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

short-range order. Therefore, glasses are typically brittle and optically transparent because they lack internal structure. The silica-based glass was undoubtedly the most studied given its multiple applications. Glasses that do not include silica as a main constituent exhibit other properties that make them useful for various applications, for example in optical fibers that work in different frequency domains than SiO2 fibers. These include fluoride glasses, tellurite glasses, aluminosilicates, phosphate glasses, borate glasses, and chalcogenide glasses. Common glasses are transparent materials in the spectral range of the visible and near-infrared region, although opaque in the far IR and UV region. The visible transparency threshold ends, for high wavelengths (λ), with UV absorption, due to electronic transitions between valence band levels and unfilled conduction band levels. For applications in photonics, there are two main categories of special glasses: chalcogenide glasses (CGs) and heavy metal oxide glasses. Chalcogenide glasses are based on the chalcogen elements S, Se, and Te. These glasses are formed by the addition of other elements such as Ge, As, Sb, Ga, etc. Heavy metal oxide and chalcogenide glasses offer the largest nonlinear response.

Most of the glasses are prepared by the melt of precursors. In solid form, glass is a non-crystalline (or amorphous) material. The deposition from a liquid solution (sol–gel method) is an alternative approach to obtain glass, especially in films form. Some compositions may otherwise be rather difficult to prepare by melt and that's why in practice this method is limited to a relatively small number of compositions. Therefore, the sol–gel processes allow the synthesis of glasses of extended composition ranges, allowing the fabrication of multiple oxide composition, but also nonoxide glasses, with a high degree of homogeneity, because reagents are mixed at the molecular level at temperatures lower than those required for conventional melting. However, the OH content of the sol–gel glasses is high and OH absorptions usually limit transmission at 1.4 μm.

Optical glasses are optically homogeneous glass that are applied in several optical functionalities. The first optical quality (flint) glasses were created at the end of the 19 century by Otto Schott, who also invented Ba crown glass, allowing the production of adjusted lenses for chromatic aberration [21]. X-ray diffraction (XRD) allows distinguishing a glass from a crystalline material. The pattern of SiO2 glass contains only a few, very broad peaks, which cannot be correlated by the Bragg law with planar distances (as in the case of crystals). SiO2 consists of a matrix of SiO4 tetrahedra (**Figure 5**) [22].

The presence of a glass modifier together with the glass formers (SiO2 or P2O5) breaks up the oxide network M–O–M (M = Si, P) and drives the transformation of the bridging oxygens (BO) into nonbridging oxygens (NBOs). The structural unit of SiO2 has Si-O atomic bonds whose electronic transitions occur in the UV range. For high λ, the transparency threshold ends due to the vibrations of the ions in the network (in resonance with the incident radiation). The amorphous character of the glass explains the absence of grain boundaries in its structure and, therefore, the absence of internal dispersion and reflection phenomena, which are always present in crystalline materials. Glasses are dielectric materials and therefore exhibit a large energy gap between the valence band and the conduction band in accordance with the band theory of solids. Their optical transmission is limited by electronic transitions (Urbach tail) for low wavelength, and multiphonon absorption at high wavelength, in the IR spectrum. The multiphonon absorption process is related to the fundamental vibration frequencies of the glass.

The transmittance spectrum varies from glass to glass, but the main differences are observed outside the transparency range (**Figure 6**). The glass has an optical transparent window which strongly depends on the compositions. Glasses made for use in the visible region have high transmittance across the entire wavelength range

#### **Figure 5.**

*A schematic representation of the structure of vitreous silica. The tetrahedral SiO4 units in silica are represented by triangular units [22].*

of 400 nm–800 nm. However, the structure of silicate glasses limits its transmission in the infrared region to above 3 μm. They have strongly bound electrons but non-bridging oxygens, with their weakly bound electrons, reduce transmission. Chalcogenide glasses, heavy metal fluoride glasses, and heavy metal oxide glasses extend this transmission to higher wavelengths. The telluride glasses have larger atoms and weaker bonds than oxide glasses and so its vibrational resonance occurs at a lower frequency, shifting the fundamental absorption cut-off to longer wavelengths (**Figure 6**).

The interest in chalcogenide glasses backs from 1950s when was reported high infrared transparency of the As2S glass, up to 12 μm [24]. The structure of chalcogenide glasses such as Ge-Sb-Se consists of covalently bonded atoms, like amorphous SiO2, with lacking periodicity. They include sulfide, selenide, and telluridebased glasses. As dielectric materials, their optical transparent window is dependent on electronic absorption at low wavelengths and multiphonon absorption at high

wavelengths. They have a band gap (Eg) that is dependent on the composition and decreases according to Sulfides < Selenides < Tellurides. A specificity of tellurides that differentiates it from the sulfides and selenides in its crystalline structure and physical properties is the large atomic number of Te. The energy gap may be taken from the glass absorption spectrum α(*ħ*ω) by extrapolating the linearized Tauc equation:

$$
\hbar \alpha \hbar \alpha \propto \left(\hbar \alpha - \mathbf{E}\_{\text{g}}\right)^{1/2} \tag{16}
$$

The absorption coefficient, α, varies exponentially with the photon energy, *ħ*ω in the Urbach tail.

It is interesting to note that *n* and *n*<sup>2</sup> and are usually directly correlated, such that low index (*n*) glasses, like certain fluorides and phosphates, have also low *n*2. On the other hand, a relationship between the material band gap and the *n*<sup>2</sup> was also established. For example, the *n*<sup>2</sup> value obtained for pure As2S3 was about 2.9 x 10<sup>18</sup> m<sup>2</sup> /W while for fused SiO2 was about 2.8 x 10<sup>19</sup> m<sup>2</sup> /W [25], which is comparatively about 10 times lower. So, materials with lower band gap seam to exhibit an increase in the nonlinear optical behavior; SiO2 has a gap of about 9 eV while that of As2S3 is 2.3 eV [19].

The increase of the nonlinear absorption coefficient (β), third-order nonlinear optical susceptibility (χ(3)), and nonlinear refractive index (n2) and decreasing the optical band gap (Eg) can be attributed to the formation of BO bonds and ions of higher polarizability in the glass matrix. It has been recognized the effect of the glass composition on the dependency of χ(3). In most multicomponent oxide glasses, there are both BO and NBO oxygens in the glass network (e.g. for a silicate glass, Si-O<sup>+</sup> Na). The NBO bonds possess larger n2 than the BO of the more covalent Si-O-Si bonds [26]. It was also established that third-order nonlinear optical susceptibility of the glasses increases with increasing optical basicity and tendency for metallization of the glasses. This fact is associated with the polarizability of the anions (F < O<sup>2</sup> < S<sup>2</sup> < Se<sup>2</sup>) and the small optical band gap [19], which is related to the increasing metallicity of the oxides [27]. The theory of metallization of the condensed matter says that in the Lorentz–Lorenz equation, the refractive index becomes infinite when metallization of covalent solid materials occurs [27]. SiO2, B2O3, and GeO2 based glasses exhibit low refractive index and have low polarizability, large metallization tendency, and small χ(3). Tellurite and TiO2 based glasses, as well as B2O3 glasses containing a large amount of Sb2O3 and Bi2O3 with high refractive index, show large polarizability, small metallization tendency, and large χ(3) (**Figure 7**). Consequently, under the point of view of polarizability, highrefractive-index glasses with an increased tendency for metallization are promising materials for application as components of nonlinear optical devices.

Glass materials are excellent non-linear optical materials, being isotropic and transparent in a wide spectral range, combining low cost of fabrication with high optical quality, manufacturable not only as bulk shapes, or fibers, but also as thin films (e.g. nonlinear planar waveguides). Furthermore, when compared to polymers, glass is more stable and has the advantage over crystals since its atomic composition is easily tailored: a nonlinear optical glass can be obtained with any refractive index in a wide range [28]. Its properties can be adjusted through doping and compositional changes to fit the specified requests of each application. Its disordered structure allows light propagation inside that medium like no other material. They also exhibit good compatibility with silica-based systems and waveguide production in which high optical intensities and long interaction lengths can be achieved [28], giving rise to nonlinear structures in integrated optical devices [29].

#### **Figure 7.**

*Line-up of the Kerr effect among various glass compositions [19].*

For the fabrication of all-optical systems in information technology and integrated photonics, the chosen materials should exhibit high nonlinearities. Rather, low nonlinearities are essential for fibers in optical communications to avoid phenomena of self-focusing, self-phase modulation, Raman and Brillouin scatterings. NLO was considered the threshold to the total of information that can be transmitted in a single optical fiber. As laser power levels increase, NLO limits data rates, transmission lengths, and the number of wavelengths that can be transmitted simultaneously. Optical nonlinearities give rise to many "secondary" effects in optical fibers. These effects can be damaging in optical communications, but they find other applications, especially for the integration of all-optical functionalities in optical networks. The optical nonlinearities can give rise to gain or amplification, the conversion between wavelengths, the generation of new wavelengths or frequencies, the control of the temporal and spectral shape of pulses, and switching [6]. Thus, they can be distinguished in two types: that from scattering (stimulated Brillouin and stimulated Raman) and that from optically induced changes in the refractive index, resulting either in phase modulation or in the mixing of several waves and the generation of new frequencies (modulation instability and parametric processes, such as four-wave mixing). So, the nonlinear refractive index, also referred optical Kerr nonlinearity (n2), offers a means to achieve switching and amplifying functions in photonic devices and produces nonlinear effects, namely self-phase modulation, and four-wave mixing. Self-phase modulation implies changes in the phase and rising frequency of a pulse, which can cause spectral broadening. Four-wave mixing is a kind of nonlinear frequency conversion generated by the Kerr nonlinearity which enables, for example, high-speed communications, frequency conversion, sensing, and quantum photonics. The effect of ultrafast response time (10 s<sup>15</sup> s) provides broad bandwidths, that can pull actual GHz electronic computing forward to PHz (1015) rates using all-optical signal processing [30]. In addition, spectral broadening, produced by changes in phase from the nonlinear refractive index, can enable the production of short-pulsed sources [30]. Four-wave mixing, on the other hand, can be used to generate optical frequency combs [30], which can measure precise frequencies of light and span spectral ranges useful for spectroscopic investigations.

Although these applications are of great practical interest, the Kerr effect (n2) is often small for common optical glasses (<sup>10</sup><sup>20</sup> to 10<sup>19</sup> <sup>m</sup><sup>2</sup> /W) [30], leading to high thresholds for nonlinear effects and requiring special sources of high-power excitation.

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

Transparent optical glasses exhibiting nonlinearities, e. g. large nonlinear refractive index and nonlinear absorption coefficient are good candidates for fiber telecommunication and for nonlinear optical devices such as optical switches, selffocusing, and white-light continuum generation. Glasses that exhibit significant nonlinearity are good candidates as Raman gains media to provide enhanced Raman gain over an extended wavelength range. Chalcogenide (As–Se) glasses and fibers are examples of good candidates as well tellurite fibers because of the high refractive index of TeO2 (2.3–2.4) [6] compared to the SiO2 (1.46). An As2S3 fiber exhibit a Raman coefficient is 300 times greater than that of silica fiber [6]. However, chalcogenide fibers have lesser chemical stability. In spite of that, chalcogenide glass has wide transparency transmission from 0.5 to 25 μm [31], enhancing their potential applications on the mid-IR. As shown in **Figure 8**, the long-wavelength cut-off edges of chalcogenide glasses depend on the mass of anionic elements and are extended between 12 and 20 μm. Their nonlinearity (Kerr effect) is 200–1000 times larger than that of the silica glass at a wavelength of 1.55 μm [32].

The nonlinear optical properties of glasses have been considered of great interest for photonic devices to be used in several technological applications with a broad spectrum of phenomena, such as optical frequency conversion, optical solitons, phase conjugation, and Raman dispersion. Most of the previous investigations were devoted to crystalline materials such as Quartz, LiNbO3, KTiOPO4, and α-BaB2O4 [19]. Nevertheless, recently the development of special glass compositions exhibiting NLO properties have extended the research into practical applications of glass transparent materials for a wide range of effects, such as fast intensitydependent index, third-harmonic generation (THG), stimulated emission (or stimulated Raman scattering), second harmonic generation (SHG) and the multiphoton absorption [29]. Nonlinear phenomena in glasses, such as nonlinear refractive index, multiphoton absorption, and Raman and Brillouin scattering, depend on the glass itself, its nature (composition and structure), which is responsible for the nonlinearity. On the other hand, in glasses doped with RE ions or semiconductor nanoparticles, in which the glass assumes the role of host, the nonlinearity is produced by interactions between dopant ions, domains, and different phases (such as in glass-ceramics).

The first nonlinear effect in history is often associated with the beginning of the NLO [33], had occurred in 1875, when J. Kerr observed changes in the refractive index of a liquid (CS2) in the presence of an electric field. The Kerr effect or quadratic electro-optic effect is directly related to the third-order nonlinearity, χ(3). Pockels, 20 years later, observed another phenomena, the linear electro-optic effect [34], through the modification of the index of refraction of light in a

**Figure 8.** *Typical infrared (IR) transmission spectra of S-, Se-, and Te-based chalcogenide (ChG) glass [32].*

non-centrosymmetric crystal (Quartz) placed by an electric field. For a long time thereafter, these phenomena were little studied and found of non-practical applications. However, the decisive prerequisite for work out such effects demands high laser pump intensities and suitable phase-matching conditions. Significant effects of NLO (e.g., frequency conversion by taking advantage of second and third harmonic generation) only began to be observed experimentally in the early 60s, after laser invention, due to the fact that such NLO effects require high electromagnetic field intensities to manifest, which was only possible using high-power lasers. P. Franken reported the first observation of the SHG in 1961 after focusing a pulsed ruby laser (λ = 694 nm) into a Quartz crystal; the red incident beam generated an emitted blue light (λ = 347 nm) [35]. THG was soon experimentally reported in 1965 [36]. Since the late of the 80s the interest in NLO properties in glass began to increase [19]. As already mentioned, the nonlinear optical response of glasses is closely related to their anionic polarizability [29, 37] which is described as the deformation of electron clouds (dipoles) when the electromagnetic field is applied. The selection of suitable glass structure and composition can contribute to efficiently optical Kerr effect, self-focusing, intensity-dependent refractive index, and other χ(3) -related effects. In the literature, several reports have shown that the Kerr effect of non-conventional glass compositions is a viable option for self-phase modulation and broadband light generation in the near-infrared [29]. The χ(3) in resonant mode is an additional possibility. Due to the bandwidth requirements for transmitting information for both long-haul and local area networks, Raman amplification is considered a good option to face out the recent developments in the telecommunications fiber industry and diode laser technology. Compared, for instance, with Er3+-doped silica fiber amplifiers, in which the wavelength is fixed at 1550 nm, Raman gain bandwidths are larger, and the operational range only varies with the pump wavelength and the bandwidth of the Raman active medium (the glass nature) [29]. It is well known that the Kerr effect and Raman gain follow the polarity of the glass medium and are deeply impacted by the structure of some specific glasses, such as TeO2 glass, which have large electronic polarizability. Additionality the small length of Te–O bond (2.01 Å) [37, 38] is considered responsible for the large third-order nonlinear optical susceptibility of these kinds of glass [38]. It <sup>χ</sup>(3) value was as high as 1.4 <sup>10</sup><sup>12</sup> esu about 50 times as large as that of SiO2 glass [38].

The field of nonlinear optics of glasses has been mainly focused on two main groups: resonant and non-resonant [28]. Non-resonant interactions occur when the light excitation falls in the transparent wavelengths range of the glass longer than its electronic absorption edge. As no electronic transitions take place, the process can be seen as lossless and so an ultrafast glass response due to third-order electronic polarization is assured. Examples are, in general, high refractive index and high dispersion glasses like heavy flint optical glasses, or heavy metal oxide glasses, or chalcogenide glasses.

The resonant ones include semiconductor (quantum dots), or metallic nanoparticles doped glasses [10, 28] and the interaction occurs when the optical field's frequencies are near the electronic absorption edge so that its high resonant nonlinearity can be exploited. However, the isotropic structure glass and its amorphous state have inversion symmetry and do not exhibit second-order nonlinearity, χ(2), or Pockels effect which is necessary for applications such as electro-optic switching and modulation or wavelength conversion in photonic technology. Indeed, glass is a good example of optically isotropic material (as well cubic crystals) that does not exhibit (in principle) any behavior that arises from that condition (e.g. optical birefringence). However, this is not always the case because secondorder nonlinearity can be achieved in glass upon appropriate modification. For
