6.973 Semiconductor OptoelectronicsLecture 20: Waveguide ConfinementRajeev J. RamElectrical EngineeringMassachusetts Institute of TechnologyOutline:• Confinement Factor• Parasitic Optical Loss• Helmholtz Equation• Slab Waveguide ModesConfinement FactorConfinement FactorMaterial gain…Gain in waveguide…Overlap of gain with optical mode…Separate Confinement Separate Confinement HeterostructureHeterostructure(SCH)(SCH)Band DiagramBand DiagramAlxGa1-xAs refractive indexelectronsholesIndex ProfileIndex Profile• Larger bandgap semiconductors have lower indices of refractionWaveguide 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)•Scattering to conserve momentumParasitic Optical LossesParasitic Optical LossesCasey & Panish• Below gap, free carrier absorption is a few cm-1per 1018cm-3of dopingParasitic Optical LossesParasitic Optical LossesParasitic Optical LossesParasitic Optical Lossesp-typen-typeFree Carrier Absorption (n-type)Intervalence Band Absorption (p-type)Free-carrier loss couples the design of doped regions to the waveguide design• rule-of-thumb dope around 5x1017cm-3Modal Gain and Confinement FactorModal Gain and Confinement FactorModal Gain and Confinement FactorModal Gain and Confinement FactorFor a traveling wave…HelmholtzHelmholtzEquationEquationMaxwell’s EquationsHelmholtz Equation…HelmholtzHelmholtzEquationEquationNeglecting 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 ModesBoundary conditionstangential cont. =tangential cont. =TE Slab Waveguide ModesTE Slab Waveguide ModesBoundary conditionsTE Slab Waveguide ModesTE Slab Waveguide ModesSolve transcendental equation for
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