Photonic Crystal Photonic Bandgap Materials and Other Nanophotonics Research at:

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• Photonic Crystal (Photonic Band-gap Materials)
  and Other Nanophotonics Research at
• MIT
• Sandia Center for Integrated Nanotechnologies
• Optical Science and Technology Center at the
  University of Iowa
• NTT
• GIT

ELEC 7970 Summer 2003 Y. Tzeng Auburn University
http//nano.sandia.gov/pdf_docs/CINT_photon20-20
allpdfversion.pdf
http//ab-initio.mit.edu/photons/
http//nano.sandia.gov/pdf_docs/CINT_photon20-2
0allpdfversion.pdf http//nano.sandia.gov/NCINTpho
tonics.htm http//ostc.physics.uiowa.edu/prineas/
Poster2.pdf http//users.ece.gatech.edu/alan/11-2
7-Yeo20Photonic20Bandgap20Fabrication.pdf
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photonic crystals (also known as photonic
band-gap materials). Photonic crystals are
periodic dielectric structures that have a band
gap that forbids propagation of a certain
frequency range of light. This property enables
one to control light with amazing facility and
produce effects that are impossible with
conventional optics. Photonic crystals are
described exactly by Maxwell's Equations, which
we can (and do) solve by the application of
massive computational power.
Introduction The MIT Photonic-Bands (MPB)
package is a free program for computing the band
structures (dispersion relations) and
electromagnetic modes of periodic dielectric
structures, on both serial and parallel
computers. It was developed by Steven G. Johnson
at MIT in the Joannopoulos Ab Initio Physics
group. This program computes definite-frequency
eigenstates of Maxwell's equations in periodic
dielectric structures for arbitrary wavevectors,
using fully-vectorial and three-dimensional
methods. It is especially designed for the study
of photonic crystals (a.k.a. photonic band-gap
materials), but is also applicable to many other
problems in optics, such as waveguides and
resonator systems. (For example, it can solve for
the modes of waveguides with arbitrary
cross-sections.)
http//ab-initio.mit.edu/mpb/
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The Color of Shock Waves in Photonic Crystals
New physical effects occur when light interacts
with a shock wave propagating through a
one-dimensional photonic crystal. These new
phenomena include frequency shifts of light
across the photonic crystal bandgap, the
bandwidth narrowing of an arbitrary input signal
with 100 efficiency. It is also possible to slow
down the speed of light propagation by orders of
magnitude.
Movie http//ab-initio.mit.edu/photons/shocked_PC
/fastup_final_thumb
http//ab-initio.mit.edu/photons/shocked_PC/shocke
d_PC.html
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Resonant Cavities By making point defects in a
photonic crystal, light can be localized, trapped
in the defect. The frequency, symmetry, and other
properties of the defect mode can be easily tuned
to anything desired.
Such a point defect, or resonant cavity, can be
utilized to produce many important effects. For
example, it can be coupled with a pair of
waveguides to produce a very sharp filter
(through resonant tunnelling). Point defects are
at the heart of many other photonic crystal
devices, such as channel drop filters. Another
application of resonant cavities is enhancing the
efficiency of lasers, taking advantage of the
fact that the density of states at the resonant
frequency is very high (approaches a delta
function).
By changing the size or the shape of the defect,
its frequency can easily be tuned to any value
within the band gap. Moreover, the symmetry of
the defect can also be tuned. By increasing the
amount of dielectric in the defect, one can pull
down higher-order modes, corresponding to the s,
p, d, etcetera states in atoms. Here, we see a
p-like state in a two-dimensional photonic
crystal (square lattice of rods). The defect was
created by increasing the radius of the center
rod by 50.
http//ab-initio.mit.edu/photons/resonant-cavities
.html
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One-dimensionally Periodic Structures By adding
a periodic structure to a conventional waveguide,
it is possible to create a one-dimensionally
periodic photonic crystal. Such structures can be
used as high-Q filters.
One-Dimensional Photonic Crystals Below is an SEM
image of a air bridge structure fabricated (and
imaged) by K. Y. Lim, G. Petrich, and L.
Kolodziejski in CMSE. This is a conventional
waveguide, surrounded by air, into which a
regular set of holes have been punched (the
center to center spacing between the holes is 1.8
µm). The periodic structure provided by these
holes creates a band gap, a one-dimensionally
periodic photonic crystal (often referred to as
simply a "one-dimensional" photonic crystal,
although it exists in three dimensions). In the
center of the bridge, a slight defect in the
crystal has been formed by leaving extra space
between the holes. This forms a resonant cavity
which can be used as a filter. (This is a
prototype design for 4.5 µm light later designs
have been scaled down for wavelengths of 1.5 µm.)
http//ab-initio.mit.edu/photons/1d-crystal.html
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Three-dimensional Structures MIT Photonic
Crystal Group have proposed (in 1994 and 2000)
structures with full three-dimensional band gaps
which, we hope, will be amenable to fabrication.
The layers themselves are an alternating stack
of the two characteristic types of 2d (or slab)
photonic crystals dielectric rods in air and air
holes in dielectric. The fundamental structure
is actually very simple an fcc lattice (possibly
distorted) of air (or low-index) cylinders in
dielectric, oriented along the 111 direction.
This results in the layered structure rendered
above, and depicted schematically below (in
vertical and horizontal cross-sections)
Typical parameters, for an undistorted fcc
lattice of air cylinders in a dielectric constant
of 12 (Si), are da/sqrt(3), xa/sqrt(2),
r0.293a, and h0.93a, where a is the fcc lattice
constant. This results in a 21 complete
three-dimensional band gap, centered at a
frequency of 0.569 c/a.
http//ab-initio.mit.edu/photons/3d-crystal.html1
994
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Waveguide Bends in Photonic Crystals In
conventional waveguides, such as fiber-optic
cables, light is confined by total internal
reflection (also known as index confinement, a
more accurate term when the guide diameter is on
the order of the wavelength). One of the
weaknesses of such waveguides, however, 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 is a serious
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 a mode that is in
the band gap. This mode is forbidden from
propagating in the bulk crystal because of the
band gap. (That is, waveguides operate in a manner
similar to resonant cavities, except that they
are line defects rather than point defects.)
Below, we see the dispersion relation for the
guided mode created in a 2d photonic crystal
(square lattice of rods) by removing a row of
rods
http//ab-initio.mit.edu/photons/bends.html
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When a bend is created in the waveguide, it is
impossible for light to escape (since it cannot
propagate in the bulk crystal). The only possible
problem is that of reflection. However, the
problem can be analyzed in a manner similar to
one-dimensional resonant tunneling in quantum
mechanics, and it turns out to be possible to get
100 transmission. The following picture depicts
the electric field in a waveguide bend exhibiting
100 transmission.
Waveguide Bends in Photonic Crystals
http//ab-initio.mit.edu/photons/bends.html
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Single mode optical waveguide in photonic
crystals
http//www.ntt.co.jp/RD/OFIS/active/2002pdfe/ct34_
e.pdf
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Channel Drop Filters
Given a collection of signals propagating down a
waveguide (called the bus waveguide), a
channel-drop filter picks out one small
wavelength range (channel) and reroutes (drops)
it into another waveguide (called the drop
waveguide). For an example of how this is useful,
imagine an optical telephone line carrying a
number of conversations simultaneously in
different wavelength bands (i.e. using wavelength
division multiplexing). Each conversation needs
to be picked out of the line and routed to its
destination, and to separate a
conversation you need a channel-drop filter. It
turns out that by using photonic crystals, one
can construct a perfect channel drop filter--that
is, one which reroutes the desired channel into
the drop waveguide with 100 transfer efficiency
(i.e. no losses, reflection, or crosstalk), while
leaving all other channels in the bus waveguide
propagating unperturbed.
Movie http//ab-initio.mit.edu/photons/ch-drop-1h
.mov http//ab-initio.mit.edu/photons/
ch-drop-2s.mov
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Waveguide Intersections In constructing
integrated optical "circuits," space constraints
and the desire for complex systems involving
multiple waveguides necessitate waveguide
crossings. The basic idea is to consider
coupling of the four branches, or "ports" of the
intersection in terms of coupling through a
resonant cavity at the center. If the resonant
cavity can be prevented by symmetry from
decaying into the crossing waveguide, then the
situation reduces to one-dimensional resonant
tunnelling, and crosstalk will be prohibited.
This situation is achieved by requiring simple
symmetries in the waveguide and resonant modes,
as shown below
http//ab-initio.mit.edu/photons/cross-pbg-empty.m
ov
http//ab-initio.mit.edu/photons/cross-pbg-3x3.mov
http//ab-initio.mit.edu/photons/cross.html
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Photonic Crystals Periodic Surprises in
Electromagnetism Steven G. Johnson a one-week
seminar (five 1.5-hour lectures) MIT MRS
Chapter, 2003 IAP tutorial series, organized by
Ion Bita This course introduced light
propagation in periodic systems, photonic
crystals and band gaps, localized defect states,
3d fabrication technology, hybrid structures and
index guiding, and photonic-crystal fibers, among
other topics. This crash course will introduce
Bloch's theorem for electromagnetism, photonic
band gaps, the confinement of light in novel
waveguides and cavities by synthetic optical
"insulators," startling sub-micron fabrication
advances, exotic optical fibers, and will upend
what you thought you knew about total internal
reflection. We will focus less on gory
differential equations than on high-level
approaches such as linear algebra, variational
theorems, conservation laws, and coupled-mode
theory the course should be accessible to anyone
with a grasp of basic electromagnetism and who
does not quake in fear at the word "eigenvalue."
http//ab-initio.mit.edu/photons/tutorial/
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http//ostc.physics.uiowa.edu/prineas/Poster2.pdf
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http//nano.sandia.gov/pdf_docs/CINT_photon20-20
allpdfversion.pdf
http//nano.sandia.gov/pdf_docs/CINT-all-about.pdf
http//nano.sandia.gov/NCINTphotonics.htm
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http//users.ece.gatech.edu/alan/11-27-Yeo20Phot
onic20Bandgap20Fabrication.pdf
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Resonant photonic bandgap structures http//ostc.p
hysics.uiowa.edu/prineas/Poster2.pdf Fabrication
of photonic bandgap structures http//users.ece.ga
tech.edu/alan/11-27-Yeo20Photonic20Bandgap20Fa
brication.pdf Finite photonic crystal theory and
simulation http//www.ifh.ee.ethz.ch/erni/PDF_Pap
er/NCCR_Tut_9C_DEF.pdf MIT photonics
tutorial http//ab-initio.mit.edu/photons/tutorial
/photonic-intro.pdf Perfect Channel Drop
Filters http//ab-initio.mit.edu/photons/ch-drop.h
tml Movie for MIT photonic crystal tutorial
5 http//ab-initio.mit.edu/photons/tutorial/fink-
10.6.wmv