By D. Sands
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Additional info for Diode Lasers (Series in Optics and Optoelctronics)
A full mathematical treatment of absorption, stimulated emission, and spontaneous emission was developed by Einstein. The relative populations of two energy levels E2 and E1 in thermal equilibrium is governed by Fermi-Dirac statistics, but under certain conditions it is possible to use the Boltzmann approximation. The two population densities are then related by and equilibrium is maintained by spontaneous and stimulated relaxation from the excited state to the ground state, with the emission of radiation.
In short, the amplitude is constant for low frequencies such that ω2o >> ω2, and at resonance, ω=ωo, the amplitude is a maximum limited by the size of the resistance. For R = 0 the amplitude would be infinite. Equations similar to (4) will be met in the treatment of refractive index in semiconductors in chapter 4 and in a treatment of the small signal modulation characteristics of diode lasers. Continuing with the electrical analogy, it is instructive to ask what exactly is meant by the term “amplitude” here.
From which The threshold current is therefore linearly dependent on the width of the guide and inversely dependent on the optical confinement. For strong guiding where Γ is close to unity, the threshold current is linearly dependent on the width of the active region, but for systems where Γ is reduced, the threshold current rises dramatically. It is difficult to separate out the contributions of optical confinement and carrier confinement to the threshold current in the homojunction device because the active region is so ill-defined.
Diode Lasers (Series in Optics and Optoelctronics) by D. Sands