laser4-研深圳大學-高等激光物理學期末復習課件

Unit4

FromamplifierstooscillatorsLightamplifiersAmplifierbandwidthGainsaturationFromamplifierstooscillatorsThelaserResonatorsPlane-mirrorresonatorsSpherical-mirrorresonatorsCavitymodesincavitieswithcurvedmirrors#Fromamplifierstooscillatorsthelaser:anopticalamplifierasourceoflightamplifier:bandwidthandgainsaturationamplifierswithpositivefeedbackopticaloscillators.laser#LightamplifiersComparingopticalamplifierswithelectronicamplifiersSimilarities:bothrelyonanexternalpowersourcetosupplyenergy;botharecharacterisedbyagaincoefficient,whichisfrequencydependent;bothareinfluencedbynoise,gainsaturation,andothernon-linearities.#DifferencesbetweenopticalandelectronicamplifiersPhaseTheopticalamplifierincreasesthemagnitudeoftheopticalfieldwhilemaintainingitsphase.Phaseisnotrelevantinelectronicamplifiers.FrequencyresponseInopticalamplifiersthebasicfrequencyselectionisdeterminedbytheenergylevelsinatomsElectronicamplifiersrelyonelectroniccircuitsmadeofcapacitors,inductors,etc#DifferencesbetweenopticalandelectronicamplifiersThesourceofexternalpowerElectronicamplifierscanonlybepoweredbyelectricalenergyOpticalamplifierscanbe‘pumped’byelectrical,optical,chemical,mechanicalandevennuclearpowersources.#AmplifierbandwidthBandwidth:amplifier’sfrequencyresponseIntheopticalamplifierthefrequencyresponseisdeterminedbythefrequencydependenceofthegaincoefficientThefrequencyresponseisproportionaltothelineshapefunctionofthegiventransition.#AmplifierbandwidthThefrequencyresponseisproportionaltothelineshapefunctionofthegiventransition.InthecaseofhomogeneousbroadeningG(

)isaLorentzianfunctionI→0GainsaturationAtlowpower,opticalamplifyfunctionI(z)=I(0)exp(Gz)theexponentialgrowthoftheintensityAthighpowerlevels,thisisnotcorrect,itwillproducegainsaturation.#GainsaturationTheintensityincreasestherateofstimulatedemissionincreasespopulationfromtheupperlevelisreducesthedegreeofpopulationinversionisreducedthegainisalsoreduced.#GainsaturationTheintensityincreasesintheamplifier,itstimulatesmoreandmoreexcitedatomstoemitphotons.Thiscanonlygoonaslongasthenumberofstimulatingphotonsislessthanthenumberofexcitedatoms.Oncethenumberofphotonsovertakesthenumberofexcitedatoms,theexponentialgrowthcomestoanend.#GainsaturationThepopulationdifferenceisafunctionoftheenergydensity:(ν=ν0)ThesaturatedgaindecreasesastheintensityincreasesThesaturationintensity

#thegaincoefficientthesaturatedgainsmall-signalgaincoefficient

Thesaturationintensity#GainsaturationFromamplifierstooscillatorsLasersaresourcesoflight.Whatisthelinkbetweenanamplifieranda

lightsource?TheOpticalfeedbackanopticalamplifierwithpositivefeedbacktheamplifierbetweenmirrorsOpticalcavityorresonatortheinitialsignaltriggersthewholeprocess.thespontaneouslyemittedphotonsOpticaloscillator--Lasertheintensitywillquicklybuildupandreachasteady-statevalue.#Tohavestableoutputfromalaser,twoconditionshavetobemet:(i)theamplifiergainshouldbelargerthanthelosses(ii)thetotalphaseshiftinaroundtripoftheradiationshouldbeequaltoanintegermultipleof2

.Boththeseconditionsarerelatedtotheopticalcavityoroptical

resonator.

#LaserResonatoranopticalcavityoropticalresonator

Electro-magnetictheory—Boundaryconditionformstandingwavesthespecialwavelengthandfrequenciseresonantwavelengthsresonantfrequenciesplane-mirror,spherical-mirrorresonators.

#Plane-mirrorresonatorsFabry-Perotresonator(F-P)Theresonantfrequencies

m,longitudinalmodefrequencyseparationbetweenthelongitudinalmodesFinesseofthecavityTheintensitydistributionofacavity,Transmissionspectrum:F--thefinesseofthecavityThefinesseisanimportantparameterofacavity#Finesseofthecavity

Thefinesseisanimportantparameterofacavityquantifiesthewidthofaresonantline.Thefinesse:

F=

/

:widthoftheresonance:theseparationoftheresonantfrequenciesforhighfinesse,highlyreflectivemirrors,thespectralresponseissharplypeakedforlowfinesse,theresonancesarebroadaroundtheresonantfrequencies.#Plane-mirrorresonatorsThreeparameters:characterisethespectralresponseofFabry-Perotresonators:(i)theresonantfrequencies:

q=(c/2d)q(ii)thespacingbetweentheresonantfrequencies:

=c/2d(iii)thewidthofeachresonance:=/FFisthefinesseofthecavity#KindofopenresonatorStableresonator.thebeamisconfinedinthecavityevenaftermanyreflectionsUnstableresonatorthebeamleavesthecavityafteronlyafewreflections#Conditionsofstabiliry:Notallunstableresonatorsareuseless.SomespecialcavityconfigurationsCavitymodesincavitieswithcurvedmirrors

q,l,m--adistinctivestandingwave--amode.Eachmode--aspecificfrequencyandintensitydistributioninthecavity.

longitudinaloraxialmodes,qwavestravellingalongtheopticalaxisofthecavity.transversemodes:l,mCavitymodesincavitieswithcurvedmirrorsl=m=0butq

0Theintensitydistribut