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Photonic Crystals
Introduction
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DefinitionPhotonic crystals are new, artificialy created materials, in which refractive index is periodically modulated in a scale compared to the wavelength of operation.
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Photonic crystals (PhC) classification
Refractive index can be modulated in 1, 2 and 3
dimensions:
• 1D PhC – multilayer filter
• 2D PhC – Photonic Crystal Fiber (PCF)
or planar PhC waveguide
• 3D PhC – ultimate photonic crystal
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Photonic crystals history
1887 1987
Periodic media with optical bandgap: “optical isolator”
2-D 3-D1-D
Actual structure can be much
more complicated
One dimensional periodic structure
Two-dimensional periodic structure
3D periodic structure
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Research statistics
0
500
1000
1500
2000
2001 2002 2003 2004 2005
Photonic Crystal*Integrated Optics
Number of scientific papers according to SCI database
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LD Niobian litu - substrate
TI:LiNbO3
Geodesic lenses
CCD
RF (analysed signal)
Integrated Acousto-optic spectrumanalyser: LiNbO3
Interdigital transducer
SAW
5 cm
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Add-drop multiplexers - comparison
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Historical introduction
Influence of periodic structures on electromagnetic radiation was first proposed by William Lawrence Bragg in 1912
Normal Plane NaCl Crystal
Diffraction Calculation
William Lawrence Bragg1890 - 1971, Nobel Prizein Physics 1915
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Bragg condition
A regular array of atoms diffracts Xrays when the Bragg condition is met. For incident Xrays of a given wavelength different planes reflect at different Bragg angles.
2 d sin θ = ν λ, ν = 1, 2, 3, ...
Bragg grating work like reflector if θ = 90o
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Bragg reflections
Bragg Scattering for Xrays. Each set of planes acts like a mirror in a small range of angles which do not overlap
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Bragg scattering for a photonic crystal
Each set of planes acts like a mirror in a large range of angles which overlap completely. Under these circumstances no radiation can penetrate into the material which is a photonic insulator. For a limit range of frequencies (the band gap) radiation is rejected whatever the incident angle.
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Technologies for fabrication of Photonic Crystals
• Multi-step micro-structuring• multi-stage lithography• two photon absorption
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The first approach – drilling (Yablonovitch)
�Yablonovite�: a slab of material is covered by a mask consisting of a triangular array of holes. Each hole is drilled through three times, at an angle 35.26° away from normal, and spread out 120° on the azimuth. The resulting criss-cross of holes below the surface of the slab produces a fully three-dimensionally periodic fccstructure.
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The very first approach (opal)
Opal comprises sub micron sized silica spheres arranged in a face centred cubic close packed structure. In this electron micrograph the individual spheres are clearly visible under a layer of surface clutter.
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Nature’s approach – micro-structuring
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Nature’s approach - microstructuring
The wing of a butterfly
consists of a series of scales
each a fraction of a millimetre
long. In this photograph of an
Adonis Blue (Lysandra
Bellargus) the small scales are
visible as striations of the blue
section of the wing. The black
spots are caused by the
occasional missing scale.
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Nature’s approach – micro-structuring
An electron micrograph of a broken scale taken from the butterfly Mitoura Grynea revealing a periodic array of holes responsible for the colour. The bar in the bottom left is one micron long.
From Helen Ghiradella’s paper on ‘light and color on the wing: structural colors in butterflies and moths’
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Multi-stage lithography
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Inexpensive technologies for large scale fabrication
• Self-organising materials• Holographic lithography
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Coloidal crystals
• Colloid scientists have perfected methods for making spherical microparticles of uniform size from polystyrene and silica.
• If left to settle under gravity from a liquid suspension, such microspheres will accumulate layer by layer in close-packed, orderly arrays called colloidal crystals.
• There is no need for any direct manipulation at all: the crystals simply self-assemble spontaneously.
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Photonic crystals at Faculty of Microsystem Electronics and Photonics,
WUTSEM photograph ofself-organized silica balls
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Holographic interferometry
PATTERN GENERATION: Holographic lithography is the alternative method to electron-beam lithography as far as fabricating nano-sized features of relatively large area in photoresist although it usefulness is limited to some selected structures. IBE (Ion Beam Etching) is a chosen method of further pattern etching.
MATERIAL: Alloys of III–Nitrides (GaN, InN and AlN) are ones of the most promising materials in modern photonics. They all have direct energy bandgap, which causes the high efficiency of photon’s emission, and absorption. In case of gallium nitride there is a possibility of forming solid solutions with InNand AlN, which allow tailoring of optical and electrical properties.
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Holographic exposure
LASER Nd -YAG355nm
DIFFRACTIONGRATING
(BEAMSPLITTER)
MIRROR 355nm
MIRROR 355nm
SPATIALFILTER
SAMPLE
SPATIALFILTER
α α
Grating period depends on exposure angle αand λ - the wavelength of the laser source:
αλ
sin2=Λ
Expo s ure ang le α [ de g re e s ] Pe rio d Λ [nm] S tripe width [nm]1,69 6000 30003,2 3170 1585
6,45 1580 79010,5 970 48515 685 342
20,4 509 255
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The 1st step– fabrication of a 1D grating
GRATING COUPLER OBTAINED WITH HOLOGRAPHIC EXPOSURE SETUP
Very useful method of producing corrugations in a photoresist film is exposing it with two interfering laser beams. It�s also known as holographic method of fabricating diffraction gratings. The photoresist patterns are made by exposing the resist, deposited on suitable substrate, to the holographic fringe pattern and immersing it in developer.
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2nd step –fabrication of the photonic crystal
TWO-STEP HOLOGRAPHIC EXPOSURE: in first step of that process one diffraction grating is produced in photoresist by exposing it with two interfering laser beams. Exposure angle a is shown in below and grating period depends on that parameter. After that sample was rotated through an angle Θ (inclination angle).
α
α
Θ
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Photonic crystals applications areas
• optics, • optoelectronics, • µ-wave technologies, • quantum engineering, • bio-photonics,• acoustics, • and many others.
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2D photonic crystals
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Photonic crystals - defects
Periodically structured materials
3D Pho to nic C rysta l with De fe c tscan collect energy inside microresonators
or guide it in waveguides
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Defects –Electron beam deposition
substrate
precursor
e-beam
e-
substrate
depositfragment
volatile
Precursors: organometallic compound hydrocarbon
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Pattern generation
Own result
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Pattern generation
Own result
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Modelling methods
� Frequency domain methods
Plane wave method(bang gap)
� Time domain method
Finite Difference Time Domain (band gap, defects, finite structure, transmission and reflectioncoefficient)
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0
( t)( t) = ( t) = -t
( t)( t) = ( t) = ( t)+t
ρ ∂∇ ⋅ ∇ ×∂
∂∇ ⋅ ∇ ×∂
B r,D r, E r,
D r,B r, H r, J r,
� Source free space
� Lossless medium : ε(r) is real in our interested region
� ε(r) linear and time invariant
� µ(r)=1
0ρ = =J
( ) ( )ε ω ε=r, r
Maxwell equations
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2
2
1 ( ) ( )( )
H r H rr c
ωε
∇× ∇× =r r
Hermitianoperator
Eigenvalue
Real
Positive value
2ω1
2
( )( )
H rH r
1
2
ωω
dla1 2( , ) 0H H =
Eigenvalue problem
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Various photonic crystal structures of different dimensions and corresponding Brillouin zones.
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Square lattice of columns
M
Γ X
Y
b2
b1
I Brillouin zoneColumns n=3.6Backgrounds n=1
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Square lattice of holes
M
Γ X
Y
b2
b1
I Brillouin zoneHoles n=1Background n=3.6
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Triangular lattice
Columns n=3.6Backgrounds n=1
b2
b1
Γ
M K
I Brillouin zone
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Photonic crystals slabSC (Semiconductor Clad)
CladHigh Aspect-Ratio
Dry Etching
AB (Air Bridge)
Selective Wet Etching
Selective Oxidization
OC (Oxide Clad)
Vol. 20, No. 11/November 2003/J. Opt. Soc. Am. A
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Photonic crystals – examples of application
• light sources including nanolasers, • waveguide components for a next era
functional circuits by photons, • passive components and fibers
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Fabrication technologies for photonic crystals
• semiconductor process techniques, • nano-manipulation techniques, • self-organization techniques, • holographic techniques,