Resonance damping and optical susceptibilities

In the formal development of optical response theory in terms of susceptibilities, proper representation of the optical frequency dependence necessitates modeling both the discrete linewidth and the finite signal enhancement associated with the onset of resonance. Such dispersion behavior is generally accommodated by damping factors, featured in both resonant and non-resonant susceptibility terms. For the resonant terms, the sign of such damping corrections is unequivocal; however the correct choice of sign for non-resonant terms has become a matter of debate, heightened by the discovery that entirely opposite conventions are applied in mainstream literature on Raman scattering and nonlinear optics. Where the two conventions are applied to electro-optical processes in fluids there are significant and potentially verifiable differences between the associated results. Through a full thorough quantum electrodynamical treatment the universal correctness of one convention can be ascertained and flaws in the counter-convention identified. Resolution of the central issue requires consideration of a number of fundamental questions concerning the nature of dissipation in quantum mechanical systems. It is concluded that optical susceptibilities formulated with correct signing of the damping corrections must fulfill several fundamental tests: satisfaction of a new sum rule; invariance of the associated quantum amplitudes under time-reversal symmetry, and a resilience to canonical transformation.