Linear response theory , nonlinear optics

The Hamiltonian (18.72) has the form (11.3), generalized to the continuous case, H = — Y jAjFj — f drA(r)F(r), that was the starting point of our discussion of linear response theory. Linear spectroscopy processes (e.g. absorption, but not light scattering) can be treated within this framework, however many important spectroscopical methods are derived from the nonlinear optical response of the material system and their description makes it necessary to go beyond linear... 

A mixed quantum classical description of EET does not represent a unique approach. On the one hand side, as already indicated, one may solve the time-dependent Schrodinger equation responsible for the electronic states of the system and couple it to the classical nuclear dynamics. Alternatively, one may also start from the full quantum theory and derive rate equations where, in a second step, the transfer rates are transformed in a mixed description (this is the standard procedure when considering linear or nonlinear optical response functions). Such alternative ways have been already studied in discussing the linear absorbance of a CC in [9] and the computation of the Forster-rate in [10]. 

All the linear and nonlinear optical properties introduced above are therefore expressed in terms of linear, quadratic and cubic response functions. They can be computed with high efficiency using analytical response theory [9] with a variety of electronic structure models [8],... 

RESPONSE FUNCTION THEORY COMPUTATIONAL APPROACHES TO LINEAR AND NONLINEAR OPTICAL SPECTROSCOPY... 

The microscopic (hyper)polarizabilities are studied by means of the so-called theory of the response functions which is of importance for aU molecular and cluster entities (Roman et al. 2006). The most commonly used approach in studying the linear and nonlinear optical properties of clusters is the so-caUed semiclassical one. According to this approach a classical treatment is used to describe the response of the cluster to an external field (radiation) while the system itself is treated using the lows and techniques of quantum mechanics. This is done by using a Hamiltonian which combines both of the above treatments ... 

Rizzo, A., Coriani, S., and Ruud, K. (2011) Response function theory computational approaches to linear and nonlinear optical spectroscopy, in Com-putational Strategies for Spectroscopy, From Small Molecules to Nano Systems, John Wiley Sons, Inc, pp. 77-135. 

Several other studies have appeared that are worthy of note. In a series of works by Keller [89-94] and Apell [95], the nonlocal nonlinear response for free-elec-tron-like metals have been examined using various theoretical approaches which are basically extensions of linear theories on the optical response of metals. The results [92] reduce to those obtained by Rudnick and Stern [26] using a similar approach when the free-electron gas is considered to be homogeneous. 

---