## 3 Results and Discussion  
Three glass samples containing gold nanoparticles of three different average particle diameters were studied and discussed in the following. Samples of gold nanoparticles in glass (plates with dimensions: 4 cm \(\times\) 4 cm \(\times\) 3 mm) were purchased from a commercial vendor. The optical absorption spectrum was recorded for light travelling  
Figure 1: Experimental set-up for measurement of quadratic electro-optic effect/Kerr coefficient. through the thickness of the sample plate. The size of the gold nanoparticle was estimated from the wavelength of the absorption peak (surface plasmon resonance) and the relative peak intensity, using the results published in the literature [4; 7]. The absorption peak appeared at shorter wavelengths and the relative intensity of the peak decreased for smaller nanoparticles. For Sample 1 (Figure 2), the peak was at about 534 nm wavelength which corresponded to a particle diameter of about 50 nm. The results of the quadratic electro-optic measurement of Sample 1 are given in Figure 3. For Sample 2, the peak was at about a 527 nm wavelength which corresponded to a particle diameter of about 25 nm. For Sample 3 (Figure 4), the peak was at about 520 nm wavelength which corresponded to a particle diameter of about 15 nm. The relative peak intensities (absorbance at SPR divided by absorbance at \(\sim\)400 nm) were also used, if needed, to ascertain the nanoparticle sizes [4]. Quadratic electro-optic measurements were made in these plates using the electric field-induced birefringence method discussed earlier. The beam at 633 nm from a He-Ne laser was passed through the long dimension (4 cm) of the plate. The results of the measurements are shown in Figures 3 and 5 for Samples 1 and 3 having particle diameters of about 50 nm and 15 nm respectively. The Kerr coefficients, as determined from the observed modulation signals, were about 2.5 \(\times\) 10\({}^{-15}\) m/V\({}^{2}\), 2.0 \(\times\) 10\({}^{-14}\) m/V\({}^{2}\) and 7.5 \(\times\) 10\({}^{-14}\) m/V\({}^{2}\), respectively, for samples 1, 2 and 3. Under the same experimental conditions no detectable modulation was observed for glasses without metal nanoparticles. Considering previous reports, subnanometer size metallic-like particles were obtained in non-conjugated conductive polymers doped with iodine. [13; 14; 15; 16; 17; 18; 19] A charge-transfer from an isolated carbon-carbon double bond to the dopant creates highly confined metallic domains/quantum dots (surface plasmon resonance of about 400 nm and radical cation of about 300 nm). The subnanometer size particles have shown the largest known Kerr coefficients and two-photon absorption coefficients of any material. The Kerr coefficient is about 3.5 \(\times\) 10\({}^{-10}\) m/V\({}^{2}\) at 633 nm for iodine-doped trans-polyisoprene [18; 19]. All the magnitudes of the Kerr coefficient stated here are for the same optical density (about 0.05 at 633 nm). As these results show, the Kerr coefficient (K) increases rapidly as particle size decreases. The increase is roughly d\({}^{-3}\), where d is the nanoparticle diameter. Therefore, we may write the following equation: K = K\({}_{0}\)d\({}^{-3}\), where K\({}_{0}\) is the Kerr coefficient for d = 1 nm. A plot of logK vs. logd is shown in Figure 6. It shows a slope of about \(-3\) implying a d\({}^{-3}\) dependence of the Kerr coefficient. This correlation between optical nonlinearity and d can be explained using an earlier theoretical treatment of metal nanoparticles in dielectric media [3]. According to this theory, \(\chi^{(3)}\) increases as d\({}^{-3}\)  
Figure 5: Quadratic electro-optic modulation data for different applied electric fields, for a particle diameter of about 15 nm. Figure 6: Kerr coefficient correlated with diameter of metallic nanoparticle. The Kerr coefficient (**K**) is proportional to \(\chi^{(3)}(\omega\); \(\omega\),0,0). In particular, **K** is proportional to the real part of \(\chi^{(3)}\).