**4. Quantum dots doped glasses**

Intensity-dependent nonlinear optical effects, such as the optical Kerr one, are very significant for all-optical data processing. Glasses with large nonlinear refractive index and nonlinear absorption coefficient are suitable materials for fiber telecommunication and nonlinear optical devices such as ultrafast optical switches and several photonic applications. Since silica and silicate glasses exhibit a small third-order nonlinear susceptibility χ(3), the strategy of combining different materials to obtain composite systems, such as glass doped with semiconductor nanocrystals (quantum dots), allowed to obtain optimized nonlinear optical properties because semiconductors exhibit larger susceptibility. Glasses doped with semiconductors nanocrystals (quantum dots, QDs) such as CdS, CdSe, CdTe, PbS, CuCl, etc., are suitable materials for resonant NLO devices with response times on the ps domain. They can be prepared through the dispersion of a nanocrystalline phase in a glass matrix. This approach, through the reduction of bulk size to nanometric scale or quasi-zero-dimensional quantum dots, allow to change the electronic properties of glasses accordingly with enhanced nonlinearity compared with the corresponding bulk semiconductors [40]. Whenever the absorption of a photon of enough energy (hν is greater than the band gap, Eg) excites an electron from the valence band to the conduction band in semiconducting materials, a free electron–hole pair may be formed. The hole and electron are attracted by Coulombic forces to keep them in a stable orbit as a bound electron–hole pair, called exciton [10]. Due to electrons and holes being confined in a small volume of radius, the radius of the exciton (distance between the electron and hole in an exciton), will change the available energy levels and the interaction with the photons. As the size of nanoparticles becomes progressively smaller, the quantum size effects of excitons confined in all three dimensions give rise to a series of discrete energy levels [10], and therefore the energy associated with them will depend on the relationship between the crystal size (R) and the exciton Bohr radius. Quantum confinement effects are quite significant in the range of *a* ≪R aB, where *a* is the lattice constant of the semiconductors, i.e. when R is similar to Bohr radius of exciton in bulk crystal (aB). In QDs doped glasses these effects give rise to the so-called blue shift of the linear optical absorption edge. The shift regarding to the bulk Eg varies with R as 1/R<sup>2</sup> . Smaller R gives rise to larger blue-shift.

The size of semiconductor particles can be calculated by [41]:

$$
\Delta \mathbf{E}\_{\rm g} = h^2 / 8 \mathsf{R}^2 \left[ \mathbf{1} / m\_e^\* + \mathbf{1} / m\_h^\* \right]
$$

$$
$$

where ΔEg is the shift of the band gap energy (due to the confinement), R is the particle size (radius), *m*<sup>∗</sup> *<sup>e</sup>* and *m*<sup>∗</sup> *<sup>h</sup>* are respectively the reduced effective masses of the electron (*e*) and hole (*h*). It is interesting to note that the second term, related to the kinetic energy of the electron and hole [41] exhibits a 1/R<sup>2</sup> dependence while the third term, the Coulomb interaction between the electron and hole, has a 1/R dependence. Although the kinetic energy of the exciton for nanoparticles of R � aB seems to be predominant, the Coulomb interaction must also be considered [42]. **Figure 9** shown that the shift of the exciton resonances to higher energy (blue shift) is a consequence of the increasing quantum confinement as R decreases [43].

The changes in absorption also lead to refractive index changes, through the Kramers-Kronig transformation:

$$
\Delta n(\alpha) = \frac{c}{\pi} \int\_0^\infty \frac{\Delta a(\alpha')}{\alpha'^2 - \alpha^2} d\alpha' \tag{18}
$$

where *c* is the speed of light and *ω* is the light frequency.

The method allows to correlate the determined change Δα in the absorption coefficient to the change Δn in the refractive index [43]. The nonlinear refractive index is then obtained by n2 = Δn/I (Eq. (8)). The value of χ(3) will be proportional to the reciprocal of the confinement volume and will increase with decreasing R [10]. Is then expected that larger non-linearities are obtained for glasses containing smaller particles and larger volume fractions of QDs [10].
