Appendix 1: Resonance Damping

to resonance, a condition which applies to an optical process when there exists a molecular state differing in energy from the initial state by an amount approaching the energy of one or more of the photons involved. The correct designation of sign for damping factors in the energy denominators of optical response tensors has been the subject of considerable debate (see for example Andrews et al. 1998, Buckingham and Fischer 2000, Stedman et al. 2001). Partly this stems from a common confusion in the literature between two entirely different forms of damping; partly it reflects attempts to impose conflicting conditions on the molecular response. The former obscurity is easily dealt with – though it forms the ground in which seeds of the latter conflict have been sown. First, note that the embodiment of photon 1) energies in the denominators of expressions such as equations (4.1.4) and (4.1.6) owes its origin to the development of the signal amplitude from equation (3.1.1). To confer analyticity on the dispersion behaviour, imaginary infinitesimals are commonly added to the photon energies in each denominator factor to displace poles from the real axis in a complex frequency plane. Each photon energy thereby acquires an infinitesimal addendum, h h is, with s 0. For example, in the polarisability equation (4.1.4), since the sign of h differs in the two energy denominators, this modification introduces addenda of –is and +is, respectively, to the two denominator expressions. The real and imaginary parts of a 185