synchronization of a ti:sapphire laser to the optical ... · design of the two-wavelength optical...

Vladimir Arsov

on behalf of the Laser-based Synchronization Team at DESY-Hamburg:

M. Bock1, M.Felber1, P. Gessler1, K.Hacker1, F.Loehl1, B.Lorbeer2, F.Ludwig1, K.-H.Matthiesen1, H.Schlarb1, B.Schmidt1, S.Schulz2, A. Winter1, L.Wißmann2, J.Zemella1

1 Deustsches Elektronen-Syncrotron (DESY), Hamburg2 Hamburg University

Synchronization of a Ti:Sapphire laser to the optical reference system

II Timing & Synchronization Workshop, ICTP, Trieste, 9 March 2009

Motivation

Vladimir Arsov II Timing & Synchronization Workshop, ICTP, Trieste, 9 March 2009

● Optical synchronization with beam based stabilization of the arrival time● High precision synchronization of lasers via optical cross-correlation ● Point-to-point synchronization ~ 10 fs rms ● Distribution over actively length-stabilized fiber links● Permanent operation and long term stability

ACC1 ACC2 ACC3 ACC4 ACC5

ACC6

seed laser

pump-probe laser

photo cathode laser

EO laser

EO

RF gun

MLO OCC OCC OCC

1.3 GHz

experimentphoton beam

dump

SASESASEseed

undulatorsundulators

bypass

BC BC

collimator

~

BAMBAM

BAMBAMBAM

to BAMs...

... ...

...

...

Layout of the two-wavelength laser synchronization

Input in the OCC from the diagnostic laser:l1 = 800 nm, dl1 = ~60 nm, t1 ~100 fs, P1 ~ 50 mW, frep = 81 MHz

Input in the OCC from the link:l2 = 1560 nm, dl1 = ~70 nm, t1 ~200 fs, P1 ~ 15 mW, frep = 216 MHz

Master Laser Oscillator

1560 nm, 216 MHz, ~0.5 nJ

stabilized link~

two-wavelength balanced optical cross-correaltor

Ti:Sapphire800 nm, 81 MHz,

~100fs, ~6nJ

81 MHz, 0.6 nJ

experiment

1.3 GHz 216 MHz, 160 fs, 0.3 nJ

error signal, 27 MHz, 528 nm

DSP control

EDFA EDFA


Layout of the balanced detection set-up

SFG

DM2DM1

DM1 – dichroic mirror HT@ l1 and l

2, HR @ l

SF

DM2 – dichroic mirror HR@ l1 and l

2, HT @ l

SF

SFG – non-linear crystal, e.g. BBOGD – group delay adjustmentF – band pass filter, HT @ l

SF

GD

F

F


Design of the two-wavelength optical cross-correlator:group delay adjustment

Assume Gaussian pulses

The convolution of two Gaussian pulses is also a Gaussian pulse:

I i t =1

i

exp−t−t i2

i2

I i t =I 1∗I 2=∫−∞

∞

I 1⋅I 2t−d = 1

122

2exp−t−t1−t 2

2

122

2 Vladimir Arsov II Timing & Synchronization Workshop, ICTP, Trieste, 9 March 2009

t

The biggest change S in the overlap is given by the derivative of the convolution:

Delay between the extrema in terms of pulse lengths (FWHM):

Ti:Sa + EDFA: t1 = 100 fs and t2= 200 fs: t = 190 fs → need a 65 - 80 fs additional delay: a double pass through a 2 – 3 mm silica slab

Examples (after accounting the group velocity delays in the crystal and the lenses):

Nd:YLF + EDFA: t1 = 11 ps and t2= 200 fs: t = 9 ps → if the same swapping technique is to be used: 20 cm SF66!

☺→ delay stage

Design of the two-wavelength optical cross-correlator:group delay adjustment

S= I 1∗I 2'=2 t−

12 2

232

exp−t−2

12 2

2

=122

2/2 ln 2


Design of the two-wavelength optical cross-correlator:choice of the crystal

Parameters to calculate: phase matching angles phase and group velocities relative group delays walk-off angle reflection losses at the crystal surfaces effective non-linear coefficients group velocity dispersion, group delay dispersion chirp, pulse broadening effective lengths phase mismatch – mix acceptance bandwidth,

mix acceptance angle, internal angular BW etc…

Guiding criteria:● highest possible efficiency● highest bandwidths● smallest background

➔ type of interaction: Type I or Type II



Geometric factors:➔ phase matching➔ cut angle➔ crystal thickness➔ focusing

Equations from:Handbook of nonlinear optical crystals, Dimitriev V.G., Gurzadyan G.G., Nikogosyan D.N., Springer Series of Optical Sciences, vol 64 (1999)


Phase matching angles for BBOλ1 = 1550 nm, λ2 = 800 nm, λSFG = 528 nm

Type I(-)(ooe): Q = 22.2°Type II(-)(eoe): Q = 27.2° Type II(-) (oee): Q = 38.8°

Phase velocities in BBO

VPh = c / n(l,Q)Type I(-)(ooe)

( ) ( )( ) ( )Θ+

Θ+=Θ22

2

0 tan1tan1

eо

e

nnnn

n(l = 1550,Q = 0°) = 1.647n(l = 800,Q = 0°) = 1.661n(l = 528,Q = 0°) = 1.656


Group velocities in BBO

Relative group delay:

Type I(-)(ooe):

( ) ( )Θ=

′=Θ

,~1,

λλ

nc

kug ( ) ( )

Θ−Θ==′

λλλλ

ω ddnn

cddkk ,,1

( ) 671.10,1550~ =°=λn

( ) 684.10,800~ =°=λn

( ) 702.12.22,528~ =°=λn

( ) ( ) ( )

Θ

−Θ

=ΘΘ2211

2121 ,1

,1,,,

λλλλτ

ggqsg uu

L

( ) mmfsg 44.0800,1550 21 −=== λλτType I(-)(ooe):


Walk-off angles for BBOFor an e-wave:S – direction of propagation of the energyK – direction of propagation of the phase

Type I(-)(ooe):

Type II(-)(eoe):

( ) ( )( )

Θ∂Θ∂

Θ−=Θ ,

,1, λ

λλρ e

e

nn

( ) mrad7.542.22,528 =°ρ

( ) mrad7.612.27,1550 =°ρ( ) mrad9.622.27,528 =°ρ

Type II(-)(oee):( ) mrad8.718.38,800 =°ρ( ) mrad4.738.38,528 =°ρ

linear walk-off:ρδ tanL=


Beam walk-off

Type I(-)(ooe): λ = 528 nm, Q = 22.2°

α

ρδ

Lδ 1

L1

mrad7.54=ρmmm /7.54 µδ =

°= 5αmmm /1001 µδ =

Reflection at the crystal surface● normal incidence● the crystal is not coated ~6% losses● difficult to simultaneously satisfy the requirements for high

bandwidth for all three wavelengths


Effective nonlinear coefficients deff [pm/V] for point group 3mType I

Available values for BBO (a negative 3m crystal) :1) Handbook of nonlinear optical crystals, Dimitriev V.G., Gurzadyan G.G.,

Nikogosyan D.N., Springer Series of Optical Sciences, vol 64 (1999)d22 = 2.3 pm/V; d31 = 0.16 pm/V;

2) Eimerl et al, J.Appl.Phys. 62(5), pp.1968-1983 (1967) d22 = 1.6 pm/V; d31 = 0.08 pm/V3) Eckard et al, IEEE-QE, vol 26, Nr.5, pp.922-933 (1990) d22 = 2.2 pm/V; d31 = ??? pm/V4) SNLO d22 = 2.2 pm/V; d31 = 0.08 pm/V

( ) ( ) ( )φρρ 3sincossin 2231 +Θ−+Θ= ddd effooe

Type II ( ) ( )φρ 3coscos222 +Θ== ddd eff

oeeeffeoe

Type I

Type II

( ) VpmnmVpmVpmd effooe /15.2528,2.22,/16.0,/3.2 =°

( ) VpmnmVpmVpmd effooe /02.2528,2.22,/08.0,/2.2 =°

( ) VpmnmVpmd effеoe /62.1528,2.27,/2.2 =°

( ) VpmnmVpmd effoее /18.1528,8.38,/2.2 =°


Design of the two-wavelength optical cross-correlator:influence of the crystal thickness on the bandwidth

(mix acceptance bandwidth)Tables 2.20 and 2.21, Handbook of nonlinear optical crystals, Dimitriev V.G., Gurzadyan G.G., Nikogosyan D.N., Springer Series of Optical Sciences, vol 64 (1999)

Example: Type I (ooe) ( ) ( ) 1

3

33

2

22322

886.0−

∂Θ∂+

∂∂−Θ−=∆

λλ

λλν

eoe

onnnn

L

Mix acceptance BW for 0.5 mm BBO


Design of the two-wavelength optical cross-correlatornon-linear conversion efficiency for Type I (ooe)

interaction between a Ti:Sa laser and EDFA

l1 = 1550 nm, t1 = 200 fs, P1 = 15 mW, frep =216 MHzl2 = 800 nm, t2 = 100 fs, P2 = 50 mW, frep = 81 MHz

➔ h = 2% @ d0 = 50 mm, LBBO = 0.5 mm

➔ h = 0.5% @ d0 = 100 mm, LBBO = 0.5 mm

choice of the crystal thickness:● h(L) < 1● L < L

eff

L, mm

hd

0 = 50 mm

d0 = 100 mm


Layout of the two-wavelength OCC for Ti:Sapphire+EDFA


Two-wavelength OCCFirst setup and signals


Layout of the Ti:Sa RF and optical synchronization


First results from the optical cross-correlator

courtesy: S.Schulz


Emphasis on the technical issues

● 50 mW input from the Ti:Saphire● Built-in piezo motors in commercial Ti:Sapphire might be

“slow” for an optical lock: 50 kHz instead of 100 kHz● The temporal overlap between the two wavelengths

requires a tool for an automatic VM scan● when the Ti:Sapphire is optically locked, the VM cannot be

used anymore for temporal overlap with the machine → an extra delay stage is required


Summary● A balanced two-wavelength cross-correlator with a BBO

crystal has been designed● Collinear propagation of 1550 nm and 800 nm, normal

incidence on the BBO● SFG, Type I interaction (ooe)...

...not background free, but:- has the highest efficiency- has the least walk off- BBO thicknesses up to 0.5 mm are possible- bandwidths up to 140 nm for l =1550 nm and

65 nm for l = 800 nm are supported● Experimental characterization is ongoing● A robust “cage” system (ThorLABSä) retains the alignment

over months● Packaging is foreseen● First error signals have been measured● Short term (~ 5 min) optical lock of the Ti:Saphhire has been

achieved● Out-of-loop measurements with two prototypes are ongoing


Thank you for your attention!

Layout of the two-wavelength OCCfor the injector laser

Ag end mirror

Ag

end

mirr

or

adjustable delay~9 ps

PMT1 PMT2

10 nm BP filter

5 mm BBODM2 DM2

telescope

telescopeDM1 DM1

DM1 – dichroic mirror HT@ 1562±20nmHR@ 1047 nm, AOI=45°

DM2 – dichroic mirror HT@ 1562±20nm & 1047 nmHR@ 627 nm, AOI=45°

l 1=104

7 nm

l2=1562 nm

lSF

=627 nm

l 1=104

7 nm

l2=1562 nm

weak focusing: d0 ~ 0.4 mm

expected efficiency ~ 2.5 %

Design of the two-wavelength optical cross-correlator:phase matching (some basics)

● optical axis (Z-axis)● principal plane: containing Z and k● ordinary (o) beam: with polarization normal to the principal plane● extraordinary (e) beam: with polarization in the principal plane


principal planeo-beam

e-beam

principal planeo-beam

e-beam

Z

neno

Z

neno

birefringence:

0≠− eo nn

no, ne – principal valuesno > ne – negative crystalno > ne – positive crystal

Design of the two-wavelength optical cross-correlator:phase matching (some basics)


vector (noncollinear):3k

1k

2k

3k

1k

2k

( )( ) ii

i

i

i

iiii nn

cn νπ

λπ

ωωωω 22

vk ====

scalar (collinear):

112233123 kkk nnn ωωω +=⇔±=

311313 ,2,k2k nn === ωω3k

2k

1k

3k

2k

1k

SFG, SHG

for isotropic crystals n1 < n3 (normal dispersion) need an anisotropic crysatal and different polarizations

k 3=k 2±k 1

Design of the two-wavelength optical cross-correlator:types of phase matching in the uniaxial crystals


I. Interacting waves ||, result ┴

Type I(-)(ooe), negative crystals

II. Interacting waves ┴, result || to one and ┴ to the other

Type II(-)(oee) or (eoe) , negative crystals

( )Θ=+ е3о2о1 kkk ( ) ( )Θ=Θ+ ее

32о1 kkk( ) ( )Θ=+Θ е

oе

321 kkk

Type I(+)(eeo), positive crystals

( ) ( ) 321 kkk оее =Θ+Θ

Type II(+)(oeo) or (eoo) , positive crystals

( ) 32о1 kkk oе =Θ+

( ) o321 kkk =+Θ oе

works in both directions:sum frequency generation (SFG) ↔ optical parametric luminescence (OPO)

( ) ( ) ( )pumpsignalidler 321 ωωω <<


Geometric factors:cut angle


Z

ncutΘ

Z

ncutΘ

Z

ncutΘ

• the phase matching depends on Q, but not on f• the conversion efficiency depends on both Q and f



The refractive index of the extraordinary wave is a function of the polar angle Q between the axis Z and the vector k

( ) ( )( ) ( )Θ+

Θ+=Θ22

2

0 tan1tan1

eо

e

nnnn

Sellmeier equations for b-BaB2O4 (BBO)

K. Kato IEEE-QE, vol.22, No7, pp.1013-1014 (1986)


22

2

22

2

01516.001667.0

01224.03753.2

01354.001822.0

01878.07359.2

λλ

λλ

−−

+=

−−

+=

e

o

n

n

no, ne – principal values of the refractive indexfor BBO no> ne (a negative uniaxial crystal)

Z

neno

Z

neno

Calculation of the nonlinear conversion efficiency

with

( ) ( ) ( )2

2

22

2

20 ,4,,

ttrP

cttrE

ctrE NL

∂∂−=

∂∂+∆

πε

( ) ( ) ( )trEtrPNL ,, 22 χ=

The field is a superposition of three interacting waves:

( ) ( ) ( )[ ]{ }∑=

+⋅−=3

1exp,

21,

iiiii CCrktjtrAptrE

ω

Assume slowly varying amplitudes → truncated equations:

( )( )

( ).expˆ,expˆ

,expˆ

21333

*13222

*23111

kzjAAjAM

kzjAAjAM

kzjAAjAM

∆−=

∆=

∆=

σ

σ

σwhere →ξξσ Mk ˆ,, ∆where →ξξσ Mk ˆ,, ∆


cijk = 2dijk = 2di(9-j-k) i , j , k∈[X Y Z١ ٢ ٣]

Calculation of the nonlinear conversion efficiency

• s - non-linear coupling coefficients• Dk – wave mismatch (spatial, thermal self-focusing, non-linear absorption, etc.)• r - walk-off angle• ug – group velocity • g – group velocity dispersion (GVD)• d - linear absorption• Q – nonlinear (e.g. two-photon) absorption

( ) ( )AQt

gtuyxk

jxz

Mg

ξξξξξ

ξ δλρ ++∂∂Θ+

∂∂+

∂∂+

∂∂+

∂∂+

∂∂= 2

2

,2

2

2

2

,212

ˆ

2333

22,12,12,1

2

4

ndk

ndk

eff

eff

πσ

πσ

=

=


Non-linear conversion effective lengths Leff

1. Aperture length (2nd term)(influence on the focal spot size)

2. Diffraction length (3rd term)(the length over which a gaussian beamwould spread by )

3. Quasi-static length (4th term)(influence of the group velocity mismatch)

4. Dispersive spread length (5th term)(influence of the dispersion on the pulse shape)

5. Non-linear interaction length (influence of the input power and the non-linear coupling)

ρ0dLa =

20kdLdiff =

2,1, ggqs uu

L−

= τ

( )Θ= ,2 λτ gLdis

( ) ( ) ( )0001

23

22

21 aaa

LNL++

=σ

Fixed field approximation (FFA): L < Leff

٢


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