Second-harmonic intensity

In the solid state, the phase matched second harmonic signal increases with increased polymeri zation(7 ). Figure 14 shows preliminary data for the second harmonic intensity of NTDA microcrystals polymerized under x-ray radiation. As the polymer forms, the second harmonic intensity... 

Figure 14. The second harmonic I2" of NTDA microcrystals relative to the second harmonic intensity of lithum iodate (LilOi) powder I2" with increasing x-ray-induced polymerization. (Reproduced with permissionfrom Ref. 7. Copyright 1980, J. Opt. Soc.)...

Figure 2. Depiction of the length dependence of second harmonic intensity. The lower curve shows the effect of decreasing the coherence length to 30% of the upper curve.

Figure 4. Temperature dependence of the induced second harmonic intensity. (Reproduced from Ref. 23. Copyright 1983, American Chemical Society.)...

From an experimental point of view, it is more practical to consider the second-harmonic intensity instead of the second-harmonic fields. For simplicity, the intensity is expressed as the square of the amplitude of the electric... 

Figures 9.10a and b show the respective s- and p-polarized components of the second-harmonic intensity recorded from a chiral thin film in transmission. The experimental data points are fitted to Eq. (42) and the values of the expansion coefficients /, g, and h are determined. Note the CD effect observed in both figures. Since fs, gs, and hp are zero for an achiral thin film or surface, (—f+g) and h cannot be simultaneously non vanishing for a particular experimental arrangement and thus no CD effect can be observed. In Figure 9.11, we compare the second-harmonic response as observed experimentally for a chiral and achiral thin film.

To determine /, g, and h the second-harmonic intensity is measured as a function of the angle of the quarter waveplate for different experimental geometries. The experimental setup is shown in Figure 9.12. A thin film is irradiated with an infrared Nd YAG laser (1064 nm, 50 Hz, 8 ns). The polarization of the input beam (p polarized) is continuously varied with a quarter waveplate... 

Figure 9.15 Second-harmonic intensity as function of rotation angle of quarter waveplate. (a) Transmitted -polarized SH signal, (b) transmitted p-polarized SH signal, (c) reflected -polarized SH signal, and (d) reflected p-polarized SH signal. Left- and right-hand circularly polarized input light is indicated with open and filled circles, respectively.

Next, the experimental results were fitted to Eqs. (42) and (43), respectively. We choose to set the imaginary part of h (hi) to zero to fix the overall phase. The second-harmonic intensity is measured in arbitrary units and we normalized the fitting parameter values to the real part of h, that is, hR = 1. Therefore, only the relative values are meaningful. The sets of parameter values found that best fit Eq. (42) to each of the waveplate data curves are given in Table 9.4. 

Second-harmonic intensity (a.u.) Second-harmonic intensity (a.u.) Second-harmonic intensity (a.u.) Second-harmonic intensity (a.u.)... 

Figure 9.25 Second-harmonic intensity of LB films as function of number of layers R/S/... structures (open dots) and R/R/... stmctures (filled dots). Solid line is quadratic fit of data points for R/R/... structures.

To analyze the second-order susceptibility, the symmetry of the films was first analyzed by measuring the intensities of the second-harmonic light. The sample was irradiated with polarized light from a Nd YAG laser incident at 45°, and the second-harmonic light emanating from the sample was detected while the sample was rotated around its surface normal. No variation in the second-harmonic intensity was observed as the sample was rotated, indicating... 

We also evaluated molecular orientation in the mixed monolayers using the SHG measurement. When the fundamental light is irradiated to the film with uniaxial molecular orientation such as LB films at an incident angle of 6, the transmitted second-harmonic intensity P2 from the film is given by... 

The ratio a can be related to the measured ratio of the p-polarized second-harmonic intensities for s- and p- polarized fundamental lights, Pp/P,. Assuming that nx n2 and L the coherence length, the relation between the ratio a and Pp/P, is described as the following equation ... 

Similar increases of the surface second harmonic intensity have been observed during the formation of alkali metal monolayers on Ge and Rh surfaces in vacuo (10-11). ... 

Recently Cresswell et al. [297] have produced alternating layer structures which they have characterised by SHG and X-ray diffraction and have obtained a partial degree of order. Era et al. [298] have produced thick alternating films which exhibit quadratic dependence of second harmonic intensity on film thickness and which show a reasonable degree of order when studied by X-ray diffraction. 

Figure 5.20. The square root of the second harmonic intensity versus number of layers obtained using the material shown in Figure 5.19. Reproduced from Decher, G., Tieke, B., Bosshard, C. and Guenter, P. 1988 J. Chem. Soc Chem. Commun. 933-4. (Reproduced by kind permission of the authors and of the Royal Society of Chemistry.)...

Figure 12. Dependence of the second harmonic intensity on the ration of the average particle size to the average coherence length after Kurtz (16). (Reprinted with permission from Williams, D. J. Angew. Chem. Int. Ed. Engl 1984, 23, 690. Copyright VCH Publishers.)...

Figure 7. Second harmonic intensity as a function of angle of incidence for transversely poled and crosslinked films of triacrylate 7 (o) and 3 wt % 18 in triacrylate 7 ( ).

Figure 8. Second harmonic intensity as a function of inter-electrode position for a longitudinally poled, crosslinked film of 22. The dotted lines indicate approximate positions of the electrodes.

Figure 9. Temperature dependence of the second harmonic intensity for a transversely poled, crosslinked film of 3 wt % 18 in triacrylate 7. Heating rate was 1 °C/min.

Fig. 5.1. Second harmonic intensity as a function of angle of rotation for Ag(lll) in 0.25 M NaC104, pH = 5.0 at -0.72 V vs. Ag/AgCl (PZC) with p-polarized 1064nm illumination. Angle of incidence (i//) is 10°. The solid lines are fits to the data generated from the theoretical expressions given in the text (Eqs. (3-11) and (3-13)). (a) p-polarized SH intensity, a/ci3) = 1.2e . (b) s-polarized SH intensity. The constant b<3) is taken to be unity. From Ref. 124.

Fig. 5.2. Second harmonic intensity at 532 nm as a function of angle of rotation for Ag(110) in 0.25 M Na2S04, pH = 5.8 at —0.2 V vs. Ag/AgCl. A p-polarized 1064 nm pump beam at a y = 310 incident angle was used, (a) p-polarized SH intensity. The theoretical curve (solid line) is generated from Eq. (3-15) in the text by setting a = 3.1, c(2) = -0.83, and c(4) = 0.08. (b) s-polariz-ed SH intensity. From Ref. 122.

Fig. 5.12. Comparison of the potential dependence in isotropic (a) and anisotropic (b) components to the second harmonic intensity from Ag(l 11) at the indicated incident wavelengths. The solution was 0.25 M Na2S04 at a pH of 3.5. An incident angle of 45° was used. From Ref. 132 and 137.

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