Laser diode rate equations

The laser diode rate equations model the electrical and optical performance of a laser diode. This system of ordinary differential equations relates the number or density of photons and charge carriers (electrons) in the device to the injection current and to device and material parameters such as carrier lifetime, photon lifetime, and the optical gain.

The rate equations may be solved by numerical integration to obtain a time-domain solution, or used to derive a set of steady state or small signal equations to help in further understanding the static and dynamic characteristics of semiconductor lasers.

The laser diode rate equations can be formulated with more or less complexity to model different aspects of laser diode behavior with varying accuracy.

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, ${\displaystyle {\tau _{n}}}$ is the carrier lifetime, G is the gain coefficient (s⁻¹), ${\displaystyle \Gamma }$ is the confinement factor, ${\displaystyle {\tau _{p}}}$ is the photon lifetime, ${\displaystyle {\beta }}$ is the spontaneous emission factor, ${\displaystyle {\tau _{r}}}$ is the radiative recombination time constant, 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.

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