WO2024216166A1 - Integrated frequency modulated optical parametric oscillator frequency combs and optical spectroscopy using same - Google Patents

Abstract

Improved optical comb generation from an integrated photonic device is obtained by intracavity optical modulation of a photonic integrated circuit optical parametric oscillator. The resulting device is referred to an FM-OPO. The comb spectrum from an FM-OPO is much broader than obtained from conventional integrated comb generators relying on the electro-optic or Kerr ef fects. There is also no mode-locking or pulse formation in an FM-OPO. Mid- IR spectroscopy is one of the most promising applications of FM-OPOs.

Description

- nrrrruunn mun rmrr un m mr.aav-aen uer.oows exaner-awan reuencs cnovmens.onreaesoeneraon o oca recseca sacree,uesncarcoms, caracerze er ‘ secra nesa serve as a nurmeeruoenc ruer’or , arensensaeoosn o us-caeacs,romrecson meroo an aomc cocs secrosco.ueeeecommunecaons an moecuar a caons,erveo mrnoaeunrzaerreacuencca c-scaeneraeevces,nown as mcroc comsno recen acceerae a a remaraeace.onovms,as ocareuenc com enona a s,rouce rou moe-oce osscersaanorssncronous ume ocaaramerc nrasrucure,s sucareaare an reure susana owerasers.s a ressuco,mexeeac ssems or - use ouseaoraor senesr csosmse.,wo anrer meosor creanneraereuenc com sournccesa - sunraeseonsoer.smaeerr,senoaeevcesave⁽³⁾een exore oca nonne voves r-orer orerr ma ar, w successuemonsraonsn ne serrae,s ssuccoanscsarcae,asncon numrnoe,aaeumnu.me acsoneesnrraeaezeusesnreesoenaencro-o.c an enec, wc nerae n-m evces. on-resonan avances, aner eseese remarae c r comsace severa caenes.ese somrs are oenmener ecenc, ex a sonau amnexaconernouna,suecerreasronmcommeneuna an enessanromeum.oreov nens or comseman sosca er,errreuenc more caenno oereae coanraosmaanerecormeeessuescarnaa rane. rovcecormrnove, o wcoaureeuaenncavcaonmcene aro oonc crcus. sromnerae sourcessw wora enaes scaae annerae source caonsn oca secrosco.e reuen s eer a sn- orou-resonan reazec mnoauaoeonoccnaeraaraemecrrccuosc.na eoxrem- evcesase on,u no meo, an ocaar rcaocnernacn,woarvemucroernarrecsaonaor,ormerom a - secon-orer no en a maera w sron rocess, suc ansnuearno mae enao,es aurmee n-woavaeem.xne - r-oucecaannoeocearaereunenacrceomue.nc-mouae moeo nonnear senerae n an - rou a secon-orer nowo, rreoceess v n e ener o um oons smuaneou rre o as sna an er. e - can reue s enerae a com o o ca reuences e enc mouaon. s mouaons reaze rou arceacero-o c eec n a connn waveue noae, wnc a maera suc asu no me o um eecroesaesrn meounae an e a e rou eecro- o ear e resonaor waveue. e w n ercan eec cane reaze a an waveen waveen sarenc wnow o e crsa. e ouu eum waoveeneenerae s conroe unn enracav a,seemmoeuraauorre.,or voae a e o rouncreassenrsoneeanccenseserneou.eu.,anw soss e o e nanooonc waveue o cann eeomer oeran waveen rane o r ca n maera. e ree eesn o eereoc-o cnane enneere me eransarenc rane o u zean ms man e waveue maerasncueu are aeras. u are rum em n sonao ana nae ,a, we.oa cnss ssou rmm eeeerma reonmoeno asss no ,asaeme ouna, an, aoner - .n some emomens, e sna - resonan e ers non-resonan, s resonan, an sn -resonan - . wc s reerre o as a a - s are suaeor o ca secrosco sources m ceane u ze oeec secmens suc asu no exosveos:.anse as, oun,s,eorooac raanseamoeasc,cesrsus,ean - wavmeeenos: eennavreosnmaenacamononsornnarearsesuc as,u no nusra conamnaon, ce enouseases, eense eecon o eam scua s s, an ewse, meca omarers,cun sances, exosves, roucon, an ar uurse.r rocess conro,oo racernacerraeseonao-r,wemoonemesnecscoanneerase on a rove momenum macn or e ree-oca oe o neracon, an anoer waveue wave mxn e rou mea eecroes saeceroncoue o e resonaorncues a waveue ne near. e or aaac couer e couer recona couer a sna or snas anne oesreecve ransm ransm n um sron . weaveumenres w ou resonan. uenc s no avaan ceonsrsasemsoaseeror ar, eseca commerca - - emomens w osnu crsas, e nanooonc eomeres enae: necaca esne waveue enaesneraon w nenoa reeuce oorn a ower consum on aener sensors euce ooncnerae crcus aseornswo comex reac waveen anw s no oss n enneern o urermore,n comarson w enu ssems. suc aserr- an oer mcrocom sources enaes: ecrure -coms, e nanooonc - um aseracroau a reuenc com emova o more susana nan a s ca orers o manue ree-secra ran e com nenens es ower wo coms c e, eseca comare oerr coms eree saencreaernaenrae,ewwc ancvreerasessmaeresoeruencoenon - sumaa-ceormesececrrcoascoanawn a.owsusn ooeecors w cu n soummenemooaem,enmsc,rosrencrecsaona, oseemon z- o a racerac. e ors are use nsea uname z-cu um noae emomen uses onn oae emnoerseoresaonwaavoeruenean, ancouwsnoreroc s emomen, mea eecroes a ens.n wa asoenerae an reaerne n suc a noae ane. eecrc e norma o e um e n some emomens, eum senerae on enesraameonnanoromoaonucmca arouo sesconreuaernmonc emomens,nvua s anor c.n some noarer ooncnerae - s arenerae no me o, waveue crcus,ncun,u an ermo couers, ers, eecro-o c asers an-oeecc moorsu,aanors,eraecrooenneeouesmensn.erae comrns enxe:maasrusemraoemen sacoaramerc source waveues mae ou o a maer nnn o ca nonnear suc as u a w secon-orer susrae o ca re m noae one ono o e eroc sonaororme ou o e waveues meneraaon- waoveeuwaevecouueersuwornne noonnceaarcav ceava eweacveroueeaanercnoeuenoeacnoesxeevrncan soourcee. eneraso.n an- s-ow oceormanenecroanceon.so com - evce c.onusra a socnemoarocureaxrearmmsenows.n e- ... s a mcroscoemae o eevce o .. coma srowse ouu secrum o eevce o eneraor. eo an ouu secrumrom an com wen mosu.ae- asnownounmonucaaera.cerzaon o e- e-s..- sowsurer caracerzaon resusor oerao.n o- seow-ener. eve arams reano conur.ao sn.owsan aernave- evce s.- sowwo aernavesor couers. eenns. on-we soewrseveermaaeereacrosex-ccounorurza-cuon.s, w an.-s asourocce.aram reano secrosco suaes.or u-sesnowsseecverroasco-a cocnaounrsa.ons secrossc.o u-snsow-roo soourcceosn.ce resusor m- nroucon nes.--. snowasreanueanrc comcosmnan. re,soannaooracna - resosnareosrucosnuncasnoumouuoaeonuaonassanceeanseerum. nensesaeca ex s w usese onena. e- . euna smeecnonarmonc as aum an ems a ne orn caareuenc.n mouaor couese ouu com.ve moes, crean an even srue sows as ree oca resonaors scemaca nuor mrrors , eecroes rovee eecrca ocaaram meoruaon, scemaca sowse e mouaonc, am scaon, scemaca sows e ouureuenc como.wsenuum, an sows r n s conce, we conser anemonsrae a ae ovvanouasesuonnoown eano mercrroccoomms,maerconmnnoensneea vccae.roeccessecsaw,our m r e soruucauroenacncoamnmonaeesrae owcaaramerc am caon an ase mouaoon o anr aesuennce-mcoavua,e oerecaacaramearncosceeaneorraon- com..emara, unen convenonaerr an ormaso,n, meannamces oun ouurmsorseecmosoenorerseesmuenauose aarreoaucen,c-meoruaaoe-reasueern.cnconmroasuaooanserrone on a sneourer comonen. s s we useas e oeraona smc caracersrae manans acevn susana roaeranwcs o coms we aanaerou mouaon aone.urermanose ecnueves rseo aa-o ouu coore, our nes w n o e me m w mos sr an, an oma secra nonneuaronesor maanmaanescaaonsa,rweues aevoeano uwnewrasn.e - conna , e - ex smressve e cenc, comvern a susana racon o eum no oeranoens. w eemann on moes owernusor moeomronssra serone sencoenr-aoreer- , weurno n- an eec. n- m as receo ca nonnear aormornerae nanoo n emere as a emonsraons o e cen moonucs rou eroca oe waveuesoaors, coms, uanum ene rreuenc converson, enneeraraoenacn r rcusa s, ao onn, r r aneseon cra aan oos nnec s won- suc ca aormmonexcoonc an uanum measurem saser conro eo erase on eens e.ece aoavereamnosnserrsaenoenrsareeween noncaneamroes seaarcaaneroveeroareanuencan o.roe⁽²⁾ esewo snc caa esorms eounamnn enerae - .oreover, our co onor movae s sron oena orarcee- os s manuacura as evence eors ncae nusr owursue n om namcs moeoo err an com eneraonunamena re on uses.conwe,vewr,c ssusreocueesnsneeraensonerormaon o sron reuenc-eenen var ouces a e com nes a eca exonaonn enens o rom e cener.noer co ena w er ose useormaons e nserae caeneose connuous-waveum ovenreascoenn uwseoasumma owaerr,oasae - carcruesasnsessu.e,ecen avancemensave sare o re man exo n aux ar esaonsancoesaarneusnnracauvseeuams.owernsaa,cuanseeormaon oer unwane nonnear es an mae co nae caenn nnerae aorms.emscoovrmaon ncororan aramercanno an - erere a easo areuenc com w ou nece mouae cav ormaon.urevceemonsrae ssan use um acroun, an secra as e cenc, reuce exensve enneern ness.n conras o e smar resus an oeraon namcs reure or aernave vers eerr coms, e - oers an coms, e -a e souon.oreover, un eure scaa an a reures on moes ower, ena n e mouaone caonsneoae sensors.es e sacn, e n coseo e cav resonance moe ose o arnamcs o our ssem sr n reseme mo euenc-mouae aser.sn areuenc- eusaen aser, we w see a e o ca reuenc o e maousa swoen.across aanw a e rae o mouaeonr.se conser e suaon w ou an eenerae soassume a we oerae e non- moe numer oseas ± ems sna an erones a ω₀ cmoosue n_oscrom a cenra moe w reuenc aoa o eum reuenc ω_p.s wenrouce cou n ron a reuenc caracerze a moe- smuaneoause, ese sna an erones are o ese eec ssuec oan an mouaon. earn con ons a marrorun e sna an er creaes mouae aser,nor e namcs o areuenc- mouaon coexs. wc ase-nsens vean an - a nreavenresumeonce-moocunaearsaesser,rome m n eavor e o e cav an ervere aeunn eween reuenc-mouae aser enr uenc . e moe-oce saes ans onso caoc an anw sncrea as seunn s reuce an e e meum or a mse o aroac eananw o osc aonanw soe e e cav serson. e serson o e cav , cara-cers me e ω = ω +n +n², wer ze moereuences n_neaerrω₀ e₀ amn₁ e coness₂eecroen,-oorureer₁ evsan ceers₂oanr,ereseeccavve.ner moe-ocn eavor. avos erans ono searae an exerenceeo scana asnneare±rn_osm_coesaareaerr orom eeacroocesesrnecesn_osc2.oreover, earamerc naure coms a o snas anaesere sremuuenacneeosu.soerrmeaoroeno e assume non-eenerae reme ,n eecve arveeunn wen, eres awas an er coms. s re we consero sna mrror ose o ar susn namcs a cose rvn,n wc coenuennucou-smorueaueencassweerewn seounse raer anuseormaon. e eec erve ven veanw s _{^^ ^^ ≡ = ^^!} ^{^} _" ^{^} _{# ^^} ^

^ ^^ ^^ ^^ ^^ ^^^& ∝ − , w e cmoorruesae aseranw reu onenceen a e eeencun-mnoun_osa_ce₂eawseeerneeunrnvea−n ocasreacnee - w- nec. ar-en eaa eonvee, raawne ea nosesoneoa raone onerrea eaore nsc,on oorsmeo axnasmo erer, a susana arer oror serson-e n_osc,a waveues a ma mac eoca snan orneere u ase-mouae save area eenemoer s. n conras o e aser, e anw annsraeea. anwrn o. e - areo ene n ennee rou serson sown ons..- s,owesomeevacseeceasuoresaeraceracevrecse. s w annracav waveue couer , wconaor on eunamena armonco resonae aows e secon armoncoraverse ee w e ena n sra secon o one racerac vce once. e oe waveue or secon- conans aeroca wereas e oer sra orer o ca nonnear , mcrowaves r racerac secon coueso waveueoou on-c eecroes . sne-ass c eneraueser asoeroca oe on e same reuenc, wceum o e a e secon-armonc usn a serse searae rom enu -an aser roves e ouus oo eeervsce.. n ouu couer raceeraae rc mrcer nso eos sncao reoerr,m eswae o en nee cre. aneer s wraeo vmw eosvuee eso.r-car . srucure ao e racerac s ao mcroeece waveue a ns w mcrowaves. e mcroe so ee nse ecs e rora n ee waveueeween e ocer,oaess.sowenonome osecone-raacremornaccmscroesrcooeca eoe mn e secon nse. e waveue cmare o n eoom-r corners aum- ern secocnu - acaereae sress,econ- anmarmonceneraon waveue. e n m. ,.ma,nrmaense.m . , rouces. ar soxowmsaeeouu un sueecorsucmoaoe - sna an erreuences usn a r moes a e o ca ower an m o ower.oueo me onnu reresens a coue-moe eor smuao e oom-r nse man esno e an arresu. e com, wereas eo-r nse sows a ea o e saecasraoenosoe w oease a- ounu,eoweecre usn . , co mu es o e cav am caoune-mo,ee eruoacoan o,eo c.a aramerc asee oneamnons-rae anneorca reuenc com eneraor srues m o o acae ona c . eevce even usn m o -an o caoweur over com nes mouaonower.om nes a m ower an m o ease ourevce on a re sace aou . z. on annsu racerac resonaorn n- m ≈ ⁶. aor w nrnscua acors o aroun _i o c s resonaoros w n an mouaor, an waveae aramerc am er an a -e cenc e n -seecve couer a near u ransms e cav nm.um w eeen e-an excaon w n wereas .. sows a scemac o eevce, evce sows a mcroscoemae o a sne - oou .reseoncaonuerennawescoureevumceaossoeserareouasae cavca.anreamserrac amseceornuasso none-reecsornoane n e nex o , ena n mouaon o e cavsaerne e nse. e oer sra secon o e cav .s, a - earoca oe waveue a rovesaramerc rn wennsume w e secon armoncsee . , eoee,no-r amsecon.-armonc mcroscoe cure o searaeeeneerraoecae o-nemum waovneueesames ceconn a eneraon.e er ou e or na um e -armonc ree on-c ers o e sameesn as enrraou couer. e secon-armoncenerao cav enaes uso aceve conserae o n e cenc usn on a sanar commerca ca um owers sows an exame - ouu se-carn aser. . ume w aroun m o unamenum wen eevces owercorresonn o aro a-armonc o ca ower an m o owuenr m o secon-armonc ea voae.n . , we,a esouvaoen o aou . usn e same ower w n e sam an com enerae comarson.e oserve a a com oe cav or an er waveen s an no rmaon aroun sna eum. e measure o susana acroun rom eor moe oe nueue a ns w our coue-moe r nse n . sowsscnrveuaeow.n eoom- secrum sace aroun . z. e oseersn a a aroun meween maxma an m ve conras o me resouon o e o ca snemcaresusrom e an e naure o e - . eo-rum anazer raer as. osooweseceorreasnuano coseeccrunr m anae ozuns er.ue nusnn a secrum, we oserve narrow nes sac e o e cav , resu n rom ee- sewemeun oes areuenc-eenen ouu couer. ver e oesecravneunseercsraannnearecoanexeosaaneanroexamuareesome- - oomramuncoue-moe eor anass.e aso use s sownano enuaooenrve,eormuaor e com anw eene moe am u wesca aoreeswe w oservaons. am uesor e n moe_n arournereseenunaemene reuenc, were n = corresonso eun a-armonc coses oa o eum reuenc.n samceonnaexm,oe reacresmens e am ue o e secon-armoncum e. seroseonnwas a naπu≈ra.rezuenc ven e cav corsre ees rrson ronv,n e reeso₁ uence nv ceav a ≡.ω_pe ann₂eπ se≈co−n-orzer as −re arameersncue e

ω, an e rve an exreme _a,o_nsasnsκ_bn.e-earsase‘cκa_bcorresonso a o aroxmae our n s couev-mo’e ane eonaes uso ormuaon.eerve a o e r nee moe arameersrom eorenecna samuaons, as we as exermena an are nass. e resu n coue-moe euaons ^^{^ ^^ ^^}

- rs,ereecaaurseewweormearnesaenroxemaumonsen eseeuaons. excaon o a ver oss moe, souon ass e susana saa varaons o eum envoavon waveue canno e reresene accur n e econ, wencue on cou n ewaeee s moe. we nore e weaer cou n n moes n an −n — numers.or exam eween moes w near n resen a e, cou n eween n an −n + cane wa n ma ecome sroner as auncon o um eve eunen amn .oevuenrnac.aveum wa . cveen an conseuen e ar anes e moears a o es.- -. soorwcomeaersec o um-waveen unn wav on, . sowsum- oueen resonuannn o e.evceess oerae as an unmouae o ca o races reaeo waveen secorume anazesr meeaesruremens. eouu macn mne ereuenc eum eween e sna an er moes w resec o secr. e c ase nes, recurrn ever ree .a rane, correson o e eoreca moe. o e s-ows aanse wum-weaveuren unn enrereuenc-mou e ren.owever, e sncronous aon ae cusers o moesune s. an e ener-conservaon nes.oro a - ca , one vson on e axs corresonso o ca sencerumnanaezeerecreaceo. ca oweror eac sma eauunsemenesououe wavuemenwaveenn e,e- rou ouu o san eu rane o ean snaecrnum.e unn sn,remormronrann en s serso cuaernacceerscescoavserve n an - unmo o.ua.ee so.e snoewscoerresonunnomeeasauvreomrennsw an rescean seecrruemacnaezeurn,nwereeaasvoreaseconasee nes waaveeurn,eassseorwsnonn. e. -.ereex, escoamscmusarersunn cwaovse oow e exece unn. ausn eum eeen o e cavmo,r w. z, wc euaesoa o aroxmae nmore. can azccesosraonw- o an . . ss.o- sowoweruna o e - . cou nwsn ecvouon o coms w e rve.s e eme reases, we oserve com row an e morese,ncaeonsnecownarsecvoemrasaasecounee−n_osc + m, nosc comne -resouonaroxmae snm m..e rom areas w eecae snas easuremens reansrom e res o e r an ow-resouon e sna aroun , nm ane.ermar ocus on , nmsecause o a mor sm c . eea aroun no e cav . . snoorwseaeameo en a um nvua osc an nesn eax-mum acsoun o cou n. eoe ne reon corres auncon o reconrom e coue-moe eor.eonso e coun rece o e com ne w e - eor w a c ase o .canum. o , we measure eeeon o e - e aroun , corresonn o e converson secocne-ncarmoonacrouennera.oneumnsesosowsnee annormaze ase neecownernascanewn - z. eeneeu smecownav-eaernmoncama π≈ an mnmumeneseeon. . sows e oxmum ower o eure as auncon o eum owuerua - eeneruaneasmeansaec-onarmoanrmconrceunenacs.nee-um n a aerrves e . ne n oases waavaesue a nonnear cou n rae π o aroxmae ozw.sa an oec maeassureecruemsaneacrzaer.eneeraen aee-evc uesn oaeraaroeusnconnn≈uous. ann rosurseme,nwaenon-eenerae moe oo o_osc accurac.eum exec euaon w aou m.e se e coeuevncera ae o, nm z mouaonewe e.- var en z an aroun z .n, weeoseorwer su e o e c .s sownn a+,ona com cveusaerrseuaenececom−n_ose_cve+o,.n_ose_cveraan −n onu_sc+e saneaer-causa _{osc o} errcvoemexsceaeesnaπ ar≈een z. or eow z are easero unersan erae w e e more useu n aracca s an moe, an resen e saes a arse a ar sem, we aso a resu n mu e - cuseerrs vaues o , an rece our eoreca anass.. ese are sna coms ueeune an om ee oer ocno e eune or car . e measure secra msre , nm corresonso a s eaae ea a aroun unamena-armoncum no e c o e or na numer o enerae nes w n eav .e coun e mean com ower an o sn ..aen owse o e areemen eween eaa, numerc rveoo coue-moe euaons an a sonuaon o e e ana ca exressonor e - svee nes an rounc.ase, wenoes. n euaon o a erve moere aens, mocoumaonnesrae - osocwer.an oeer w n − rom e a-o mean aroune -o oeernauesswecon-armeoncenc, convern nes. rs, enracav conv c no com , exceen ,ase on erson e cenc s measuremen n ..e coseum eeon s se-ca ran eo useeeonecause e cenc as an enaes uso cacuae e maxma an mnema ono eeconnorrmaaszeewseeecnonemeasure vs e wenunn eum -armoncower, nse.ex, en waveen , as sownn e cav esc racav com s ou-coue w e e cenca oe e cenc _a ≈., wc ms eoa conve ourevce.oe a eeeon an e srerson e cenc o no een on e rve umnow.ero awnevers,maxemezecaencarouenenoson e o ca reso. e ouu ower o e -ur remes e ca eavor o an unmouae n semes a we oserve a reso o aou m s . ,n wc an nonnear econ-armoncower rece co se mzu a, n rae π ≈ z,ower an e erec a cwnc we

arueo oeran a non- ou se-conane com eneraors. ase asers scusson nereaeave cosmucceesnseruaoraenmonessraaesaenewsueno oeran rnc es.urevceem amena r ness, anes onsraes exce ona oeraona namcss.anncereascnencewanew rean ann ursonus - oeanonruneacroereesnoreuwenc ecnoamen−e socrcne,rean rou veoc macn sna an er w e sense. enneern aramercananw o cov nae – m, exann e use o e - n mer as muc as secrosco. ven a ourn a em -nrare as eoena or mare mrove onsraon s anw serson enneern,menson o ca resonan enancem wer consum on mrove en an o ca converson e cenc o a new ca osus-ocoueno,aes orecaa rroeuuenocencsomse.ooor e a caon o ese co r sec mso eroems o aowrosco, e versa o e maera aorm nrasreo,resnaecrna coeverrauseernomeuessuc asnmoecea m- raonuocsocns,anrovcaerssoucsonnrousrnaarseccuure,oo com ee sacn o our curren ors . ou e z, our aorm can ac evcess aroun . eecom sanars an eveve an o zo mee esa se mouaors.ene excee z, ven comsenerae reore, we ancae a-o sourcesn erwcom - so n a caons as nvauaeor ranmnun acaocna sosnsemuss.noreover,reeuenacre moanuane. connuou - r s wave eecon an u emena normaon n mores.ea-. sow. some asecs o e reevan scs aramerc a sows reevan eneresor nowo omons aca 1oann. 2e.reanerum conoseornvaaon₀resuress - ee₀c=ro₁-o+₂ca. cou.n. soewrsermeoeuvaan eneresor reuenc an reuenc easoon eo a reuences + an -. sowsmseson a um unn on e ouu reuenc o e eec o ecro-o c cou n a reuen osc aon. am ues o oons a reuenc coues e am e w n e rane o ceesaram±e, a e owerar o ure. rc am er crcu .m seows an aernave an smer oonc exame o menaon o e - . ersrom e ouer. us.eu om n e on-c reuenc ncae. m ere neesoe a ₀,as couere - cav esnnvoves annracav sna anesneeroreruaennsceers.a secouer acanee sana or esvrae rnc uecsco uen rna co e, w cu eoruer e we w = wo,eawcow eoave eeru.es. aencs suc a ranser a e_{1 2}a eensre rsesne o a sare enou o avo cou ne ouence ωω,an.e aaan scomceouemeor,maens, enracav couers an ncueswo waveusesece n . sesn varn w .n e r, sane , eac w a sow an ave w s w an w, reo . , waveues se o , wave₃ues₂ asecve.n ee w, resecve. eran n ave w s w₄an s₁ess aceve s oneween e r an e a mes, rou raua waveue w aers. a .owernce weanveounweasvearueseearameovn ancouene - raecoen wransraonuas sorwancsomerarweaveoueecou,rnovre eween ewo waveues. e aaac cou coe ae sens veo waveen an e recona uresr.ess ase oenerxemeawrave- sources o s wor are u ue ece no x-cu n m no m noae or oer maera w secon-orer snnear .s an exame, a n m o um noae saonree o a susrae, suc asu no me o wav or s con oxe.n some emomens, e sreucuureesccaanneeoaccae onsuasceanrreernwaaerr., eenre s con or um noaen e case o or exame, susrae. e n m caneeroca s coon oxe ero aernn aer e w a oc mea eecroe an sonmans asvoneeaeeuosersovoeeua csr-saas,ewmaccnnv.ers mea eeec-roes canose coue o e e rou waveue. . eocnes nex o e resonaor waveue a an exame cross-secon o a mea n eecroes.n e -cou n secon,wo e r eeecroes a, areos one ono ses o some emo wamveenue , rec on e n m .n aer .ns,a ce waveues covere a ca n o e ca n aser, e eecroes connec o eo or rec eecrca cou ece vas , wc aows susrae. onnecon.ere s e n z-cnusome emomens, e sources areaerne mxoes.n sumcanseo,aeecrevscae’saneoumseereunerasmenroam e n-couaveerzs-coun.wave.ue,ewcerseaeercroscaaz-axose um - surcecaosnsruacreureoscanoneerevaerzecar.oueraoaceon o eecsersoe o rnn mea u no o e m an a n voae u verca . e eecroeeomer n e z-cu ver m noaeesn reures an eecrc e onn -.ca .wooss eeomeres areece n s. aovene wa.v , one eecroe s ace rec e ses.neu.e, a,n e oers a, are ace o waveue, an e oe ereeceroe s aove e susraeaer . croe sure uner e msoourcmeesnsoroseceronsvceon,onasarsecseumaacaeorsuoswenas e oc aram o .. er n nu an o e aaserum , o e - evocnea . asere arerove asnus reuenc com asescre a su n ouu eama an rom same soeveeceumnnaeeesc soarme. oenner saomeemeumomeencosm,smuw nee sreuences are use orwo - s on e same c seeeame o ca cav com secrosco eow.n som scr on o ua- sourcesncue o a e emomens, a voae voae. e ouu eamsasseevce w consan secmen, an s asor oes rou a -asorn nens .n some emnosecrumsmrne on e enerae, e c mens, werewo coms are rou ane searae eore one o emasses meos suecsecmen. na , e seece usn eecon,a ass,uoo noo me o, rec oooe anazer, an wav eeecon w an secrum measur een -resovn secromeers. e uane smeeacsurruemcsanecemenusr.enrsuosmeeemooemnens,ane - csanecemneenr,aweacnaccaonusacerexceaeeocnewennsaesaoroe n.e secro sscnoer-ec, asecsauoswenonesou.rceemcane use or reuenc mouaon an canenc sson ex s asor on ne saes. e c e rec scan over sowwo wasorove a son uraons o s. - secrosco. n . ,ouwroceoroua-com eecroes . e exame o .nes arae su e o evces sose on e same c , w esrw oou - comne n a comne searae ouuss auss o on. ere a,, a o an ar ,, a,, a,, an a, eeroec waaveuoee resonaseocrs,ones,ecanrooeus,uum couers, resecve, o ewo - evces. wcouers, enerae rov n eren onesoo ecoms are a an . urereas onua-com seecroes oow. ewo - evces canearca crosco eren ree secr e w ernav a ranes an . one oroe, e erence cane conroe unn me o ecav es w mecansms, suc asu no aer c ecro-o c an ermo-o c eecs.n e e sameaser,eeseecwora-rane.evces canearcae w comsu wa cosm secroscoerenemroeeswo o ca reuenc aua-com senera secra ranes. rs, rane an om werreoemom w ree secra e er one oro coms a secra rane -.ex, same o neres. reasse rou an asorn asse ro n cases were on one o e comss eeecour e same,o coms are s rove o sameoo.ws:e owerransmsson rou e - _{^^ ^^ = ^^} ^':;< w_!9 ere ^_{&3 ^^ ^^} sa ^ ^^s e asor on coe cen o e ana e anme, s con o awraee veeea nnen o rou e ana e, un_{in out} .uouu owers on e same as a asoreo rneaeavueresowwerso e com nesocae near om an om s comecrease. en e romo ooeecor, raore ne an ocuse ono a a reuences ^^₃ = ^^ wueernecnesaannonesewer,aneo_nsersvee sreecuernucmcoonaensn-seceraa no-er.anseareaonreuenc e o ca asor on secrum ormaonrom aroaces,wo - coms c.omare o oer sma erencen e aneenerae w a ver sacn ewe ree secra rane. e smaer ne en com nes enaes uso man more as w n e same anw , wc means a ower rnowerese caencoersuswe. eran an eer nose eneraneonewreanzaasonn, eua-com source cane . .ere, a sueeros- evce reazaon a e o e cav , a reuoen o wo rves are reazaon,o coms are nces an -.n s e rom e ouu wasen o e ouu waveue. n a er or usn a veue cane coece e er ana esacn ree saceens, en sen o an secroo.ooeecororua-com asor on w n aneorenercraevazarouonn,-rwoesnncsan-encevces eren ree secra ranes, - caneae on a sne c . . snas canrverecawoe - ceaavc ceasva. aenwo -ou,urocoumcsncaancom sourcerom oeern a sne waveue u e ere comne ouu searae sn a waveue couer or ssem c . an, e er ers or aree sace ua- an coec e ouu , wc cane use or ranecomew seeencroescowo.caveesere cnacneen eree secra voae source a e o e - eeune usn a 's asooss eor oe zero.croe . . unmou. sows aroa unn roeres o an w ae - ume a um. serson enneern, encances enuannea nanoes.ooenrec,neeruamowna,vaowsor c emeraure are use n conu een an emsson over nm,ncu nconoune e e . n a sn can oronn can reso.ve nasrroows a anunmouae - ’s ouu swe wo er-roaene as nes o meane resoveen eum aser. mouae - cou reuenc-emo saumeaaesoermssononesaweueressrreecc ove e asor on ne sae. r e -. umseowsa renmu.enc com eneraonrom a esneoave successu emonsrae e a o s a wor non-eenerae n e m-nrare, cnasem,or=an sm,ecra= r.eomn,aonrse=crosmc.o.ennra-s rersao onn vsa₀ emor a an o.a n-cma₁c cou resaner o ons owewe res₂ ane o rouraonssmron mm a e. um waveen o um, eevcerouces a o - w₁avaenen₂. aneecmssoenmesrauunrae.e varn um c s wor can sowcase eunae secroscoc raeaon. es o e - esnn e m-nrare w rs, eevces coarse une usn um oaveen an emeraure so a e er a ₂ svcearnasewum rweaveonesno mweaeneaesor on nes. en, we xe on a cav moe sna waveen sas canen a ₁. ener conservaon, e waveen ,uma woawvenenusoresscuansovenramucaneean er eauresn meane . .mon e s-or on n e m-nrare rane w aow sam n esn corresonn o a e acces waveen s smuaneous. s e resonaor moes

Claims

- . araus comrsn: a susrae monroar s wavcs ea o uenca reesornaar aeame or onrce osscusaraoreanncun a maer waereanvne a sresconwavoeruereorescoananoornnnceauresars nra wcaevrenaese mrosuwaavoerue resonaorncues an oc waerearnamerorvconscrasoruamn rarovaonnaorers snaoe aresasn aracrasvocaase s emsson o mroeuueancorcoema.so .reueenacacroamussonocaamu,sewerraennneersme oomcaan. .re aaraus o cam, weren areuenc o e esrs swanvaeusewresonnaor.o aree secra rane o r.esoneaaorarsaruessoonancaomr,owesrenna aenrserwarvaeuaeon. r.esoneaaraus o cam, wereners waveue raaaoorn.s resonanor eer sna raaon or er - r.esoneaaoaraus o cam, wereners waveue resonaorr,sa cconure asoonc crcu ar-ero rn resonaor.rcuar rn resonaor or as a racerac .avne aasaercauso cam, wereners maera oeoroovne orearseomaccanno.nnear seroca r.esoneaaoaraus o cam, wereners waveue z-cu rnucmuneosare.e waveuesarcaen x-cu or .ouee aaraus o cam,urer comrsn areuenc werern moounou racaa nerae one susrae, an rsum raaonoonrroemresr oeuecnacouerse oscaor. aramerc .e aaraus o cam,urer comrsn: um ararasonumo coueer conureo coueers coun sna orrser warvaeuaeonresonaor wou waveue resonaor an ou o ers r ars ouu couer con reomeeremnersrwaacveounoeresonsaonu rare . anoo croueer araaon .e aaraus o cam, - conssurner o c:omrosoneeaceecor seeceromerou secrum anazers, waveeonrs,-reosooeecors coueo acousceecors an vn secromeers, an sec wroesrceoncmeeaasuraermaenussosncaonsamureeusonerorm an usn ersreuenc com as an ocae seouercceo.r n.cueesaaararsus o conaeman,awseecroenneoner,s sna rsreuenc comsene werene werene sec rae ers one, an reuenc como snuerosoeneweaseo emrsssorneouenacseccoomn. u.reer acomarrasuess:o cam, werene susrae mono a seccoan oncearaaeramoenrceosscaor secon waveue resonaor usrae anncun a seconwemraeenrae saevconnawasveecouneorreesronoaorcancnounesneaar seconwernernacaveseconasewamvoeuuaeorresonaorncues a aramweerrecnoscrovaonrasneconroum raaonoe oca e seconnra vn a secon snao a secon ocacavreuencase commo.uaoreaso emsson o