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Observation of optical turbulence in a single mode homogeneously broadened optically pumped molecular laser
~ollllllc
54.
lluIIIll~!: ?
Instabilities leading 10 chaos in the emission from laser systems have receivedconsidcrablc attention since the first prediction of such behaviour by I lakcu for a hornogcneously broadened system [I].
Rcccnt-
ly we here able IO demonsrrute chaotic pulsations in the 100 ns emission from a truly homogeneously broadened laser system; VL! a mid-infrared ( 12.8 pm and 12.08 ~ni wavelength) NH, laser optically pumppulsed CO2 laser radiation 12J. In IIICpresent paper we extend our results to essentially steady state
et1
by
conditions and use a short laser cavity length to cnsure sin@ ;utial ~nodcoperalion. To our krrowlcdgc this represenls the firsr dcrrmsiration of chaos in a single mode homogeneously broadened laser sysrcm. Wc iio1c hcrc the iwent dmonstration of period doubling by Weiss cl al. 13 ] in an extrerncly low prcssure system \iir an oprically pumped fdr infrared Cl I, l:2 laser. Routes to chaos via period doubling and also; inlermilicncy are clearly idernificd in our s]slcm. The gcncrarion of instabilities was
li~~nd IO
critically
dcpcnd on cavity length. NH3 was sclccred here OII l,hc basis of ils well docunienlcd discrete spectroscopic lixture, highly efficient mid-infrared king emission and ills0 our carlicr demonstration of instabilir its in this gas under passive (non-lasing) condilion (4 I. ‘I’cmporally smooth TC’Mt,,-, pump pulses wcrc dcrixxl iiottt a hybrid CO2 laser [S 1, the I’EA SW ion of which was a I .urrronics K-021 IIW~UIC. L.ong puks
(FWHM -2 /AS) 4 peak power 250 kW wcrc &t;lined by operating the low pressulc section above t hrcshold and using a N,-rich gas mixture in the TEA secrion 161 (see fig. I). The (10, laser operating on the FIR16 lint (1076 cm l ) pu~npcd the aR(6. 0) NH, lransition I .3 GI Ix below the lint centre. The Fabry-Perot St I, laser cavity. slightly offset to eliminate feedback to the CO2 laser cavity, was 24 cm long giving a frccspectral range of 624 MHz and consisicd of a gold CCXICRYC (2 111radius of curvature) mirror provided with piczoelectric runing (P7.T) I’acility and 21plane Gf! mirror (705 rcllcctiviity ilf 12.8 clnl and 8.5%.at 9 pm: for achcrnaticdetails see fig. 1). The NH, cmissiim occurred at 12.8 pm (aI’@. 0) transition) and lhc pulse duralion was approximately 2 PS compared to lhc cavity round lrip iimc (It<) of I.6 ns. For cxpcrimcnls on a dispcrsivc cavity. used lo tlccouplc the rotliati<)n aiicr a single l)ilss rhrough tllc NH’,
~IIIII~
vclllrlllr
OI’I’K’S (‘OU~~I’YI(‘A’I’IOFiS
.%I. Illllllllc! 1
cdl. il KBr prislll was WXX~irisidc lhc Fihry-t’crol
cilvi-
200 t-6
1~. The St I 3 hscr sigmls wcrc rccortlctl b> iI sensiriw
II
pholorcsisl& tlcrcclor antI clisplayctl orI a ‘I’cklrollix 51oilcl 7 IO4 i~scilloszi~pc: lord rcsponsc liinc - I 11s. 1 llC INllrlI) INJISCWilS SUilllhIy ilIxxlUrCd 11)giVCil gilUSSiill1 sIXlli;ll tlislriburion (bl!illll waisl ilt I/i’ - 7 111111) illld 1IllJS prouiilcd Ilighesl giIil1 011 the ‘I’l~W~~~~ motlc li)r I hc NH, laser. Transvcrsc sc;ms ol’ IIIC Sll; luscr cniissioii ixmtiriricd a iieilr gaussiari Spiltiill in- .’ Iclisil~ tlisllil~tJrioll
wirli no significanr tliffcrcficc iii
IIIC illSlill>lliliCS s;llnpletl across ItIC bCarll. In ill1 SubSCtIllr’Hl lIlCiISUrCIIIClllS IIIC WIIOICbCilll1 signal WilS rlli~lcli)le iixx)riIciI. (‘IlilOlli ;llld ;X’riOlIk plISillk~ll hdlilViOlJl ill IIIC UI 1,; ~:llilssioll u’;ls li~tlllil lo bc very smsitivc 10 CiIVily lciipll~ liiiiiiip ;Irid occulrcd incr ill1 Sllj pcssiirc I.lle IOlill IiIIIlX 01’ 5 0 lorr ~0IIICUllilt Slllilllcr I111111 rilflp! .! I I Iorr I’or H tiicli IilSillg mission WBS lh5cncJ. 5losl t~roiiouricctl Cl’lL’cls. IllOSCiJW lmwnlprcssurc -8 Ion. :Il lliis
cc! Iicrc. wc’rc l~tlliliIll!ll
iII il
prosurc’
t~r0iltlc’l1ill~ ( 140 MI I/ I’roiii
lioiii0pciICotIS
h-1.. I7 1) doiiiili;iia incr Ih~t~~~h:ri’I’l’C;lS (74 511 I/ ISI ) bliicli ;iri’ iic’~crllii%*sa ill11 alriull~ rCItiVillll sillcc icily oiic wlocil! grout) 01’ iiiolcculcs is iiiwrlccl rlic OI)lkill IxJlliI~ilip. II is sigliilii:llll I0 ll0IC Iicrc lllill \Vcis:,Cl 31. IlilS t,rctlida! 1’)I IlOllllK$.?llLVNlSl~
I,
I~ll~illlCll~*llcx~lldiliolls I’or ;I I’:lr-iiil’i;ircd oplliilll~ piii1llWI \I I ; l;lw 1%liidl is ~llilril
I’Z’I’
#ilS ioiiliriiicd
from IIIC
01 lllC Cil\il> ICllplll: IilSillg bciiip 0hl:iiiicil 0~1’10l:lJ ill~l~lll OIICcIllilrlcr 01’ iii I’rci’ Ctll’i’l rill lilllgc’ (I’Slij. hi.! IlOtU licre Illill IIIC LilVil! lllllilig IilllgC OicI ?iilIl
wllicll IilSlllI! oci’iirlcil
SiillCll lillCil!I!’ # iili
illl(l w:lh ill f!OOd iI~!rCCIIIc1III willi
orcssiirc
IIIC t~rctlicld
~~;I111 I~illllI\b’kI~Ilbil!d OII 11I)l’CSSlll’C hlOildCllt%IVilIlJC01 17.040 VI I/ lorl li)r Ihis IrilllSllirlll 171.
I’ip. 2 illO#a II 2OilrbCI’%‘1 GIlI IilkCll ill CtIllill iiiIclVillS ;ii’rosh IIW Ir!giOll 01’ IIIC t.SH incr \vliicli lilbillg o~allrctl. O;dlircll~C ol’iiislat~ilili~~s W’ilS li~tllltl lo t,c iIS~l!llllc’lriL%ll~ tlC~~Ch!lll OII Ciliil> llllllll~ illlll is silllilar IO IIILY rhSCl\illil)ll oi’\Vciss ard KIiwIIc 1.31. ‘I’Ho plll~illillll lwrioils here 1’011~1~1 lo oc’i’lli for dighi-
PA’ acllillpa ill IIIC lillll_‘t for wliic’li iitIllC~illlCll piaiotisl>. Olli: ill L’IOSL!It) 2/j< pcl ioil ilIlll I Iic oi Iier 0i’ rchiwly slow pcrioil willi 110 ohvioiib !~il’ur~:Ilioil icl:itionsliit~ Ii) 2flt (‘l’lir’ \ViI\c’IOIIII WilS illWil>S li,uiiil IO IN IICiII Iriilll~lllilr.) II is Ilk! I> ilifi~icill
slahlilic.3
4ow pci iotlic iiiodiil:ili~~ii tlisliiicl Iy lciiprli
twriotl iiliiillg
iloiit~lirig Idorc
(lig. .iil) wliidli
cxliibiwd
(lip. 3h:) wilh icr>’ lint iil\‘ipoillp irllo liigli pcriotl cliaod I IS
~OtlJlll“ .I 54 . Illllllbl!i “
oI’rI~‘s
100ns
50ns
I I
I I
Fig. 4(;1) shows iI kind 01’inlcrnii~lcnq
[ lO(
(jig. 32).
\I
wlicrc flicre is a tlircct
I]
I! WtC
into ;I
lirll0MWl
t)y
( oHML:YI(‘A’rIoS~
transiticln
frwii
ai1
oidcr-
Ill~liiStilt~l~CllilOS Vir! il CllilOliC pciiod
ill1
abrupt l.riinsilion
IO order iIS llilh rc-
lhwi discusscil by Shill cl ill. 1I2 I. Inlcnniltell1 dliM)liC hrsls arc c~iilcnt in tip. 4(b). The Iwling cl’l’ccls so_xI in fig. 4(c) Uilrl hc ihrilicd wil II
cciilly
heavy hrcalliiiig
1I.31 wldc
l&s. 4(1l) and 4(e)
2llilOS I IO dciir
TIN
ill
CIOSC!IO 2! t( is c’\i-
dc’is 0I’i’ig. 4.
llilllSllliltCd pUlllp
prorioiiikxl I II
1. ‘1’llCt)ilSLLpcric~il
iii Ilie
icspw-
and (‘1~11~tl~~~l~l~d
tidy lypii’y Cxi~llIt~lCSoi’wlk
ilisiorlion
IO cl;lril’> using
pUlSC
did
1101 SllOW
iIll!
iii ortlei
role oi’ l~cdbwk 01’ the
il dispcrsivc
licr. \hliich
collld
lcsl cxpcriiiicnls
42lEXlS
signal
pu~np
wcrc cimluclctl
I:ilt?r~-I'CrOl syslelll. dcscritml SllSlilillOnly
rcrice of’ IilSCr instahilirics Illill[IICW
iIrk:
in
Sli!
this
mission. sysrciu
I’roni IllCiIi'tiW
WI-
Occur-
corilirnwtl OpliCill
CilVil~
iIlOl1~. bC
011 iI ring pulsations will1 cvi-
llilbr!ills0 ~X~llllll~lCd cxpcrinlcllls
i'ilVil>'Kli,:
IilWr. Wliilc
tlciiuc of’ pcriotlic S!3ll!lll
eft’cct. Nwcrthclci:,
IIIC
Ilir iilvily.
within
tlwblirig
WilS ncvcr ilrivcn
bllilMl)ly ill<0 IlOfC
periodic
were I’oimd lo il
1lW 10 Iioii-oprinlised licrc
lo
otmr
CllilOliC Icgiiir:
C;lVitj
lllillIllC I'ilhr~-RrOl
cordiIions.
CilVil!
tllc
pre-
\hC
is yencral-
a
e I.i$. 4. RcprcscntiJlivc ewllll~l~! 01’ \I13 lrscr cmisdion (covlly ib iii I’Jp.2, H livr
~i~cmil;~l~lc &IO~
(I)) illwr-
IIIIIKWI
“hild CilVil)” rcc~llirl!lllcrll h
SUCtl Operution.
H’C
l’urllicl IioIc’ llial our .Ycvcl high pin 1IS] op~icallj IJllHlI3ctl her SyStClll lllily hC ;MOCiiltCd witI1 il WllIn ci~nclusion
WC Ilavc obbcrvcd piiilll
illslilt~ilitics
Irally tlippcd pain (as S~OWII tJy I’imock iJIId Tcmkin
illld ClliiOS t’lf_lJll il single IlllllIk! llOl~l~~~~Il~~~~~Sl~brOiltlCll-
1Ib( ); il Silllihr
Cd OlHicilll> plllttlWd mid iril’riiretl
I’crcnl ill origin being responsible
luscr. ‘I’llill I IICSCCl-
kClS ilrc’ SIJSlilillCd ilS IlOll-(ICCilyirlg Cl’fCClS I’Or INJISC~
01’ illSlability
mission
S>SlClllS
0f’dllrilliOn
-2 ps coircspondirig lo -, I.300
/I< CSlilbliSlleS Sti%tl) SlilfC contlilion lilr OLJr ol!scr\ilIiOI~. I lowcver, CiJlClJl~~tilMlSSIIOW IlliJl for 0lJr SySl~3tl lllc laser cavity liriewidili (-80 %tll/) dots no1 2xCWd lhc I~oJnogcnc0lls lincwitlt Ii Of’llie IilWr mxliuril ( I SO Mlir) which is ilt b7lriilncC wil Ii llw prctlicictl
flXllJre
ilIlIlOU~Il
[ 17. IX I ill gle:llly
hroatlcJlcd laser rcdiiml thshold f0 tlic
I’or homogeneously IO
lilll~ (Illillllll’~
prctliclctl
b!
hroadencd S~SICIIIS. Fur-
l her c!Xpc’riIIICIIIiII ilrltl ltlcorctical navsSary
li)r lhc occi~~rencc
in inh0JnogcilcOUSl~
proliihil hcly lligli VilllJC. originally tl:lkPtI:
I’LJIldiJlllCI1lJJII~ dif-
invesligariona
iIrC
0lJr ohscrvaliolls.
I IS
illstahilitio
and chaos have been rcportcd b) Weiss
et ill. [Is) 1 fi)r a resonantly exciled fiir infrared fwo tt!\cl s>SlClTl. acknowledge the SI:RC for partial
We graldutty
support of Ihis progrmmc. D.J.B. wishes to thank Rhahha .Alomic Rcsci\rdl Centrc for grating him lcavc oi’i~bscncc. I4c thank W.J. I%h. J. Maloney illld I. AI-Saidi iiN IlClplill discussions.
.I. (.BXllll. SyC57rov IL(llill I lillblr’: I .: I IHI !!I] (.‘. IWlirntl. II 6 (,;!;Glr- :III~ I IMI. \;!;)I. I’h>3. I cl:. 10 (IYXZ) 655 Op:ic\ ( QI:;III 5! 1iOh PI ( .() Heis> :Incl U Klww. 47 LlOl N.B. .Qrrli;r~u. I. (‘II! h. 11. (‘olcm:u~. K.S. (;iogd;b. S.J. Ili~hs, I..Y. Ildr’cr, S.Y. lb. M. 5iadn imtl .I.(‘. Wcsson. in: I.ecturc Xotcs in Plwicc. Vol. I82 (Spririgc’i Vcrlag. 1983) p. 105. fI.!:I!. I’ll). III, y. I’OIIlC:IU illlil I’. Villlll~~IIIc’. ~‘Oll:ll’llll. ‘4 I I 08(J) I HO I -I ” V.L. SIIIII. I’.\! Viloriiii :iIld 1.K. I~kc’rlbill:. :o Iv ITi I .U.
l;l>ll~l.
(1983)
pul~lirlietl.
References
I I .‘?I 1..,\.
LIl~!liil~~. I.. M. Xard:JCL’l. I) C. l1illXl> .Illtl ( 2
Pcnnhe. Opriir
II. Il;lkcn.
PII)\.
It (I. Ili~rr~w~ tlYh;l
l.c~r. 5.iA flY75)
and I.A. Al-Saidi.
77. Optics ~‘onm.
14
II!?
I{.(;
Ilxrwn.
I.Cll
53 IlYH4I
U.J. I iah and I.:\. II-Sdidi. I%)>. Kc\. 2.58; I< (I Ilillrl*~!fl. \..I. I irth. (‘. I.mblIiJr~ iIIld I:\. :\I-Silltll. l’ll)~. I<\?. I.~‘11 51 IlYti3) 562 \. ( ;t~rItlI:illtvkill. S.K. Ilskcnbclg iId I . IIoI/II~II~cI. I’ll!\
I Cll. -lo:1 I IYY.“rb 229.
5 I< Ilcckcnlxr;, ;wl!li~llcrl
t to
A.K.
Kw ml
.I.(; II. Va~lwa.
(‘omc:. 46 [I OX.\I h-l Ilodpes. I .R. I’OOI~ and I< I). ILvl. \;)pi. I%y, I i:rl. 29 (IV761 662. 1151 11.1). Uoi:iron. I3.K (Arwle ilnd I I~cIcI. II I I .I Oui~nt. I’lwrion 2(! I I YH4! I M!i I If-1 K.1. Ihock and I7 J. Iankill. II I’I J QIL~III I Icc:on 141 I’). I
IO Ix
II_
S I. Ilentlua antI Il. Siirpwl
Ill.
Op:ics ( ~II~II*: 4!!
I 108’1_ .ik5. I..\\ (‘ii,pCr\,o~l. II’! I J. ()lJillll. I ir!::-on 14 l,lY’?j tih 256 I IO C.O.H&c, \h. Klnd~. P.S. I rlrl!’ iIll \I (‘~H~;wI. ()I’liL*u (‘ornm. 52 I lYHS)Ji)S.
54.
lluIIIll~!: ?
Instabilities leading 10 chaos in the emission from laser systems have receivedconsidcrablc attention since the first prediction of such behaviour by I lakcu for a hornogcneously broadened system [I].
Rcccnt-
ly we here able IO demonsrrute chaotic pulsations in the 100 ns emission from a truly homogeneously broadened laser system; VL! a mid-infrared ( 12.8 pm and 12.08 ~ni wavelength) NH, laser optically pumppulsed CO2 laser radiation 12J. In IIICpresent paper we extend our results to essentially steady state
et1
by
conditions and use a short laser cavity length to cnsure sin@ ;utial ~nodcoperalion. To our krrowlcdgc this represenls the firsr dcrrmsiration of chaos in a single mode homogeneously broadened laser sysrcm. Wc iio1c hcrc the iwent dmonstration of period doubling by Weiss cl al. 13 ] in an extrerncly low prcssure system \iir an oprically pumped fdr infrared Cl I, l:2 laser. Routes to chaos via period doubling and also; inlermilicncy are clearly idernificd in our s]slcm. The gcncrarion of instabilities was
li~~nd IO
critically
dcpcnd on cavity length. NH3 was sclccred here OII l,hc basis of ils well docunienlcd discrete spectroscopic lixture, highly efficient mid-infrared king emission and ills0 our carlicr demonstration of instabilir its in this gas under passive (non-lasing) condilion (4 I. ‘I’cmporally smooth TC’Mt,,-, pump pulses wcrc dcrixxl iiottt a hybrid CO2 laser [S 1, the I’EA SW ion of which was a I .urrronics K-021 IIW~UIC. L.ong puks
(FWHM -2 /AS) 4 peak power 250 kW wcrc &t;lined by operating the low pressulc section above t hrcshold and using a N,-rich gas mixture in the TEA secrion 161 (see fig. I). The (10, laser operating on the FIR16 lint (1076 cm l ) pu~npcd the aR(6. 0) NH, lransition I .3 GI Ix below the lint centre. The Fabry-Perot St I, laser cavity. slightly offset to eliminate feedback to the CO2 laser cavity, was 24 cm long giving a frccspectral range of 624 MHz and consisicd of a gold CCXICRYC (2 111radius of curvature) mirror provided with piczoelectric runing (P7.T) I’acility and 21plane Gf! mirror (705 rcllcctiviity ilf 12.8 clnl and 8.5%.at 9 pm: for achcrnaticdetails see fig. 1). The NH, cmissiim occurred at 12.8 pm (aI’@. 0) transition) and lhc pulse duralion was approximately 2 PS compared to lhc cavity round lrip iimc (It<) of I.6 ns. For cxpcrimcnls on a dispcrsivc cavity. used lo tlccouplc the rotliati<)n aiicr a single l)ilss rhrough tllc NH’,
~IIIII~
vclllrlllr
OI’I’K’S (‘OU~~I’YI(‘A’I’IOFiS
.%I. Illllllllc! 1
cdl. il KBr prislll was WXX~irisidc lhc Fihry-t’crol
cilvi-
200 t-6
1~. The St I 3 hscr sigmls wcrc rccortlctl b> iI sensiriw
II
pholorcsisl& tlcrcclor antI clisplayctl orI a ‘I’cklrollix 51oilcl 7 IO4 i~scilloszi~pc: lord rcsponsc liinc - I 11s. 1 llC INllrlI) INJISCWilS SUilllhIy ilIxxlUrCd 11)giVCil gilUSSiill1 sIXlli;ll tlislriburion (bl!illll waisl ilt I/i’ - 7 111111) illld 1IllJS prouiilcd Ilighesl giIil1 011 the ‘I’l~W~~~~ motlc li)r I hc NH, laser. Transvcrsc sc;ms ol’ IIIC Sll; luscr cniissioii ixmtiriricd a iieilr gaussiari Spiltiill in- .’ Iclisil~ tlisllil~tJrioll
wirli no significanr tliffcrcficc iii
IIIC illSlill>lliliCS s;llnpletl across ItIC bCarll. In ill1 SubSCtIllr’Hl lIlCiISUrCIIIClllS IIIC WIIOICbCilll1 signal WilS rlli~lcli)le iixx)riIciI. (‘IlilOlli ;llld ;X’riOlIk plISillk~ll hdlilViOlJl ill IIIC UI 1,; ~:llilssioll u’;ls li~tlllil lo bc very smsitivc 10 CiIVily lciipll~ liiiiiiip ;Irid occulrcd incr ill1 Sllj pcssiirc I.lle IOlill IiIIIlX 01’ 5 0 lorr ~0IIICUllilt Slllilllcr I111111 rilflp! .! I I Iorr I’or H tiicli IilSillg mission WBS lh5cncJ. 5losl t~roiiouricctl Cl’lL’cls. IllOSCiJW lmwnlprcssurc -8 Ion. :Il lliis
cc! Iicrc. wc’rc l~tlliliIll!ll
iII il
prosurc’
t~r0iltlc’l1ill~ ( 140 MI I/ I’roiii
lioiii0pciICotIS
h-1.. I7 1) doiiiili;iia incr Ih~t~~~h:ri’I’l’C;lS (74 511 I/ ISI ) bliicli ;iri’ iic’~crllii%*sa ill11 alriull~ rCItiVillll sillcc icily oiic wlocil! grout) 01’ iiiolcculcs is iiiwrlccl rlic OI)lkill IxJlliI~ilip. II is sigliilii:llll I0 ll0IC Iicrc lllill \Vcis:,Cl 31. IlilS t,rctlida! 1’)I IlOllllK$.?llLVNlSl~
I,
I~ll~illlCll~*llcx~lldiliolls I’or ;I I’:lr-iiil’i;ircd oplliilll~ piii1llWI \I I ; l;lw 1%liidl is ~llilril
I’Z’I’
#ilS ioiiliriiicd
from IIIC
01 lllC Cil\il> ICllplll: IilSillg bciiip 0hl:iiiicil 0~1’10l:lJ ill~l~lll OIICcIllilrlcr 01’ iii I’rci’ Ctll’i’l rill lilllgc’ (I’Slij. hi.! IlOtU licre Illill IIIC LilVil! lllllilig IilllgC OicI ?iilIl
wllicll IilSlllI! oci’iirlcil
SiillCll lillCil!I!’ # iili
illl(l w:lh ill f!OOd iI~!rCCIIIc1III willi
orcssiirc
IIIC t~rctlicld
~~;I111 I~illllI\b’kI~Ilbil!d OII 11I)l’CSSlll’C hlOildCllt%IVilIlJC01 17.040 VI I/ lorl li)r Ihis IrilllSllirlll 171.
I’ip. 2 illO#a II 2OilrbCI’%‘1 GIlI IilkCll ill CtIllill iiiIclVillS ;ii’rosh IIW Ir!giOll 01’ IIIC t.SH incr \vliicli lilbillg o~allrctl. O;dlircll~C ol’iiislat~ilili~~s W’ilS li~tllltl lo t,c iIS~l!llllc’lriL%ll~ tlC~~Ch!lll OII Ciliil> llllllll~ illlll is silllilar IO IIILY rhSCl\illil)ll oi’\Vciss ard KIiwIIc 1.31. ‘I’Ho plll~illillll lwrioils here 1’011~1~1 lo oc’i’lli for dighi-
PA’ acllillpa ill IIIC lillll_‘t for wliic’li iitIllC~illlCll piaiotisl>. Olli: ill L’IOSL!It) 2/j< pcl ioil ilIlll I Iic oi Iier 0i’ rchiwly slow pcrioil willi 110 ohvioiib !~il’ur~:Ilioil icl:itionsliit~ Ii) 2flt (‘l’lir’ \ViI\c’IOIIII WilS illWil>S li,uiiil IO IN IICiII Iriilll~lllilr.) II is Ilk! I> ilifi~icill
slahlilic.3
4ow pci iotlic iiiodiil:ili~~ii tlisliiicl Iy lciiprli
twriotl iiliiillg
iloiit~lirig Idorc
(lig. .iil) wliidli
cxliibiwd
(lip. 3h:) wilh icr>’ lint iil\‘ipoillp irllo liigli pcriotl cliaod I IS
~OtlJlll“ .I 54 . Illllllbl!i “
oI’rI~‘s
100ns
50ns
I I
I I
Fig. 4(;1) shows iI kind 01’inlcrnii~lcnq
[ lO(
(jig. 32).
\I
wlicrc flicre is a tlircct
I]
I! WtC
into ;I
lirll0MWl
t)y
( oHML:YI(‘A’rIoS~
transiticln
frwii
ai1
oidcr-
Ill~liiStilt~l~CllilOS Vir! il CllilOliC pciiod
ill1
abrupt l.riinsilion
IO order iIS llilh rc-
lhwi discusscil by Shill cl ill. 1I2 I. Inlcnniltell1 dliM)liC hrsls arc c~iilcnt in tip. 4(b). The Iwling cl’l’ccls so_xI in fig. 4(c) Uilrl hc ihrilicd wil II
cciilly
heavy hrcalliiiig
1I.31 wldc
l&s. 4(1l) and 4(e)
2llilOS I IO dciir
TIN
ill
CIOSC!IO 2! t( is c’\i-
dc’is 0I’i’ig. 4.
llilllSllliltCd pUlllp
prorioiiikxl I II
1. ‘1’llCt)ilSLLpcric~il
iii Ilie
icspw-
and (‘1~11~tl~~~l~l~d
tidy lypii’y Cxi~llIt~lCSoi’wlk
ilisiorlion
IO cl;lril’> using
pUlSC
did
1101 SllOW
iIll!
iii ortlei
role oi’ l~cdbwk 01’ the
il dispcrsivc
licr. \hliich
collld
lcsl cxpcriiiicnls
42lEXlS
signal
pu~np
wcrc cimluclctl
I:ilt?r~-I'CrOl syslelll. dcscritml SllSlilillOnly
rcrice of’ IilSCr instahilirics Illill[IICW
iIrk:
in
Sli!
this
mission. sysrciu
I’roni IllCiIi'tiW
WI-
Occur-
corilirnwtl OpliCill
CilVil~
iIlOl1~. bC
011 iI ring pulsations will1 cvi-
llilbr!ills0 ~X~llllll~lCd cxpcrinlcllls
i'ilVil>'Kli,:
IilWr. Wliilc
tlciiuc of’ pcriotlic S!3ll!lll
eft’cct. Nwcrthclci:,
IIIC
Ilir iilvily.
within
tlwblirig
WilS ncvcr ilrivcn
bllilMl)ly ill<0 IlOfC
periodic
were I’oimd lo il
1lW 10 Iioii-oprinlised licrc
lo
otmr
CllilOliC Icgiiir:
C;lVitj
lllillIllC I'ilhr~-RrOl
cordiIions.
CilVil!
tllc
pre-
\hC
is yencral-
a
e I.i$. 4. RcprcscntiJlivc ewllll~l~! 01’ \I13 lrscr cmisdion (covlly ib iii I’Jp.2, H livr
~i~cmil;~l~lc &IO~
(I)) illwr-
IIIIIKWI
“hild CilVil)” rcc~llirl!lllcrll h
SUCtl Operution.
H’C
l’urllicl IioIc’ llial our .Ycvcl high pin 1IS] op~icallj IJllHlI3ctl her SyStClll lllily hC ;MOCiiltCd witI1 il WllIn ci~nclusion
WC Ilavc obbcrvcd piiilll
illslilt~ilitics
Irally tlippcd pain (as S~OWII tJy I’imock iJIId Tcmkin
illld ClliiOS t’lf_lJll il single IlllllIk! llOl~l~~~~Il~~~~~Sl~brOiltlCll-
1Ib( ); il Silllihr
Cd OlHicilll> plllttlWd mid iril’riiretl
I’crcnl ill origin being responsible
luscr. ‘I’llill I IICSCCl-
kClS ilrc’ SIJSlilillCd ilS IlOll-(ICCilyirlg Cl’fCClS I’Or INJISC~
01’ illSlability
mission
S>SlClllS
0f’dllrilliOn
-2 ps coircspondirig lo -, I.300
/I< CSlilbliSlleS Sti%tl) SlilfC contlilion lilr OLJr ol!scr\ilIiOI~. I lowcver, CiJlClJl~~tilMlSSIIOW IlliJl for 0lJr SySl~3tl lllc laser cavity liriewidili (-80 %tll/) dots no1 2xCWd lhc I~oJnogcnc0lls lincwitlt Ii Of’llie IilWr mxliuril ( I SO Mlir) which is ilt b7lriilncC wil Ii llw prctlicictl
flXllJre
ilIlIlOU~Il
[ 17. IX I ill gle:llly
hroatlcJlcd laser rcdiiml thshold f0 tlic
I’or homogeneously IO
lilll~ (Illillllll’~
prctliclctl
b!
hroadencd S~SICIIIS. Fur-
l her c!Xpc’riIIICIIIiII ilrltl ltlcorctical navsSary
li)r lhc occi~~rencc
in inh0JnogcilcOUSl~
proliihil hcly lligli VilllJC. originally tl:lkPtI:
I’LJIldiJlllCI1lJJII~ dif-
invesligariona
iIrC
0lJr ohscrvaliolls.
I IS
illstahilitio
and chaos have been rcportcd b) Weiss
et ill. [Is) 1 fi)r a resonantly exciled fiir infrared fwo tt!\cl s>SlClTl. acknowledge the SI:RC for partial
We graldutty
support of Ihis progrmmc. D.J.B. wishes to thank Rhahha .Alomic Rcsci\rdl Centrc for grating him lcavc oi’i~bscncc. I4c thank W.J. I%h. J. Maloney illld I. AI-Saidi iiN IlClplill discussions.
.I. (.BXllll. SyC57rov IL(llill I lillblr’: I .: I IHI !!I] (.‘. IWlirntl. II 6 (,;!;Glr- :III~ I IMI. \;!;)I. I’h>3. I cl:. 10 (IYXZ) 655 Op:ic\ ( QI:;III 5! 1iOh PI ( .() Heis> :Incl U Klww. 47 LlOl N.B. .Qrrli;r~u. I. (‘II! h. 11. (‘olcm:u~. K.S. (;iogd;b. S.J. Ili~hs, I..Y. Ildr’cr, S.Y. lb. M. 5iadn imtl .I.(‘. Wcsson. in: I.ecturc Xotcs in Plwicc. Vol. I82 (Spririgc’i Vcrlag. 1983) p. 105. fI.!:I!. I’ll). III, y. I’OIIlC:IU illlil I’. Villlll~~IIIc’. ~‘Oll:ll’llll. ‘4 I I 08(J) I HO I -I ” V.L. SIIIII. I’.\! Viloriiii :iIld 1.K. I~kc’rlbill:. :o Iv ITi I .U.
l;l>ll~l.
(1983)
pul~lirlietl.
References
I I .‘?I 1..,\.
LIl~!liil~~. I.. M. Xard:JCL’l. I) C. l1illXl> .Illtl ( 2
Pcnnhe. Opriir
II. Il;lkcn.
PII)\.
It (I. Ili~rr~w~ tlYh;l
l.c~r. 5.iA flY75)
and I.A. Al-Saidi.
77. Optics ~‘onm.
14
II!?
I{.(;
Ilxrwn.
I.Cll
53 IlYH4I
U.J. I iah and I.:\. II-Sdidi. I%)>. Kc\. 2.58; I< (I Ilillrl*~!fl. \..I. I irth. (‘. I.mblIiJr~ iIIld I:\. :\I-Silltll. l’ll)~. I<\?. I.~‘11 51 IlYti3) 562 \. ( ;t~rItlI:illtvkill. S.K. Ilskcnbclg iId I . IIoI/II~II~cI. I’ll!\
I Cll. -lo:1 I IYY.“rb 229.
5 I< Ilcckcnlxr;, ;wl!li~llcrl
t to
A.K.
Kw ml
.I.(; II. Va~lwa.
(‘omc:. 46 [I OX.\I h-l Ilodpes. I .R. I’OOI~ and I< I). ILvl. \;)pi. I%y, I i:rl. 29 (IV761 662. 1151 11.1). Uoi:iron. I3.K (Arwle ilnd I I~cIcI. II I I .I Oui~nt. I’lwrion 2(! I I YH4! I M!i I If-1 K.1. Ihock and I7 J. Iankill. II I’I J QIL~III I Icc:on 141 I’). I
IO Ix
II_
S I. Ilentlua antI Il. Siirpwl
Ill.
Op:ics ( ~II~II*: 4!!
I 108’1_ .ik5. I..\\ (‘ii,pCr\,o~l. II’! I J. ()lJillll. I ir!::-on 14 l,lY’?j tih 256 I IO C.O.H&c, \h. Klnd~. P.S. I rlrl!’ iIll \I (‘~H~;wI. ()I’liL*u (‘ornm. 52 I lYHS)Ji)S.