Lesson 2 2
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Transcript of Lesson 2 2
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:
where E is the electric field strength of an applied optical wave, ε0 is the free-space permittivity,
)3()2()1( ,, and are the first-order (linear), second-order, third-order susceptibility of the medium.
...... )3()2()1()3()2()1(0 PPPEEEEEEP
Second-order nonlinear optical processes are generated by the second-order nonlinear polarization:
EEP )2(0
)2(
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)
12 2 123
isp
Optical parametric amplification (OPA)
(a), (b), (c) - OPO; (d) - OPG; (e) - OPA
Non-linear crystal
ωs
ωp ωp
ωs
ωi
ωp= ωs+ ωi
ωp > ωs > ωi
p-pump
s – signal
i - idler
pk
sk ikCollinear OPA
α β
pk
sk
ik
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
Optical axisθ
θ
Parametric process
Monochromatic plane wave propagating along z-axis: zktjzAtzE ssss exp)(Re),(
Nonlinear induced polarization at ips tjzPtzP sNLs
NLs exp)(Re),(
zdAd
kzdAd s
ss 22
2
2
2
02
2
02
tP
tEE NL
Equation of electric field propagation
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):
)exp(exp)()(2
)exp()(2
)2(0
00 zkjzkkjzAzAnc
jzkjzPnc
jzdAd
sipips
ss
NLs
s
ss
)exp(
)exp(
)exp(
zkjAAcn
dj
dzAd
zkjAAcn
dj
dzAd
zkjAAcn
dj
dzAd
isp
effpp
spi
effii
ips
effss
isp kkkk
2
)2(effd , effective nonlinear optical coefficient [m/V]
, wave-vector mismatch
,0k perfect phase-matching
G. Cerullo at al, Rev. Sci. Instrum., 74, 1 (2003); R. Dabu et al, “Optica neliniara…”, Editura Univ. Bucuresti, 2007
Efficient parametric process: )()()(0
0
iiissspppisp
isp
nnnkkk
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 Ti:sapphire:~ 1 μs after the pump pulse10-100 ns precision of pump and signal pulse synchronisation
During the pump and signal pulse temporal overlapping
Pump and signal pulse of the same durationPump-signal pulse synchronisation <(pump/signal pulse duration)/10
Thermal loading
Part of the pump energy (~ 33% in case of Ti:sapphire) is dissipated in the amplifying medium
No thermal loading
Nonlinear crystal are transparent for the interacting beams wavelength
Lp hh
Parametric gain
)0()0( ps AA small initial signal amplitude
0)0( iA no initial idler beam
)0()( pp ALA neglected pump depletion; L, length of nonlinear crystal
Parametric gain
where 2
22
2
kgcnnn
IdcnnnId
ispis
peff
pis
peffis
0
22
30
22 82
Low parametric gain, 2kg
22
2222
2
22
)(0
2sin
2
2sin
)(
LLGk
LkcLLk
Lk
LLG
S
S
High parametric gain,
2
22 )(sinh
)0()0()(
)(g
gLI
ILILG
s
sss
4)2exp()(0
4)2exp()(
2)exp()sinh(,1 2
2
LLGk
gL
LGLg
LggL
S
S
R. Dabu et al, “Optica neliniara…”, Editura Univ. Bucuresti, 2007
OPA with ultrashort pulses
G. Cerullo at al, Rev. Sci. Instrum., 74, 1 (2003)
Frame of reference moving with GV of pump pulse, gpv
zt
)exp(
)exp(11
)exp(11
zkjAAcn
dj
zA
zkjAAcn
dj
Avvz
A
zkjAAcn
dj
Avvz
A
isp
effpp
spi
effii
gpgi
i
ips
effss
gpgs
s
GVM between pump and signal/idler pulses limits the interaction length of parametric amplification:
isj
vv
L
gpgj
jp ,,11
GVM between signal and idler pulses determines the phase-matching band-width for the parametric amplification process
Gain band-width is given by :
)0(21)( kGkG ss
Wave-vector mismatch, Δk:
Collinear OPA: phase-matching band-width within large gain approximation
1. First order wave-vector mismatch, Δk(1) ≠ 0
FWHM phase matching band-width:
gigsi
i
s
s
vv
LkkL 11
1)2(ln21)2(ln2 21
21
21
21
)1(
...)3()2()1( kkk
...0
...)(61)(
21)()()(
0)()()(
,0
)3()2()1(
33
3
3
32
2
2
2
2
00
00)0(
0000
kkk
kkkkkkkkkk
kkkk
i
i
s
s
i
i
s
s
i
i
s
siisspp
iisspp
iissisp
Phase matching
2. Second order wave-vector mismatch, Δk(1) = 0, Δk(2) ≠ 0Broad band-width:
21
41
41
21
2
2
2
2
41
41
)2(
)()(
1)2(ln21)2(ln2
is
i
i
s
s GVDGVDLkkL
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:
dzzInB )(22
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,
gigsis vv
011)1(
gigsi
i
s
s
vvkk
k
mmLcmGWInmItypeBBO PP 8,/1,532, 2
21
41
41
21
2
2
2
2
41
41
)2(
)()(
1)2(ln21)2(ln2
is
i
i
s
sGVDGVDLkkL
Collinear OPCPA
Signal/idler wavelength [nm]
θ [degree]
Bandwidth [nm]
Pulse duration [fs]
λS = 750λI = 1830
21.6 4.4 189
λS = 800λI = 1588
22.1 5.4 173
λS = 850λI = 1422
22.4 7.7 137
λS = 900λI = 1301
22.6 13.1 91
λS = λI = 1064
22.8 99.8 17
Broad-band OPCPA
b) Non-collinear OPCPA - NOPCPA
α β
pkik
sk
0sinsin)(
0coscos)(
ipy
ispx
kkk
kkkk
Phase matching:
y
x
θ
s
i
s
ip
i
gigsi
i
s
s
ss
isi
iy
ss
isi
is
s
sx
is
nn
vvkk
kk
k
kkk
k
ddkmismatchphaseorderFirst
11
1sinsin
cos0cos
0cossin)(
0sincos)(
0
)1(
)1(
)1(
λ p=532 nm
Noncollinear phase-matching in BBO crystal
λ s= 800 nm λi = 1588 nm
θ
βpump
signalα
Crystal optical axis
0
0
0
8.6
3.2
7.23
(internal)
BBO crystal
R. Butkus, LEI-2009, Brasov
Dependence of spectrum on pump-signal angle
BBO-I noncollinear OPCPA
300 ps
Amplified signal spectra a, b, c for α=41.5, 41and 30 mrad
X. Yang et al, Appl Phys B, 73, 219 (2001)
θ=24.50 Φ=00
c) Multi-beam pumped OPCPA
E. Žeromskis et al, Opt. Commun. 203, 435 (2002).
Nd:glass pump (1 ps)
Broad band OPCPA
165 cm-1 -> ~ 8.6 nm
Ultra-broad-band OPCPA
a) Noncollinear OPCPA, first-order and second-order phase mismatch terms: 0)()( )2()1( kk
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, 0)()( )2()1( kk
α β
pkik
sk
yθ 0sinsin)(
0coscos)(
ipy
ispx
kkk
kkkk(1) Phase matching, (Δk)(0) = 0
(2) First order phase-mismatch, (Δk)(1) = 0
cos0cos gigsi
i
s
s vvkk
(3) Second order phase-mismatch, (Δk)(2) = 0
Crystal optical axis
0sincossincos 2
2
2
2
2
2
2
2
igs
isigsi
i
s
s
kvGVDGVD
kvdkd
dkd
a) Noncollinear OPCPA, first-order and second-order phase mismatch terms 0
0)()( )2()1( kk
V.V. Lozhkarev et al, Laser Physics, Vol. 15, 1319 (2005)
Β-BaB2O4 (BBO) – I crystal:
KD2PO4 (DKDP,KD*P) – I crystal: KH2PO4 (KDP) – I crystal:
IP = 1 GW/cm2 Uniaxial negative crystals, ne < no
nmnmnmnm
fsnmnm
S
S
S
11091070750
6,155850800
0
0
0
fsnmnms 9,135,9100 fsnmnms 20,75,10540
Conditions to obtain the ultra-broad-band amplification bandwidth
KDP DKDP BBO
Critical wavelength, λ*: 984 nm 1120 nm 1430 nm
(ultra-broad-band PM) Never fulfiled
~ 910 nm ~ 800 nm
max02
2
valoarevd
kdgs
nmp 527
s
2
p
2
p 2
p
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)
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
Short-pulse source at 910 nm –suitable seed for high energy OPCPA systemCentral 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.
)1(
)1(2
0
0
tctb
ta
SS
PP
Y.Tang et al, Opt. Lett, Vol. 33, 2386 (2008)
OPCPA – phase matching conditions in uniaxial nonlinear crystals
1. Collinear phase-matching sp ,i
ii
s
ss
p
pp
isp
nnn
)()(),(
111
,i
2. Non-collinear phase-matching, broad bandwidth
→
sp ,
cos
0cos)()(
cos),(
0sin)(
sin),(
111
gigs
i
ii
s
ss
p
pp
i
ii
p
pp
isp
v
nnn
nn
,,,, is→
→ ,,,i
3. Non-collinear phase-matching, ultra-broad bandwidth
p
Uniaxial crystal, Sellmeier equations: )(),( eo nn
0sincos
cos
0cos)()(
cos),(
0sin)(
sin),(
111
2
2
2
2
2
2
igsi
i
s
s
gigs
i
ii
s
ss
p
pp
i
ii
p
pp
isp
kvdkd
dkd
v
nnn
nn
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