Multimode Rate Equations
In the multimode formulation, the rate equations model a laser with multiple optical modes. This formulation requires one equation for the carrier density, and one equation for the photon density in each of the optical cavity modes:
where: N is the carrier density, P is the photon density, I is the applied current, e is the elementary charge, V is the volume of the active region, is the carrier lifetime, G is the gain coefficient (s−1), is the confinement factor, is the photon lifetime, is the spontaneous emission factor, M is the number of modes modelled, μ is the mode number, and subscript μ has been added to G, Γ, and β to indicate these properties may vary for the different modes.
The first term on the right side of the carrier rate equation is the injected electrons rate (I/eV), the second term is the carrier depletion rate due to non-radiative recombination processes (described by the decay time ) and the third term is the carrier depletion due to stimulated recombination, which is proportional to the photon density and medium gain.
In the photon density rate equation, the first term ΓGP is the rate at which photon density increases due to stimulated emission (the same term in carrier rate equation, with positive sign and multiplied for the confinement factor Γ), the second term is the rate at which photons leave the cavity, for internal absorption or exiting the mirrors, expressed via the decay time constant and the third term is the contribution of spontaneous emission from carrier non-radiative recombination.
Read more about this topic: Laser Diode Rate Equations
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