**2. Chalcogenide glasses and their properties**

The term "chalcogen" – meaning "ore former" (from "*chalcos"* old Greek for "ore") – is a characteristic name that was proposed by Fischer in 1932 to refer to the group of elements O, S, Se, and Te (Fischer, 2001). "Chalcogenides" is used to address chalcogen's compounds with elements such as As (arsenic), Ag (silver), Bi (bismuth), Cu (copper), Cd (cadmium), Fe

Thin Chalcogenide Films for Photonic Applications 145

of the chalcogenide media. Photoinduced darkening or bleaching, expressed by the shift of the absorption edge towards longer or shorter wavelengths, accompanied by increase or decrease of the refractive index and sometimes by contraction or expansion of the films are among the linear effects. The listed phenomena have been of a continuous interest for the scientific groups, dealing with chalcogenides (Barik et al., 2011; Skordeva et al., 2001) and will not be in the focus of the considerations in this section, but further. We will just report here some characteristic values for the photoinduced refractive index change of our materials since, as it will be shown in the next sections, a target parameter in the fabrication of PhC is the high optical contrast, that can be post-tuned by simply exposing the structure to light, accounting namely on the induced modifications in the photosensitive medium.

n/n\*100 [%]

Fig. 2. a) Refractive index (at λ = 1.55 µm) of as-deposited and light irradiated films of AsSe, depending on the thickness and absolute relative (to the as-deposited) refractive index change after exposure of thin films from b) As-Se, c) As-S-Se and d) As-S-Se-Ge systems

As seen from Fig. 2, the photostimulated refractive index changes can reach up to 7 % in the system As-Se (fig. 2b), up to 4 % in the system As-S-Se (fig 2 c) and up to 5.8 % in As-S-Se-Ge system (fig. 2d). The data, presented in fig. 2 is a confirmation of the well-known fact that the sensitivity of As-containing chalcogenide films increases with the addition of arsenic. Though a tendency is observed for enhancing the photosensitivity of the coatings with the increase of the selenium in the As-S-Se system, the refractive index change is poorly influenced by the substitution of Se for sulphur. For the compositions within As-S-Se-Ge system (fig. 2d), obtained by co-evaporation of AsSe and GeS2 - the details of which were published elsewhere (Tasseva et al., 2005) – it can be concluded that films enriched in AsSe undergo higher photoinduced changes. The poorest is the sensitivity of the coatings, containing equal fractions

(n/n)\*100 [%]

24 28 32 36 40 44 48 52 56 60 64

6 d)

0.0 0.2 0.4 0.6 0.8 1.0 <sup>1</sup>

+AsSe)

GeS2 /(GeS2

Composition of As [at.%]

7 b)

0 200 400 600 800 1000 2.3

at = 1,55 m

Thickness of the film [nm]

 As28(S+Se)72 As33(S+Se)67 As40(S+Se)60

0.0 0.2 0.4 0.6 0.8 1.0

Se/(S+Se)

as-deposited

2.7 a) irradiated

2.4

1.5 2.0 2.5 3.0 3.5 4.0 c)

(n/n)\*100 [%]

2.5

Refractive index at = 1.55 m

2.6

(iron), Ga (gallium), Ge (germanium), In (indium), Pb (lead), Na (sodium), Sb (antimony), Si (silicon), Sn (tin), Tl (thallium), Zn (zinc), etc. As suggested by the above variety of elements entering in the formation of the chalcogenide glassy alloys, chalcogenides offer wide range of variation in their properties – e.g., in their index of refraction and optical band gap, as seen in the figure below. It is seen that the refractive index could be freely varied with the composition in 2 – 3.6 range and the optical band-gap from 1.5 to nearly 2.8 eV.

Fig. 1. Compositional variation of the refractive index and optical band-gap of chalcogenide glass thin films. The data depicted is taken from own studies and published elsewhere (Todorov et al., 2001, 2003; Tasseva et al., 2005, 2007, 2010; Kincl et al., 2009; Knotek et al., 2009; Petkov et al. , 2009).

Chalcogenide glasses, as implied by the latter term, are characterized by lack of a long-range order in the arrangement of the structural units within the glassy network, and are consequently in their nature – metastable. That fact is determining for the interesting effects resulting from the light-matter interactions in chalcogenides – electromagnetic radiation leads to modification of their structure and structural bonds. Chalcogens are two-fold coordinated with their atoms being in possession of lone-pair electrons, occupying states at the top of the valence band. Thus, exposure to light is associated with absorption of photons with certain energy, consumed for excitation of these anti-bonding electrons. That results to the formation of structural defects of one- or threefold coordinated chalcogen units (Kastner et al. 1976, Fritzsche, 1998, Liu et al., 2005). Considering all of the above and keeping in mind that the optical band gap for these materials is defined as the difference between the energies corresponding to the top of the valance and those, separating localized from delocalized states in the conductive band, we can interpret the above given values of the optical band gap as energies below which our materials are transparent. That provides transparency in the visible to IR region, where main telecommunication wavelengths are positioned, as well as the characteristic features of the so-called greenhouse gasses (water vapour, carbon dioxide, methane, nitrous oxide, and ozone) and biological molecules are located. That well-known fact can be utilized in fabrication of mid-IR guiding optical fibers for space and underground CO2 storage monitoring (Houizot et al., 2007, Charpentier et al., 2009), optical biosensors (Anne et al., 2009), etc.

To follow the thread started above for the interesting interactions between light and chalcogenides, we should say that these interactions when low- or high-intensity electromagnetic field involved are manifested respectively as a linear or nonlinear response

(iron), Ga (gallium), Ge (germanium), In (indium), Pb (lead), Na (sodium), Sb (antimony), Si (silicon), Sn (tin), Tl (thallium), Zn (zinc), etc. As suggested by the above variety of elements entering in the formation of the chalcogenide glassy alloys, chalcogenides offer wide range of variation in their properties – e.g., in their index of refraction and optical band gap, as seen in the figure below. It is seen that the refractive index could be freely varied with the

Fig. 1. Compositional variation of the refractive index and optical band-gap of chalcogenide glass thin films. The data depicted is taken from own studies and published elsewhere (Todorov et al., 2001, 2003; Tasseva et al., 2005, 2007, 2010; Kincl et al., 2009; Knotek et al.,

Chalcogenide glasses, as implied by the latter term, are characterized by lack of a long-range order in the arrangement of the structural units within the glassy network, and are consequently in their nature – metastable. That fact is determining for the interesting effects resulting from the light-matter interactions in chalcogenides – electromagnetic radiation leads to modification of their structure and structural bonds. Chalcogens are two-fold coordinated with their atoms being in possession of lone-pair electrons, occupying states at the top of the valence band. Thus, exposure to light is associated with absorption of photons with certain energy, consumed for excitation of these anti-bonding electrons. That results to the formation of structural defects of one- or threefold coordinated chalcogen units (Kastner et al. 1976, Fritzsche, 1998, Liu et al., 2005). Considering all of the above and keeping in mind that the optical band gap for these materials is defined as the difference between the energies corresponding to the top of the valance and those, separating localized from delocalized states in the conductive band, we can interpret the above given values of the optical band gap as energies below which our materials are transparent. That provides transparency in the visible to IR region, where main telecommunication wavelengths are positioned, as well as the characteristic features of the so-called greenhouse gasses (water vapour, carbon dioxide, methane, nitrous oxide, and ozone) and biological molecules are located. That well-known fact can be utilized in fabrication of mid-IR guiding optical fibers for space and underground CO2 storage monitoring (Houizot et al., 2007, Charpentier et al.,

To follow the thread started above for the interesting interactions between light and chalcogenides, we should say that these interactions when low- or high-intensity electromagnetic field involved are manifested respectively as a linear or nonlinear response

1,6 1,8 2,0 2,2 2,4 2,6 2,8 3,0

Ge-S-Tl

As-S-Tl

Ge-S

Optical band gap [eV]

As-S-Ge

As-S-Ag

As-S

Ge-S-In Ge-S-Bi

As-S-Se

As-S-Se-Ge

As-Se

As-S-Se-Ag

As-Se-Ag

composition in 2 – 3.6 range and the optical band-gap from 1.5 to nearly 2.8 eV.

2,0 2,2 2,4 2,6 2,8 3,0 3,2 3,4 3,6

Refractive index, n (at = 1.5 m)

2009), optical biosensors (Anne et al., 2009), etc.

As-S-Se-Ag

As-Se-Ag

As-S-Se-Ge

As-S-Ag

As-S-Se As-Se

Ge-S-Tl Ge-S-In Ge-S-Bi As-S-Ge

2009; Petkov et al. , 2009).

As-S-Tl

Ge-S

As-S

of the chalcogenide media. Photoinduced darkening or bleaching, expressed by the shift of the absorption edge towards longer or shorter wavelengths, accompanied by increase or decrease of the refractive index and sometimes by contraction or expansion of the films are among the linear effects. The listed phenomena have been of a continuous interest for the scientific groups, dealing with chalcogenides (Barik et al., 2011; Skordeva et al., 2001) and will not be in the focus of the considerations in this section, but further. We will just report here some characteristic values for the photoinduced refractive index change of our materials since, as it will be shown in the next sections, a target parameter in the fabrication of PhC is the high optical contrast, that can be post-tuned by simply exposing the structure to light, accounting namely on the induced modifications in the photosensitive medium.

Fig. 2. a) Refractive index (at λ = 1.55 µm) of as-deposited and light irradiated films of AsSe, depending on the thickness and absolute relative (to the as-deposited) refractive index change after exposure of thin films from b) As-Se, c) As-S-Se and d) As-S-Se-Ge systems

As seen from Fig. 2, the photostimulated refractive index changes can reach up to 7 % in the system As-Se (fig. 2b), up to 4 % in the system As-S-Se (fig 2 c) and up to 5.8 % in As-S-Se-Ge system (fig. 2d). The data, presented in fig. 2 is a confirmation of the well-known fact that the sensitivity of As-containing chalcogenide films increases with the addition of arsenic. Though a tendency is observed for enhancing the photosensitivity of the coatings with the increase of the selenium in the As-S-Se system, the refractive index change is poorly influenced by the substitution of Se for sulphur. For the compositions within As-S-Se-Ge system (fig. 2d), obtained by co-evaporation of AsSe and GeS2 - the details of which were published elsewhere (Tasseva et al., 2005) – it can be concluded that films enriched in AsSe undergo higher photoinduced changes. The poorest is the sensitivity of the coatings, containing equal fractions

Thin Chalcogenide Films for Photonic Applications 147

where Ep = 21 eV, K is found to be 3.1 x 10-8 in units such that Ep and Egopt are measured in

3 3 26 3 2(1 2 ) (1 2 ) 4 4 ( ) <sup>64</sup>

2[ ] [] <sup>40</sup> *cn n esu SI* 

Originally developed for crystalline materials, Eq. 2 was shown to be applicable as a rough approximation as well for glasses (Tanaka, 2007), providing with a possibility for calculation of the dispersion of the nonlinear refractive index. In the same approximation, the two photon absorption, β, defined by α = α0 + βI (where α0 is the linear absorption coefficient of

> <sup>2</sup> <sup>2</sup> <sup>3</sup> (2 / ) *<sup>p</sup> opt g opt*

> > 3/2

*x*

and F2(2x) = 0 otherwise. That means that two photon absorption may occur for photon energies higher than at least half of the optical band-gap. It was shown (Mizrahi, 1989) that high values of β, that are likely to accompany the high values of the nonlinear refractive index, γ, would impose strong limitations upon the applicability of any third order nonlinear material. Qualitatively, that limitation would be expressed through a simple criterion set upon the so called figure-of-merit (FOM). For the effective operation of a given

> <sup>2</sup> *FOM* <sup>1</sup>

The above criterion implies that when optimizing chalcogenide compositions in order to enhance devices performance, we should carefully consider the trade-off between high nonlinearity and low optical losses due to two photon absorption. Following below, the results are depicted from the calculations of two photon absorption, nonlinear refractive

Chalcogenides, as suggested in table 1, offer a nonlinear refractive index up 700 times higher than that of fused silica, simultaneously detaining low two photon absorption, i.e. FOM. It is seen that small additions of silver (the thickness of the silver layer used for the process of photodiffusion, as reported elsewhere (Tasseva et al., 2010), was 25 nm) increase 3 times γ

*g*

*n E*

2 5 (2 1) (2 ) <sup>2</sup> *<sup>x</sup> F x*

*E K FE*

2 6

is measured in m2/W, ħ is the Dirac's constant, c the speed of light in vacuum and

2 3 4 5 3/2

*x*

*xxx x x x x*

(3)

(5)

for 2х > 1 (6)

(7)

(4)

are related by:

eV, and 

where

*G2* - a universal function:

*G x*

the medium), can be expressed:

where is the Heaviside step function. *n2* and

nonlinear device, the inequality should be observed:

index and FOM for thin films from As2S3, As2Se3 and GeS2 (Fig. 3).

AsSe and GeS2 (50 %). The lower sensitivity of the GeS2 films in respect to the AsSe ones and in general to the bi-component As-containing films is justified by the fact that the tetrahedral structural units forming the amorphous network of the Ge-containing glasses are with a greater volume and therefore are hardly reoriented in comparison with the structural units of As-containing glasses (Raptis et al., 1997). The microhardness measurements, presented in our previous work (Tasseva et al., 2005) come also to support that suggestion. At this point it should be emphasized the result from our investigation that the refractive index value is not affected by the thickness of the film in the range 80 – 1000 nm (fig. 2a). The deviation from the plateau observed for the film of 40 nm thickness is possibly attributed to voids due to the sooner interruption of the deposition process, depriving the initial formations of the possibility to grow as an integral coating. The possibility to produce films with invariable refractive index still varying their thickness has a special importance for the fabrication of multilayered structures, as would be seen in the next sections.

Further, the discussed possibilities to modify the refractive index either by exposing the coatings to light or simply changing their composition within a chalcogenide system are utilizable in the production of focusing elements – microlenses or diffraction gratings (Wágner & Ewen, 2000; Saithoh et. al., 2002; Kovalskiy et al., 2006; Eisenberg et al., 2005; Teteris & Reinfelde, 2004; Arsh et. al. 2004; Freeman et. al. 2005; Beev et. al. 2007; Vlaeva et. al. 2011). The phenomenon of total internal reflection staying at the basis of applications such as optical fibers or planar waveguides (Su et. al. 2008; Liao et. al. 2009; Conseil et. al. 2011; Savović & Djordjevich, 2011, Ung & Skorobogatiy 2011, Rowlands et. al. 2010, Ganjoo et al. 2006; Riley et al. 2008), could also benefit from the opportunity of retaining interface losses low when creating refractive index profile in compatible materials.

Let us now consider the non-linear response of the chalcogenide medium to intense light with photon energies lower than the optical band-gap. We know that two-photon absorption will be involved in the interband transitions in that case (Boyd, 2003). One of the associated effects is the induction of a non-linear refractive index, *n2 [esu]* or  *[m2/W]* that gives the rate at which the intensity dependent refractive index *n*' changes with increasing light intensity, *I*:

$$m' = n + \mathcal{N} = n \quad + \frac{n\_2}{2} \|E\|^2 \tag{1}$$

where *n* is the linear, weak-field refractive index, *I* - the intensity and E denotes the strength of the applied optical field. A detailed discussion on the origin of the nonlinear response in chalcogenides is published in (Bureau et al., 2004, Zakery & Elliott, 2007, etc). The electron shells of the chalcogens are such that favor the induction of polarization under strong electromagnetic field that is, in general, directly associated with the nonlinearity (Boyd, 2003). It is discussed in (Bureau et al., 2004) that the coordination of the chalcogen atoms is always pseudo-tetrahedral, consisting of two bonding and two anti-bonding electron pairs. One consequence of the presence of the unpaired electrons is that they occupy levels in the energy diagram, located between the bonding and non-bonding levels, significantly lowering in that way the optical band gap. The latter strongly influences the non-linear refractive index, according to the formula developed by Sheik-Bahae et al. (1990):

$$\gamma = K \frac{\hbar c \sqrt{E\_p}}{2n^2 E\_\mathcal{g}^{opt4}} G\_2(\hbar \alpha / E\_\mathcal{g}^{opt}) \tag{2}$$

where Ep = 21 eV, K is found to be 3.1 x 10-8 in units such that Ep and Egopt are measured in eV, and is measured in m2/W, ħ is the Dirac's constant, c the speed of light in vacuum and *G2* - a universal function:

$$G\_{2}(\mathbf{x}) = \frac{-2 + 6\mathbf{x} - 3\mathbf{x}^{2} - \mathbf{x}^{3} - \frac{3}{4}\mathbf{x}^{4} - \frac{3}{4}\mathbf{x}^{5} + 2(1 - 2\mathbf{x})^{3/2}\Theta(1 - 2\mathbf{x})}{64\mathbf{x}^{6}}\tag{3}$$

where is the Heaviside step function. *n2* and are related by:

$$m\_2[esu] = \frac{cn}{40\pi}\gamma[SI] \tag{4}$$

Originally developed for crystalline materials, Eq. 2 was shown to be applicable as a rough approximation as well for glasses (Tanaka, 2007), providing with a possibility for calculation of the dispersion of the nonlinear refractive index. In the same approximation, the two photon absorption, β, defined by α = α0 + βI (where α0 is the linear absorption coefficient of the medium), can be expressed:

$$\beta = K \frac{\sqrt{E\_p}}{n^2 E\_g^{\text{opt3}}} F\_2(2\hbar \text{co} / E\_g^{\text{opt}}) \tag{5}$$

where

146 Photonic Crystals – Innovative Systems, Lasers and Waveguides

AsSe and GeS2 (50 %). The lower sensitivity of the GeS2 films in respect to the AsSe ones and in general to the bi-component As-containing films is justified by the fact that the tetrahedral structural units forming the amorphous network of the Ge-containing glasses are with a greater volume and therefore are hardly reoriented in comparison with the structural units of As-containing glasses (Raptis et al., 1997). The microhardness measurements, presented in our previous work (Tasseva et al., 2005) come also to support that suggestion. At this point it should be emphasized the result from our investigation that the refractive index value is not affected by the thickness of the film in the range 80 – 1000 nm (fig. 2a). The deviation from the plateau observed for the film of 40 nm thickness is possibly attributed to voids due to the sooner interruption of the deposition process, depriving the initial formations of the possibility to grow as an integral coating. The possibility to produce films with invariable refractive index still varying their thickness has a special importance for the fabrication of multilayered

Further, the discussed possibilities to modify the refractive index either by exposing the coatings to light or simply changing their composition within a chalcogenide system are utilizable in the production of focusing elements – microlenses or diffraction gratings (Wágner & Ewen, 2000; Saithoh et. al., 2002; Kovalskiy et al., 2006; Eisenberg et al., 2005; Teteris & Reinfelde, 2004; Arsh et. al. 2004; Freeman et. al. 2005; Beev et. al. 2007; Vlaeva et. al. 2011). The phenomenon of total internal reflection staying at the basis of applications such as optical fibers or planar waveguides (Su et. al. 2008; Liao et. al. 2009; Conseil et. al. 2011; Savović & Djordjevich, 2011, Ung & Skorobogatiy 2011, Rowlands et. al. 2010, Ganjoo et al. 2006; Riley et al. 2008), could also benefit from the opportunity of retaining interface

Let us now consider the non-linear response of the chalcogenide medium to intense light with photon energies lower than the optical band-gap. We know that two-photon absorption will be involved in the interband transitions in that case (Boyd, 2003). One of the associated effects

<sup>2</sup> <sup>2</sup> <sup>|</sup> <sup>|</sup> <sup>2</sup>

where *n* is the linear, weak-field refractive index, *I* - the intensity and E denotes the strength of the applied optical field. A detailed discussion on the origin of the nonlinear response in chalcogenides is published in (Bureau et al., 2004, Zakery & Elliott, 2007, etc). The electron shells of the chalcogens are such that favor the induction of polarization under strong electromagnetic field that is, in general, directly associated with the nonlinearity (Boyd, 2003). It is discussed in (Bureau et al., 2004) that the coordination of the chalcogen atoms is always pseudo-tetrahedral, consisting of two bonding and two anti-bonding electron pairs. One consequence of the presence of the unpaired electrons is that they occupy levels in the energy diagram, located between the bonding and non-bonding levels, significantly lowering in that way the optical band gap. The latter strongly influences the non-linear

*<sup>E</sup> <sup>n</sup>*

 *[m2/W]* that gives the rate at which

*I n* (1)

(2)

losses low when creating refractive index profile in compatible materials.

'

*n n* 

the intensity dependent refractive index *n*' changes with increasing light intensity, *I*:

refractive index, according to the formula developed by Sheik-Bahae et al. (1990):

*g*

*c E K GE*

*n E* 

<sup>2</sup> <sup>2</sup> <sup>4</sup> (/ ) <sup>2</sup> *p opt g opt*

is the induction of a non-linear refractive index, *n2 [esu]* or

structures, as would be seen in the next sections.

$$F\_2(2\mathbf{x}) = \frac{\left(2\mathbf{x} - \mathbf{1}\right)^{3/2}}{2\mathbf{x}^5} \text{ for } 2\mathbf{x} \ge \mathbf{1} \tag{6}$$

and F2(2x) = 0 otherwise. That means that two photon absorption may occur for photon energies higher than at least half of the optical band-gap. It was shown (Mizrahi, 1989) that high values of β, that are likely to accompany the high values of the nonlinear refractive index, γ, would impose strong limitations upon the applicability of any third order nonlinear material. Qualitatively, that limitation would be expressed through a simple criterion set upon the so called figure-of-merit (FOM). For the effective operation of a given nonlinear device, the inequality should be observed:

$$FOM = \frac{\mathfrak{D}\mathfrak{R}}{\mathfrak{Y}} < 1\tag{7}$$

The above criterion implies that when optimizing chalcogenide compositions in order to enhance devices performance, we should carefully consider the trade-off between high nonlinearity and low optical losses due to two photon absorption. Following below, the results are depicted from the calculations of two photon absorption, nonlinear refractive index and FOM for thin films from As2S3, As2Se3 and GeS2 (Fig. 3).

Chalcogenides, as suggested in table 1, offer a nonlinear refractive index up 700 times higher than that of fused silica, simultaneously detaining low two photon absorption, i.e. FOM. It is seen that small additions of silver (the thickness of the silver layer used for the process of photodiffusion, as reported elsewhere (Tasseva et al., 2010), was 25 nm) increase 3 times γ

Thin Chalcogenide Films for Photonic Applications 149

Photonic crystals are artificial structures usually comprising two media with different dielectric permittivity arranged in periodic manner with periodicity of the order of wavelength for the visible spectral range. Generally photonic crystals are divided into one-, two- or three dimensional PhC referred to as 1D, 2D and 3D PhC, depending on the

Photonic crystals occur in nature. Spectacular examples can be found in the natural opal, multilayered structures of pearls, flashing wings of some insects etc. A close inspection with an electron microscope shows that many species of butterflies and beetles have photonic crystal structures in some part of their bodies, resulting in a variety of optical effects such as

Although photonic crystals have been studied in one form or another since 1887, the term "photonic crystal" appeared about 100 years later, after Eli Yablonovitch and Sajeev John published two papers on photonic crystals (see Yablonovitch, 1987, John, 1987). It is very important to note that the periodicity is not a sufficient condition for a certain structure to be called photonic crystal. There is another requirement, namely the optical contrast, i.e. the difference between dielectric permittivity of the two constituent media, to be high enough

One of the most striking features of photonic crystals is associated with the fact that if suitably engineered, they may exhibit a range of wavelengths over which the propagation of light is forbidden for all directions. The band of forbidden wavelengths is commonly referred to as "photonic band gap-PBG" and as "complete (or 3D) photonic band gap" if it is realized for all light propagation directions. These photonic bands enable various

As mentioned above, the concept of 3D PBG materials was independently introduced by Yablonovitch (1987) and John (1987). Extensive numerical calculations conducted few years later (Ho et al. 1990) shown that 3D structures with a certain symmetry do indeed exhibit complete PBG. The "ideal" photonic crystal, defined as the one that could manipulate light most efficiently, would have the same crystal structure as the lattice of the carbon atoms in diamond. It is clear that diamonds cannot be used as photonic crystals because their atoms are packed too tightly together to manipulate visible light. However, a diamond-like structure made from appropriate material with suitable lattice constant would create a large "photonic bandgap". The first 3D photonic crystal was fabricated in 1991 in the group of Eli Yablonovitch (Yablonovitch et al., 1991) and is called Yablonovite. It had a complete photonic band gap in the microwave range. The structure of Yablonovite had cylindrical holes arranged in a diamond lattice. It is fabricated by drilling holes in high refractive index

Two-dimensional structures with a complete photonic band gap are neither known, nor likely to occur. Nevertheless, there is a growing scientific interest in 2D structures. The scientific efforts are focused on introduction of functional defects in 2D structures in order to

**3.1 Short description of theory of photonic crystals** 

applications of PhC in linear, non-linear and quantum optics.

realize waveguide structures (Brau et al., 2006).

dimensionality of the periodicity.

structural colours, for example.

(Yablonovitch, 2007).

material.

**3. Theory** 

still keeping low values of the two photon absorption. The values of the non-linear refractive index predicted for thin As-S-Se films are commensurable with those measured for bulk samples (Cardinal et al., 1999). The ultrafast response, i.e. the induction of nonlinear refractive index in chalcogenides exposed to the influence of strong electromagnetic field could be explained in the terms of the electronic structure of the glasses, considering ionization of the atom and distortion of the electron orbits (Liu et al., 2005).

Fig. 3. Dispersion of the a) nonlinear refractive index, b) two photon absorption and c) FOM of thin chalcogenide films, calculated from eqs (2), (5) and (7)


Table 1. Nonlinear refractive index values, and FOM for low-loss thin chalcogenide films of various compositions at λ = 1.55 µm

In the process of selection of chalcogenide compositions for optimized photonic applications, as discussed in the lines above, one should be careful in tailoring the properties of the materials. It should be taken account for transparency of the films in the designation spectral region, high nonlinearities and low nonlinear absorption, high photosensitivity.
