Fluctuation-dissipation theorems for driven non-linear media at optical frequencies

Abstract

The conventional symmetrized definition of a noise current power spectrum is shown to be inappropriate at optical frequencies. A new definition is developed which takes account of the fact that optical detection is accomplished by photon annihilation. Using this definition, fluctuation-dissipation theorems are established for a medium in thermal equilibrium and for a pumped Raman-active medium. The theorems relate the power spectrum to the first- and third-order conductivity tensors in the thermal equilibrium and Raman-active cases respectively, the zero-point fluctuation noise is absent in both cases. The consequences of time reversal invariance and the emission of Stokes, anti-Stokes and spontaneous radiation are discussed.