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INFLPR. Amplificarea pulsurilor laser ultrascurte. CPA in Ti:safir sau OPCPA? Solutii pentru laserul ELI-RO. (Partea II). R. Dabu Sectia Laseri, INFLPR. INFLPR. CUPRINS 1. Amplificarea pulsurilor laser cu deriva de frecventa (“chirped pulse amplification” - CPA) in Ti:safir.

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

(Partea II)

R. Dabu

Sectia Laseri, INFLPR



  • 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,

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)


Optical parametric amplification (OPA)


s – signal

i - idler

ωp=ωs+ ωi

ωp> ωs> ωi

Non-linear crystal






Optical axis


Collinear OPA




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


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


Distinct features of laser medium amplification and OPA


Parametric gain

small initial signal amplitude

no initial idler beam

neglected pump depletion; L, length of nonlinear crystal

Parametric gain


Low parametric gain,

High parametric gain,

R. Dabu et al, “Optica neliniara…”, Editura Univ. Bucuresti, 2007


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)


Collinear OPA: phase-matching band-width within large gain approximation

Wave-vector mismatch, Δk:

Phase matching

  • First order wave-vector mismatch, Δk(1) ≠ 0

  • FWHM phase matching band-width:

2. Second order wave-vector mismatch, Δk(1) = 0, Δk(2) ≠ 0

Broad band-width:


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:

n2 – nonlinear index quantifying the Kerr nonlinearity, I(z) – signal intensity

B < 1; ifB > 3-5, self-focusing could appear


Broad-band OPCPA

a) Near degeneracy,

Collinear OPCPA


Broad-band OPCPA

b) Non-collinear OPCPA - NOPCPA

Phase matching:







Noncollinear phase-matching in BBO crystal

Crystal optical axis






BBO crystal


λp=532 nm

λs= 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:

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,

Crystal optical axis

(1) Phase matching,(Δk)(0) = 0





(2) First order phase-mismatch, (Δk)(1) = 0

(3) Second order phase-mismatch, (Δk)(2) = 0


a) Noncollinear OPCPA, first-order and second-order phase mismatch terms 0

IP = 1 GW/cm2

Uniaxial negative crystals, ne < no

Β-BaB2O4 (BBO) – I crystal:

KD2PO4 (DKDP,KD*P) – I crystal:

KH2PO4 (KDP) – I crystal:

V.V. Lozhkarev et al, Laser Physics, Vol. 15, 1319 (2005)


Conditions to obtain the ultra-broad-band amplification bandwidth

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

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)


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


Femtosecond PW class lasers over the world

  • 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