6.973 Semiconductor OptoelectronicsLecture 23: Semiconductor LasersRajeev J. RamElectrical EngineeringMassachusetts Institute of TechnologyOutline:• Single Mode Rate Equations• Multimode Rate Equations•Lasing ThresholdSingle Mode Rate EquationsSingle Mode Rate EquationsWaveguide AnalysisWaveguide AnalysisIndex ProfileIndex ProfileFor a symmetric guide the parasitic modal loss is..Rule-of-thumb is that for a well designed waveguide the confinement factors is approximately 2% per QWWaveguide dispersion slows group velocity of light..Gain AnalysisGain AnalysisTransport AnalysisTransport AnalysisJn Jp11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5050100150200250300350400Position (um)Current (A/cm2)hole currentelectroncurrentelectronsholesBand DiagramBand DiagramPhenomenology of a LaserPhenomenology of a Laseroutput power (mW)current (mA)thresholdhigh spectral purityhigh efficiencySingle Mode Rate EquationsSingle Mode Rate EquationsSingle Mode Rate EquationsSingle Mode Rate EquationsIn the absence of non-radiative recombination…Single Mode Rate EquationsSingle Mode Rate EquationsIdeal DeviceIdeal DeviceIn the absence of non-radiative recombination, a truly single modedevice has a linear relationship between current and outputstimulated emissionspontaneous emissionWhat is missing from this analysis ?Multimode Rate EquationsMultimode Rate EquationsC=0C=0Multimode Rate EquationsMultimode Rate Equationssingle lasing mode, C=0single lasing mode, C=0If only mode 1 builds up sufficient photon density,Multimode Rate EquationsMultimode Rate Equationssingle lasing mode, C=0single lasing mode, C=0Only a single lasing mode, but multiple modes into which photons are emitted by spontaneous emissionMultimode Rate EquationsMultimode Rate Equationssingle lasing mode, C=0single lasing mode, C=0Only keep track of photons emitted into the single lasing mode…output power (mW)current (mA)thresholdMultimode Rate EquationsMultimode Rate Equationssingle lasing mode, C=0single lasing mode, C=0Threshold results because of competition for injected electrons…At low bias, is very smallBelow threshold…Multimode Rate EquationsMultimode Rate Equationssingle lasing mode, C=0single lasing mode, C=0at high bias, can be large (for a good cavity)Multimode Rate EquationsMultimode Rate Equationssingle lasing mode, C=0single lasing mode, C=0Above threshold…output power (mW)current (mA)thresholdMultimode Rate EquationsMultimode Rate Equationssingle lasing mode, C=0single lasing mode, C=0log currentlog powerBelow thresholdAbove thresholdSpontaneous Emission FactorSpontaneous Emission FactorRam IEEE PTL (1996)Vahala, Nature 424, 839 - 846 (2003) Approaches to eliminate spontaneous emission into unwanted modes…currentradiative non-radiativeQW captureleakageinternal lossmirror lossfiber coupledphotonsoutput power (mW)current (mA)thresholdLaser ThresholdLaser ThresholdIn steady state:(valid for all bias)gain can never equal the loss.gain is alwayssmaller than the lossgain defecit depends on how much smaller gain is than lossSteadySteady--State Solution of Rate EquationsState Solution of Rate EquationsLaser ThresholdLaser ThresholdCavity AnalysisCavity AnalysisBut we forgot to add spontaneous emission !! Laser ThresholdLaser ThresholdLaser ThresholdLaser ThresholdCavity AnalysisCavity
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