(Solved): The gain coefficient of a semiconductor laser amplifier is given by =82r1(v)fg ...

The gain coefficient of a semiconductor laser amplifier is given by $$?=\frac{{?}^2}{8?}\frac{1}{{?}_r}?(v)f_g(v)$$ where $$f_g(v)$$ is the Fermi inversion factor, and $$?(v)$$ is the optical joint density of states $$?(v)=\frac{1}{?{?}^2}{\left(2m_r\right)}^{3/2}{\left(hv?E_g\right)}^{1/2}$$ a) Considering a GaAs laser amplifier operating at $$300\mathrm{K}(Eg=1.42\mathrm{eV})$$, if the injection current through the device is such that the separation between the quasi Fermi levels is $$1.48\mathrm{eV}$$, draw a schematic representing the variation of gain with photon energy. (Briefly explain the nature of the curve) b) What is the amplification frequency-range $$(?v)$$ of this amplifier? c) If the gain medium (at a) above) is cooled to $$200\mathrm{K}$$, what qualitative changes one would see in the gain variation? (Show this change in the same diagram drawn at a) above. Neglect the temperature dependence of $$Eg$$.)