Second harmonic signal

Nonlinear Optical Devices. A transparent, optically active, sol—gel-derived organic—inorganic glass has been synthesized (68). This hybrid consists of a 2,4-dinitroaminophenylpropyl-triethoxysilane covalently bound to a siUcon alkoxide-derived siUca network. This hybrid exhibits a strong electric field-induced second harmonic signal and showed no signs of crystallization. 

A very simple equation exists that relates spontaneous polarization to the intensity of the second harmonic signal. Spontaneous polarization is conceived as the sum of the products of each of the charges in a dielectric material by each of their displacements from the centrosymmetric positions. Hence, the relationship between spontaneous polarization and the second harmonic signal value can be presented as follows ... 

Recently, Eisenthal and coworkers have developed time-resolved surface second harmonic techniques to probe dynamics of polar solvation and isomerization reactions occurring at liquid liquid, liquid air, and liquid solid interfaces [22]. As these experiments afford subpicosecond time resolution, they are analogous to ultrafast pump probe measurements. Specifically, they excite a dye molecule residing at the interface and follow its dynamics via the resonance enhance second harmonic signal. 

FIG. 3 Solvation dynamics dependence of coumarin 314 probe molecule orientation at the air-water interface. Signals are generated with a 420 nm pump photon and probed by surface second harmonic signal with 840 nm (SH at 420), x Sx element. The normalized change in SH field is plotted vs. pump delay, r is derived from a single exponential fit to the data, (a) Pump polarization S (inplane), (b) Pump polarization P (out-of-plane). (Reprinted from Ref 24 with permission from the American Chemical Society.)... 

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 9.9 Simulated normalized line shapes of -polarized (a-c) and p-polarized (if-/) second-harmonic signals for quarter waveplate measurements (a) and (if) hypothetical achiral surface (hs = 0.5 fp = 0.75, gp = —0.5), (b) and (if) hypothetical chiral surface with in-phase chiral coefficient (fs = 0.75, hs = 0.5 fp = 0.75, gp = —0.5, hp = 0.25), (c) and (/) hypothetical chiral surface with out-of-phase chiral coefficient ( fs = 0.75 0.25i, hs = 0.5 fp = 0.75, gp = —0.5, hp = 0.25z). Upper (solid line) and lower (dashed line) sign in expansion coefficients correspond to two enantiomers. Rotation angles of 45° and 225° (135° and 315°) correspond to right-hand (left-hand) circularly polarized light and are indicated for one of enantiomers with open and filled circles, respectively.

Figure 9.10 (a) and (b) Example of a circular-difference effect from an isotropic Langmuir-Blodgett film composed of enantiomerically pure chiral molecules. Experimental data points are fitted to Eq. (42) (solid curve), (a) The -polarized second-harmonic signal, fit coefficients fs = 0.87 + 0.39z and hs = —0.38. (b) The / -polarized second-harmonic signal, fit coefficients fp = 0.63 — 0.20i, gp = 0.12 + 0.003z, and hp = 1.24. The right- and left-hand circular polarization are indicated by open and filled circles. 

The coefficients /, g, and h are unique for each second-harmonic signal and depend on the three susceptibility tensors. We normalize the relative values of the tensor components to = 1- The task is then to determine the complex values of the other 14 tensor components (see Table 9.2). A sufficient number of 8 independent measurements is provided by the p- and s--polarized components of the reflected and transmitted second-harmonic signals for the two orientations of the sample shown in Figure 9.17. The change in sample orientation corresponds to a coordinate transformation that reverses the... 

Figure 9.18 Eight measured second-harmonic signals. Waveplate rotation angle of 0° corresponds to p-polarized fundamental field. Dots are experimental data and lines fit to Eq. 42 with polarization control by quarter waveplate. (a-d) Film-side incidence, (e-h) glass-side incidence (a) and (e) transmitted -polarized (b) and (/) transmitted p-polarized (c) and (g) reflected -polarized (if) and (h) reflected p-polarized.

The nonlinearity of the sample was analyzed using the experimental procedure described in Section 3.3 The polarization of the fundamental beam of a YAG laser was continuously varied by means of a quarter waveplate, and the intensity of the second-harmonic signal was measured as a function of the rotation angle of the quarter waveplate. The obtained polarization pattern were then fitted to Eq. (42), which yields the relative values of the expansion coefficients /, g, and h. The experimental results for the transmitted, glass-side-incidence, s-polarizcd signal are shown in Figure 9.20. 

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.

Figure 9.23 s-Polarized second-harmonic signal detected in transmitted direction as function of the azimuthal rotation angle. Twofold pattern clearly indicates C2 symmetry of sample. 

We can quantitate the relative surface coverage of adsorbed hydrogen, 0, from the second harmonic signal, I (2C0) ... 

Figure 1. The current (a) and the second harmonic signal (b) obtained during the potential cycling (10 mV s"1 scan rate) from a polycrystalline silver electrode in a 0.1M LiClC>4 aceto nitrile solution.

Figure 4. The relative surface coverage of adsorbed hydrogen as a function of electrode potential for acetic acid. The circles are calculated from the second harmonic signal using Equation 1, and the solid line is the theoretical curve predicted from the reaction mechanism (Equations 2 and 3).

In spite of this uncertainty, we can quantitate this increase in the second harmonic signal due to chemisorption through the use of Equation 1. Since, in this case, the hydrogen is chemisorbed prior to the formation of molecular hydrogen, we can also monitor the surface coverage of hydride by the charge passed during the deposition. A plot of "c9"... 

Figure 6. The function c0 ( = [I (2(0)/I (2(0) 0]1/2 - 1 ) determined from the second harmonic signal plotted versus the charge passed due to hydrogen chemisorption on the platinum electrode.

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