UNIVERSITY OF LJUBLJANA FACULTY OF MATHEMATICS AND PHYSICS

PHYSICS DEPARTMENT

SEMINAR

ARTIFICIAL OPALS

Ivan Jamnik

Advisor: dr. Irena Drevenšek Olenik

Abstract Opals are three-dimensional photonic crystals, self-assembled from dielectric spherical beads

into a face-centered lattice. Their periodic structure results in interesting optical properties, such as photonic band gaps. With their relatively easy and cheap fabrication, they look a promising material for elements in optical circuits. By introducing intentional defects in the crystal lattice, one can manufacture nanoscale optical devices such as filters, waveguides, resonators, lasers…

Ljubljana, April, 2006

Table of Contents

1 Introduction................................................................................................................................ 3 2 Optical Properties....................................................................................................................... 4

2.1 Maxwell’s Equations in Periodic Media............................................................................ 4 2.1.1 Wave equation ........................................................................................................... 4 2.1.2 Effects of Discrete Translation Symmetry................................................................. 5 2.1.3 Solutions of the Wave Equation ................................................................................ 5

2.2 One Dimensional Case....................................................................................................... 6 2.3 Three-Dimensional Case.................................................................................................... 7

3 Fabrication of Opals................................................................................................................... 8 3.1 Self-assembly Techniques ................................................................................................. 9

3.1.1 Gravitational Sedimentation ...................................................................................... 9 3.1.2 Centrifugation .......................................................................................................... 10 3.1.3 Vertical Deposition Method..................................................................................... 10

3.2 Optical Characterization .................................................................................................. 12 4 Inverse Opals15 5 Applications ............................................................................................................................. 16

5.1 Waveguides (line defects)................................................................................................ 16 5.2 Resonant Cavities (point defects) .................................................................................... 17 5.3 Filters ............................................................................................................................... 17

6 Conclusion ............................................................................................................................... 18 7 References................................................................................................................................ 19

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1 Introduction

Opals are three-dimensional photonic crystals with dielectric spheres of radius from 200 to 600 nm that are arranged into a heksagonal or cubic (fcc) close- packed lattice. As well as occurring naturally, opals of all varieties have been synthesized experimentally and commercially. The discovery of the ordered sphere structure of precious opal led to its synthesis by Pierre Gilson in 1974.

The research field of photonic crystals has, during the last years, gained a considerable interest. Photonic crystals are media possessing a periodic modulation of the refractive index, in one, two, or three dimensions and their possibility of separating spectral domains of light and suppressing spontaneous emission are key issues in applications such as optical switching and light generation1 . In this respect opals are of particular interest since they provide a three-dimensional photonic structure enabling a full three-dimensional photonic band gap, which effectively can prohibit the spontaneous emission in light-matter interaction.Due to their simple fabrication they are highly scalable also up to macroscopic sizes in range of millimeter.

A natural opal is , hydrated silicon dioxide, with water content sometimes being as high as 20%, but usually between three and ten percent. Opals range from colorless through white, milky blue, gray, red, yellow, green, brown and black. The precious opal consists of spheres of silica, whose sizes may vary from 200 to 600 nm, packed into close-packed planes which are stacked together. Synthetics are further distinguished from naturals by the formers lack of fluorescence. Synthetics are also generally lower in density.

2 2SiO nH O−

Ordered silica spheres produce colors by causing the interference and diffraction of light passing through the microstructure of the opal. It is the regularity of the sizes of the spheres and of the packing of these spheres that determines the quality of the precious opal. If distance between the regularly packed planes of spheres is approximately half the wavelength of a component of visible light, the light of that wavelength may be subject to diffraction from the stacked planes.

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The spacing between the planes and the orientation of planes with respect to the incident light determine the colors observed. When looking at a natural opal, one observes many colours. The phenomenon is called play of colour. The process can be described by the Brag’s law of diffraction.

2 Optical Properties As stated in the introduction, opals are photonic crystals, which are periodically structured

electromagnetic media possessing photonic band gaps. These are ranges of frequency in which light can not propagate through the structure. Structural periodicity, whose length scale is proportional to the wavelength of light in the band gap, is the electromagnetic analogue of a crystalline atomic lattice, which acts on the electron wave function to produce the familiar band gaps in semiconductors.

Figure 1: Schematic drawings of 1-D, 2-D and 3-d photonic crystals, for which the periodicity is in the material structure of the crystal. Red end yellow portions of the crystal represent materials with different refractive indices.

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2.1 Maxwell’s Equations in Periodic Media

2.1.1 Wave equation Felix Bloch (1905-1983) proved that waves in a periodic structure can propagate without

scattering. For dielectric crystals we can use source-free and current-free ( 0, =ρ j ) Maxwell’s equations. We also take into account the held relations ( ) ( ) ( )rε0=D r ε E r and μ0=B H , assuming that μ for most dielectrics is one. We can write:

. 0 0

. 0

t

t

μ

εε

0

0 0

∂∇ = ∇× + =

∂∂

∇ = ∇× − =∂

HH E

ED H (2.1)

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We look for solutions at a fixed frequency ω , which have the form of ( , ) ( ) i tt e ω=H r H r and ( , ) ( ) i tt e ω=E r E r and substitute them into Eq. (2.1). We join both rotor equations, so that we can

write down the wave equation for : ( )H r

2

1( ( )) ( )) c

ωε

2

∇× ∇× =(

H r H rr

(2.2)

The solution for is then simply obtainable with ( , )tE r

1( ) ( ))iωε

= ∇×(

E r H rr

(2.3)

from . ( )H r

The Eq. (2.2) is an eigenvalue equation, with eigenvalue ( 2cω2

) and an eigen-operator

1()ε

Θ =∇× ∇×(r

which is Hermitian (its eigenvalues are real and positive and its eigenstates are

orthogonatal).

2.1.2 Effects of Discrete Translation Symmetry A photonic crystal in three dimensions can be described by a periodic dielectric modulation ) i )ε ε( = ( +r r R corresponding to some set of primitive lattice vectors . The Bloch-

Floquet theorem for periodic eigenproblems states that the solutions of Eq. ( 1, 2,3)i i =R(2.2) can be written in

the form with eigenvalues ,( ) ( )i= krn kH r e u r ,n kω ,where is a periodic envelope function

satisfying . , ( )n ku r

( ) ( )= +u r u r RThe eigenvalues ,ωn k are continuous functions of k , forming discrete “bands” when plotted

versus , in a “band structure” or dispersion diagram. Moreover, the eigensolutions are periodic functions of as well: the solution at k is the same as the solution at

kk i+k G , where is a

primitive reciprocal lattice vector defined by iG

,2i j i jπ= δR G . Thanks to this periodicity, one need only compute the eigensolutions within the primitive cell of these reciprocal lattice called the first Brillouin zone.

2.1.3 Solutions of the Wave Equation The simplest way to find the solutions of Eq. (2.2) is the plane wave expansion method that

follows very closely from the corresponding nearly free electron approximation. Since the dielectric function is periodic, therefore the solution is expanded in an infinite Bloch sum of plane waves for each wave vector in the Brillouin zone.

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( ),

1 1

1 1 1 3

( ) ,

,

1 .

i

i

i

cell cell

h e

and e

where is givenby e dV

λ λλ

ε ε

ε ε ε

+

=1,2

− −

− − − −

=

( ) =

=

∑ ∑

∑

∫

k G rG

G

GrG

G

GrG G

H r e

r

r

(2.4)

The sum in Eq. (2.4) is over all reciprocal lattice vectors and the two possible transverse

polarization vectors G

λ =1,2 and ,h λG is the coefficient of the H component along the axes eλ .Inserting Eq.(2.4) into Eq. (2.2), one obtains:

1' 2

'( ) ( ( ') )

cωε

2−− + × + × =∑ G G

Gk G k G h hG . (2.5)

The result is similar to that from electron in a weak periodic potential. We are left with matrix eigenvalue equation, that is usually solved numerically1, . Descriptions of some other methods like Transfer matrix method, can be found in the reference list 1, .

2

2

2.2 One Dimensional Case In order to describe a formation of the band gap, let us consider the simplest possible structure;

i.e. one-dimensional (1D) structure, composed of alternating layers of two dielectrics (see Figure 1).

Figure 2: Band structures for three different multilayered films . (a) Homogenous GaAs, (b) GaAs and GaAlAs multilayered film. The difference in refractive indices is small and the band gap is small. (c) Multilayered GaAs-air film with large refractive index difference (a is the lattice length and c is the vacuum speed of light).

4

3

6

For a totally homogenous material the dispersion relation is simply

.ck ckn

ωε

= = (2.6)

Because of the structural periodicity we show only the dispersion relation in the 1. Brilluine

zone, therefore the line is folded back into the zone (Figure 2a). When an incident wave enters a periodic array of dielectric sheets, the wave is partially reflected at the boundaries of dielectric layers. If the partially reflected waves are superimposed and in phase, they form a total reflected wave, which means that incident wave is unable to enter the medium.

In one-dimensional case the band gap arises at the zone boundaries at kaπ

= , where is the

lattice constant. Here the harmonic modes are standing waves. The nodes of these standing waves are located either in the middle of lower or higher index layer. Harmonic modes with lower frequencies concentrate their energy in higher

a

ε layers, while higher frequency modes condensate

in ε regions ( ckn

ω = ). These means that the waves just above the band gap, with energy

concentrated in lower ε regions, will have a bit higher frequencies, than in homogenous media and vice versa for lower frequencies, leading to band gap creation (Figure 3). In one-dimension a bangap is created as soon as 1 2ε ε≠ and the bigger is the difference 1( )ε ε2− the bigger band gap we get (Figure 2).

Figure 3: The origin of the band gap in 1D photonic crystals with . Band gap arises

at the zone boundaries at

41n n> 2

kaπ

= , where is the lattice constant. Here the harmonic modes

are standing waves, with the nodes located either in the middle of lower or higher index layer.

a

2.3 Three-Dimensional Case In the one-dimensional periodical crystals we always obtain a band gap. In three-dimensions

that is not usually the case, becouse lower bands in some directions of a crystal overlap with the hihger bands in other directions (Figure 4b). We often get only partial band gaps, which means that

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total reflection only appears in some directions. An important role, in achieving a perfect gap, plays the difference in dielectric constants. Usually, to achieve a complete bandgap the ratio has to be 4 / 9ε ε1 2 > .

Figure 4: Photonic bandstucure for 3D opal structures. a) Bandstructure for spheres of radius 160nm with theoretically high refractive index (ε =12 ) . There is a clear band gap (yellow) in all directions and an illustration of the 1. Brillouin zone for a fcc lattice 5 b) Photonic bandstructure for a fcc lattice of closed packed air spheres (inverse opal) located in a silicon matrix ( 0ε =1 .9 ). The frequency is plotted in units of a/2πc, where a is the cubic lattice constant and c denotes the vacuum speed of light. Clearly visible is the complete band gap between bands 8 and 9 . 6

The direct opal structure, e.g. an arrangement of polystyrene or silica spheres in air, does

produce a well-defined stop band in some directions of light propagation . Instead, the inverse opal structure, i.e. air spheres in TiO2 or in silicon, produces a strong effect on the photonic DOS (density of states) and may even result in a complete photonic band gap, if the dielectric constant and the filling fraction of the infiltrated material are large enough (

7,8,9,10,11

7 Figure 4).

3 Fabrication of Opals Traditionally have been two approaches have been to fabricate photonic crystals:

nanolithography and self assembly of colloidal crystals. Engineers have used nanolithography successively with remarkable precision 8, . Opals can not be fabritated by nanolithography. Most widely used are layer- by –layer and holographic lithography. In the first case holes are etched into the substrate and then filled with dielectric material. Then you add another layer of substrate and redo the process and so on. In holographic lithography four laser beams and photosensitive monomers and liquid crystals are used. Where all the laser beams cross (highest intensity), the monomeres polymerize, resulting in a different refractive index (

9,11

0.2nΔ ≤ ). If these polymerized regions occur periodically, a photonic crystal is made. However, this method is expensive, slow

8

and capable of producing materials only a few structural layers thick. The self-assembly of colloidal crystals (the so-called ‘‘bottom-up’’ approach) is simpler, inexpensive and can yield crystalline samples with thickness of a few to several hundred structural layers . 7,8

3.1 Self-assembly Techniques This approach involves the crystallization of a colloidal dispersion of spheres of silica,

polystyrene or polymethylmethacrylate (PMMA) to form a material with a three-dimensional periodic structure (fcc) in which 24% of the volume is air (opal). Theoretical and experimental 8 studies have shown, that a pseudo photonic band gap exists in the [111] direction for fcc arrangements of silica or polymer spheres. These opals do not poses a complete photonic band gap, since the gap position and hence frequencies of light allowed to propagate within the crystal, vary with the angle of incidence op incoming waves. The ratio / 1sphere air .5ε ε ∼ is not enough for a complete gap as stated in Optical Properties section in this paper.

Opal crystals of spheres are mostly fabricated by three self-assembly methods: gravitational

sedimentation, centrifugation and vertical deposition method. For all these techniques we need a colloidal solution of spherical particles. Their fabrication is

well described in the literature 9, . 10,11

For example11 , silica nanospheres are synthesized via hydrolysis of tetraethyl-ortho-silicate using as a catalyst and ethanol as a solvent. The reaction is controlled in a thermostatic cell (30˙C). The colloidal suspension is centrifugated to extract the spheres, then it is successively rinsed and redispersed in distilled water with a sonicator. By using different reagent concentrations, one can obtain controlled sphere diameters within the range of 160–640 nm.

3NH

3.1.1 Gravitational Sedimentation Colloidal particles have very little horizontal correlation . Gravitational force is driving the

spheres down towards the bottom of the container. Accounting the hard-core interaction (spheres do not overlap) a fcc crystal is constructed (

12

Figure 5). With this method large scale crystals can be manufactured, depending of course on the quantity of the material that dispersed in the solution12 (Figure 6a). The crystals grow eighter in (100) or (111) orientation (Figure 6b) Procedure is as follows. Colloidal suspension with spheres is left in open glass at 25 C 8, . After 3–5 weeks water evaporates to leave, well-ordered photonic crystal. Then colloidal crystals are then left to dry in air at 25 C for a further 1–2 weeks, resulting in well ordered opals.

9,10,12

9

Figure 5: Gravitational sedimentation method using colloidal suspension of silica spheres 9 . Due to gravity force spheres sediment to the botom of the container, where they form fcc lattice photonic crystals (opals) 9 .

3.1.2 Centrifugation In this technique colloidal suspensions are loaded into tubes and then centrifuged at about 1500

rpm 9 and 10˙C for 24 h. Then the crystals are left to dry in air at 25˙C for 1–2 weeks. The method is obviously similar to gravitational sedimentation. The difference is thatthe gravitational force is substituted with the centrifugal force. This gives us more controlled process and faster fabrication (larger terminal velocity of the spheres).

Figure 6: SEM images 8 of opals prepared with sedimentation method. a) Fractured surface showing fcc array of spheres and (b) colloidal crystal exhibiting domains of both (111) and (100) orientations.

3.1.3 Vertical Deposition Method Centrifugation and sedimentation methods often lead to polycrystalline structures. Vertical

deposition method proved to make more ideal crystals. In this method a glass or some other substrate12 is dipped in the colloidal solution. The plate is in a vertical position or slightly tilted. At the surface of a liquid a meniscus is formed on the contact bounding with object (Figure 7). The contact angle between the suspension surface and the substrate is influenced by the solvent, the substrate, and the tilt angle of the substrate relative to the solution. A more detailed model is

Θ

10

presented in the literature14 .Important parameters are also the viscosity of the solution and particle diameter. Some relations are shown in Figure 8.

As the liquid level in the container decreases, a thin colloidal crystal layer is deposited on the glass slide (Figure 7). This technique proved very effective for uniformly covering large areas. Film thickness could be varied by changing the concentration of spheres in the colloidal suspension or by changing the speed of the surface level decreasing (Figure 8).

Figure 7: Vertical deposition method: a) A glass slide is dipped in the colloidal solution in an almost vertical position . With solvent vaporization the liquid surface is lowered , which produces crystal growth in the meniscus region of the slide due to capillary forces in the meniscus. b) The vaporization is substituted with lifting of the slide out of the colloidal solution, also leading to crystal growth in the meniscus region.

4

In literature 9 one can find different procedures for this technique. One way for crystal

growth is lifting the substrate from the solution as shown in ,11,15,15

Figure 7b. The lifting speeds are very slow, in the range of about millimeter per hour. Another way is to decrease the liquid surface with the help of a peristaltic pump. The advantage of this method is that the substrate is fixed in the colloidal suspension and the shaking problem during lift-up of the substrate can be avoided. The lift-up speed of the substrate is solely controlled by the motor. In pumping method the dropping velocity of the liquid surface is determined by the pumping flow rate and the cross-sectional area of the container. As a result, by using a common peristaltic pump the dropping velocity of the liquid surface can be easily controlled. For example, the smallest velocity that can be achieved in pumping method is 0.0232 /m sμ , while it is 0.1 /m sμ in the lifting method.

Also widely used is the evaporation method. Here the surface dropping velocity is determined by evaporation rate of solvents11 . See Figure 7 for illustration. Heating liquids is almost always accompanied by convection currents. In both previous methods, however, there is an unwanted process: sedimentation. Experiments take place for a few hours and spheres constantly sediment to the bottom of the container resulting in lower concentrations at the surface. Convective currents partially hold the concentrations constant.

With sedimentation method one can make almost unlimited thick crystals. In VDP method this is not the case. In Figure 8 some parameters are shown, that affect the number of layers of the resulting crystal. One can observe linear dependence of number of layers versus inverse sphere diameter (Figure 8a) and volume fracture of spheres in the solution (Figure 8b). Number of deposited layers can also be controlled by changing the pump flow velocity (Figure 8c) or the lifting or evaporation speeds.

11

When dried, opals are very fragile. For opals this problem is solved by sintering at temperature in range from 900 to 1100°C for 3 hours15 . The result is sphere overlaping and strengthening the crystal. Furthermore, spheres can be etched to make smaller necks between spheres as shown in

2SiO

Figure 9c. This is achieved by soaking the crystal in a 1% solution of HF in distilled water.

Figure 8: Controllable parameters for vertical deposition method13 . a) Number of opal layers versus inverse particle diameter for fixed volume fraction of the spheresφ =1% and pump flow velocity V. b) Number of colloid layers versus the volume fraction (particle diameter is 560 nm). c) Number of layers versus inverse pump flow velocity (d=560nm, φ =1%).

Figure 9: a) SEM image of a multilayer opal structure prepared by vertical deposition method. b) Photograph of vertical deposition grown, dried opal, fabricated from 290 nm silica spheres12 . c) SEM image of an opal showing the of necking of spheres.

12

8

3.2 Optical Characterization Reflection and transmission spectroscopy are customary techniques, which reveal stop bands

as increased reflection or decreased transmission. The position of stop bands (band gaps) in the fcc photonic crystals can be estimated using a modified form of Bragg’s law (Eq. (3.6)), which takes

12

into account refraction of light in the composite structure and the incident angle of the incoming light.

Figure 10: a) Illustration of Snell’s law in Eq. (3.2) . b) Illustration of Bragg’s law (Eq. (3.1)). Both are used in deriving modified Bragg’s law written in Eq. (3.6)

The derivation of modified Bragg’s law is as follows. The wavelength of the reflection peak

can be calculated using the simple equation for Bragg diffraction Figure 10b. max 2 sinhklm dλ = Θ . (3.1)

, where maxλ is the wavelength of the maximum reflectance (i.e. the position of the photonic band gap), is the interplanar spacing between hkl planes, m is the order of the Bragg diffraction.

hkld

On the other hand, a more precise description of the angular position of the resolved reflection

peaks can be done by combination Bragg's law and Snell's law (Figure 10b). The modified form of Bragg's law, which takes into account the reduced angle with respect to the normal at which light travels in the opal. Snell’s law or law of refraction can be written:

1 2sin sinn n φΘ = (3.2)

or

sin ,sin

λλ φ1

2

Θ= (3.3)

where is the refractive index of the material and of the medium of the incoming wave or in out case air, thus and .

2n 2n

1 1n = 2 1n n> Θ is the angle of the incident wave and she surface normal and φ the angle of the ray in the higher index media(opal) and the normal. Starting from Bragg’s law on using Snell’s law one obtains:

max 2 cohkl avgm d n sλ φ= (3.4)

and Snell’s law yields the relation

13

2

2 22

1sin sin

sin1 sin 1 cos .

avg

avg

n

n

φ

φ φ

= Θ

Θ− = − =

(3.5)

Joining Eq.(3.4) and Eq.(3.5) yields the modified Bragg’s law:

2 2max

2 sin .hklavg

d nm

λ = − Θ (3.6)

The is the average refractive index of the photonic structure. For silica spheres in air we calculate the average index like

avgn

avg silica silica air airn n f n f= + (3.7)

, where silican = 1.542, = 1.000, airn silicaf and airf are the volume fractions occupied by spheres and air in the structure (generally 74% and 26% for a fcc lattice). In the most general case, the refractive index is a rank-2 tensor (a 3 by 3 matrix), which cannot simply be described by refractive indices except for polarizations along principal axes, but in our case both materials are isotropic and Eq. 3.7 holds. For cases where spheres are not mede of silica one can leave refractive index dependent on the direction and can thenbe obtained by a fitting methotod from an angle dependent reflectance spectra.

Due to small dielectical contrast of silica and polystyrene ( 1.5n = ) opals do not have a complete photonic gap. But they do form a pseudogap associated with the (111) family of planes (Figure 11). Theoretical calculations that are made with plane wave expansion method and are usually performed for infinite crystals. Measurements in Figure 11 were made on a 25 layer crystal. Calculated bandgap width corresponds to the measured ones for crystals 30 layers thick or thicker, when the gap becomes constant14 So we have an excellent agreement with the theory.

Figure 11: a) Dispersion relation for the infinite system calculated using the plane wave expansion method. Experimental and calculated normal incidence reflectivity spectra for sample 23 layers thick are shown as thick and thin solid lines. Reflectivity peak is in the calculated band gap14 . b) The Brillouin zone of the fcc lattice. The (111) direction corresponds to LΓ direction in reciprocal space.

14

4 Inverse Opals Due to their low dielectric constant, opals made of silica or polystyrene spheres do not exhibit

a full band gap phenomena. A better solution could be inverse opals. Regular opals structure are spheres arranged in a crystal with air filled voids in between. The

inverse opal is like a negative image of a regular opal, where voids are filled with a material and spheres are removed, leaving air spheres. We can fill those voids with a large number of substances like semiconductor (Si, GaAs, InP and CdS), superconductor (Pb, Bi, In, Sn) ferromagnetic media (e.g. Fe, alloys) and fluorescent (ZnO, oxides and chlorides) or high ε materials ( , Ge 2ZrO , ) with refractive indexes above the theoretical threshold for bandgap phenomena.

2TiO

Figure 12: (a) and (b) are SEM images of inverse opals 8 (c) Scheme of inverse opal production technique. (d) Ag coating of usual opals improves the reflectance18 .

2TiO

15

The voids are filled by using high pressure techniques (800˙C, 100bar) or a sol-gel method. In sol-gel method we gave gel like substance containing selected material. Gel is then inserted in the matrix and than the solvent (with evaporation) is removed, leaving selected material in a solid state.

The sphere substance (for ) is then removed by etching in aqueous solution of hydrofluoric acid. The result is an inverse opal structure with air spheres surrounded by selected material.

2SiO

To achieve a complete PBG for the visible and infrared regions, inverse opal structures with refractive index contrast of at least 2.9 are required. Inverse opals of (n = 2.5) and . (n = 2.4) made

2TiO 2CeO8 from methamethycrilate opal templetes are interesting materials. Also semiconductor

materials have high refractive index and silicon ( 3.4n = ) inverse opals have been made6, that has a complete band gap.

Another method to enhance the reflectance of the artificial opal is by silver (Ag) coating of the

polymethylmethacrylate microspheres to form a metallodielectric artificial opal. The authors studied the angle-resolved reflection spectra of the metallodielectric opals. By a suitable coating of the microspheres, the reflectance of the opals is enhanced without changing the reflection wavelength18 (Figure 12).

5 Applications

5.1 Waveguides (line defects) In conventional optical waveguides, such as fiber-optic cables, light is confined on the basis of

total internal reflection. One of the weaknesses of such waveguides, is that creating bends is difficult. Unless the radius of the bend is large compared to the wavelength much of the light will be lost. This represents a problem in creating integrated optical "circuits," since the space required for large-radius bends is unavailable.

Photonic crystal waveguides operate on a different principle. A linear defect is created in the crystal which supports modes that are in the band gap, analogous to the impurity states in the semiconductor band gap. Below, we see the dispersion relation for the defect mode (Figure 13a). A defect can be a missing sphere, a smaller sphere, combination of both or spheres from different materials (Figure 9).Impurity mode is forbidden from propagating in the bulk crystal because of the band gap. Due to sharp bends optical circuits can be made much smaller for optoelectronic devices (example is the computer industry).

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Figure 13:a) Bandgap (yellow) structure 3 with allowed modes for propagation in defects region of crstal(red). b) and c) are two variations of bend waveguides made with a photonic crystal.

3

When a bend defect line is created in the waveguide, it is impossible for light to escape from

the waveguide (since it cannot propagate in the bulk of the crystal), hence it is possible to get 100% transmission 19 .

5.2 Resonant Cavities (point defects) When a point defect is created in a photonic crystal, it is possible for that defect to pull a light

mode into the band gap. Because such a state is forbidden from propagating in the bulk crystal, it is trapped. The mode decays exponentially into the bulk.

In other words, a resonant cavity replaces mirrors in the usual resonator. Application of resonant cavities is enhancing the efficiency of lasers. By changing the size or the shape of the defect, its frequency can easily be tuned to any value within the band gap.

5.3 Filters A straightforward use of artificial opals, photonic crystals is frequency filters. When incident

light, with frequencies in the photonic gap tries to enter the crystal, it is reflected. Other frequencies can propagate trough the crystal. If we introduce defects, only a narrow range of frequencies can pass.

17

6 Conclusion The direction of present day technology is planar technology, therefore, for the density of

elements to increase further, a change to three- dimensional nanosystems is required for increasing the density of elements such as optical chips, waveguides for increasingly evolving optoelectronics. Such systems are able to operate at current densities up to four orders of magnitude lower than planar devices . Opals present a fast and cheap production of such materials. In future, more work will be done for better techniques for introducing defects into opals, hopefully achieving mass production in computer technology. The goal is to replace electrons as the information carriers with photons.

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Furthermore, beside optical devices, inverse opals are a promising approach in making highly ordered and porous materials, usable in battery and fuel cell technology. They can increase active surfaces of electrodes or in medicine as a template for drug containers allowing very small dosage. The techniques, for incorporating new materials in opal matrices, have to be improved.

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