Polarity/polarization second harmonic generation

H. Watanabe, S. Yamaguchi, S. Sen, A. Morita, and T. Tahara,/. Chem. Phys., 132, 144701 (2010). Half-Hydration At the Air/Water Interface Revealed by Heterodyne-Detected Electronic Sum Frequency Generation Spectroscopy, Polarization Second Harmonic Generation, and Molecular Dynamics Simulation. 

The second term on the right-hand side, a component oscillating at frequency 2co, represents the second harmonic of the incident beam. This component of the polarization vector can radiate light at the frequency 2co. Observation of the second harmonic generation was demonstrated in the early 1960s using mby lasers (59). 

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. 

For crystalline solids, comparative quantities for second harmonic generation and the linear electrooptic coefficient are given by Miller s delta and the polarization optic coefficient f. The quantity 6 is defined by the relation... 

The value of 3 and its dispersion for a molecule, or polymer chain, can be experimentally determined by DC induced second harmonic generation (DCSHG) measurements of liquid solutions -1 2). The experimental arrangement requiring an applied DC field E° to remove the natural center of inversion symmetry of the solution is described in Figure 4. The second harmonic polarization of the solution is expressed as... 

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. 

Without going into too much detail, it is relatively easy to intuitively understand optical rotation in second-harmonic generation from a chiral thin film by simply considering the nonvanishing polarization components generated in a chiral and achiral film. For example, for an achiral thin film with CXA, symmetry and for the experimental situation shown in Figure 9.5, the nonvanishing components of the polarization can be written as ... 

Figure 9.8 Second-harmonic generation from thin film (or surface). Fundamental beam at frequency > i p or. v polarized) is incident on film at angle 0. The p- and. s-polarized second-harmonic fields (frequency 2 co) are generated in reflection and transmission. 

Figure 9.20 Intensity of s-polarized second-harmonic signal generated in transmitted direction for glass-side incidence as function of rotation angle of quarter waveplate. Note significant difference in response for right- (45° and 225°) and left-hand (135° and 315°) circularly polarized light. Points represent experimental data, solid line fit to the model described in Section 3 with nonvanishing g, and the dashed line the fit with vanishing g.

The symmetry of the LB films was determined by polarized ultraviolet-visible (UV-Vis) absorption spectroscopy, optical rotation, and second-harmonic generation. All studies showed that the constructed LB films are anisotropic in the plane of the film and that the symmetry of the film is C2 with the twofold rotation axis perpendicular to the film plane. For example, when the SH intensity is plotted as a function of the azimuthal rotation angle (rotation around an axis perpendicular to the plane of the film), the twofold symmetry becomes evident (Figure 9.23). Isotropic films generate an SH signal independent of the azimuthal rotation angle. On the other hand, the LB... 

In LB films not only the interaction of chromophores but also their orientation can be controlled at the molecular level. Molecular orientation of chromophores has been determined by several methods including polarized UV/vis or IR absorption, second harmonic generation (SHG), Electron Spin Resonance (ESR), or resonance Raman scattering. We have measured the incident angle and polarization angle dependencies of polarized UV/vis absorption to study the molecular orientation of alloxazine, porphyrin, and carbazolyl chromophores, or 4,4 -bipyridinium radical cations in LB films[3-12]. Usually in-plane components of transition dipoles of chromophores are... 

Dombeck, D. A., Kasischke, K. A., Vishwasrao, H. D., et al. 2003. Uniform polarity microtubule assemblies imaged in native brain tissue by second harmonic generation microscopy. Proc. Natl. Acad. Sci. USA 100 7081. 

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... 

In second harmonic generation, light of angular frequency oo pass through a crystal and generates a beam of angular frequency 2 . With conventional light sources the electric polarization induced in the medium depends linearly on the electric held ... 

Optical frequency up-conversion, or second harmonic generation (SHG), in nanostructured surfaces can be also considered as a kind of field enhance-menf [61]. In general, SHG efficiency is proportional to the square of nonlinear polarization ha (x [P (2second order susceptibility. For a nanostructured surface, the incident field is transformed to the local field given by Eq. 19, yielding ... 

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