Derivative techniques, nonlinear optics

TDHF [52, 53] is one of the most widely-employed ab initio techniques to evaluate nonlinear-optical response tensors. The fDHF approach is size consistent but cannot account for the finite lifetime of the excited states. The matrices of the TDHF equation are expanded in a Taylor series of the perturbation due to the static and/or dynamic electric fields and are solved for each order [52, 53], The so-obtained successive field-derivatives of the density matrix are then inserted into the expressions for the hyperpolarizability,... 

A series of new ( )-4,4 -bis(diphenylammo)stilbene derivatives have been synthesized to investigate nonlinear absorptivities with attention paid to the peripheral substituent effect and multibranched modification effect by the open aperture femtosecond Z-scan technique and the nanosecond nonlinear optical transmission (NET), respectively [36]. Two-photon fluorescence for ( )-4,4 -bis(di-phenylamino)stilbene in THE was detected. It was found that substituent group attached to the periphery of BDPAS has no obvious contribution to TPA enhancement and that the dramatic increase in effective TPA cross sections of multibranched samples in nanosecond regime strongly suggested their larger excited-state absorption. 

Explicit formulas for the nonlinear susceptibilities xljL Xuu derived by working out the coefficients c (t), c (r),..., respectively, in the time-ordered expansion (1.96). Straightforward evaluation of the integrals in the time-ordered expansions rapidly becomes unwieldy, and an efficient diagrammatic technique is developed in Section 11.1 for writing down the contributions to cj r) that are pertinent to any multiphoton process of interest. In Sections 11.2 and 11.3, we apply this technique to obtaining the nonlinear susceptibilities for two important nonlinear optical processes, SHG and CARS. Experimental considerations that are unique to such coherent optical phenomena are also discussed. 

In the attempt to evaluate the optical nonlinearities that can be obtained with the vibrational method, both theoretical and experimental approaches have been undertaken [244-246,250]. In the first case, quantum-chemical ab initio calculations were used to compute /3 (0 0,0) and y (0 0,0,0) using standard derivative techniques and and Y using calculated vibrational intensities. On the other hand, experimental Raman and infrared absolute intensities were used to measure and /. Experimental values for /S and y determined with traditional methods (EFISH, THG, etc.) can be found in the literature. In both cases (theoretical and experimental), the agreement between the NLO coefficients determined in the traditional way and their vibrational counterparts is astonishingly good. 

---