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6.973 Semiconductor OptoelectronicsLecture 21: Waveguide ConfinementRajeev J. RamElectrical EngineeringMassachusetts Institute of TechnologyOutline:• Slab Waveguide Modes• Effective Index• Normalized Parameters• Confinement Factor•Group VelocityWaveguide OptimizationWaveguide OptimizationBand DiagramBand DiagramIndex ProfileIndex ProfileelectronsholesWaveguide optimization requires:•Maximizing modal gain•Minimizing the loss from the doped regionsParasitic Optical LossesParasitic Optical Lossesp-typen-typeFree Carrier Absorption (n-type)Intervalence Band Absorption (p-type)Parasitic loss couples the design of doped regions to the waveguide design• rule-of-thumb dope around 5x1017cm-3Confinement FactorConfinement FactorGain in waveguide…Overlap of gain with optical mode…HelmholtzHelmholtzEquationEquationMaxwell’s EquationsHelmholtz Equation…Neglecting currents and free charge motion at optical frequencies..Slab Waveguide ModesSlab Waveguide ModesTE solutions:TM solutions:Slab Waveguide ModesSlab Waveguide Modes1. (upper cladding)2. (core)3. (lower cladding)Slab Waveguide ModesSlab Waveguide ModesSlab Waveguide ModesSlab Waveguide ModesBoundary conditionstangential cont. =tangential cont. =TE Slab Waveguide ModesTE Slab Waveguide ModesSymmetricSymmetricBoundary conditionsEffective IndexEffective IndexSymmetricSymmetriceffective indexSolve transcendental equation for …Solutions for Slab WaveguideSolutions for Slab Waveguide• at long wavelengths, effective index is small• at short wavelenths, effective index is largeNormalized ParametersNormalized ParametersNormalized frequency: Normalized wavevector:Normalized ParametersNormalized ParametersNormalized ParametersNormalized ParametersSymmetricSymmetricsingle mode…# of modesDiode Lasers and Photonic Integrated CircuitsL. A. Coldren, S. W. CorzineAsymmetric WaveguideAsymmetric WaveguideNormalized ParametersNormalized ParametersSymmetric guide:Diode Lasers and Photonic Integrated CircuitsL. A. Coldren, S. W. CorzineWaveguide Confinement FactorWaveguide Confinement Factor= fraction of mode within coreWaveguide Confinement FactorWaveguide Confinement Factorfor fundamental mode where is not large.Diode Lasers and Photonic Integrated CircuitsL. A. Coldren, S. W. Corzine*neglectingWaveguide Confinement FactorWaveguide Confinement FactorBand DiagramBand DiagramIndex ProfileIndex ProfileelectronsholesFor a symmetric guide the parasitic modal loss is..Group VelocityGroup Velocitylow group velocityVelocity of wavepacket..Waveguide DispersionWaveguide Dispersionhttp://people.deas.harvard.edu/~jones/ap216/lectures/ls_1/ls1_u8/ls1_unit_8.htmlSuppressing Higher Order ModesSuppressing Higher Order ModesStrategy: keep V constant as λ decreases (koincreases)• reduce as increases• increase as increasesso a highly dispersive cladding can help keep waveguide single mode (V const.)for wide range of frequency.Diode Lasers and Photonic Integrated CircuitsL. A. Coldren, S. W. CorzinePhotonic Crystal WaveguidesPhotonic Crystal Waveguidesafter Knight, Optics & Photonics News, March 2002• effective index of “cladding” increases at shorter λ• results in V value which becomes nearly independent of


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MIT 6 973 - Waveguide Confinement

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