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

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 dimensionality of the periodicity.

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 structural colours, for example.

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 (Yablonovitch, 2007).

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

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 material.

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

Thin Chalcogenide Films for Photonic Applications 151

in Eqs 9 and 10 that for high reflectance the stack should be terminated with high refractive

Transmittance and reflectance of the stack are finally obtained from the respective matrix

The short and the long wavelength edges of the band are function of *nH*, *nL* and the angle of incidence *θ.* They are calculated according to (Kim et. al, 2002) and are presented in Fig. 4a. Fig. 4 b,c and d presents the reflectance of the stack for p and s-polarized light incident at angles of 0, 45o and 85o as a function of the wavelength calculated from Eqs 12 and 13. It is seen that for higher incident angles the band shifts towards smaller wavelengths becoming wider for s-polarization and narrower for p-polarization. The shaded area in fig. 4 indicates the omnidirectional reflectance (ODR) band that is the spectral area of high reflectance for all incident angles and polarization types. It is seen that ODR band opens between short wavelength edge for 0o and long wavelength edge for p-polarization at

0 10 20 30 40 50 60 70 80 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100

00

**(b)**

Fig. 4. a) Reflection band edges for both polarizations as a function of incident angle;

Reflectance of the stack as a function of wavelength for incident angles of b) 0°, c) 45° and d)

The short and long wavelength edges of ODR band can also be expressed explicitly as (Kim

1

 

*ODR <sup>H</sup> <sup>L</sup> short <sup>n</sup> <sup>n</sup> <sup>n</sup> <sup>n</sup>* cos

2

  2

2

1 cos ( , )

> 1 1 2 1 ( , ) ( , )

*<sup>Q</sup> <sup>R</sup>* and

*p*-pol s-pol

*P*

*P <sup>P</sup> <sup>P</sup> <sup>Q</sup>* *ns*

2

*<sup>Q</sup> <sup>R</sup>* (13)

**(c) (d)**

**c**

850

(14)

*Rs*

*Rs*

*R* [%] *R* [%]

1

 

 

*H L*

*R* [%]

 *Rp Rp*

450

(12)

1 cos ( , )

*s*

<sup>0</sup> <sup>0</sup> 1 1

2

1 1 2 1 ( , ) ( , )

*S S <sup>S</sup> Q*

cos

*<sup>n</sup> <sup>T</sup>*

*s s <sup>S</sup> n Q*

*<sup>s</sup>* <sup>0</sup> sin <sup>0</sup> sin . Note

where the angle *θs* is associated with *θ*0 by the Snell-Decarte's law *n*

<sup>0</sup> <sup>0</sup> 1 1

and

cos

*<sup>n</sup> <sup>T</sup>*

angle of incidence [deg]

85°. The shaded area represents the ODR band.

**(a)**

*s s <sup>P</sup> n Q*

index layer.

elements *Q*(*i*,*j*):

incident angle of 90o.

1000

et. al., 2002):

1200

1400

[nm]

1600

1800

2000

The widely accepted concept for a one-dimensional photonic crystal is a quarter-wave stack of alternating low- and high-refractive index layers (Joanopoulus et al., 1997). For a wave propagating normally to the stack (zero angle of incidence), a one-dimensional photonic band gap exists that is shifted towards smaller wavelengths with increasing the incident angle. Considering all possible angles and polarizations, one can mistakenly conclude that a 1D structure has no three-dimensional photonic band gap. Fortunately, it has been shown that if the optical contrast (the difference in dielectric permittivity between stack constituents) and number of the layers are sufficiently high, an omnidirectional (OD) reflectance band could be open (reflectance of the stack is close to unity for all incident directions and polarization of light) (Fink et al., 1998). As it will be shown in the next section, there are special requirements for low and high refractive index values of the two media of the stack.

Here we will give some details of calculation of the photonic band gap in the case of 1D PhC. The calculation methods for 2D and 3D cases are not presented here because they are out of the scope of this chapter. Very comprehensive description can be found in (Sakoda K., 2005) for example.

As already mentioned, 1D PhC can be realized by deposition of alternating high and low refractive index layers with a quarter-wave optical thicknesses. If the refractive index and thicknesses of the materials are represented by *ni* and *di*, where the subscripts *i* is H or L for high and low refractive index material, then the characteristic matrices *MP* and *MS* of each layer for p and s – polarization can be written in the form:

$$M\_P = \begin{pmatrix} \cos \Delta\_i & \frac{-i n\_i \sin \Delta\_i}{\cos \theta\_i} \\ \frac{-i \cos \theta\_i \sin \Delta\_i}{n\_i} & \cos \Delta\_i \end{pmatrix} \text{ and } M\_S = \begin{pmatrix} \cos \Delta\_i & \frac{-i \sin \Delta\_i}{n\_i \cos \theta\_i} \\ -i n\_i \cos \theta\_i \sin \Delta\_i & \cos \Delta\_i \end{pmatrix} \tag{8}$$

In eq.8 *<sup>i</sup>* 2*nidi* cos *i* is the optical phase thickness of the layer and *θ<sup>i</sup>* is connected with the angle of incidence *θ*0 by the Snell-Decarte's law *n ni <sup>i</sup>* <sup>0</sup> sin <sup>0</sup> sin , where *n*0 is the refractive index of incident medium.

The multilayered stack composed of *q* pairs of high (H) and low (L) refractive index layers, is presented by the matrix multiplication:

$$Q\_{\mathcal{P}} \equiv (n\_s/n\_0)^\* \mathcal{I}^\* \mathcal{H}^\*(\mathcal{L}H)^\* \mathcal{S} \text{ , for } \mathbf{p}\text{-polarization} \tag{9}$$

$$Q\_{\mathbb{S}} \equiv 0.5^{\ast} l^{\ast} H^{\ast} (LH) \mathbb{q}^{\ast} S \text{ , for } \text{s-polarization},\tag{10}$$

where the sign "\*" denotes matrix multiplication, the matrices *H* and *L* are the characteristic matrices *MP* and *MS* for high and low refractive index materials; *I* and *S* are the characteristic matrices of the two surrounding media, usually air and substrate with refractive indices *n*<sup>0</sup> and *n*s, respectively:

$$I\_P = \begin{pmatrix} 1 & \frac{-n\_0}{\cos\theta\_0} \\ 1 & \frac{-n\_0}{\cos\theta\_0} \end{pmatrix}, \quad I\_S = \begin{pmatrix} 1 & \frac{-1}{n\_0 \cos\theta\_0} \\ 1 & \frac{1}{n\_0 \cos\theta\_0} \end{pmatrix}, \quad S\_P = \begin{pmatrix} 1 & 1 \\ \frac{-\cos\theta\_s}{n\_s} & \frac{\cos\theta\_s}{n\_s} \end{pmatrix} \text{ and } \ S\_S = \begin{pmatrix} 1 & 1 \\ -n\_s \cos\theta\_s & n\_s \cos\theta\_s \end{pmatrix} \tag{11}$$

The widely accepted concept for a one-dimensional photonic crystal is a quarter-wave stack of alternating low- and high-refractive index layers (Joanopoulus et al., 1997). For a wave propagating normally to the stack (zero angle of incidence), a one-dimensional photonic band gap exists that is shifted towards smaller wavelengths with increasing the incident angle. Considering all possible angles and polarizations, one can mistakenly conclude that a 1D structure has no three-dimensional photonic band gap. Fortunately, it has been shown that if the optical contrast (the difference in dielectric permittivity between stack constituents) and number of the layers are sufficiently high, an omnidirectional (OD) reflectance band could be open (reflectance of the stack is close to unity for all incident directions and polarization of light) (Fink et al., 1998). As it will be shown in the next section, there are special requirements

Here we will give some details of calculation of the photonic band gap in the case of 1D PhC. The calculation methods for 2D and 3D cases are not presented here because they are out of the scope of this chapter. Very comprehensive description can be found in (Sakoda K.,

As already mentioned, 1D PhC can be realized by deposition of alternating high and low refractive index layers with a quarter-wave optical thicknesses. If the refractive index and thicknesses of the materials are represented by *ni* and *di*, where the subscripts *i* is H or L for high and low refractive index material, then the characteristic matrices *MP* and *MS* of each

> 

and

The multilayered stack composed of *q* pairs of high (H) and low (L) refractive index layers,

 *QP*=(*ns*/*n0*)\**I*\**H*\*(*LH*)q\**S* , for p-polarization (9)

 *QS*=0.5\**I*\**H*\*(*LH*)q\**S* , for s-polarization, (10) where the sign "\*" denotes matrix multiplication, the matrices *H* and *L* are the characteristic matrices *MP* and *MS* for high and low refractive index materials; *I* and *S* are the characteristic matrices of the two surrounding media, usually air and substrate with refractive indices *n*<sup>0</sup>

 

*S*

*M*

*in*

 

*s s* is the optical phase thickness of the layer and *θ<sup>i</sup>* is connected

 

*i*

*ni*

cos

*i i i i*

cos sin cos

 

, (8)

 

<sup>1</sup> 1 (11)

*i i i*

cos sin

*n i*

*<sup>i</sup>* <sup>0</sup> sin <sup>0</sup> sin , where *n*0 is the

and

 *<sup>s</sup> <sup>s</sup> <sup>s</sup> <sup>s</sup> <sup>S</sup> <sup>n</sup> <sup>n</sup> <sup>S</sup>* coscos

  *i*

*i i i*

for low and high refractive index values of the two media of the stack.

layer for p and s – polarization can be written in the form:

*in*

cos

 

*<sup>n</sup> IS* ,

 

*S* cos

*s s P*

 cos

*n n*

1 1

 

0 0

0 0

cos sin

with the angle of incidence *θ*0 by the Snell-Decarte's law *n*

*i*

*i i i*

*n*

cos sin

cos 

2005) for example.

 

*i*

refractive index of incident medium.

is presented by the matrix multiplication:

*P*

*M*

and *n*s, respectively:

cos <sup>1</sup>

cos <sup>1</sup>

*IP* ,

*n*

 

   

*n*

*n*

In eq.8 *<sup>i</sup>* 2

*nidi* cos *i*  where the angle *θs* is associated with *θ*0 by the Snell-Decarte's law *n ns <sup>s</sup>* <sup>0</sup> sin <sup>0</sup> sin . Note in Eqs 9 and 10 that for high reflectance the stack should be terminated with high refractive index layer.

Transmittance and reflectance of the stack are finally obtained from the respective matrix elements *Q*(*i*,*j*):

$$T\_P = \frac{n\_s \cos \theta\_s}{n\_0 \cos \theta\_0} \left| \frac{1}{Q\_P(1, 1)} \right|^2 \text{ and } T\_S = \frac{n\_s \cos \theta\_s}{n\_0 \cos \theta\_0} \left| \frac{1}{Q\_s(1, 1)} \right|^2 \tag{12}$$

$$R\_P = \left| \frac{Q\_P(2,1)}{Q\_P(1,1)} \right|^2 \text{ and } \quad R\_S = \left| \frac{Q\_S(2,1)}{Q\_S(1,1)} \right|^2 \tag{13}$$

The short and the long wavelength edges of the band are function of *nH*, *nL* and the angle of incidence *θ.* They are calculated according to (Kim et. al, 2002) and are presented in Fig. 4a. Fig. 4 b,c and d presents the reflectance of the stack for p and s-polarized light incident at angles of 0, 45o and 85o as a function of the wavelength calculated from Eqs 12 and 13. It is seen that for higher incident angles the band shifts towards smaller wavelengths becoming wider for s-polarization and narrower for p-polarization. The shaded area in fig. 4 indicates the omnidirectional reflectance (ODR) band that is the spectral area of high reflectance for all incident angles and polarization types. It is seen that ODR band opens between short wavelength edge for 0o and long wavelength edge for p-polarization at incident angle of 90o.

Fig. 4. a) Reflection band edges for both polarizations as a function of incident angle; Reflectance of the stack as a function of wavelength for incident angles of b) 0°, c) 45° and d) 85°. The shaded area represents the ODR band.

The short and long wavelength edges of ODR band can also be expressed explicitly as (Kim et. al., 2002):

$$\mathcal{A}\_{\text{short}}^{ODR} = \frac{\pi}{2} \left[ \cos^{-1} \left( -\frac{n\_H - n\_L}{n\_H + n\_L} \right) \right]^{-1} \tag{14}$$

Thin Chalcogenide Films for Photonic Applications 153

It is well known that during the fabrication of the stack deviations of both refractive indices and thicknesses of the layers from their target values may occur. Our calculations showed that the deviation of refractive index influences mostly the optical phase thickness of the *L*layer, while the deviation in thickness from the target values is pronounced by changes in the phase thickness of the *H*-layer. If the error in *n* is Δ*n*=±0.02, than the phase

the thickness leads to 1.9 % and 2.9 % changes of phase thicknesses of low and high refractive index layers. Fig. 6 presents the influences of the error in thickness and small losses in the layers on the reflectance band for the particular case of As2S3/PMMA stack with target refractive indices *nH*=2.27, *nL*=1.49 and thicknesses *dH*=170 nm and *dL*=260 nm. From Fig 6(a) it is seen that the alteration of thicknesses with 5 nm leads to the band shift of 44 nm. The small absorption of the layers leads to decrease in *R* of 0.5 % for *k* =0.001 and 2.1

1.4 1.6 1.8 2.0 2.2

0

25

50 80

Reflectance [%]

Fig. 6. a) Shift of reflectance band of As2S3 ( *nH*=2.27, *dH*=170 nm) / PMMA (*nL*=1.49, *dL=*270 nm) stack due to error of 5 nm in thicknesses; b) influence of small absorption of layers on

90

b)

99.9

Fig. 5. Value of reflectance band for normal light incidence as function of number of the

 0 +5 -5

*nH/nL*

100 *k*

1000 1500 2000 2500

Wavelength [nm]

 0 0.001 0.005

changes with 1.3 % for *i*=*L* and 1 % for *i*=*H*. The deviation of 5 nm in

100

thickness *<sup>i</sup>* 2

*nidi* 

% for *k*=0.005. (Fig. 6 (b)).

4

layers in the stack and ratio of their refractive indices

a) *d* [nm]

1000 1500 2000 2500

Wavelength [nm]

0

the reflectance value.

25

50

Reflectance [%]

75

100

8

12

Number of layers

16

20

$$\mathcal{A}\_{\text{long}}^{\text{ODR}} = \frac{\pi}{4} \left( \frac{n\_L \sqrt{n\_H^2 - n\_0^2} + n\_H \sqrt{n\_L^2 - n\_0^2}}{n\_H n\_L} \right) \left[ \cos^{-1} \left( \frac{n\_H^2 \sqrt{n\_L^2 - n\_0^2} - n\_L^2 \sqrt{n\_H^2 - n\_0^2}}{n\_H^2 \sqrt{n\_L^2 - n\_0^2} + n\_L^2 \sqrt{n\_H^2 - n\_0^2}} \right) \right]^{-1} \tag{15}$$

Knowing *nH* and *nL* it is easy to calculate the width and position of ODR band using eqs. 14 and 15. It was shown (Kim et. al., 2002) that as higher is the optical contrast between the stack's constituents as wider is the ODR band. It is interesting to note that the smallest value of *nH* for ODR to be opened is 2.264 (Kim et. al., 2002). It is clear from eqs 14 and 15 that the lowest refractive index for existence of ODR band can be calculated at a fixed *nH.* For *nH* = 2.264 the lowest *nL* is 1.5132, i.e the smallest optical contrast Δ*n* is around 0.75.

From material and technological viewpoint, there are various materials and deposition methods suitable for successful preparation of quarter-wave stacks with good optical contrast resulting in wide reflectance band with high reflectance value. But for achieving ODR band low and high refractive index materials should be carefully chosen to fulfil the additional requirements - *nH* > 2.264 and Δ*n* ~ 0.75.

One good opportunity is combining calcogenide glasses (*nH* > 2.3 at 1550 nm, see Fig. 1) and polymer layer (*nL* ~ 1.5-1.7). Quarter-wave stacks from As33Se67 (*nH* = 2.64), Ge20Se80 (*nH* = 2.58) and Ge25Se75 (*nH* =2.35) as high refractive index materials and polyamide–imide films (PAI) (*nL* = 1.67) and polystyrene (PS) (*nL* = 1.53) as low refractive index materials are prepared (Kohoutek et. al., 2007a, Kohoutek et. al., 2007b*)* exhibiting high reflection band around 1550 nm. We prepared a quarter wave stack combining As2S3 with *nH* = 2.27 at 1550 nm and Poly(methyl methacrylate) (PMMA) polymer with *nL* = 1.49 thus achieving an optical contrast of about 0.78. Further it is shown that the addition of thin Au film with thickness of 50 nm as a layer close to the substrate in Ge33As12Se55 / PAI stack increases the width of ODR band three times (Ponnampalam et. al., 2008) ).

Another possibility for achieving ODR band is combining two suitably chosen chalcogenide glasses, i.e fabrication of all-chalcogenide reflectors. Combinations of Ge-S / Sb-Se (Kohoutek et al. 2009) with optical contrast of more than 1 and exposed As2Se3 / GeS*2* with optical contrast more than 0.8 have been already realized. (Todorov et al. 2010b).

### **3.2 Factors which influence the properties and quality of 1D photonic crystals**

In section 3.1 it was shown that both the optical contrast between the two component of 1D PhC and *nH* values are factors that influence the width of the omnidirectional reflectance band. Here we will show that the number of the layers and small optical losses due to absorption or scattering are additional factors that should be considered during the design of an OD reflector.

Fig. 5 presents the value of the reflectance band for normal light incidence as a function of the number of the layers in the stack and the ratio of their refractive indices. It is seen that the reflectance increases both with increasing the number of the layers and the ratio of their refractive indices. Besides, the lower optical contrast can be compensated to some extent by increasing the number of layers in the stack. For example if *nH*/*nL* = 1.8 then 20 layers will be required for 100% reflectance whereas for *nH*/*nL* =2.2 only 14 layers will be sufficient.

 

Knowing *nH* and *nL* it is easy to calculate the width and position of ODR band using eqs. 14 and 15. It was shown (Kim et. al., 2002) that as higher is the optical contrast between the stack's constituents as wider is the ODR band. It is interesting to note that the smallest value of *nH* for ODR to be opened is 2.264 (Kim et. al., 2002). It is clear from eqs 14 and 15 that the lowest refractive index for existence of ODR band can be calculated at a fixed *nH.* For

From material and technological viewpoint, there are various materials and deposition methods suitable for successful preparation of quarter-wave stacks with good optical contrast resulting in wide reflectance band with high reflectance value. But for achieving ODR band low and high refractive index materials should be carefully chosen to fulfil the

One good opportunity is combining calcogenide glasses (*nH* > 2.3 at 1550 nm, see Fig. 1) and polymer layer (*nL* ~ 1.5-1.7). Quarter-wave stacks from As33Se67 (*nH* = 2.64), Ge20Se80 (*nH* = 2.58) and Ge25Se75 (*nH* =2.35) as high refractive index materials and polyamide–imide films (PAI) (*nL* = 1.67) and polystyrene (PS) (*nL* = 1.53) as low refractive index materials are prepared (Kohoutek et. al., 2007a, Kohoutek et. al., 2007b*)* exhibiting high reflection band around 1550 nm. We prepared a quarter wave stack combining As2S3 with *nH* = 2.27 at 1550 nm and Poly(methyl methacrylate) (PMMA) polymer with *nL* = 1.49 thus achieving an optical contrast of about 0.78. Further it is shown that the addition of thin Au film with thickness of 50 nm as a layer close to the substrate in Ge33As12Se55 / PAI stack increases the

Another possibility for achieving ODR band is combining two suitably chosen chalcogenide glasses, i.e fabrication of all-chalcogenide reflectors. Combinations of Ge-S / Sb-Se (Kohoutek et al. 2009) with optical contrast of more than 1 and exposed As2Se3 / GeS*2* with

In section 3.1 it was shown that both the optical contrast between the two component of 1D PhC and *nH* values are factors that influence the width of the omnidirectional reflectance band. Here we will show that the number of the layers and small optical losses due to absorption or scattering are additional factors that should be considered during the design

Fig. 5 presents the value of the reflectance band for normal light incidence as a function of the number of the layers in the stack and the ratio of their refractive indices. It is seen that the reflectance increases both with increasing the number of the layers and the ratio of their refractive indices. Besides, the lower optical contrast can be compensated to some extent by increasing the number of layers in the stack. For example if *nH*/*nL* = 1.8 then 20 layers will be required for 100% reflectance whereas for *nH*/*nL* =2.2 only 14 layers will be

optical contrast more than 0.8 have been already realized. (Todorov et al. 2010b).

**3.2 Factors which influence the properties and quality of 1D photonic crystals** 

*nH* = 2.264 the lowest *nL* is 1.5132, i.e the smallest optical contrast Δ*n* is around 0.75.

 

2 0

2 2

0

*long* cos

*n n n n n n n n*

*H L*

2

*ODR L H H L*

additional requirements - *nH* > 2.264 and Δ*n* ~ 0.75.

width of ODR band three times (Ponnampalam et. al., 2008) ).

4

of an OD reflector.

sufficient.

 

1

(15)

 

 

2 0

2 0

2 2 2

 

2 2 2

0

*H L L H H L L H*

*n n n n n n n n n n n n*

0

2 2

2 2

1

 

It is well known that during the fabrication of the stack deviations of both refractive indices and thicknesses of the layers from their target values may occur. Our calculations showed that the deviation of refractive index influences mostly the optical phase thickness of the *L*layer, while the deviation in thickness from the target values is pronounced by changes in the phase thickness of the *H*-layer. If the error in *n* is Δ*n*=±0.02, than the phase thickness *<sup>i</sup>* 2*nidi* changes with 1.3 % for *i*=*L* and 1 % for *i*=*H*. The deviation of 5 nm in the thickness leads to 1.9 % and 2.9 % changes of phase thicknesses of low and high refractive index layers. Fig. 6 presents the influences of the error in thickness and small losses in the layers on the reflectance band for the particular case of As2S3/PMMA stack with target refractive indices *nH*=2.27, *nL*=1.49 and thicknesses *dH*=170 nm and *dL*=260 nm. From Fig 6(a) it is seen that the alteration of thicknesses with 5 nm leads to the band shift of 44 nm. The small absorption of the layers leads to decrease in *R* of 0.5 % for *k* =0.001 and 2.1 % for *k*=0.005. (Fig. 6 (b)).

Fig. 5. Value of reflectance band for normal light incidence as function of number of the layers in the stack and ratio of their refractive indices

Fig. 6. a) Shift of reflectance band of As2S3 ( *nH*=2.27, *dH*=170 nm) / PMMA (*nL*=1.49, *dL=*270 nm) stack due to error of 5 nm in thicknesses; b) influence of small absorption of layers on the reflectance value.

Thin Chalcogenide Films for Photonic Applications 155

Direct laser writing method through multi-photon absorption is another method for producing 3D PhC. The light from the laser is focused on a small spot of the dye-doped polymer used as a recording medium. The energy of the laser excites the dye molecules that initiate a local polymerization in the spot thus changing the refractive index of the polymer in the illuminated spot. A spatial resolution of 120 nm is reported in the literature (Kawata et al., 2001). The problem is that the optical contrast is very small and infiltration of the structure is needed. Another possibility is using the laser writing in high refractive index material. Promising candidates are chalcogenide glasses, particularly As2S3 that undergo

Conventional lithography and selective etching were used mainly for fabrication of 2D PhC. For producing 3D PhC a concept of layer-by-layer deposition has to be implemented that comprises repeated cycles of photolithography, wet and dry etching, planarization, and

The holographic lithography is very promising method enabling large-area defect-free 2D and 3D periodic structure to be produced in a single-step. In holographic lithography the sensitive medium (a photoresist) is exposed to a multiple-beam interference pattern (for Ndimensional structures at least N+1 beams are required) and subsequently developed, producing a porous structure. The interbeam angles and polarizations and the number of beams determine the type of symmetry of the recorded structures. It has been theoretically shown that all 14 Bravais lattices could be produced (Cai et. al., 2002). Usually SU-8 photoresist with refractive index of around 1.67 is used. A recognized drawback is the need for infiltration of the produced structure with high refractive index material. Otherwise the optical contrast is not sufficiently high for opening a complete photonic band. Difficulties such as optical alignment, vibrational instability, and reflection losses on the interface air/photoresist further complicate the recording processes. One possibility for overcoming the problem is rotating the sample between two consecutive exposures (Lai et. al., 2005). The second approach is implementation of specially design diffraction mask that provides the required number of beams with correct directions and polarizations reducing the alignment

complexity and vibration instabilities in the optical setup (Divlianski et. al., 2002).

**4.2 Experimental procedure for deposition of 1D photonic crystals** 

Two-dimensional structures have already been fabricated in chalcogenide glasses using holographic lithography (Feigel et. al., 2005; Su et. al., 2009). To the best of our knowledge holographic lithography has not been used yet for fabrication of 3D PhC from chalcogenide glasses. The three dimensional wood-pile photonic crystals made in chalcogenide glasses are fabricated by direct laser writing (Nicoletti et. al., 2008) or through layer-by-layer deposition

In the present work we used the concept of layer-by-layer deposition of quarter-wave stacks of alternating suitably chosen films with low and high refractive indices for producing of

The bulk chalcogenide glass was synthesized in a quartz ampoule by the method of melt quenching from elements of purity 99.999 %. The chalcogenide layers were deposited by thermal evaporation at deposition rate of 0.5 – 0.7 nm/s. The X-ray microanalysis showed

that the film composition is close to that of the bulk samples (Todorov et al., 2010b).

changes in solubility upon exposure to light.

growth of layers (Blanco et. al., 2004).

(Feigel et. al., 2003).

one-dimensional photonic crystals.

The comparison between the real and ideal 1D-PhC from As2S3 / PMMA is presented in Fig. 7. It is seen that there is an insignificant shift between the reflectance bands of both structures. The difference of 1.1 % between the measured and calculated reflectance can be due to slight absorption and scattering of the layers as well as to measurements errors. The most significant difference between the fabricated and simulated structures is in the side peaks. Note for example the first minima that are very high for the real structure and zero for the simulated one. Most probably this difference is due to random deviations of phase thicknesses of the constituent layers leading to violation of the conditions for destructive interference.

Fig. 7. Measured and simulated reflectance band of As2S3/PMMA stack
