Nonlinear Susceptibility and Intensity-Dependent Refractive Index

NONLINEAR SUSCEPTIBILITY AND INTENSITY-DEPENDENT REFRACTIVE INDEX 

In Chapter 2, we discuss the refractive indices of hquid ciystals in terms of the induced polarization P and the optical electric field E, where P is linearly related to E. Generally speaking, a material is said to be optically nonlinear when the induced polarization Pis not linearly dependent on E. This could happen if the optical field is very intense. It could also happen if the physical properties of the material are easily perturbed by the optical field. In this chapter we describe the general theoretical framework for studying these processes. Specific nonlinear optical phenomena observed in liquid crystalline systems will be presented in Chapter 12. 

There are two basic approaches. In many systems (e.g., atoms, molecules, and semiconductors), the primary processes responsible for nonlinear polarizations are associated with electronic transitions. To describe such processes and obtain the correct polarization, it is necessary to employ quantum mechanical theories. On the other hand, many processes are essentially classical in nature. In liquid crystals, for example, processes such as thermal and density effects, molecular reorientations, flows, and electrostrictive effects require only classical mechanics and electromagnetic theories. In this chapter the fundamentals of nonlinear optics are described within the framework of classical electromagnetic theories. Some of the quantum mechanical aspects of electronic nonlinearities were given in Chapter 10. 

All optical phenomena occurring in a material arise from the optical field-induced polarization P. In general, the total polarization P may be written in the form. 

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

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NONLINEAR SUSCEPTIBILITY AND INTENSITY-DEPENDENT REFRACTIVE INDEX 275... 

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