Photonic Crystals for Various Applications

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Photonic Crystals for Various Applications Durdu
O. Guney EECS -Microelectronics Sabanci
University, Istanbul TR
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Light l
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Perfect Photonic Band Gap Materials
Periodic along one direction, and extends
infinity along other directions. Periodic
along two axis, and extends infinity along the
third axis. Periodic along three axes (x, y,
z) and can be obtained by filling (eg. sphere,
bar) a unit cell of any three dimensional lattice
and duplicating through space
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The idea of Photonic Crystals was first
introduced by Yablonovitch1 and John2
1. E Yablonovitch, Phys Rev Lett 58 2059
(1987) 2. S John, Phys Rev Lett 58 2486 (1987)
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The idea of a Photonic Crystal is based on
drawing analogies between light and
electrons Because both have a wave-like nature
and can therefore be diffracted !
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Consider Electrons and the Electronic Bandgap
first
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The electronic bandgap of an insulator arises
from the diffractive interaction of the electron
wavefunction with the atomic lattice, resulting
in destructive interference at certain
wavelengths
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What about Photons (ie, Light) and Origin of the
Photonic Bandgap ?
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Interaction of l i g h t with m a t t e r
Materials refractive index (or dielectric
constant e) describes the interaction of light
with matter !
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Setting up a periodic refractive index (like a
periodic potential of an atomic lattice) can
result in a similar band theory for photons
where certain frequencies cannot propagate
In other words, the photonic equivalent of an
insulator !
However,
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Electrons and photons are not on the
same wavelength scale
Wavelength of Visible Light l 400 nm-700
nm Wavelength of Electron l 0.1
nm
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To see the diffractive effects, we must make
large artificial atoms on the same scale as
the wavelength
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Computer models for doing the calculations for
semiconductors cannot be used for photons !
Schrodingers equation governs electrons,
but Maxwells equations describe the behavior of
light. With photons, one cannot safely neglect
polarization the way one can with electrons
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The electromagnetic properties of the photonic
crystals are completely determined by the
solutions of the macroscopic Maxwells equations
Periodicity of e(r) is described by the Bravias
lattice associated with the crystal
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denotes the lattice periodic part of the Bloch
function, i.e.,
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Restricting the Bloch vector to the first BZ,
corresponds to a back-folding of the dispersion
relation in the infinitely extended k-space into
the 1st BZ by means of translations through
reciprocal lattice vectors
This introduces a discrete band index n?N such
that the band structure is described by the set
associated with
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(transverse unit vectors)
(expansion coefficients - to be determined...)
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l/4nH
Light l
l/4nL
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nH1.52 nL1.38
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a
(square lattice of dielectric rods, e 8.9 r
0.2a)
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2D Hexagonal lattice structure (e 13, r 0.48a
)
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(Joannoupouloss group / MIT)
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(Joannoupouloss group / MIT)
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Face centered tetragonal lattice symmetry
fw/d0.28 c/d1.414
Complete bandgap (0.46c/a - 0.56c/a)
S Y Lin et al Nature 394 251 (1998)
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O Toader and S John, Science 292 1133(2001)
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What we did ...
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Working Principle
A 2D PBG Structure for Surface Temperature
Mapping Based on BB Radiation Characteristics
of the Target
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I(li,T)
Intensity
I(lj,T)


I(lk,T)
I(l,T) 2phc2/l5(ehc/lkT-1)
O(li,T)
O(lk,T)
O(lj,T)
I(l,T) ? O(l,T) SgI(l,T)
li lj lk
wavelength
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Proposed PBG Structure Design Parameters
2D Photonic Crsytal Slab Triangular array
(ie, 2D Hexagonal)of air holes GaAs Lossless
around 1.55-mm r/a 0.3 (a 0.382 -mm) e
11.4 Complete TE band-gap 0.213-0.280 (c/a)
Defect radii 0.51a, 0.54a, 0.57a.
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Relation between measured optical power and
resonant wavelengths (output radiation and BBR
are linked)

Ratio of optical powers for any two defects i and
j

Discrete formulisation for numerical analysis
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Notation

Analytical Solution

Obtain temperature, T

Constant scaling factors
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(A line defect is introduced in the periodic
array)
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Defect Size r 0.51a
waveguide region
point-defect region
localisation
Surface plot for the intensity of Hy component of
EM field for the defect radius of 0.51a,
corresponding to the resonant wavelength of 1.73
mm.
Amplitude of the Hy component of the field in
a.u. for the defect, 0.51a. The each colored line
indicates one slice passing through the isolated
point defect.
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Defect Size r 0.54a
waveguide region
point-defect region
localisation
Surface plot for the intensity of Hy component of
EM field for the defect radius of 0.54a,
corresponding to the resonant wavelength of 1.699
mm.
Amplitude of the Hy component of the field in
a.u. for the defect, 0.54a. The each colored line
indicates one slice passing through the isolated
point defect.
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Defect size r 57a
waveguide region
point-defect region
localisation
Amplitude of the Hy component of the field in
a.u. for the defecct, 0.57a. The each colored
line indicates one slice passing through the
isolated point defect.
Surface plot for the intensity of Hy component of
EM field for the defect radius of 0.57a,
corresponding to the resonant wavelength of 1.658
mm.
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Calculated input and output radiations and
coupling ratios, corresponding to the resonant
wavelengths in the first column, are illustrated.
Second column gives the corresponding defect
radii, while the third column indicates the
relative power coupling for these defects, which
is calculated by the FDTD method, in terms of a
constant ?. In the fourth and fifth columns are
given the input radiation in BB radiation form
and output radiation, which is emitted from the
crystal structure, respectively. Note that the
output radiation has a constant scaling factor S,
which our method for temperature reading makes
use of. Blue colour (last row) indicates the
fourth defect, which has a different profile than
the others.
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Few sensor applications in literature PBG
Tech. in IR-based Devices
Temperature mapping of delicate miniature
devices Explored the resonant properties of the
defects Remarkable for division multiplexing in
optical comm. Systems Highlights the
possibilities for - Optical MEMS - Advanced
Quantum Network Technology
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SOME OTHER PC APPLICATIONS
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Ultra-small optical integrated circuits by 3D
Photonic Crystals
ultra-small wavelength DEMUX circuit
ultra-small multiwavelength light source
(S Noda, Kyoto University, Japan)
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2D PBG Laser
H Park et al, APL79 3032(2001)
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Photonic Crystal Waveguide
(A Mekis,et al Phys. Rev Lett. 77 (1996)
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Crosstalk Reduction Using Photonic Crystal
Resonators
(Johnson et al, Optics Letters, Dec 1998)
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Tapped Delay Line Filter RF Signal Modulated on
Optical Carrier
(MIT Lincoln Laboratory)
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New Ways to Guide Light
J C Knight and P St Russell, Science 296 276
(2002)
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...and Finally, Quantum state transfer from one
node to another node, or Nam-i diger our failed
project !