Maximizing the mode instability threshold of a fiber amplifier

0.1 MB·English

by  Arlee V. Smith

Maximizing the mode instability
threshold of a fiber amplifier
∗
ArleeV.Smith andJesseJ.Smith
AS-Photonics,LLC,8500MenaulBlvd.NE,SuiteB335,Albuquerque,NMUSA87112
∗[email protected]
3
1
0
Abstract: We show by detailed numerical modeling that stimulated
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thermalRayleighscatteringcanaccountforthe modalinstabilityobserved
n
in high power fiber amplifiers. Our model illustrates how the instability
a
J threshold power can be maximized by eliminating amplitude and phase
modulation of the signal seed and the pump, and by careful launch of the
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1 signal seed. We also illustrate the influence of photodarkening and mode
specificlossonthethreshold.

]
s © 2013 OpticalSocietyofAmerica
c
OCIScodes:(060.2320)Fiberopticsamplifiersandoscillators;(060.4370)Nonlinearoptics,
i
t fibers;(140.6810)Thermaleffects;(190.2640)Stimulatedscattering,modulation,etc
p
o
s. Referencesandlinks
c 1. T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber,
i
s J. Limpert, and A. Tu¨nnermann, “Experimental observations of the threshold-like on-
y set of mode instabilities in high power fiber amplifiers,” Opt. Express 19, 13218 (2011).
h http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-19-14-13218.
p 2. H.-J.Otto, F. Stutzki, F.Jansen, T.Eidam, C. Jauregui, J.Limpert, and A. Tu¨nnermann, “Temporal dynam-
[ ics of mode instabilities in high-power fiber lasers and amplifiers,” Opt. Express 20, 15710–15722 (2012).
http://www.opticsexpress.org/abstract.cfm?URI=oe-20-14-15710.

1 3. N.Haarlammert,O.deVries,A.Liem,A.Kliner,T.Peschel,T.Schreiber,R.Eberhardt,andA.Tu¨nnermann,
v “Buildupanddecayofmodeinstabilityinahighpowerfiberamplifier,”Opt.Express20,13274–13283(2012).
9 http://www.opticsexpress.org/abstract.cfm?URI=oe-20-12-13274.
8 4. F. Stutzki, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, A. Tu¨nnermann. “High-speed modal
4 decomposition of mode instabilities in high-power fiber lasers”, Opt. Letters 36, 4572–4574 (2011).
3 http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-36-23-4572.
5. A.V.SmithandJ.J.Smith,“Modeinstabilityinhighpowerfiberamplifiers,”Opt.Express19,10180–10192
.
1 (2011).http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-19-11-10180.
0 6. A. V. Smith and J. J. Smith, “Influence of pump and seed modulation on the
3 mode instability thresholds of fiber amplifiers,” Opt. Express 20, 24545–24558 (2012).
1 http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-22-24545.
: 7. K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Thermally induced
v
mode coupling in rare-earth doped fiber amplifiers,” Opt. Letters 37, 2382–2384 (2012).
Xi http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-37-12-2382.
8. A.V.SmithandJ.J.Smith,“Asteady-periodicmethodformodelingmodeinstabilityinfiberamplifiers,”ArXiv
r e-prints(2013).http://arxiv.org/abs/1301.1296.
a
9. K.D.Cole,“Steady-periodic Green’sfunctions andthermal-measurementapplications inrectangular coordi-
nates,”JournalofHeatTransfer128,DOI:10.1115/1.2194040(2006).
10. B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities
in large mode area fiber amplifiers,” Opt. Express 20, 11407–11422 (2012).
http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-20-10-11407.
11. M.Laurila,T.T.Alkeskjold,M.M.Jorgensen,S.R.Petersen,J.Broeng,andJ.Lægsgaard,“Highlyefficienthigh
powersingle-modefiberamplifierutilizingthedistributedmodefilteringbandgaprodfiber,”in“Proc.SPIE,”,
vol.8237,E.C.HoneaandS.T.Hendow,eds.(2012),vol.8237,p.823710.
12. M.Laurila,M.M.Jorgensen,K.R.Hansen,T.T.Alkeskjold,J.Broeng,andJ.Lægsgaard,“Distributedmode
filteringrodfiberamplifierdelivering292wwithimprovedmodestability,”Opt.Express20,5742–5753(2012).
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5742.
13. H.Uranus,H.Hoekstra,andE.vanGroesen,“Modesofanendlesslysingle-modephotoniccrystalfiber:afinite
elementinvestigation,”Proc.11thIEEESymp.Commun.andVehicularTechnol.(SCVT)(2004).
14. Z.JiangandJ.R.Marciante,“Mode-areascalingofhelical-core,dual-cladfiberlasersandamplifiersusingan
improvedbend-lossmodel,”J.Opt.Soc.Am.B23,2051–2058(2006).
15. B. G. Ward, “Bend performance-enhanced photonic crystal fibers with
anisotropic numerical aperture,” Opt. Express 16, 8532–8548 (2008).
http://www.opticsexpress.org/abstract.cfm?URI=oe-16-12-8532.
16. F. Stutzki, F. Jansen, C. Jauregui, J. Limpert, and A. Tu¨nnermann, “Non-hexagonal large-
pitch fibers for enhanced mode discrimination,” Opt. Express 19, 12081–12086 (2011).
http://www.opticsexpress.org/abstract.cfm?URI=oe-19-13-12081.
1. INTRODUCTION
Aboveasharppowerthresholdtheoutputbeamfromamultimodefiberamplifierisradically
altered[1,2,3,4].IfthefundamentalLP modeisinjectedatthefiberinput,slightlyabovethe
01
thresholdtheoutputislargelyinLP .Thismodalinstabilityiscausedbyastimulatedthermal
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Rayleigh scattering (STRS) process[5, 6, 7]. Quantum defect heating creates a temperature
grating,and consequentlya refractiveindexgrating,that is responsibleforcouplingbetween
the two fibermodes.Numericalmodelsof the STRS processshow that,like otherstimulated
Rayleigh scattering processes, the gain has a dispersive shape[6, 7] similar to that shown in
Fig. 1. A frequencyoffsetbetweenthe two coupledmodesis necessaryto producethe phase
shiftessentialformodecoupling[5, 7],andpowertransfer istowardthemodewith thelower
frequency.
80
40
m]
B/
d
ain [ 0
G
al
ot
T
−40
−80
−100 −75 −50 −25 0 25 50 75 100
∆ν [kHz]
Fig.1.SamplegainofmodeLP versusitsfrequencyoffsetfrommodeLP .Thegain
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includesbothlasergainandmodecouplinggainduetoSTRS.Lasergainaccountsforthe
upwardshiftofapproximately15dB/m.
Thepurposeofthispaperistoprovidesomeguidanceonhowthemodeinstabilitythreshold
canbeheldatthehighestpossiblepower.Therearetwoapproachestothis:optimizingthefiber
design,oroptimizingtheoperatingconditions.Thispaperisprimarilyconcernedwithfinding
theoptimumoperatingconditions.
2. NUMERICALMODEL
WereportedelsewhereourdetailednumericalmodeloftheSTRSprocess[5,8]basedontheas-
sumptionthatthepowersofthetwocoupledmodesandthetemperaturevaryonlyperiodically.
Thissteady-periodicassumptionallowstheuseofasteady-periodicGreen’sfunctiontocom-
pute the time-dependenttemperature profiles responsible for mode coupling[9]. The Green’s
functiontemperaturesolveriscombinedwithasplit-stepfast-Fouriertransformbeampropaga-
tionmethodtomodelmodecoupling.Thisapproachhastheadvantagethatallfibermodesare
simultaneouslyincluded,andthepopulationinversionprofilesarerealistic.Thehighlynumer-
icalnatureofthe modelmakesit relativelyeasy to addother physicaleffects.Thismodelal-
lowsustopredictthefrequencyshiftbetweenLP andLP whichproducesmaximummode
01 11
coupling gain. Our predicted frequenciesare in good agreement with observed signal output
modulationfrequencies[2,10].Anotherkeyfeatureofthemodelistheinstabilitythresholdis
well-defined,with a sharpchangeof LP contentwithincreasingpumppower,asillustrated
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inFig.2.
Inthefollowingsectionswewillexaminehowtheinstabilitythresholdisimpactedbypump
andsignalamplitudemodulation,photodarkening,andmodespecificloss.Wealsosuggestthe
possibilityofrestoringthethresholdbycounteringthepumpmodulationwithsignalmodula-
tion.Asabaselinecase,withoutanyoftheseinfluences,we modeltheLPF45fiberamplifier
described by Otto et al.[2], using the parameters listed in Table 1. This is a photonic crystal
fiber,butwesimulateitusingaco-pumped,stepindexfiberwiththecoresizeandnumerical
apertureadjusted to give an LP modeclose to the reportedsize. For the baseline amplifier,
01
weuseasignalseedpowerof10−16 WinthefrequencyshiftedLP modetosimulatequan-
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tumnoiseseeding.Thisiscalculatedusinganoisespectralpowerdensityofhn multipliedby
the amplified bandwidth of approximately 500 Hz. The baseline amplifier has a threshold at
a normalizedpump input powerof 1.0. We will compareother thresholdsto this normalized
value.Thresholdisdefinedhereasthepumpinputpoweratwhich5%oftheoutputsignalisin
thehigherordermodeLP .Sincethispaperisonlyconcernedwithqualitativebehavior,and
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weexpectsimilarbehaviorsforco-andcounter-pumpedfibers,wemodelonlytheco-pumped
case. Theexperimentalmodecouplingperformanceof the LPF45 fiberhasbeenreported[2],
permittingcomparisonsofsomeofourpredictionswithlaboratoryresults.
Table1.LPF45fiberamplifierparametersusedinthenumericalmodel.
d 81m m d 63m m
core dope
d 255m m P 10W
clad 01
l 976nm l 1060nm
pump signal
s a 2.47×10−24m2 s e 2.44×10−24m2
pump pump
s a 5.8×10−27m2 s e 2.71×10−25m2
sig sig
n 1.45015 n 1.45
core clad
N 3.0×1025m−3 L 1.2m
Yb
3. MODULATEDSIGNALSEED
While seeding the LP mode with quantum noise is unavoidable, additional sources of fre-
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quencyshiftedLP lightcandramaticallyreducethethreshold.Forexample,iftheinputsig-
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nallightis amplitudemodulated,frequencycomponentswithin the STRS amplificationband
canbepopulated.Ifsomeofthisfrequencyshiftedseedlightisaccidentallyinjectedintomode
LP , it will seed the amplified mode.Amongotherpossibilities, such amplitudemodulation
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willbepresentiftheseedisanASEsource.Itisalsopresentatsomelevelinanyothersource
oftheseedlight.
1
0.8
nt
e
nt
o
c 0.6
al
d
o
m
ge 0.4
a LP
er 01
Av LP
11
0.2 LP
12
LP
02
0
0 0.5 1 1.5
Normalized Input Pump Power [arb.]
Fig. 2. Fraction of the signal power in various modes versus the input pump power (in
normalizedunits).Here,thefrequencyshiftedLP isseededbyquantumnoisesimulated
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by10−16W.Thesharpmodeinstabilitythresholdoccursnearthenormalizedpumppower
of1.0.
We modelan amplitudemodulatedseed with 9.9W injectedintoLP and 0.1W injected
01
intoLP .Thefrequencyisadjustedformaximummodecouplinggain.Figure3demonstrates
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theinfluenceofincreasingdepthofsignalmodulationonthethresholdwherethebaselinecase
correspondstozeromodulation.Asthefigureshows,thethresholdisstronglyreducedevenfor
smalllevelsofmodulation.
1
el.] 0.8
er [r
w
o 0.6
p
p
m
u
d p 0.4
ol
h
es
hr 0.2
T
0
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
Signal Modulation
(Peak−to−Peak)
Fig.3.Normalizedpumppoweratmodeinstabilitythresholdvs.magnitudeofsignalam-
plitudemodulation.Themagnitudeisdefinedasthepeak-to-peakpowervariationnormal-
ized totheaveragepower. Thresholdisdefined as5%of thesignal output inLP .The
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leftmostpointcorrespondstothebaselinecase.
The importantthing is the strength of the seed in the frequency-shiftedlight in LP . The
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threshold reductionis similar if onlythe light in LP is amplitudemodulatedratherthen all
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theseedlightaswasthecasefortheresultspresentedinFig.3.Thismeanssmallmechanical
vibrations that affect the amount of light accidentally injected into LP could produce the
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amplitude modulation in the amplified band. It is also unimportantwhether the seed light is
amplitudemodulatedorphasemodulated.Theyproducesimilarthresholdreductions.
4. MODULATEDPUMP
Evenif thesignalseedisunmodulated,pumpmodulationproducesalmostthesameeffectas
signalmodulation.A modulatedpumpquicklyimpressesamplitudemodulationonthesignal
light in LP , leading to population of the frequency shifted signal sideband. We model this
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effectbyseedingLP with9.9WandLP with0.1W,bothunmodulated.We modulatethe
01 11
inputpumpbyvaryingamountsatthefrequencyofmaximummodecouplinggain.Theresults
are shown in Fig. 4 with the baseline case correspondingto zero modulation. Again a small
amountofmodulationleadstoastrongreductioninthreshold.
1
0.9
el.] 0.8
er [r 0.7
w
o 0.6
p
mp 0.5
u
p
d 0.4
ol
esh 0.3
hr
T 0.2
0.1
0
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
Pump modulation
(Peak−to−Peak)
Fig.4.Normalizedpumppoweratmodeinstabilitythresholdvs.magnitudeofpumpampli-
tudemodulation.Themagnitudeisdefinedasthepeak-to-peakpowervariationnormalized
totheaveragepower.Thresholdisdefinedas5%ofthesignaloutputinLP .
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5. COUNTERMODULATIONOFSEEDANDPUMP
The similarity of Figs. 3 and 4 suggests that perhapsa small pump modulationcan be coun-
teracted by an appropriately adjusted signal modulation. We tested this idea using a pump
amplitudemodulationof 0.001,and show in Fig. 5 the results whenthe signalmodulationis
optimizedinamplitudeandphase.Wecouldnotfullyrestorethethreshold,butdidimproveit
by15%.
6. PHOTODARKENING
Photodarkeningcanalsostronglyreducetheinstabilitythreshold.Wemodelthisusingavery
simplephotodarkeningmodel.Weassumeauniformlinearabsorptionofthesignallightacross
the full doped region of the fiber. A more realistic model would account for the transverse
shape of the absorptionat each z location,butourmodelshouldgive a reasonableindication
oftheinfluenceofphotodarkening.Italsoshowsthe effectothersourcesoflinearabsorption
mighthave.We assumetheabsorbedpowerisfullyandinstantaneouslyconvertedtoheat,so
theheatingprofilematchestheirradianceprofileoverthedopedregion.
Figure6showsinthebluetrace(circles)howthethresholdfallswithincreasingsignalab-
sorption.Itisimportanttorealizethatattheabsorptions consideredheretheefficiencyofthe
amplifierisonlyslightlyreduced,asshowninthegreencurve(squares).Areductionof60%
1
el.] 0.8
er [r
w
o 0.6
p
p
m
u
d p 0.4
ol
h
es
hr 0.2
T
0
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
Pump Modulation
(Peak−to−Peak)
Fig.5.ThisisthesameasFig.4withtheadditionofthestarindicatingtheimprovement
byoptimizedcountermodulationoftheinputsignal.
in threshold correspondsto a reduction in efficiency of only 7%. One importantsignature of
actual photodarkeningis that it turns on graduallyin the presence of pumping,and it can be
reversedbyopticalbleachingorthermalbleaching[11,12].
1 95
0.9 94
el.] 0.8 93
mp power [r 000...567 999012ciency [%]
eshold pu 00..34 8889Slope effi
Thr 0.2 87
0.1 86
0 85
00 00..0055 00..11 00..1155 00..22 00..2255 00..33 00..3355 00..44 00..4455 00..55
Linear absorption [dB/m]
Fig.6.Threshold(circles)andefficiency(squares)dependenceonlinearabsorption.Here,
LP isseededwith10WandLP isseededwith10−16Watthefrequencyofmaximum
01 11
gain.Efficiencyisdefinedastheincreaseinsignalpowerdividedbythereductioninpump
power.
7. MODESPECIFICLOSS
IfthelossofLP canbemadelargewithoutsignificantlyaffectingLP ,itshouldbepossible
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to increase the instability threshold while maintaining overall efficiency. Such loss for LP
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mightbe created by bend loss orby cleverfiber engineering.We introducean LP loss that
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isconstantalongthefulllengthofthefiber,withzerolossto LP , withtheresultsshownin
01
Fig. 7. We seed LP with 10 W and the frequency shifted LP with 10−16 W so the zero
01 11
losspointisagainthebaselinecase.Itisclearfromthefigurethatlargemodespecificlosses
arerequiredtosignificantlyincreasethethreshold.Thisisnotsurprisingbecausethebaseline
modecouplinggainislargerthan170dBatthreshold,andthe gainisapproximatelylinearin
pumppower.
Severalstudies ofmodediscriminationby fiberdesignorbendinghave suggestedthe pos-
siblityoflargemodespecificloss[13,14,15,16].Unfortunately,itiscommonthatreportsof
experimentalobservationsof modeinstability thresholds neglectto includemention of mode
specificlosses.
1.5
el.]
er [r 1
w
o
p
p
m
u
p
d
ol 0.5
h
es
hr
T
0
0 10 20 30 40 50 60 70
LP −specific loss (dB/m)
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Fig. 7. Influence of mode LP losson therelative threshold pump power ina quantum
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seededamplifier.
8. CONCLUSION
Careful characterization of fiber amplifiers will be required to maximize the mode instabil-
ity threshold. All pump lasers and seed sources have some degree of spectral and amplitude
modulation,andweshowedthatevensmallmodulationscanstronglyreducethethreshold.It
shouldbeclearthatthepumpandseedinputsmustbeextremelywellcontrolledtomaximize
thresholds,andthattheircharacterizationis an essentialpartof meaningfulreportson modal
instability.Additionally,preciseaccountingofthesignalandpumppowersmaybenecessary
inordertodetectanysmalllinearlossessincetheyalsostronglyreducethresholds.Further,it
isclearthatattemptstoraisethemodeinstabilitythresholdsignificantlybyengineeringlosses
forthehigherordermodeswillrequirelargelosses.Doublingthethresholdfromthebaseline
requiresabout170dBoflossforLP .
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