Nonlinear Optical Probes and Processes in Polymers and Liquid ...

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work I am presenting here describes several nonlinear optical techniques and their
applications for the study of physics of organic optical materials such as polymer
composites and liquid crystals.
In nonlinear optics, the nonlinear optical response is described by expressing the
dipole moment per unit volume, or polarization density P (t) of a material, as a power
series in the electric field E(t) as [1]
P (t) = P0 + χ (1) E(t) + χ (2) E 2 (t) + χ (3) E 3 (t) + ..., (1.1)
where P0 is the intrinsic polarization, χ (1) is the linear susceptibility, χ (2) and χ (3)
are the second- and third-order nonlinear optical susceptibilities. Generally, the nth
order optical susceptibility χ (n) is a tensor of rank n + 1.
The polarization density is important for the description of nonlinear optical phe-
nomena since a time-varying polarization acts as a source of new components of the
electromagnetic field. This is described by the wave equation in nonlinear optical
form as
∇ 2 E − n2
c 2
∂2E 4π
=
∂t2 c2 ∂2P ∂t2 where n is the refractive index and c is the speed of light in vacuum.
(1.2)
For nonlinear optical studies, it appears convenient to work in the frequency do-
main rather than in the time domain. In this case, if the optical electric field of a
laser beam is represented as E(t) = E exp(−iωt)+c.c., then the ω Fourier component