Second harmonic polarization calculation

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. 

Fig. 5.24. Second harmonic intensity at 532 nm as a function of angle of rotation for Au(l 11) in 0.01 M H2S04 at (a) -0.1 V and (b) +0.7 V vs. SCE. s-polarized excitation and s-polarized SHG detection in both cases. For comparison purposes the calculated polar plots of the rotational anisotropies for s/s-polarization of a threefold symmetry surface with (a) and without (b) a onefold symmetry superimposed are also shown. From Ref. 156.

We have obtained SERS and second harmonic generation (SHG) from the doublehole structures with different hole distances. The dependence of the SHG efficiency on the spacing between the holes in the basis is shown in Fig. 11 for two polarizations of the fundamental beam. It can be seen that, as expected from the calculations shown in Fig. lOd, the SHG signal maximizes when the two holes overlap [63,64]. This optimum distance has also been observed in SERS experiments using the double-hole basis [65]. The double-hole structure offers two degrees of freedom, shape and periodicity, for electric field optimization and enhanced spectroscopy. 

The experimental arrangement is shown in Fig. 2.48. The output of a tunable dye laser at X = 486 nm is frequency-doubled in a nonlinear crystal. While the fundamental wave at 486 nm is used for Doppler-free saturation spectroscopy [261] or polarization spectroscopy [278] of the Balmer transition 2Si/2- P /2 the second harmonics of the laser at X = 243 nm induce the Doppler-free two-photon transition 15 i/2 25 i/2. In the simple Bohr model [279], both transitions should be induced at the same frequency since in this model v(lS-2S) = 4v(2S-4P). The measured frequency difference Av = v(lS-2S) — 4v(2S-4P) yields the Lamb shift vlCI ) = Av — 8v] 2S) — Avfs(45 i/2 4Pi/2) <5vl(45 ). The Lamb shift (5vl(2/S) is known and Avfs(45i/2-4Pi/2) can be calculated within the Dirac theory. The frequency markers of the FPI allow the accurate determination of the hfs splitting of the 15 state and the isotope shift Avis( H- H) between the 1S-2S transitions of hydrogen and deuterium (Fig. 2.38). 

Most calculations have focused on determining the nonlinear coefficients for second-harmonic generation. By anology with the formalism for discussed above, the relevant polarization can be written as... 

Ab initio calculations can give a variety of molecular properties besides energy. By changing the SCAN command to OPT in the above list of input statements, the value of the HCl bond length can be optimized to give the lowest energy and the bond length can then be compared with the value determined experimentally in Exp. 37. Addition of FREQ and POLAR commands to the second line yields properties such as the harmonic vibrational frequency (vj, the dipole moment ijl, and the polarizabihty tensor elements a , etc. The calculated dipole moment can be contrasted with that determined... 

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