Table Of ContentMode Locking At and Below the CW Threshold
Shai Yefet and Avi Pe’er∗
Department of physics and BINA Center of nano-technology, Bar-Ilan university, Ramat-Gan 52900, Israel
∗e-mail: [email protected]
CompiledDecember 11,2013
WeexploreexperimentallyanewregimeofoperationformodelockinginaTi:SapphirelaserwithenhancedKerr
nonlinearity,wherethethresholdforpulsedoperationisloweredbelowthethresholdforcontinuous-wave(CW)
operation. Even though a CW solution cannot exist in this regime, pulsed oscillation can be realized directly
3 fromzeroCWoscillation.Inthisregime,thepointofmaximumstrengthoftheKerrnonlinearprocessprovides
1 a ”sweet spot” for mode locking, which can be optimized to considerably lower the pump power threshold.
0 Thepropertiesofthe”sweetspot”areexplainedwithaqualitativemodel. (cid:13)c 2013 OpticalSocietyofAmerica
2 OCIS codes: 140.3538, 140.3580,140.7090
n
a OC
J Theultra-broadgainbandwidthoftheTi:Sapphire(TiS) HR
2 laser renders it the ’work-horse’ of the last decades for
generationofultrashortpulsesbymodelocking(ML)[1].
s] The nonlinear mechanism responsible for ML is self- M1 2f M2
c focusing of the beam due to the optical Kerr effect
i
pt wdeitnhtinlostshemTecihSancrisymstatlh,aitntfraovdourscipnuglsaens oinvteerncsoitnytidneupoeuns-- BK7 f f TiS
o Z
. wave (CW) operation [2]. A known feature of ML is Pump source @ 532 nm
s
c the abrupt transition between CW and ML operation Fig.1.Cavityconfiguration.Thegainmediumisa3mm
i intermsofpump power[3].Onlywhenthe pump power longBrewster-cutTiScrystalwith0.25wt%doping.The
s
y crosses a certain threshold, ML can be initiated from a curvedmirrors(M1,M2)radiusofcurvatureisR=15cm,
h noise-seeded fluctuation (either by a knock on a cavity withhighreflector(HR)anda95%outputcoupler(OC)
p elementorbyexternalinjectionoflongpulses).Another asendmirrors.Anadditionalplanar-cutBK7windowis
[ common feature is that the threshold pump power for insertednearthe imagepointofthe TiScrystal,created
1 ML is higher than the CW threshold. It seems as if a by the two-lens telescope of focal length f=10cm. The
v certainamountofCWoscillationsisnecessary,andonly short cavity arm is 42cm long and the long arm (90cm)
6 ontopofanexistingCWcananintensityfluctuationbe contains a prism-pair of BK7 glass (60cm). Each cavity
3
amplified to create the pulse. mirror except the OC provides GDD≈−55fs2.
2
The threshold-like behavior of ML was elegantly ex-
0
. plained by the theory of statistical light-mode dynam-
1
ics (SLD) [4], where the transition from CW to ML
0 OurlinearTiScavityisillustratedinFig.1.Byadding
is described as a first order phase transition, in which
3 a lens based 1x1 telescope between the curved mirrors
1 the order parameter (analogous to temperature) is T ∼
thefocusinsidetheTiScrystalisimagedtowardsmirror
v: 1/(γsP2), where γs represents the strength of the rele- M1, allowing us to enhance the nonlinearity of the cav-
Xi vantnonlinearityandP isthetotallasercavitypower.It ity in a controlled manner by introducing an additional
wasdemonstrated[5]thatontopofanexistingCW,ML
Kerrmediumneartheimagedfocuswhilevaryingitspo-
r can occur only when T is lowered below a critical value
a sition. We first introduced a 3mm long planar window
of Tc. Yet, to our knowledge, the question whether the
of BK7 glass, which was AR coated and set near nor-
preliminary existence of a CW oscillation is a necessary
mal incidence. As opposed to Brewster windows, where
conditionforMLoperationwasnotdirectlyexploredand
the beam expands in one dimension due to refraction,
isnottrivialtoanswerapriori.Herewedemonstrateex-
thereby reducing the nonlinear response and generating
perimentally that an initial CW power need not exist.
anastigmaticKerrlens,withnormalincidencetheintra-
TheadditionofasecondintracavityKerrmediumwas
cavity beam retains its small size, which enhances the
exploredinthepastusingdifferentcombinationsofgain
nonlinearity and provides an astigmatic-free Kerr lens.
and Kerr media [6–11], and was shown to lower the ML
If we define δ as a measure for the distance between
threshold. Here, we further enhance the nonlinear Kerr
M1andM2withrespecttoanarbitraryreferencepoint,
mechanism, observing a new regime of mode locking,
two separate bands of δ values [δ1,δ2], [δ3,δ4] allow sta-
where: 1. the intracavity CW power needed to initiate
bleCWoperationofthecavity.Thesetwostabilityzones
ML can be reduced to zero, 2. pulses can be sustained
are bounded by four stability limits (δ4 >δ3 >δ2 >δ1)
evenbelowtheCWthresholdandthepumppowerneces-
and the working point for ML in our experiment is near
sary for pulsed operationcan be considerably improved.
thesecondstabilitylimitδ2 [2].Nearthislimitthe addi-
1
tionalnonlinearKerrlens causes adecreaseof the mode Fig.2(c)and(d)forin-focusposition.TheML threshold
sizeattheOCforML.InordertofavorML,onecanex- (Fig.2(c)) is reduced by the added nonlinearity, and the
ploit the Kerr lens in one of two ways:either by placing MLthresholdcurveeventuallycrossestheCWthreshold
anapertureneartheOCtoselectivelyinducelossonthe atZc ≈1.2mmwheretheintracavityCWpowerdropsto
CW mode, or by increasing the distance δ between the zero, marking the transition point to a different regime.
curved mirrors a little bit beyond the stability limit of At Zc, ML can be achieved from pure fluorescence with
δ2, which passively induces diffraction losses to the CW noCWoscillation.ThecorrespondingCWandMLintra-
mode. For pulsedoperation,the additionalKerrlens re- cavitypowersattheMLthresholdareshowninFig.2(d).
stabilizes the cavity, eliminating the diffraction losses. Beyondthe crossing point (Z >Zc), stable ML can still
In this manner increasing the distance δ is equivalentto be initiated, but only by first raising the pump power
closingaphysicalapertureonthebeam,whichincreases up to the CW threshold, locking, and then lowering the
the threshold for CW due to loss, and requires higher pump again. At the CW threshold the pump power is
powerinML forthe nonlinearlens toovercomethe loss. too highandmode lockinggeneratesa pulse with a CW
spike attached to it, which can be eliminated by lower-
4.3 3 ing the pump power below the CW threshold. The ML
d (W) (a) (c) threshold in Fig.2(c) for Z > Zc is the minimal pump
ol power needed to maintain a clean pulse.
h
s
hre Wecanunderstandtheneedtofirstincreasethepump
mp t MCWL power to the CW threshold and than lower it by noting
u
P that the CW threshold marks the crossoverbetween de-
1.4 1.1
4.3 2.6 cayandamplificationin the cavity.For ML to occur,an
W) (b) (d)
er ( intensityfluctuationmustfirstbe linearlyamplifiedtoa
ow sufficient peak power to initiate the Kerr-lensing mech-
p
vity anism.ForZ >Zc,one mustpump the lasersufficiently
a
ac for a noise-induced fluctuation to be amplified (rather
Intr 0 0 than decay) in order for it to reach the peak intensity
0.5 1.8 0.5 1.6
required to mobilize the Kerr-lensing process. After re-
Z (mm)
ducing the pump power to the ML threshold, a clean
Fig.2.ML(red)andCW(blue)operationparametersas pulseoperationisobtained,butifMLisbrokenthecav-
a function of Z =δ−δ2 for two3mm long BK7 window ity will not mode-lock again.
positions: off-focus (a)+(b) and in-focus (c)+(d). Toinvestigatetheappearanceofthenewregime(Z >
Zc) for in-focus window position, we plot the ratio of
The measured ML and CW operation parameters are CW to ML powers γe ≡PCW/PML as a function of Z,
plotted in Fig.2 as a function of Z = δ −δ2. Measure- for windows of variable thickness (Fig.3). γe represents
ments were taken for two positions of the BK7 window: an experimental measure for the strength of the Kerr
1. at the imaged focus, where considerable nonlinear- effect, which demonstrates a ”sweet spot” where γe is
ity is added by the window (in-focus). 2. several cen- minimal and the nonlinear mechanism is most efficient.
timeters away, much beyond the Rayleigh range of the The apparent tendency from Fig.3 is that for increased
intracavity mode (off-focus), where the added nonlin- nonlinearity,thesweetspotispushedtolargerZ andthe
earity is negligible and the cavity acts as a standard γe value at the sweet spot is reduced.We find that for a
TiS cavity (with some additional material dispersion). 2mmthickwindowtheγe curvetouchesonzeronearthe
Fig.2(a) plots the CW threshold and the ML threshold sweet spot, marking the onset of the new regime. For a
asafunctionofZ foroff-focusposition.The MLthresh- 3mmthickwindowthecurvecrosseszeroatZ=Zc.Well
old is defined as the minimum pump power required to above Z >Zc pulsed operation becomes unstable, and
initiate pulsed operation. As expected, the CW thresh- we could not observe the reappearance of the γe curve
old increases with Z,due to increased diffraction losses. for larger values of Z. At every experimental point the
The ML threshold also increases (since higher power is prismswereadjustedtoprovidethebroadestpulseband-
needed for ML to overcomethe loss),yet with a varying width. The maximum bandwidth was obtained near the
slope as Z increases. Fig.2(b) plots the CW and ML in- sweetspotduetothemaximizedKerrstrength,reaching
tracavitypowersat the ML threshold as a function of Z ≈100nmforallofthewindowthicknesses.Thisindicates
for off-focus position. As typical for ML lasers, the ML that the bandwidth was limited mainly by high order
threshold is always larger than the CW threshold and dispersion of the prisms-mirrors combination, and not
CW oscillationmustexist to initiate the ML process.In by the added dispersion of the windows. Although the
addition,althoughMLoperationisfavorableovertheen- pulse temporal width was not measured, we expect the
tire range of Z, it is most favorable at the ”sweet spot” pulses to be nearly transform limited based on previous
(Zss ≈ 1.1mm) where the CW oscillation required to experience with similar TiS cavities.
start the ML process reaches a minimal value. To provide a qualitative model for the dynamics of
The same CW and ML parameters are plotted in the ”sweet spot” with increasing Kerr nonlinearity we
2
1.2 measuresfortheKerrstrength,thecalculationofγs pro-
0 mm 1 mm
Zss ≈1.1 Zss ≈1.25 vspidoetsforeratshoenidnigffefroerntthweinmdeoawsutrheidckbneehsasevsio.r of the sweet
InconclusionwenotethattheperformanceoftheML
(a) (b)
γ
0 laserreportedhere atthe criticaldistanceZc,where the
e 1.2 thresholdsforpulsedandCWoperationmeetinFig.2(c),
2 mm 3 mm
canbecomparedtorecentlypublishedrecord-results[14]
Z ≈1.35 Z (?)>1.35
ss ss that reported a mode-locked TiS laser with low pump
power of 2.4W using an OC of 99% and curved mirrors
(c) (d)
0 radii of R = 8.6cm with output power of 30mW and
0.5 1.8 0.5 1.8
intracavity power of 3W. Here, we have achieved ML
Z (mm)
from zero CW oscillation with similar repetition rate
Fig.3.Experimentaldefinition ofthe Kerrstrengthasa (≈ 80MHz) using pump power of 2.3W with far less
function of Z for BK7 window with different lengths. stringentconditions.Inourexperiment,theOChadonly
95% reflectivity (5 times more losses), coupling more
power out (≈ 85mW) with lower intracavity power of
examine a commonly used theoretical measure for the
1.7W and using curved mirrors of radius R = 15cm.
Kerr Strength:
Withfurtheroptimizationoftheaddedwindowmaterial
γs ≡ Pc dω, (1) and cavity parameters, this may allow the development
ω dP
of ultra-low threshold ML sources in the future.
where ω is the mode radius at the OC and P is the
This research was supported by the Israeli science
pulse peak power normalized to the critical power for
foundation (grant 807/09).
self-focusing Pc [12]. This Kerr strength, which repre-
sents the change of the mode size due to a small in-
References
crease in the ML power P, is a convenient measure for
mode-locking with an aperture near the OC. Yet, since 1. H. A. Haus, IEEE J. Sel. Topics Quantum Electron. 6,
increasing Z beyond δ2 is equivalent to closing an aper- 1173–1185 (2000).
ture, γs is useful also for our configuration. Usually, γs 2. T.Brabec,P.F.Curley,C.Spielmann,E.Wintner,and
A.J.Schmidt,J.Opt.Soc.Am.B10,1029–1034(1993).
is calculated at zero power (P = 0) [13] to estimate the
3. H. Haken and H. Ohno, Opt. Commun. 26, 117118
tendencyofsmallfluctuationstodevelopintopulses.We
(1978).
note however that the dependence of γs(P) on power is 4. A. Gordon and B. Fischer, Opt. Commun. 223, 151156
mostimportant.Specifically,alarge(negative)value for
(2003).
γs indicates that only a small increase in the ML power
5. A.Rosen,R.Weill,B.Levit,V.Smulakovsky,A.Bekker,
(or threshold) will be necessary to overcome a small re- and B. Fischer, Phys. Rev.Lett. 105, 013905 (2010).
ductionoftheaperturesize(orincreaseinZ).Thepower
6. G. Gabetta, D. Huang, J. Jacobson, M. Ramaswamy,
whereγs is mostnegativewillrepresentasweetspotfor E. P. Ippen, and J. G. Fujimoto, Opt. Lett. 16, 1756–
mode locking. 1758 (1991).
7. G. P. A. Malcolm and A. I. Ferguson, Opt. Lett. 16,
-2 1967–1969 (1991).
3mm TiSonly
8. G.W.Pearson,C.Radzewicz,andJ.S.Krasinski,Opt.
3mm TiS+ 2mm window
Commun. 94, 221–226 (1992).
γ 9. C.Radzewicz,G.W.Pearson,andJ.S.Krasinski,Opt.
Commun. 102, 464–468 (1993).
s
10. M. A. Larotonda, A. A. Hnilo, and F. P. Diodati, Opt.
Commun. 183, 485491 (2000).
11. R.Ell,U.Morgner,F.X.Kartner,J.G.Fujimoto,E.P.
Ippen, V. Scheuer, G. Angelow, T. Tschudi, M. J. Led-
-12
0 P / P 0.15 erer, A. Boiko, and B. Luther-Davies, Opt. Lett. 26,
373–375 (2001).
c
12. G. Fibich and A. L. Gaeta, Opt. Lett. 25, 335–337
Fig. 4. Theoretical definition of the Kerr strength as a
(2000).
function of P for TiS crystal with added window.
13. V.Magni,G.Cerullo,andS.D.Silvestri,Opt.Commun.
101, 365–370 (1993).
Figure 4 plots γs(P) for no added Kerr window (TiS 14. C. G. Durfee, T. Storz, J. Garlick, S. Hill, J. A.Squier,
only) and for a 2mm long added window, demonstrat- M. Kirchner, G. Taft, K. Shea, H. Kapteyn, M. Mur-
ing a clear minimum (sweet spot) on both curves. Fur- nane, and S. Backus, Opt. Express 20, 13677–13683
thermore, as Kerr material is added (enhanced Kerr (2012).
strength), the minimum point is deepened and pushed
towards higher power P (larger Z), similar to the ob-
served γe. Although γs and γe are somewhat different
3
