Spontaneous growth of Raman Stokes and anti-Stokes waves in fibers

Using the quantum theory of light, we derive general analytical expressions of Stokes and anti-Stokes spectral photon-flux densities that are spontaneously generated by a single monochromatic pump wave propagating in a single-mode optical fiber. We validate our results by comparing them with experimental data. Limiting cases corresponding to interesting physical situations are discussed.