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