Optical response function

Our starting point is again the Hamiltonian for the molecular system, M, the radiation field, R, and their mutual interaction, 

In fact, we continue to assume that the field is weak enough to allow the use of a perturhation series in the field-molecule interaction to any desired order. 

and// given by Eq. (3.72). However, since we no longer limit ourselves to weak radiation fields and to the RWA, we adopt the semiclassical level of description, treating the radiation field as a classical object. In this case our starting point is the Hamiltonian for the material system under the influence of an external oscillating field (cf Eq. 3.73) 

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 

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INTRODUCTION. A standard and universal description of various nonlinear spectroscopic techniques can be given in terms of the optical response functions (RFs) [1], These functions allow one to perturbatively calculate the nonlinear response of a material system to external time-dependent fields. Normally, one assumes that the Born-Oppenheimer approximation is adequate and it is sufficient to consider the ground and a certain excited electronic state of the system, which are coupled via the laser fields. One then can model the ground and excited state Hamiltonians via a collection of vibrational modes, which are usually assumed to be harmonic. The conventional damped oscillator is thus the standard model in this case [1]. 

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]. 

A pronounced change in the absorption spectrum which accompanies the spin transition can be utilised to select an appropriate optical response function (e.g. a difference between HS and LS absorption at a certain wavenumber). The optical response function possesses a shape which copies the shape of the (xT) versus T curve of the magnetic measurements, including the hysteresis width. The hysteresis is utilised as an information-keeping function (memory effect). 

Figure 3. Effective electro-optic response function measured at the frequency of the applied ac field (solid squares) and at the second harmonic (open squares), for different frequencies of the applied voltage. The inset shows the configuration of the set-up.

FuIIerenes. - Perpete, Champagne and Kirtman have computed the vibrational contributions to the main non-linear optical response functions for the fiillerene Ceo- They use normal co-ordinates obtained in a DFT approximation combined with Hartree-Fock ab initio calculations of the electrical properties. Vibrational contributions to the electro-optic Kerr effect and degenerate four wave mixing are found to be comparable with the electronic effects. 

Linear and nonlinear infrared spectroscopy are powerful tools for probing the structure and vibrational dynamics of molecular systems." In order to take full advantage of them, however, accurate models and methods are required for simulating and interpreting spectra. A common approach for modeling spectra is based on computing optical response functions (ORFs)." Unfortunately, exact calculations of quantum-mechanical ORFs are not feasible for most systems of practical interest due to the large number of DOF. Instead, mixed quantum-classical methods ean provide suitable alternatives." " " ... 

Figure 8.14 Effective electro-optic response functions of the DMNPAA ...

The optical response functions characterizing the dephasing processes for a pair of states that are entangled in a coherent superposition can be obtained directly or via the second order cumulant expansion." The cumulant expansion approximation together with the FT of the ACF provides additional information about the dephasing process. The cumulant dephasing function is obtained by double integration and exponentiation of the unnormalized ACF, Equation (2.4). 

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