Digital optical communication systems utilizing Raman amplification

Analytical expressions for the optical powers of the signal, pump, and first Stokes wave are derived using a series forms as functions of the pumping power, signal wavelength, relative refractive index, and fiber radius parameters. This is done through the series solution of three first-order nonlinear coupled equations relating the three signals. The criteria employed to find the repeater spacing limit are based on the fact that the input signal power and the minimum detectable power at a detector are 10 and -40 dBm, respectively, which in turns means a 30-dB loss