Amplificarea pulsurilor laser ultrascurte. CPA in Ti:safir sau OPCPA? Solutii pentru laserul ELI-RO.

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Amplificarea pulsurilor laser ultrascurte. CPA in
Tisafir sau OPCPA? Solutii pentru laserul
ELI-RO. (Partea II)
R. Dabu Sectia Laseri, INFLPR
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• CUPRINS
• 1. Amplificarea pulsurilor laser cu deriva de
  frecventa (chirped pulse amplification - CPA)
  in Tisafir.
• - Caractersiticile Tisafir ca mediu
  amplificator laser.
• - Probleme legate de amplificarea pulsurilor
  de femtosecunde de mare energie.
• 2. Ce este amplificarea parametrica si, in
  particular, OPCPA.
• - Oscilatia, generarea si amplificarea
  parametrica ca fenomene in optica neliniara.
• - Relatiile care guverneaza fenomenele
  parametrice.
• - Castigul unui amplificator parametric, banda
  de frecventa.
• 3. Amplificare parametrica optica (OPA) de banda
  larga si de banda foarte larga.
• - Conditiile de obtinere a amplificarii
  parametrice de banda larga sau foarte larga.
• - Cum se calculeaza pentru un cristal dat
  parametrii de functionare in cele doua cazuri.
• - Potentialul aplicarii pentru laserii cu
  pulsuri ultrascurte de mare putere.
• - Amplificarea parametrica a pulsurilor
  largite cu deriva de frecventa OPCPA.
• - Metode de obtinere a amplificarii de banda
  larga la degenerescenta, amplificare
  necoliniara, folosirea mai multor laseri de
  pompaj. Exemple.
• - Metode de obtinere a amplificarii de banda
  foarte larga. Benzile de amplificare foarte larga
  in cristale BBO si DKDP pentru laserii din clasa
  PW.
• 4. Prezentarea unor sisteme laser amplificatoare
  in domeniul PW
• - Laserul rusesc cu oscilator in fs la 1250 nm
  (Crforsterite) si amplificare in cristale DKDP.
• Laserul englez (910 nm) cu amplificare de mare
  energie in DKDP.

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Second-order nonlinear wave mixing
Polarization - electric dipole moment per unit
of volume Polarization vector P induced in a
medium
where E is the electric field strength of an
applied optical wave, e0 is the free-space
permittivity,
are the first-order (linear), second-order,
third-order susceptibility of the medium.
Second-order nonlinear optical processes are
generated by the second-order nonlinear
polarization
Second-order nonlinear three-wave
interactions Second-harmonic generation (SHG)
Sum/difference frequency generation (SFG, DFG)
Optical parametric generation, amplification and
oscillation (OPG, OPA, OPO)
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Optical parametric amplification (OPA)
p-pump s signal i - idler
?p ?s ?i ?p gt ?s gt ?i
Non-linear crystal
?p
?p
?s
?s
?i
Optical axis
?
Collinear OPA
?
a
ß
Non-collinear OPA - NOPA
(a), (b), (c) - OPO (d) - OPG (e) - OPA
Byer, R.L. Optical Parametric Oscillators. In
Quantum Electronics A Treatise, Rabin, H. Tang,
C.L., Eds Academic Press, New-York, San
Francisco, London, 1975 Vol. 1, Nonlinear
Optics, Part B, 587-702. R. Dabu,
Parametric Oscillators and Amplifiers in
Encyclopedia of Optical Engineering, Marcel
Dekker, New York, published online in 2004
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Parametric process
Monochromatic plane wave propagating along z-axis
Equation of electric field propagation
Nonlinear induced polarization at
Assuming collinear wave-vectors
slowly-varying-amplitude approximation
Propagation equation for the signal amplitude
Coupled equations that describe the parametric
amplification process (neglected waves absorption
in crystal)
, wave-vector mismatch
perfect phase-matching
, effective nonlinear optical coefficient m/V
Efficient parametric process
G. Cerullo at al, Rev. Sci. Instrum., 74, 1
(2003) R. Dabu et al, Optica neliniara,
Editura Univ. Bucuresti, 2007
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Distinct features of laser medium amplification
and OPA
Laser medium amplification OPA
During the existence of the inverted population (energy accumulated on the upper laser level) For Tisapphire 1 µs after the pump pulse 10-100 ns precision of pump and signal pulse synchronisation During the pump and signal pulse temporal overlapping Pump and signal pulse of the same duration Pump-signal pulse synchronisation lt(pump/signal pulse duration)/10
Thermal loading Part of the pump energy ( 33 in case of Tisapphire) is dissipated in the amplifying medium No thermal loading Nonlinear crystal are transparent for the interacting beams wavelength
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Parametric gain
small initial signal amplitude
no initial idler beam
neglected pump depletion L, length of nonlinear
crystal
Parametric gain
where
Low parametric gain,
High parametric gain,
R. Dabu et al, Optica neliniara, Editura
Univ. Bucuresti, 2007
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OPA with ultrashort pulses
Frame of reference moving with GV of pump pulse,
GVM between pump and signal/idler pulses limits
the interaction length of parametric
amplification
GVM between signal and idler pulses determines
the phase-matching band-width for the parametric
amplification process Gain band-width is given by

G. Cerullo at al, Rev. Sci. Instrum., 74, 1 (2003)
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Collinear OPA phase-matching band-width within
large gain approximation
Wave-vector mismatch, ?k
Phase matching

• First order wave-vector mismatch, ?k(1) ? 0
• FWHM phase matching band-width

2. Second order wave-vector mismatch, ?k(1) 0,
?k(2) ? 0
Broad band-width
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Basic papers
- A. Dubietis, G. Jonusauskas, and A. Piskarskas.
Powerful femtosecond pulse generation by chirped
and stretched pulse parametric amplification in
BBO crystal. Optics Commun. 88, 437 (1992). -
Ross, I.N. Matousek, P. Towrie, M. Langley,
A.J. Collier, J. The prospects for ultrashort
pulse duration and ultrahigh intensity using
optical parametric chirped pulse amplifiers.
Optics Commun. 144, 125-133 (1997). - Collier,
J. Hernandez-Gomez, C. Ross, I.N. Matousek,
P. Danson, C.N. Walczak, J. Evaluation of
ultrabroadband high-gain amplification technique
for chirped pulse amplification facilities.
Appl. Opt., 38, 7486-7493 (1999). - I. N. Ross,
J. L. Collier,, K. Osvay, Generation of
terawatt pulses by use of optical parametric
chirped pulse amplification, Appl. Opt. 39, 2422
(2000).
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Optical parametric chirped pulse amplification -
OPCPA
Key principle of OPCPA A broad bandwidth
linearly chirped signal pulse is amplified with
an energetic and relatively narrow-band pump
pulse of approximately the same duration

• Key features
• High signal gain (up to ten orders of magnitude
  per cm)
• Broad bandwidth (ultrashort re-compressed
  pulses)
• Small B integral
• Negligible thermal loading
• High signal - noise contrast ratio
• High energy pulses in available large non-linear
  crystals, no transversal lasing
• Unlike ultrafast pulses OPA, there is no
  practical restriction concerning GVM of pump and
  signal/idler pulses (crystal length)
• Precise time/space synchronization of signal and
  pump pulses
• High intensity and high quality pump beams
  required
• Short (ps-ns) pump pulse duration

B integral total on-axis nonlinear phase-shift
accumulated through the amplifier chain
n2 nonlinear index quantifying the Kerr
nonlinearity, I(z) signal intensity B lt 1 if B
gt 3-5, self-focusing could appear
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Broad-band OPCPA
a) Near degeneracy,
Collinear OPCPA
Signal/idler wavelength nm ? degree Bandwidth nm Pulse duration fs
?S 750 ?I 1830 21.6 4.4 189
?S 800 ?I 1588 22.1 5.4 173
?S 850 ?I 1422 22.4 7.7 137
?S 900 ?I 1301 22.6 13.1 91
?S ?I 1064 22.8 99.8 17
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Broad-band OPCPA
b) Non-collinear OPCPA - NOPCPA
Phase matching
?
a
ß
y
x
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Noncollinear phase-matching in BBO crystal
Crystal optical axis
?
pump
a
ß
signal
BBO crystal
(internal)
? p532 nm
? s 800 nm
?i 1588 nm
R. Butkus, LEI-2009, Brasov
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Dependence of spectrum on pump-signal angle
BBO-I noncollinear OPCPA
300 ps
?24.50 F00
Amplified signal spectra a, b, c for a41.5,
41and 30 mrad
X. Yang et al, Appl Phys B, 73, 219 (2001)
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Broad band OPCPA
c) Multi-beam pumped OPCPA
Ndglass pump (1 ps)
165 cm-1 -gt 8.6 nm
E. Žeromskis et al, Opt. Commun. 203, 435 (2002).
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Ultra-broad-band OPCPA
a) Noncollinear OPCPA,

first-order and second-order phase mismatch
terms
b) Pre-chirp control ? collinear OPCPA,
relatively
broad-band linearly chirped pump laser pulse,
nonlinearly ultra-broad
bandwidth chirped signal pulse
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a) Noncollinear OPCPA, first-order and
second-order phase mismatch terms 0,
Crystal optical axis
(1) Phase matching, (?k)(0) 0
?
a
ß
y
(2) First order phase-mismatch, (?k)(1) 0
(3) Second order phase-mismatch, (?k)(2) 0
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a) Noncollinear OPCPA, first-order and
second-order phase mismatch terms 0
IP 1 GW/cm2
Uniaxial negative crystals, ne lt no
?-BaB2O4 (BBO) I crystal
KD2PO4 (DKDP,KDP) I crystal
KH2PO4 (KDP) I crystal
V.V. Lozhkarev et al, Laser Physics, Vol. 15,
1319 (2005)
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Conditions to obtain the ultra-broad-band
amplification bandwidth
KDP DKDP BBO
Critical wavelength, ? 984 nm 1120 nm 1430 nm

(ultra-broad-band PM) Never fulfiled 910 nm 800 nm
V.V. Lozhkarev et al, Laser Physics, Vol. 15,
1319 (2005)
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• The principle of pre-chirp control
• If we adjust the chirp ratio between the pump and
  the signal to compensate the group velocity
  mismatch and group velocity dispersion mismatch,
  we could increase the energy transfer efficiency
  of the parametric process.
• At the same time, the gain bandwidth would match
  the parametric bandwidth.

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Collinear OPCPA, pumping by a relatively
broad-band linearly chirped pump laser pulse
Collinear chirp-compensated amplifier-
ultra-broad-band generation around degeneracy
Linear chirp in the pump pulse requires a signal
with quadratic chirp to provide temporal overlap
of phase matched spectral components.
J. Limpert et al, Opt. Express, Vol. 13, 7386
(2005)
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Collinear chirp-compensated amplifier-
experimental set-up
UV pump pulses are positively stretched in the
prism sequence to 550 fs Supercontinuum is
generated in a 5-cm length photonic crystal fiber
J. Limpert et al, Opt. Express, Vol. 13, 7386
(2005)
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Short-pulse source at 910 nm suitable seed for
high energy OPCPA system
Central Laser Facility, Rutherford Appleton
Laboratory, Chilton, Oxon, UK
Linearly negative GVD stretched pump seed pulses
2 nm/ps SHG at 400 nm in 0.2 mm BBO crystal,
6.8 nm bandwidth, 110 µJ pulse energy, 1 nm/ps
linear chirp Signal seed pulse at 714 nm the air
and glass stretcher were adjusted to get the
desired combination of nonlinear and linear
signal chirp (18 nm/ps) Idler at 910 nm, 7 µJ
pulse energy, 165 nm bandwidth, was obtained
after two-pass amplification. Calculated Fourier
transform-limited pulse duration 14.5 fs.
Y.Tang et al, Opt. Lett, Vol. 33, 2386 (2008)
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OPCPA phase matching conditions in uniaxial
nonlinear crystals
Uniaxial crystal, Sellmeier equations
?
1. Collinear phase-matching
2. Non-collinear phase-matching, broad bandwidth
?
3. Non-collinear phase-matching, ultra-broad
bandwidth
?
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Femtosecond PW class lasers over the world

• OPCPA laser systems
• Nijnii-Novgorod, Russia
• Rutherford Appleton Laboratory, UK
• PFS, MPQ Garching, Germany
• 2. Tisapphire amplification
• XL III, Beijing, China
• Center for Femto-Atto Science and Technology
  Advanced Photonics Research Institute, Korea
• 3. Hybrid laser system
• Apollon 10, Paris, France