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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. ==Multimode rate equations== In the multimode formulation, the rate equations〔G. P. Agrawal, "Fiber-Optic Communication Systems", Wiley Interscience, Chap. 3〕 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, 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. 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 all 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 the carrier radiative recombination into the laser mode. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「laser diode rate equations」の詳細全文を読む スポンサード リンク
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