Nonlinear optical effects second harmonic generation

Keywords Diamondoid net Metal-organic framework Noncentrosymmetric MOFs Nonlinear optics Octupolar symmetry Push-pull effect Second harmonic generation... 

Fig. 8. Examples of some of the donor-acceptor substituted TEEs prepared for the exploration of structure-property relationships in the second- and third-order nonlinear optical effects of fully two-dimensionally-conjugated chromophores. For all compounds, the second hyperpolarizability y [10 esu], measured by third harmonic generation experiments in CHCI3 solution at a laser frequency of either A = 1.9 or 2.1 (second value if shown) pm is given in parentheses. n.o. not obtained...

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. 

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). 

Tang, S., Krasieva, T. B., Chen, Z., Tempea, G., and Tromberg, B. J. 2006. Effect of pulse duration on two-photon excited flourescence and second harmonic generation in nonlinear optical microscopy./. Biomed. Opt. 11 020501. 

Second harmonic generation (SHG) is one of the most intensively studied nonlinear optical effects that have ever been combined with near-held scanning optical microscopy (Shen et al. 2000 Zayats and Sandoghdar 2000 Zayats and Sandoghdar 2001 Takahashi and Zayats 2002). SHG, which is an even-order nonlinear process, is forbidden in centrosymmetric media under the dipole approximation (Shen 1984). Non-centrosymmetric molecules and lattices are allowed to exhibit SHG light. The second-order nonlinear polarization for SHG (T shg) is given in a scalar form by... 

This tutorial deals with nonlinear optical effects associated with the first nonlinear term in expression for the polarization expansion described in the next section. The first nonlinear term is the origin of several interesting and important effects including second-harmonic generation, the linear electrooptic or Pockels effect,... 

Two of the most important nonlinear optical (NLO) processess, electro-optic switching and second harmonic generation, are second order effects. As such, they occur in materials consisting of noncentrosymmetrically arranged molecular subunits whose polarizability contains a second order dependence on electric fields. Excluding the special cases of noncentrosymmetric but nonpolar crystals, which would be nearly impossible to design from first principles, the rational fabrication of an optimal material would result from the simultaneous maximization of the molecular second order coefficients (first hyperpolarizabilities, p) and the polar order parameters of the assembly of subunits. (1)... 

Amino-5-nitropyrimidine, cocrystallization, 455 Amorphous polymers, criteria for use in second harmonic generation, 250-251 Amphiphilic molecules polar Z-type Langmuir-Blodgett films, formation, 473-479 structures, transfer behavior, and contact angles, 474,476-477r Anharmonic oscillator models, nonlinear optical effect-microstructure relationship, 361... 

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