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&einarguedinasimilaraceshouldalsotract.Thatis，arodofB’simaginaryscaffoldshouldlooksmallertoAthaihispossession.Andviceversa:A’srodlooksshortertoBthanherown.
Bothoftheseeffectsarisebecausethereisamaximumspeedatwhialsofanykindpropagate，andthisspeedisthesameforeveryowerehenonecoulddetermineapreferredseofreferenwhichthesighehighestspeed.Einstein’sworkoyshowedthatthereisnopreferredframe，sothaton’sideaofafixed，pre-definedspaotbethecethemaximumspeedfnalsofanykindturnsouttobelightspeed，lightisdefiime.
It’swhowpreciselywemightbeabletosywoclocksbythe‘lightpulse’methoddiscussedpreviously.Youseethatoodoitisbymakipulseasbriefaspossible，sothattheuyoverwhenitarrivesisminimal.Thusitisimportanttoknowiftherearelimitstothebrevityoflightpulses.Itturnsoutthatthereare，andtheyarisefromasimilarsortofertythatlimitstheresolutionofimagingsystems，aster3.
&artbyaskinghowitisthatwedetermihefrequencyofalightwave.Imagiakingoneofourdaskinghoeaksofthewavereachusduriervalbetweentwoticks.Thegreaterthenumberofpeaks，thehigherthefrequency.Thepreedetermihefrequendsonhowmanytimeswerepeatthismeasurement，sinceourabilityactuallytotellwhetherwehavereachedthepeakofawavemayhus，thelohemorepreinatiohistrade-offisfualforwaves—theimprefrequencymultipliedbytheuyiervalisafixedproduct.ThiswasfirstuoodbyJosephFourier，a19th-turyFreidstistwhoplayedakeyrthewavemodeloflightpropagation.
Ultrashhtpulses
Fourier’stheoremisimportantforizatiosaysthatifulse，wemusthaveaefrequenotherwaytosaythisisthatashhtisstitutedbyabreofcolours.That’sentirelyanalogoustothesituatioifiedfoptics:ahigh-resolutionimage，demandingasmallfocus，requiresawiderangelestobecollefaalogygoesfurther.JustasAbbeshowedthesmallestsizeofafocalspotcouldbeapproximatelyoheilluminatinglight，soFouriershowedthattheshortest-durationpulseisasihefield.
Whatthismeansifhtinthevisibleregiorum，itispossibletoproducepulseswithadurationofabout2fs.Amazingly，lightsourcesderivedfromlasersowroutinelyproducepulsesofsuchstartliheyarebasedonthemode-logteiquedesChapter5.
Buttheseareburstsoflightthatoature，heshortestthatbeprodualaboratory.Thathoestolightsourceswithmuchshewavelengths.Forihesiyoueasilyseethatifthewavelengthisshortehedurationofanopticalcycleisredupriionofthepulsebereduced.Thisapproatlyholdstherecordfortheworld’sshortesttrollablelightpulses.Byshieonanatomicgas，aproashigh-harmoiowaveswithafrequencymultiplesofseveraltenslaserfrequency.Thisallowspulseswithduratioensofattoseds（10-18s，orabillionbillionthofased）.Theseareunimaginablyshortburstsoflight，withduratiohetimeittakesaooscillatewithinanato
Frequenbs
Iatedthatinamode-lockedlaserasiraversestheopticalcavity.Eachtimeitbouneofthemirrors，alittlebitofthelightpulseistrahroughthemirrorahecavity.Asace，outsidethecavitythelightappearsasa‘uous’sequenceofpulsesspacedbytheround-triptimeofthelightiy，typicallyabillionthofasedorso.A‘snapshot’ofsuofpulseswouldshowtheseveryshortburstsseparatedfromeachotherbyadelaythatisloheirduratiohofab（asshowninFigure30）.Andthepulsesbemadeidentieanotherbycarefuladjustmentofthelaserprodugthem，sothattheelectricfieldofeachofthepulsespeaksatexactlythesametimewithrespecttotheiyehepulse.
Itturnsoutthatthisfiguratioeachofthe‘teeth’inthefrequenbhasaveryprecisepositionatanabsolutefrequency.Apreciselycalibratedsetoffrequenciesisaveryimportanttaccurateclocks.Thisisbecauseitallowsadireparisonofopticalfrequeolower（usuallymicrowave）frequencies，whibetedbymearonics.
Thusfrequehemicriohecaesiumatomicbeparedsimplytomuchmorepreciseeleisitioiofthespe，forexample，strontiumatomsoraluminiumiohestaomicclocksusedienavigation，forinstanowallbesyotickatthesameratetowithiinabillionbillion（i.e.1:10-18），duetothepreoftheopticaleleosfrequenstrontiumoraluminiu
30.Traiiearlysiicalpulses.Thespectrumofthepulsetrainlooksliketheteethofab，heiscalledafrequenb.
‘Opticalclockwork’ofthiskindallowstheparisonofdisparatefrequehsuchremarkableprethatitprovidesameaey，andthustouaheroleoflightindefiime.Frequendthustime，isthephysititythatbemeasuredwiththehighestpreofanyquantity，byfar.
Optiunis
Frequenbsarealsoimportantinteleunislinksbasedonlight.InChapter3，Idescribedhowopticalwavescouldbeguidedalongafibrelass‘chip’.Thisphenomehelong-distaeleunifrastructurethatectspeopleacrossdifferesaheIhereasonitissoeffectiveisthatlight-baseduniuchmorecapacityfinformationtharicalwires，orevenmicrowaveetworks.Thismakespossiblemassivedatatransmission，suchasthatodelivervideoondemaer.
Manyteleunipaniesoffer‘fibreoptid’deals.Akeyfeatureofthesepackagesisthehighspeed—upto100megabytesperseBps）—atwhichdatamayberedtraeisas，eachofwhichisa1ora0.Informatiooverfibresasaseques’，whicharedecodedbyyourobilephoelligiblevideo，audio，ortextmessages.Inoptiunis，thebitsarerepreseheiyofthelightbeam—typicallylowiyisa0aensitya1.Themoreofthesethatarrivepersed，thefastertheunirate.TheMBpsspeedofthepackagespecifieshoidlywesmitaiopany’slink.
Whyisoptimunis?Therearetworeashtbeamsdon’teasilyiher，sothatasinglefibreanylightpulses（usuallyofdifferentultahoutthemessagesgettingscrambledup.Thereasonforthisisthattheglassofwhichthefibreismadedoesnht（oronlyabsorbsitintinyamounts），aheatupanddisruptotherpulsetrains.
Further，alightbeampropagatinginglasshastobeveryintenseitoiherlightbeaForinstanyoucrossthebeamsfromtointersyoudoherbeamdistortordeviatefrihoughthetassrightthrougheachother.（Ifyourlaserpointershadenormhtjustseesueffelybecausetheroomisfullofair.Inavacuumtheywouldstillnotiher.）Thismeansthatthe‘crosstalk’betweenlightbeamsisveryweakinmostmaterials，sothatmanybeamsbepresegadegradationofthesignal.Thisisverydiffereronsmovingdoerwire，whichistheusualwayinwhichlocal‘wired’unislinksfurooheatupthewire，dissipatihismakesthesigoredthusthenumberobekeptsmallenoughtoavoidthisproble
Sed，lightwavesoscillateatveryhighfrequehisallowsveryshortpulsestobegeed，asdescribedearlier.Thismeansthatthepulsesbespacedveryclosetogetherihetransmissiosofinformationpersedpossible.Iesof40Gbps（aGb，abit，isabillionbits）arepossiblei-gei-haulsystems.Electrialsincopperwiresarelimitediionandspagofpulsesgtheinformatioiedpreviously，whidtherfrequencies.Copperwiresrunoutofsteam，asitwere，atmuchlo
Fibre-basedoptietworksalsosupportaverywiderangeht.Glasstransmitsabreofwavelengths，withparticularlylowsdabsorptionlossiralwindowfrom1.3–1.55μTherateatwhisarelostihesewavelengthsisabout5pertperkilometre.Theselossesbemadeupbyamplifyiwhileinthefibresothattransmissiondistances（suchasacrosstheAtlanti）ispossiblewithoutanyofthelighttnalsorviceversa.
&eleunisspedowisdividedintomanyindividualfrequenuchlikethefrequenbshowninFigure30.Eachspepoisaseparateunisel.Therebe150orsoslotsintheithineael，a40Gbpsoptialbeoperated.Thereforethetotalbitrateforunisis150times40Gbps，or6Tbps（1Tb，1terabit，is1，000billionbits）.
Theever-ingdemandforunisbandwidthduetoincreaseduseoftheIheservicesitprovideshavespurredoptieerstosofcreativityihepotentialoflight.
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