**5. Metal-doped glasses**

Metal doped glass possesses linear and nonlinear optical properties. Great interest has driven the study of the third-order nonlinear susceptibility of metal particles embedded in dielectric matrices, like glasses [44], which are influenced not only by the type and size of the metal particles but also by the metal-dielectric constant. The most significant effect of the confinement of metal particles in optical properties of nanocomposite glasses is the appearance of the surface plasmon resonance, which

**Figure 9.** *Absorption spectra of CuCI-doped quantum dot glasses: 22 Å (solid); 27 Å (dot); 34 Å (dash) [43].*

deeply enhances the glass χ(3) responses with picosecond temporal responses. For example, the optical absorption spectrum of Ag-doped silica sol–gel glass shows the presence of an absorption band of surface plasmon resonance due to Ag nanoparticles at �420 nm (**Figure 10**).

Plasmons deals with a coherent interaction between the free-electron gas surrounding metal and the incident radiation. The motion of these free electrons can be described by the plasma Drude model, along with a plasma frequency of the bulk metal ωp. In accordance with the Drude free-electron model, the dielectric constant of metal particles is given by [45]:

$$
\epsilon\_m = \epsilon\_m' - i\epsilon\_m'' = \mathbf{1} - \alpha\_P^2 / [\alpha(\boldsymbol{\alpha} - \mathbf{i}/\tau)] \tag{19}
$$

Where τ is the time between collisions among electrons. The real (ε') and imaginary (ε") parts of the complex dielectric constant are expressed as [45]:

$$\boldsymbol{\epsilon}\_{m}^{\prime} = \boldsymbol{n}^{2} - \boldsymbol{k}^{2} = \mathbf{1} - \boldsymbol{\alpha}\_{P}^{2} \boldsymbol{\tau}^{2} / \left[\mathbf{1} + \left(\boldsymbol{\alpha}\boldsymbol{\tau}\right)^{2}\right] \tag{20}$$

$$
\epsilon\_m'' = 2nk = \alpha\_\text{P}^2 \tau / \left\{ \alpha \left[ 1 + \left( \alpha \tau \right)^2 \right] \right\} \tag{21}
$$

From the above equations is possible to infer the existence of an interaction between the free-electron gas and the incident electromagnetic field, which gives rise to an excitation of the electrons at the metal surface, associated with collective oscillations of electrons in the metal nanoparticles, called surface plasmon. The large value of χ(3) of metal-doped glasses arises predominantly from the local electric field enhancement near the surface of the metal nanoparticles (Ag, Cu, Ni, or other metal nanoparticles) due to their surface plasma resonance, leading to a variety of optical effects.

When the diameter (*d*) of metal particles is much lower than the wavelength of light (λ), scattering is negligible. As well, the total collisional impacts of the electrons with the particle surfaces become significant and a new-found relaxation time, τeff, appeared, given by [45]:

$$\mathbf{1}/\tau\_{\rm eff} = \mathbf{1}/\tau\_{\rm b} + \mathbf{2}v\_{\rm F}/d\tag{22}$$

**Figure 11.**

*Transmission electron microscopy micrographs of Au-SiO2 thin films: a) cross section view of a film with Au volume fraction p = 23%, and b) plan view of a film of Au volume fraction* p *= 8% [46].*

where τ<sup>b</sup> is the bulk value and vF is the electron velocity at the Fermi energy. Spherical metal nanoparticles embedded in a glass matrix with a real dielectric constant ε<sup>d</sup> exhibit NLO properties. **Figure 11** exhibits homogeneous size distribution of spherical Au nanoparticles in a SiO2 thin film on a metal substrate [46]. For the conditions.

The equation usually considered to obtain the χ(3) of metal/glass composites, is given by [45]:

*Optical Nonlinearities in Glasses DOI: http://dx.doi.org/10.5772/intechopen.101774*

$$\chi^{(3)} = \mathbf{3}pf^4 \chi^{(3)}\_{m} \tag{23}$$

Where *χ* ð Þ3 *<sup>m</sup>* is the bulk metal third-order susceptibility, *f* is the local electric field near the metal particles and p is the metal volume fraction. The optical response of metal particle/glass composites can be determined by the local field enhancement inside the nanoparticles (dielectric confinement):

$$f = \frac{E}{E\_0} = \frac{3\varepsilon\_d}{\varepsilon\_m + 2\varepsilon\_d} \tag{24}$$

*f* is given by the ratio between the field E inside a metal particle and the applied field E0, with ε<sup>d</sup> the dielectric constant of the glass matrix and ε<sup>m</sup> the one of the metal.

So, if one assumes *χ* ð Þ3 *<sup>m</sup>* independent of particle size, then χ(3) will increase as the volume fraction of metal particles and their size increases [45].
