Raman amplifier model in single-mode optical fiber

Equations to describe the process of Raman amplification in single-mode optical fiber and Stokes and anti-Stokes spontaneous emission generation with conservation of photon number are derived from first principles. The numerical simulation of Stokes and anti-Stokes spontaneous emission is in good agreement with experimental results. The importance of the sometimes-omitted anti-Stokes spontaneous emission terms in wavelength-division-multiplexed situations for optical signal-to-noise ratio is demonstrated by the simulation of light propagation through transmission fiber with and without Raman amplification.