Polarization, nonlinear light interaction

As described at the end of section Al.6.1. in nonlinear spectroscopy a polarization is created in the material which depends in a nonlinear way on the strength of the electric field. As we shall now see, the microscopic description of this nonlinear polarization involves multiple interactions of the material with the electric field. The multiple interactions in principle contain infomiation on both the ground electronic state and excited electronic state dynamics, and for a molecule in the presence of solvent, infomiation on the molecule-solvent interactions. Excellent general introductions to nonlinear spectroscopy may be found in [35, 36 and 37]. Raman spectroscopy, described at the end of the previous section, is also a nonlinear spectroscopy, in the sense that it involves more than one interaction of light with the material, but it is a pathological example since the second interaction is tlirough spontaneous emission and therefore not proportional to a driving field... 

Now there seems to be one immediate and important question to be addressed if the particle and wave pictures of light are two versions of the same thing, how can we understand nonlinear light-matter interactions when the electric field is represented by a plane wave The answer lies in a generalization of Eq. (2) which lets the polarization be expressed as a Taylor series in the electric field strength... 

Passive all-optical switching, also known as nonlinear self-action effects, offers a practical solution to such challenges. In these processes, the incident light interacting with the nonlinear optical material creates the complex phase shift necessary to change its polarization state, transmission, and other spatio-optical characteristics. 

Light-matter interactions can be described via an induced polarization, i.e., the induced dipole moment per unit volume. Ultrafast laser pulses, which are used in laser scanning microscopes, have high enough intensity to induce a nonlinear polarization in various materials. For intense optical electric field E, the polarization vector P can be expanded in the power series (Boyd 1992)... 

The extensive jt-delocalized system of metal-dithiolene complexes is also responsible for the nonlinear optical properties (NLO) which have been recently reviewed . The interaction of radiation with the matter induces an instantaneous displacement (polarization Pq = /X = aE, where a is the linear polarizability) of the electronic density away from the nucleus at small field (linear optics). At high fields (laser light) the polarizability of the molecule can be driven beyond the linear regime and a nonlinear polarization is induced (NLO) = aE + fiE" + y E + and for the bulk material... 

The TPA cross section (7>) is proportional to the second-order nonlinear polarizability y. This is derived by consideration of interactions of light with matter causing a change in the dipole moment that is the induced dipole moment /iirld. Induced polarization Pind is proportional to /(ind and the field strength E of the incident light, Eq. (7) [50, 73] ... 

A comparison has been made between the reorientational behavior of a series of copolymers of DR with MMA (13, Figure 4) and that of series of blends of a DR homopolymer (12) with PMMA to elucidate the sequential effect of the DR monomer units on the orientability caused by intramolecular interactions between dye chromophore groups in polymer solids.79 The maximum birefringence induced by linearly polarized light for the blends80 increased linearly with an increase in the DR fraction. In contrast, the copolymers showed a nonlinear... 

In order to introduce some notation, we first recall a few of the well-known properties of the interaction of light pulses with molecules in the linear approximation. Frequently, the signals in nonlinear optical experiments are expressed in terms of the polarization induced in the medium by the incident pulses. The complex linear polarization P t) vector for a distribution of identical two-level systems is obtained from an elementary calculation of the density matrix using the Liouville equation of a system perturbed by an electric field and proceeding as follows ... 

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