Undergrad How to get plot (optical gain of GaAs)?

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To calculate the optical gain plot for GaAs based on photon energy dependence and injected carrier density, one must utilize the effective masses of electrons and holes, along with the given parameters like the energy band gap and recombination lifetime. The energy of the photon, ħω, must exceed the band gap energy, Eg, which is 1.43 eV for GaAs. The relationship between wavelength and frequency can be established using ω = c/λ, allowing for the determination of ω0 if λ0 is known. For further understanding, recommended resources include textbooks on semiconductor physics and laser technology. Assistance is sought for both calculations and foundational knowledge in semiconductor lasers.
yeyintkoko
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How can i calculate this plot (photon energy dependence of the optical gain (or loss = negative gain) of GaAs with the injected carrier density as a parameter?
Show calculated plot based on this equation
plot.jpg
equ.jpg

Given parameter:
mc=0.067 me; (effective mass of electrons in conduction band)
mv=0.48 me; (effective mass of holes in valence band)
T2~0.5 ps; (lifetime for coherent interaction of electrons with a monochromatic field)
Eg=1.43 eV; (energy band gap of GaAs)
taung~3x10-9s; (recombination lifetime)
1/mr=1/mc+1/mv; ( reduced effective mass)
n= 3.6: (refractive index for GaAs)

How can i find this value
ħω (energy of photon)- this should be ħω>Eg. How can i determine this energy?
λ0
ω0 ( if i known λ0, can i get ω0? (ω=c/λ))
[ƒc(ω)-ƒv(ω)]

Really I need your help. I am new for semiconductor laser. Please anyone help me.
Thanks!
 
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please suggest me the books, where from you got this equation ?????
 
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