Second harmonic generation , nonlinear

Vollmer R 1998 Magnetization-induced second harmonic generation from surfaces and ultrathin films Nonlinear Optics in Metals e6 K H Bennemann (Oxford Clarendon) pp 42-131... 

Campagnola P J, Wei M D, Lewis A and Loew L M 1999 High-resolution nonlinear optical imaging of live cells by second harmonic generation Biophys. J. 77 3341-9... 

In the single-domain state, many ferroelectric crystals also exhibit high optical nonlinearity and this, coupled with the large standing optical anisotropies (birefringences) that are often available, makes the ferroelectrics interesting candidates for phase-matched optical second harmonic generation (SHG). 

Only certain types of crystalline materials can exhibit second harmonic generation (61). Because of symmetry considerations, the coefficient must be identically equal to zero in any material having a center of symmetry. Thus the only candidates for second harmonic generation are materials that lack a center of symmetry. Some common materials which are used in nonlinear optics include barium sodium niobate [12323-03-4] Ba2NaNb O lithium niobate [12031 -63-9] LiNbO potassium titanyl phosphate [12690-20-9], KTiOPO beta-barium borate [13701 -59-2], p-BaB204 and lithium triborate... 

Barium sodium niobium oxide [12323-03-4] Ba2NaNb 02, finds appHcation for its dielectric, pie2oelectric, nonlinear crystal and electro-optic properties (35,36). It has been used in conjunction with lasers for second harmonic generation and frequency doubling. The crystalline material can be grown at high temperature, mp ca 1450°C (37). 

Microscopy methods based on nonlinear optical phenomena that provide chemical information are a recent development. Infrared snm-frequency microscopy has been demonstrated for LB films of arachidic acid, allowing for surface-specific imaging of the lateral distribution of a selected vibrational mode, the asymmetric methyl stretch [60]. The method is sensitive to the snrface distribntion of the functional gronp as well as to lateral variations in the gronp environmental and conformation. Second-harmonic generation (SHG) microscopy has also been demonstrated for both spread monolayers and LB films of dye molecules [61,62]. The method images the molecular density and orientation field with optical resolution, and local qnantitative information can be extracted. 

Lamberth, C. Murphy, D. M. Mingos, D. M. P. Second Harmonic Generation Properties of Some Coordination Compounds Based on Pentadionato and Polyene Ligands. In Organic Materials for Nonlinear Optics II Harm, R. A., Bloor, D., Eds. Royal Society of Chemistry London, 1991 pp 183-189. 

Nonlinear second order optical properties such as second harmonic generation and the linear electrooptic effect arise from the first non-linear term in the constitutive relation for the polarization P(t) of a medium in an applied electric field E(t) = E cos ot. 

The first and third order terms in odd powers of the applied electric field are present for all materials. In the second order term, a polarization is induced proportional to the square of the applied electric field, and the. nonlinear second order optical susceptibility must, therefore, vanish in crystals that possess a center of symmetry. In addition to the noncentrosymmetric structure, efficient second harmonic generation requires crystals to possess propagation directions where the crystal birefringence cancels the natural dispersion leading to phase matching. 

These effects Q.2) are all driven by the same third-rank frequency dependent nonlinear susceptibility x2(-u>3 w,, u>2).d is sometimes preferred for second-harmonic generation (SHG). 

Experimental and theoretical results are presented for four nonlinear electrooptic and dielectric effects, as they pertain to flexible polymers. They are the Kerr effect, electric field induced light scattering, dielectric saturation and electric field induced second harmonic generation. We show the relationship between the dipole moment, polarizability, hyperpolarizability, the conformation of the polymer and these electrooptic and dielectric effects. We find that these effects are very sensitive to the details of polymer structure such as the rotational isomeric states, tacticity, and in the case of a copolymer, the comonomer composition. 

We have shown in this paper the relationships between the fundamental electrical parameters, such as the dipole moment, polarizability and hyperpolarizability, and the conformations of flexible polymers which are manifested in a number of their electrooptic and dielectric properties. These include the Kerr effect, dielectric polarization and saturation, electric field induced light scattering and second harmonic generation. Our experimental and theoretical studies of the Kerr effect show that it is very useful for the characterization of polymer microstructure. Our theoretical studies of the NLDE, EFLS and EFSHG also show that these effects are potentially useful, but there are very few experimental results reported in the literature with which to test the calculations. More experimental studies are needed to further our understanding of the nonlinear electrooptic and dielectric properties of flexible polymers. 

Nonlinear Optical Activity in Second-Harmonic Generation... 

In the following sections we will first in Section 2 briefly discuss the necessary background to understand optical activity effects in linear and nonlinear optics and to illustrate the similarities and differences between both types. In Section 3 we present a more thorough analysis of nonlinear optical effects in second-harmonic generation, both from a theoretical and an experimental point of view. Section 4 deals with experimental examples that illustrate the usefulness of nonlinear optical activity in the study of chiral thin films and surfaces. Finally, in Section 5 we give an overview of the role of chirality in the field of second-order nonlinear optics and show that chiral molecules can be useful for applications in this field. 

Figure 9.3 Schematic illustration of second-order nonlinear optical effects, (a) Second-harmonic generation. Two light fields at frequency go are incident on medium with nonvanishing / 2. Nonlinear interaction with medium creates new field at frequency 2 go. (b) Frequency mixing. One light field at frequency GO and one at frequency go2 is incident on nonlinear medium. Nonlinear interaction with medium creates new field at frequency goi + go2. (c) electro-optic effect. Static electric field E (0) applied over nonlinear medium changes phase of an incoming light field.

The proportionality constants a and (> are the linear polarizability and the second-order polarizability (or first hyperpolarizability), and x(1) and x<2) are the first- and second-order susceptibility. The quadratic terms (> and x<2) are related by x(2) = (V/(P) and are responsible for second-order nonlinear optical (NLO) effects such as frequency doubling (or second-harmonic generation), frequency mixing, and the electro-optic effect (or Pockels effect). These effects are schematically illustrated in Figure 9.3. In the remainder of this chapter, we will primarily focus on the process of second-harmonic generation (SHG). 

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