“…In the above system of equations is the pump power along the fiber, and are the phase velocities of the pump and signal, and are the fiber (host) linear attenuation coefficients per meter for the pump and signal wavelengths, represents the signal powers travelling in forward and backward directions, and are the absorption and gain coefficients for the pump and signal per meter, and are the absorption and emission cross sections of Yb 3 + ions in pm 2 , h is the Planck constant, c is the speed of light in free space, and are the pump and signal wavelengths, N 0 is the dopant concentration in fiber core, N 1 and N 2 are the populations of the lower and upper states, τ is the upper state life time, and are the unitless pump and signal overlapping factors. The last RHS term in Equation (5) describes the interaction of spontaneous emission with the laser beam, here the normalized Planck emission term over the ASE range is multiplied by a small angle geometrical approximation for the beam [ 26 ] and the presence of is to consider the division of ASE range to K channels. The parameter values that are used in our simulations can be found in Section 5.…”