Laser Diode Rate Equations - The Modal Gain

The Modal Gain

G_μ, the gain of the μth mode, can be modelled by a parabolic dependence of gain on wavelength as follows:

where: α is the gain coefficient and ε is the gain compression factor (see below). λ_μ is the wavelength of the μth mode, δλ_g is the full width at half maximum (FWHM) of the gain curve, the centre of which is given by

where λ₀ is the centre wavelength for N = N_th and k is the spectral shift constant (see below). N_th is the carrier density at threshold and is given by

where N_tr is the carrier density at transparency.

β_μ is given by

where

β₀ is the spontaneous emission factor, λ_s is the centre wavelength for spontaneous emission and δλ_s is the spontaneous emission FWHM. Finally, λ_μ is the wavelength of the μth mode and is given by

where δλ is the mode spacing.