Amplificarea pulsurilor laser ultrascurte. CPA in Ti:safir
sau OPCPA? Solutii pentru laserul ELI-RO.
(Partea II)
R. Dabu
Sectia Laseri, INFLPR
CUPRINS
1. Amplificarea pulsurilor laser cu deriva de frecventa (“chirped pulse amplification” CPA) in Ti:safir.
- Caractersiticile Ti:safir 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 (Cr:forsterite) si amplificare in cristale DKDP.
- Laserul englez (910 nm) cu amplificare de mare energie in DKDP.
- Laserul german cu amplificare pe ~ 900 nm.
- Laserul francez cu amplificare pe 800 nm in BBO si Ti:safir.
- Comparatie intre diferite sisteme de amplificare (China, Korea, Japonia, Rusia, Franta,
Germania si Anglia). OPCPA versus amplificare in Ti-safir: avantaje si dezavantaje.
5. Care ar fi cea mai buna solutie pentru laserul ELI-RO? Ce e de facut pentru realizarea
la timp si la parametrii propusi a sistemului laser ELI-RO?
Second-order nonlinear wave mixing
Polarization - electric dipole moment per unit of volume
Polarization vector P induced in a medium:


P   0  (1) E   ( 2) E  E   (3) E  E  E  ...  P (1)  P ( 2)  P (3)  ...
where E is the electric field strength of an applied optical wave, ε0 is the free-space permittivity,
 (1) ,  ( 2) , and  (3) 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:
P ( 2)   0  ( 2) E  E
Second-order nonlinear three-wave interactions:
Second-harmonic generation (SHG)
2  2 1
Sum/difference frequency generation (SFG, DFG)
3  2  1
Optical parametric generation, amplification and oscillation (OPG, OPA, OPO)
 p  s  i
Optical parametric amplification (OPA)
p-pump
ωp= ωs+ ωi
s – signal
ωp > ωs > ωi
i - idler
Non-linear crystal
ωp
ωp
ωs
ωs
ωi
Optical axis
kp
θ
Collinear OPA
ks
ki
kp
θ
(a), (b), (c) - OPO; (d) - OPG; (e) - OPA
α
β
ks
ki
Non-collinear OPA - NOPA
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
Parametric process
Monochromatic plane wave propagating along z-axis:
2 E
 2 P NL
 E   0 2   0
t
t 2
2
Equation of electric field propagation
Nonlinear induced polarization at
Es ( z, t )  ReAs ( z) exp js t  k s z 
s   p  i


PsNL ( z, t )  Re PsNL ( z) exp js t 
Assuming: collinear wave-vectors
d 2 As
d As

2
k
s
dz
d z2
slowly-varying-amplitude approximation:
Propagation equation for the signal amplitude:
d As
 c
 c
  j 0 s PsNL ( z ) exp( j k s z )   j 0 s  0  ( 2) Ap ( z ) Ai ( z ) exp  j k p  k i z exp( j k s z )
dz
2 ns
2 ns


Coupled equations that describe the parametric amplification process (neglected waves absorption in crystal):
 s d eff
d As
j
A p Ai exp( j k z )
dz
ns c
 i d eff
d Ai
j
A p As exp( j k z )
dz
ni c
d Ap
dz
j
 p d eff
npc
As Ai exp( j k z )
k  k p  k s  ki , wave-vector mismatch
k  0, perfect phase-matching
d eff 
 ( 2)
2
, effective nonlinear optical coefficient [m/V]
 p   s  i  0
Efficient parametric process: k  k  k  0   n ( )   n ( )   n ( )
p
s
i
p p
p
s s
s
i i
i
G. Cerullo at al, Rev. Sci. Instrum., 74, 1 (2003); R. Dabu et al, “Optica neliniara…”, Editura Univ. Bucuresti, 2007
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)
During the pump and signal pulse
temporal overlapping
For Ti:sapphire:
~ 1 μs after the pump pulse
10-100 ns precision of pump and signal
pulse synchronisation
Pump and signal pulse of the same
duration
Pump-signal pulse synchronisation
<(pump/signal pulse duration)/10
Thermal loading
h p  h L
No thermal loading
Part of the pump energy (~ 33% in case of
Ti:sapphire) is dissipated in the amplifying
medium
Nonlinear crystal are transparent for the
interacting beams wavelength
Parametric gain
As (0)  Ap (0)
small initial signal amplitude
Ai (0)  0
no initial idler beam
Ap ( L)  Ap (0)
Parametric gain
neglected pump depletion; L, length of nonlinear crystal
2
I s ( L)  I s (0)
2 sinh ( gL)
G s ( L) 

I s (0)
g2
 k 
where g     
 2 
2
2
2
 
2
Low parametric gain, g 
2
2  s  i d eff
Ip
n s ni n p  0 c 3

2
8  2 d eff
Ip
n s ni n p  s i  0 c
k
2
 k L 
sin 2 

2 

2 2
2 2
2  k L 
G S ( L)   L


L
sin
c


2
 2 
 k L 


 2 
k  0  G S ( L)   2 L2
exp(g L)
 2 exp(2  L)
 G S ( L) 
High parametric gain, gL  1, sinh(g L) 
2
4g2
k  0  GS ( L) 
exp(2  L)
4
R. Dabu et al, “Optica neliniara…”, Editura Univ. Bucuresti, 2007
OPA with ultrashort pulses
Frame of reference moving with GV of pump pulse,   t  z
v gp
 s d eff
 As  1
1  As


j
A p Ai exp( j k z )
z  v gs v gp  
ns c
i d eff
 Ai  1
1  Ai


j
A p As exp( j k z )
z  v gi v gp  
ni c
 Ap
 p d eff
j
As Ai exp( j k z )
z
npc
GVM between pump and signal/idler pulses limits the interaction length of parametric amplification:
L jp 

1
1

v gj v gp
, j  s, i
GVM between signal and idler pulses determines the phase-matching band-width for the
parametric amplification process
Gain band-width is given by :
Gs (k ) 
1
Gs (k  0)
2
G. Cerullo at al, Rev. Sci. Instrum., 74, 1 (2003)
Collinear OPA: phase-matching band-width within large gain approximation
Wave-vector mismatch, Δk:
 p   s 0  i 0  0   s   s 0   , i  i 0  
k ( 0)  k p ( p )  k s ( s 0 )  k i (i 0 )  0
Phase matching
 k
k
k  k p ( p )  k s ( s 0 )  k i (i 0 )   s  i
  s i
0  k (1)  k ( 2)  k (3)  ...

1   2 k s  2 ki
  

2
2
2



 s i

1   3 k s  3 ki
( ) 2  

  3   3
6
i

 s
k (1)  k ( 2)  k (3)  ...
1.
First order wave-vector mismatch, Δk(1) ≠ 0
FWHM phase matching band-width:

(1)

2 (ln 2)
1
2


 
 L
1
2
1
k s k i

 s i

2 (ln 2)
1
2


 
 L
1
2
1
1
1

v gs v gi
2. Second order wave-vector mismatch, Δk(1) = 0, Δk(2) ≠ 0
Broad band-width:

( 2)

2 (ln 2)

1
4

 
L
1
4
1
 k s  ki

 s2  i2
2
2
1

2
2 (ln 2)

1
4

 
L
1
4
1
(GVD) s  (GVD) i
1
2

( ) 3  ... 


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).
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:
B
2

 n I ( z ) dz
2
n2 – nonlinear index quantifying the Kerr nonlinearity, I(z) – signal intensity
B < 1; if B > 3-5, self-focusing could appear
Broad-band OPCPA
a) Near degeneracy,
 k
k
k (1)   s  i
  s  i
s  i  vgs  vgi

( 2)

2 (ln 2)

Collinear OPCPA
BBO typeI , P  532nm, I P  1GW / cm2 , L  8 mm
Signal/idler
wavelength
[nm]
θ
[degree]
Bandwidth
[nm]
Pulse
duration
[fs]
λS = 750
λI = 1830
21.6
4.4
189
λS = 800
λI = 1588
22.1
5.4
173
λS = 850
λI = 1422
22.4
7.7
137
λS = 900
λI = 1301
22.6
13.1
91
λS = λI =
1064
22.8
99.8
17
1
4
 1

1 
  

  0
v

v
gi 

 gs

 
L
1
4
1
 2 k s  2 ki

 s2  i2
1

2
2 (ln 2)

1
4

 
L
1
4
1
(GVD) s  (GVD) i
1
2
Broad-band OPCPA
b) Non-collinear OPCPA - NOPCPA
Phase matching:
kp
θ
α
(k ) x  k p cos  k s  k i cos   0
ki
β
(k ) y  k p sin   k i sin   0
y
ks
x
 
First order phasem ism atch  k
(1)
0
d s  d i
(k ) (x1)  
(k ) (y1) 

k s
k

 s  i cos   s  k i sin 
 s  0
 s
 i
 s
k i

sin   s  k i cos 
 s  0
 i
 s
k s
k
cos   i  0  v gs  v gi cos 
 s
 i
sin   sin 
ni
np
1
1
i
s




1 i
s
Noncollinear phase-matching in BBO crystal
Crystal optical axis
θ
pump
α
β
signal
BBO crystal
  23.7 0
  2.30 (internal)
  6.8 0
λ p=532 nm
λ s= 800 nm
λi = 1588 nm
R. Butkus, LEI-2009, Brasov
Dependence of spectrum on pump-signal angle
BBO-I noncollinear OPCPA
300 ps
θ=24.50
Φ=00
Amplified signal spectra a, b, c for α=41.5, 41and 30 mrad
X. Yang et al, Appl Phys B, 73, 219 (2001)
Broad band OPCPA
c) Multi-beam pumped OPCPA
Nd:glass pump (1 ps)
165 cm-1 -> ~ 8.6 nm
E. Žeromskis et al, Opt. Commun. 203, 435 (2002).
Ultra-broad-band OPCPA
a) Noncollinear OPCPA,
first-order and second-order phase mismatch terms: (k ) (1)  (k ) ( 2)  0
b) Pre-chirp control → collinear OPCPA,
relatively broad-band linearly chirped pump laser pulse,
nonlinearly ultra-broad bandwidth chirped signal pulse
a) Noncollinear OPCPA, first-order and second-order phase mismatch
terms  0, (k ) (1)  (k ) ( 2)  0
Crystal optical axis
(1) Phase matching, (Δk)(0) = 0
kp
θ
α
β
(k ) x  k p cos  k s  k i cos   0
ki
(k ) y  k p sin   k i sin   0
y
ks
(2) First order phase-mismatch, (Δk)(1) = 0

k s
k
cos   i  0  v gs  v gi cos 
 s
i
(3) Second order phase-mismatch, (Δk)(2) = 0
d 2ks
d 2 k i sin 2 
sin 2 
cos  
 2
 GVD s cos   GVD i  2
0
d s2
di2
v gs k i
v gs k i
a) Noncollinear OPCPA, first-order and second-order phase mismatch
terms  0
(k ) (1)  (k ) ( 2)  0

IP = 1 GW/cm2
Β-BaB2O4 (BBO) – I crystal:
S 0  800  850nm    155nm,   6 fs
S 0  750nm 
  70 nm
S 0  910nm 
  110nm
Uniaxial negative crystals, ne < no
KD2PO4 (DKDP,KD*P) – I crystal:
KH2PO4 (KDP) – I crystal:
s 0  910nm,   135nm,   9 fs s 0  1054nm,   75nm,   20 fs
V.V. Lozhkarev et al, Laser Physics, Vol. 15, 1319 (2005)
Conditions to obtain the ultra-broad-band amplification bandwidth
Critical wavelength, λ*:
KDP
DKDP
BBO
984 nm
1120 nm
1430 nm



2
d k
 0  v gs  valoare max
d 2
 p  527nm
s (ultra-broad-band PM)
p 
2
Never
fulfiled
p 
2
~ 910 nm
p 
2
~ 800 nm
V.V. Lozhkarev et al, Laser Physics, Vol. 15, 1319 (2005)
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.
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)
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)
Short-pulse source at 910 nm –suitable seed for high energy OPCPA system
Central Laser Facility, Rutherford Appleton Laboratory, Chilton, Oxon, UK
 P   P 0 (1  a t )
 S   S 0 (1  b t  c t 2 )
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 twopass amplification. Calculated Fourier transform-limited pulse duration ~ 14.5 fs.
Y.Tang et al, Opt. Lett, Vol. 33, 2386 (2008)
OPCPA – phase matching conditions in uniaxial nonlinear crystals
Uniaxial crystal, Sellmeier equations:
no ( ), ne ( )
1
1. Collinear phase-matching
p
 p , s

1
s
n p ( p ,  )
p
1
p
2. Non-collinear phase-matching,
broad bandwidth
 p , s

1
s

n p ( p ,  )
p
n p ( p ,  )
p
1

i

n s ( s )
s

ni ( i )
i ,
→
i
1
i
ni ( i )
sin  
i
cos 
sin   0
n s ( s )
s

ni ( i )
i
→ i , ,  , 
cos   0
 gs  v gi cos 
1
p
3. Non-collinear phase-matching,
ultra-broad bandwidth

1
s

n p ( p ,  )
p
p
n p ( p ,  )
p
1
i
sin  
cos 
ni (  i )
i
sin   0
n s ( s )
s

ni (  i )
i
 gs  v gi cos 
d 2ks
d 2 k i sin 2 
cos  
 2
0
d s2
d i2
v gs k i
cos   0
→ s , i , ,  , 
Femtosecond PW class lasers over the world
1. OPCPA laser systems
-
Nijnii-Novgorod, Russia
-
Rutherford Appleton Laboratory, UK
-
PFS, MPQ Garching, Germany
2. Ti:sapphire 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