et al. Opt. Express 20, 3076 (2012) 19

20. Multi-10-TW sub-5-fs Optical Parametric Synthesizer
− Relativistic intensity sub-5-femtosecond laser pulses
and their applications
Laszlo Veisz1, Daniel Rivas1, Gilad Marcus1, Xun Gu1, Daniel Cardenas1, Jiancai Xu1, Julia Mikhailova1, Alexander Buck1,2, Tibor Wittmann1, Christopher M. S. Sears1, Daniel Herrmann3, Olga Razskazovskaya2, Vladimir Pervak2, Ferenc Krausz1,2
1 Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, Garching, Germany
2 Ludwig-Maximilians-Universität München, Am Coulombwall 1, Garching, Germany
3 Lehrstuhl für BioMolekulare Optik, Department für Physik, Ludwig-Maximilians-Universität,Oettingenstrasse 67, München, Germany 20

21. Fourier plane optical parametric amplification (FOPA)
Faux pas L
grating
Laser source y
grating
This is part of OPCPA
PUMP

22. A collimated Gaussian beam of 2 mm diameter FWHM, 800 nm, is incident
on a pair of gratings of 1700 grooves/mm, at an angle of incidence of 30
degrees (see Fig. ). The spacing between the gratings is L = 10 cm. After
the gratings, the diffracted beam is incident on 4 independent modulators,
each of height Δy = 2 mm.
Assuming a Gaussian pulse of g = 40 fs duration, calculate the duration and
chirp of the pulse entering each 2 mm section (you are sampling a fraction
of the spectrum of the pulse diffracted by the gratings). You can make
abstraction of the spatial problem for this question.
Two approaches possible:
(a) see which wavelength correspond to each section boundaries. That
defines the spectrum. The inverse of the spectrum gives the pulse
duration
(b) Calculate the second order dispersion of the pair of gratings. That give
the pulse broadening and chirp introduced by the pair of gratings.

23. (b) Calculate the second order dispersion of the pair of gratings
(b) Calculate the second order dispersion of the pair of gratings. That give
the pulse broadening and chirp introduced by the pair of gratings.

24. TIME
SPACE

25. the pulse broadening and chirp introduced by the pair of gratings.
(b) Calculate the second order dispersion of the pair of gratings. That give
the pulse broadening and chirp introduced by the pair of gratings.
If m is the order of diffraction, the angle of incidence
and the diffraction angle are related through the grating equation

26. (a) see which wavelength correspond to each section boundaries. That
defines the spectrum. The inverse of the spectrum gives the pulse
duration