## 3 Results and Discussion
As these results show, electroabsorption/the imaginary part of Kerr coefficient (K) increases rapidly as particle size is decreased. For particles of diameters 25 nm and 50 nm, the magnitudes of K\({}^{\prime}\) were too small to measure. Comparing with doped nonconjugated conductive polymer, the increase roughly goes as d\({}^{-3}\), where d is the nanoparticle-diameter. This is identical to the dependence of the real part of Kerr coefficient (K) on d as reported earlier [6]. For quadratic electro-optic measurements, the magnitudes of modulations were large enough to measure for all three sizes of gold nanoparticles in glass [6]. As in the case of quadratic electro-optic effect, this correlation between electroabsorption and d can be explained using an earlier theoretical treatment as well as more recent theory on dimensionally confined electronic systems [3; 4; 22; 23; 24; 25]. According to these theories \(\chi^{(3)}\) should increase as d\({}^{-3}\). The Kerr coefficient is proportional to \(\chi^{(3)}\) (\(\omega\); \(\omega\),0,0). In particular, K is proportional to the real part of \(\chi^{(3)}\) and K\({}^{\prime}\) is proportional to the imaginary part. The measurements reported here were made at 633 nm which is near the onset of the surface plasmon resonance. Therefore, \(\chi^{(3)}\) at this wavelength is complex with real and imaginary parts. The theoretical treatment mentioned above predicts that the maximum value of \(\chi^{(3)}\) is proportional to T\({}_{1}\)T\({}_{2}\)(1-d/d)\({}^{3}\), where T\({}_{1}\) is the excited state life-time, T\({}_{2}\) is the dephasing time, d\({}_{0}\) is a characteristic threshold diameter of the system, and d is the diameter of the nanoparticle. Therefore, for d \(<\) d\({}_{0}\), \(\chi^{(3)}\) increases as d\({}^{-3}\). The particle concentration would alter absorption coefficient the same way as it would alter Kerr coefficient. Since the optical density is about the same for all samples (at 633 nm) we can compare the magnitudes of Kerr coefficients at the fundamental level. As the results show, the Kerr coefficient follows the theory and increases as \(\sim\)d\({}^{-3}\). An alternative interpretation of the d\({}^{-3}\) dependence is that for any given excitation the fraction of electrons excited in a nanoparticle is higher in a smaller particle since the total number of electrons in a smaller nanoparticle is less. Therefore, a larger optical nonlinearity is expected. This is essentially a result predicted by the phase-space filling model [22; 23; 24; 25] which states that \(\delta\)/f = \(-\)(N/N\({}_{\rm s}\)), where \(\delta\)f represents change in oscillator strength (f), N represents the number of electrons excited, and N\({}_{\rm s}\) represents the total number of electrons participating in the excitation process. The value of N\({}_{\rm s}\) is proportional to the particle volume (\(\sim\)\(\pi\)d\({}^{3}\)/6) that confines the electrons. Therefore, the change in absorption coefficient \(\Delta\alpha\) which is proportional to the change in oscillator strength \(\delta\)f, should have a d\({}^{-3}\) dependence. As a result, K\({}^{\prime}\) also has a d\({}^{-3}\) dependence. Metallic nanoparticles within transparent dielectric media are expected to have various applications in ultrafast electro-optic switching/modulation, Kerr cells and others. As the absorption coefficient is small (\(\sim\)0.2 cm\({}^{-1}\) at 633 nm), the figure of merit for applications is high for these materials. Although this report involves metal nanoparticles in glass, the results presented can be extended to metal nanoparticles in other transparent dielectric media.