Electronic Optical Nonlinearities

In this chapter we treat those nonlinear optical processes in which the electronic wave functions of the liquid crystal molecules are significantly perturbed by the optical field. Unlike the nonelectronic processes discussed in the previous chapters, these electronic processes are very fast the active elections of the molecules respond almost instantaneously to the optical field in the form of an induced electronic polarization. Transitions from the initial level to some final excited state could also occur. 

Such processes are obviously dependent on the optical frequency and the resonant frequencies of the liquid crystal constituent molecules. They are also understandably extremely complicated, owing to the complex electronic and energy level stracture of liquid crystal molecules. Even calculating such basic quantities as the Hamiltonian, the starting point for quantum mechanical calcnlations of the electronic wave function and energy levels and linear optical properties, requires very powerful numerical computational techniques. 

We shall adopt a greatly simplified approach where the liquid crystal molecule is represented as a general multilevel system. Only dipole transitions among the levels are considered. Using this model, we quantitatively illustrate some important basic aspects of the various electronic nonlinear optical processes and their accompanying nonlinearities. Special features pertaining to liquid crystalline materials are then discussed. 

DENSITY MATRIX FORMALISM FOR OPTICALLY INDUCED MOLECULAR ELECTRONIC POLARIZABILITIES 

Liquid Crystals, Second Edition By lam-Choon Khoo Copyright 2007 John Wiley Sons, Inc. 

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In the rest of this chapter, we address these and other macroscopic symmetry properties of liquid ciystalline electronic optical nonlinearities. 

It is important to note that since the thermal/density and order parameter changes could be induced in microseconds or tens of nanoseconds (cf preceding chapters), these director-axis-reorientation or order-parameter-change mediated limiting actions will work well for sensor protection in these time scales. For shorter laser pulses, for example, nanosecond and picosecond or subpicosecond laser pulses, the response will not be able to build up sufficiently in time to provide the necessary attenuation effect. In those time regimes, electronic optical nonlinear mechanisms, in particular, nonlinear photonic absorptions, have to be employed. This is discussed in... 

For measurements carried out closer to resonances, thermal contributions to the optical nonlinearity, given by the following formula, can compete with electronic contributions (54,55) ... 

As a result of the unique molecular electronic properties and geometrical structure, liquid crystals also tend to be optically nonlinear materials meaning... 

Sheik-Bahae, M., Said, A. A., Wei, T. H., Hagan, D. J. and Van Stryland, E. W. (1990) Sensitive measurement of optical nonlinearities using a single beam. IEEE J Quantum Electron., 26, 760-769. 

Another source of variability, which can have still different characteristics, is comprised of the interaction of any of the above factors with a nonlinearity anywhere in the system. These nonlinearities could consist of nonlinearity in the detector, in the spectrometer s electronics, optical effects such as changes in the field of view, and so on. Many of these nonlinearities are likely to be idiosyncratic to the cause, and would have to be characterized individually and also analyzed on a case-by-case basis. 

The optical and electronic functions of polysilanes owe to their delocalized highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) that are occupied by holes and conduction electrons, respectively. The polymer does not show high conductivity or optical nonlinearity if the electrons or holes are localized on a small part of the polymer chain. To elucidate the structure of HOMO and LUMO is therefore important for the molecular design of polysilanes as functional materials. 

Second-order optical nonlinearities result from introduction of a cubic term in the potential function for the electron, and third-order optical nonlinearities result from introduction of a quartic term (Figure 18). Two important points relate to the symmetry of this perturbation. First, while negative and positive p both give rise to the same potential and therefore the same physical effects (the only difference being the orientation of the coordinate system), a negative y will lead to a different electron potential than will a positive y. Second, the quartic perturbation has mirror symmetry with respect to a distortion coordinate as a result, both centrosymmetric and noncentrosymmetric materials will exhibit third-order optical nonlinearities. If we reconsider equation 23 for the expansion of polarization of a molecule as a function of electric field and assume that the even-order terms are zero (i.e., that the molecule is centrosymmetric), we see that polarization at a given point in space is ... 

The optical nonlinearity is strongly dependent on the extent of ir-electron delocalization from one repeat unit to another in the polymer (or oligomer) structure. This effective delocalization is not always equally manifested but depends on the details of repeat unit electronic structure and order. For example, in a sequentially built structure, the ir-delocalization effect on Y is found to be more effective for the thiophene oligomers than it is for the benzene oligomers (5). 

The third-harmonic generation method has the advantage that it probes purely electronic nonlinearity. Therefore, orientational and thermal effects as well as other dynamic nonlinearities derived from excitations under resonance condition are eliminated (7). The THG method, however, does not provide any information on the time-response of optical nonlinearity. Another disadvantage of the method is that one has to consider resonances at oj, 2w and 3o> as opposed to degenerate four wave mixing discussed below which utilizes the intensity dependence of refractive index and where only resonances at a) and 2a) manifest. 

Electron correlation effects are expected to play an important role in determining optical nonlinearities. Both the configuration interaction and Moeller-Plesset perturbation correction approaches have been used to incorporate electron-correlation effects (26,27) ... 

The search of third-order materials should not just be limited to conjugated structures. But only with an improved microscopic understanding of optical nonlinearities, can the scope, in any useful way, be broadened to include other classes of molecular materials. Incorporation of polarizable heavy atoms may be a viable route to increase Y. A suitable example is iodoform (CHI ) which has no ir-electron but has a value (3J ) comparable to" that of bithiophene... 

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