## 1 Introduction  
Nonlinear optics in metal nanoparticles within transparent dielectric media has been studied extensively [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12]. In particular, third order optics using ultrashort (femtosecond) laser pulses in such metal nanoparticle systems have been widely studied and reported. The metallic nanoparticles of smaller diameters (<about 10 nm) are also called quantum dots since many of their properties can be understood by considering the quantum confinement of the electrons within nanometer dimensions. The third-order susceptibilities (\(\chi^{(3)}\)) and response times of various metallic nanoparticles in dielectric media have been measured for different diameters of nanoparticles. However, as our literature review revealed no measurement of the quadratic electro-optic effect in such systems has been published or is known in the prior art and no correlation between third order susceptibility and particle size have been established. Using high intensity, short pulse, second order optical effect has been shown for specific nanoparticles utilizing the asymmetry in the shapes/interfaces [12]. Second order optics has no relevance to the quadratic electro-optic effects presented here. Quadratic electro-optic effects have applications in ultrafast electro-optic modulation/switching and also as Kerr cells, Kerr-gates for mode-locking, Q-switching, and other applications in optoelectronics.  
The focus of the present report is on the measurement of quadratic electro-optic/Kerr effects in metal nanoparticles of various sizes with an objective of further elucidating the mechanisms of nonlinear optics in these important systems. The quadratic electro-optic effect is given by: \(\Delta\)n = K\(\Delta\)E\({}^{2}\), where \(\Delta\)n is the change in the refractive index (induced birefringence), \(\mathbf{K}\) is the Kerr coefficient, \(\mathbf{\lambda}\) is the wavelength and \(\mathbf{E}\) stands for the applied electric field. Thus a change in the refractive index occurs when an electric field is applied. This change in the refractive index leads to electro-optic switching/modulation and any related device application. The larger the Kerr coefficient is, the larger the change in the refractive index for any given electric field and optical path length through the sample.  
Since the magnitude of **K** is typically small in these samples (as will be shown in the following), a long, up to about 4 cm, sample was used to obtain detectable electro-optic modulation signal. Such samples are difficult to come by and that is probably part of the reason such measurements have not previously been made or reported. The advantage of making these measurements compared to four-wave mixing or optical Kerr effect with ultrashort optical pulses is that thermal contribution is expected to be minimal in the quadratic electro-optic measurements. This is because the metal nanoparticles in glass are insulators that allow no detectable or only an extremely small electrical current and, thus, lead to minimal thermal effects. Therefore, these measurements may provide evidence of a correlation of nonlinearity with particle size, while such a correlation could be obscured by thermal effects in the other nonlinear optical measurements involving intense laser pulses.