THEORY OF 2ND-ORDER OPTICAL PROCESSES FROM A LUTTINGER LIQUID

We develop a theory for the total optical secondary emission from a 1D interacting electron system modeled as a Tomonaga-Luttinger liquid. We separate the emission into two parts which may originate in hot luminescence (HL) and Raman Scattering (RS) respectively when we neglect the interference effect. We find a peak around Delta omega = upsilon(f)\q\ in the RS part which does not come from a structure factor peak. In general the total emission cannot be separated into HL and RS. However at resonance, and taking into account the k dependence of the optical matrix element, a part of the RS is proportional to the structure factor S(q(1) - q(2),omega(1) - omega(2))