**Optimized Dipole Antennas on Photonic Band Gap Crystals**. R.
BISWAS, S. D. Cheng, E. Ozbay, S. McCalmont, W. Leung, G. Tuttle, K.-M. Ho,
*Microelectronics Research Center, Ames Laboratory*, and Department of
Physics and Astronomy, Iowa State University, Ames, IA 50011*.

- - -
Photonic band gap crystals have been used as a perfectly reflecting
substrate for planar dipole antennas in the 12-15 GHz regime. Photonic
band gap crystals with alumina rods and photonic band gaps between 12 and
14 GHz have been utilized. The position, orientation, and driving
frequency of the dipole antenna on the photonic band gap crystal surface
have been optimized for antenna performance and directionality. Virtually
no radiated power is lost to the photonic crystal resulting in gains and
radiation efficiencies larger than antennas on other conventional
dielectric substrates. Modeling of the antenna radiation patterns will
also be discussed.

**Microwave Applications of Photonic Crystals**. E. R. BROWN
(1), O. B McMahon (1), C. D. Parker (1), C. D. Dill III (1), K. Agi (2), K.
J. Mallory (2), 1. *Lincoln Laboratory, Massachusetts Institute of
Technology, Lexington, MA 02173*, 2. *Center for High Technology
Materials, University of New Mexico, Albuquerque, NM 87131*.

- - -
Photonic crystals are two- and three-dimensional periodic dielectric or
metallic structures that display a frequency gap in their electromagnetic
dispersion relation and an associated stop band in their transmission
characteristic. As such, photonic crystals are well suited to a number of
microwave and millimeter-wave applications for which conventional materials
and components are unsatisfactory. This talk will address the application
of planar antennas, transmission lines, and cavity reflectors. For
example, in the antenna application, a three-dimensional photonic crystal
acts as a substrate with its stop band designed to encompass the range of
operational frequencies of the antenna. In this case, the photonic crystal
rejects the majority of power radiated by the antenna into the free space
above the substrate. This makes the planar antenna much more efficient
than the same antenna placed on a homogeneous substrate made from the same
dielectric and/or metallic materials as the photonic crystal. Since the
high rejection of the three-dimensional photonic crystal occurs, by
definition, for all wave vectors, in principle, the high antenna efficiency
can be maintained over all directions of the antenna pattern above the
substrate. This feature makes the photonic-crystal antenna particularly
attractive for phased arrays. A key factor in each application is the
development of new types of photonic crystal structures that are superior
mechanically to conventional crystals or crystals that display enhanced
stop-band characteristics. For example, we have developed a new
face-centered-cubic (fcc) dielectric photonic crystal by stacking plates
that contain a triangular lattice of air atoms. The stacking is done in an
alternating close-packed (i.e., ABCABC . . .) fashion, so that a flat and
rigid surface is left on top for the fabrication of antennas, transmission
lines, and other planar circuits.

**Elastic Waves in Periodic Composite Materials**. E. N.
ECONOMOU*, M. Kafesaki*, *Research Center of Crete/FORTH, P.O. Box 1527,
71110 Heraklion Crete, Greece*.

- - - The question of spectral gaps in
the propagation of elastic waves in periodic composite materials has been
studied using the plane wave method. Elastic waves exhibit a richer
behavior than electromagnetic waves because they possess both longitudinal
and transverse components, each of a different propagation velocity, and
because they encounter mass density mismatch as well. By generalizing the
basic idea of the method of LCAO employed in electronic propagation, we can
predict and interpret the gross features of the elastic wave band structure
from the single sphere scattering cross-section. In particular, the
existence of a wide gap and its midgap frequency can be extracted from this
cross-section.

* Also at the University of Crete, Department of Physics.

**Coherent Potential Approximation for Classical Waves**. E. N.
ECONOMOU*, *Research Center of Crete/FORTH, P.O. Box 1527, 71110
Heraklion Crete, Greece*.

- - - The basic idea behind the Coherent
Potential Approximation (CPA) will be presented and elucidated by
considering a simple random tight-binding model. The successes and the
shortcomings of the CPA will be discussed. The difficulties associated
with the application of the CPA to classical waves will be emphasized and
various ways to overcome these difficulties (while keeping the
calculational scheme relatively simple) will be presented. Attention will
be focused on the question of the energy velocity.

* Also at the University of Crete, Department of Physics.

**Photonic Band Gap Materials**. K. M. HO, *Ames Laboratory*
and Department of Physics and Astronomy, Iowa State University, Ames, IA
50011*.

- - - We will review the progress in photonic band gap materials
at Iowa State University. Most of the work is based on structures [1,2]
which are designed for easy fabrication in a layer-by-layer fashion.
Results for both dielectric and metallic structures will be presented. We
will also discuss applications of these materials in the microwave and
millimeter wave regime as well as progress in the fabrication of these
structures at infra-red and optical wavelengths.

**The Magical World of Photonic Crystals: I and II**. J. D.
JOANNOPOULOS, *Massachusetts Institute of Technology*.

- - - A
tutorial introduction and survey of the fundamental concepts underlying
photonic bandgap materials are presented. New capabilities for the general
controls and manipulation of light are discussed and exciting specific
applications to optoelectronics highlighted.

**Theory of Photonic Bandgaps Materials**. S. JOHN,
*Department of Physics, University of Toronto, Toronto, Ontario,
Canada*.

- - -I review the recent history as well as the underlying
physics of light localization in periodic and disordered dielectric
materials. These materials are the photonic analogues of semiconductors in
the electronic industry. I describe the occurrence of photon-atom bound
states in these materials, as well as novel forms of laser activity and
co-operative quantum phenomena predicted to arise from photon localization
in these systems.

**Collective Phenomena in a Photonic Band Gap**. S. JOHN, T.
Quang, *Department of Physics, University of Toronto, 60 St. George
Street, Toronto, Ontario, Canada M5A 1A7*.

- - - We present a
theoretical overview of collective phenomena in a photonic band gap (PBG)
materials. This includes superradiance, photon hopping conduction, and a
novel quantum optical spin-glass state of *N* two-level impurity
atoms.

We show that near the edge of a PBG, the collective time scale
factor is equal to *N*$\phi$, where $\phi$=2/3 for an isotropic band
gap, and $\phi$=1 or 2 for anisotropic two-dimensional or three-dimensional
band edges, respectively [1]. These anomalous collective decay rates give
rise to peak intensities proportional to *N*$^{5/3}$, *N*$^2$,
and *N*$^3$, respectively. That is, the collection of atoms near a
3-d band edge can radiate faster (~*N*$^2$) and more intensely
(~*N*$^3$) than Dicke superradiance in free space. We show that a
fraction of the superradiant emission remains localized in the vicinity of
the atoms leading to a steady state in which the atomic system acquires a
macroscopic polarization and nonzero atomic population in the excited state
[2]. It suggests that a light emitting diode operating near a photonic
band edge will exhibit very high modulation speed and coherence properties
without recourse to external mirrors or even a true cavity mode. This
spontaneous symmetry breaking also suggest the possibility of observing
macroscopic coherent superpositions of states in superradiant devices.

Inside a PBG, where spontaneous emission is suppressed, the
resonant dipole-dipole interaction (RDDI) becomes the dominant interaction
mechanism between atoms. The random impurity atom positions are modeled by
means of Gaussian random distributions of RDDI's. This leads to a number
of interesting collective effects within the resulting photonic impurity
band. In particular, the collective hopping conduction (energy transfer)
rate is shown to be strongly enhanced [3]. In the presence of a localized
dielectric defect mode, collectively induced transparency occurs, i.e.,
there is almost no absorption of the resonant photon in the cavity mode by
a large collection of unexcited impurity atoms. In the presence of
fluctuations in the RDDI, quantum collapse of the defect mode photon
occurs. We also show that under certain nonequilibrium boundary
conditions, the system of two-level impurity atom in a PBG can tend to a
novel collective steady state, an optical analogue of a quantum spin-glass
state [4]. Such a state may be relevant to optical neural networks and for
optical information storage.

**Photonic Band Structures of Systems with Components
Characterized by Frequency-Dependent Dielectric Functions**. A. A.
MARADUDIN, *Department of Physics, University of California, Irvine, CA
92717*, V. Kuzmiak, *Institute of Radio Engineering and Electronics,
Czech Academy of Sciences, Chaberska 57, 182 51 Praha 8, Czech
Republic*, A. R. McGurn, *Department of Physics, Western Michigan
University, Kalamazoo, MI 49008*.

- - - In these lectures we describe
methods for calculating photonic band structures of systems that contain
components characterized by frequency-dependent dielectric functions, and
present results obtained by their use. Such components can be metallic, in
which case the dielectric function is assumed to have the simple, free
electron form $\epsilon (\omega ) = 1- \big( \omega_p^2 /\omega_2$, where
$\omega_p$ is the plasma frequency of the electrons; or they can be
fabricated from cubic, diatomic, polar semiconductors, in which case the
dielectric function has the form $\epsilon (\omega ) = \epsilon_{\infty}
\big( \omega_L^2 - \omega^2 \big) / \big( \omega_T^2 - \omega^2 \big)$,
where $\epsilon_{\infty}$ is the optical frequency dielectric constant,
while $\omega_L$ and $\omega_T$ are the frequencies of the longitudinal
optical and transverse optical vibration modes of infinite wavelength,
respectively. We first consider a one-dimensional, periodic array of
alternating layers of vacuum and a dielectric characterized by one or the
other of the frequency-dependent dielectric functions described above.
This is a model system whose photonic band structure can be calculated by
(1) a transfer matrix approach, which also yields the transmissivity of the
system as a function of frequency for comparison; (2) a search for the
zeros of a determinant; (3) transformation to a standard eigenvalue problem
for a real symmetric matrix; and (4) transformation to the solution of
several standard eigenvalue problems. The resulting band structure
displays an absolute band gap below the lowest frequency band in the case
that the dielectric medium is a metal, and nearly dispersionless bands in
the frequency range in which $\epsilon (\omega )$ is negative for both
forms of the dielectric function used. We then apply two of these methods,
viz. the transformation of the calculation into a standard eigenvalue
problem, and the determinantal approach, to obtain the photonic band
structures of an infinite array of parallel, infinitely long rods of
circular cross section fabricated from the materials described above,
embedded in a vacuum, whose intersections with a perpendicular plane form a
square or triangular lattice. The determinantal approach is then used to
obtain the photonic band structure of metal spheres arranged in a face
centered cubic array. The features observed in these band structures are
discussed in terms of the electromagnetic modes supported by each of the
cylinders or spheres forming these systems in isolation.

**Layer-by-Layer Methods in the Study of Photonic Crystals and
Related Problems**. A. MODINOS (1), V. Karathanos (1), N. Stefanou
(2), 1. *Department of Physics, National Technical University of
Athens, Zografou Campus, GR-15780, Athens, Greece*, 2. *Solid
State Section, University of Athens, Panepistimiopolis, GR-15784,
Athens, Greece*.

- - - We have developed a formalism [1] which
allows one to calculate the transmission, reflection and absorption
coefficients of electromagnetic waves incident on structures with
two-dimensional periodicity parallel to a given surface. One can also
calculate the complex frequency-band-structure corresponding to a given
surface of an infinite crystal. the structures considered are single
layers or multilayers of non overlapping spheres embedded in a host
material of a different dielectric function. The formalism is an
extension of the methods which have been developed in relation to
low-energy-electron diffraction by crystals.

A special case of multilayer is a slab of photonic crystal. We
describe a photonic crystal which exhibits an absolute frequency-gap and
examine the dependence of the gap on the geometry of the crystal. We
calculate the transmittance through a slab of the crystal, and show that
planar defects in the slab produce interface states of the electromagnetic
field at frequencies within the gap, manifested by sharp resonances in the
transmittance of these systems [2].

Using the same formalism, we demonstrate the possibility of
optically active photonic crystals, capable of turning the plane of
polarization of light transmitted through them through a considerable angle
[3].

Finally, we point out other applications of the above formalism,
and of variants of it, relating to scattering of electromagnetic waves by
periodic and non-periodic arrays of spherical scatterers [4].

**Micromachined Photonic Band Gap Crystals: From Microwave to
Far-Infrared Frequencies**. E. OZBAY, *Microelectronics Research
Center and Ames Laboratory*, and Department of Physics, Bilkent University,
Bilkent, Ankara 06533, Turkey*.

- - - We have recently developed a new
technique for building photonic band gap crystals with frequencies ranging
from microwave to far-infrared. The fabrication technique takes advantage
of a new dielectric rod-based design which can be easily achieved by
micromachining (110) silicon wafers. By stacking micromachined wafers in a
special order, we have built photonic crystals with full photonic band
gaps. A variety of crystals with different photonic band gap frequencies
are fabricated and tested by means of millimeter wave and terahertz
spectroscopy techniques. These results correspond to the highest frequency
photonic band gap results ever reported in scientific literature. The new
technique offers readily available photonic band gap materials for a
variety of millimeter and infrared wave applications.

**Transfer Matrix Techniques for EM Waves and Applications to
Photonic Materials**. J. B. PENDRY, P. M. Bell, *Department of
Physics, Imperial College, London, SW7, 2BZ, United Kingdom*.

- - -
Transfer matrix techniques have been adapted to the computation of the
electromagnetic response of photonic structures. They are proving a
powerful methodology. Drawing on analogies with low energy electron
diffraction theory, the whole calculation proceeds at a fixed frequency and
therefore has no difficulty taking account of materials such as metals
where $\epsilon$ is a strong function of $\omega$. In fact, photonic
structures that incorporate metals show some remarkable and unexpected
effects which we shall describe.

The main thrust of these lectures will be the practical one of
introducing the audience to the OPAL suite of computer codes. Detailed
notes on background theory will be available, and several test cases will
be presented. It will be possible, for those who wish, to leave with a
copy of the codes or to have them e-mailed immediately after the
conference.

**Optical Stop Bands and Photonic Band Gaps: Physics and
Applications**. P. St. J. RUSSELL, *Optoelectronics Research Center,
University of Southampton, Southampton SO17 1BJ, United Kingdom*.

- - -
The first clue of the presence of a periodic structure is often the
reflection of waves at certain specific wavelengths and angles of
incidence. The natural world is full of visually attractive examples of
this - moth and butterfly wings, snake scales, bird feathers and some gem
stones show bright flashes or "rainbows" of color upon rotation in
sunlight. The ranges of reflection where waves are rejected are commonly
known as *stop-bands*. Stop-bands govern the physics of, for example,
acousto-optics, X-ray, electron and neutron diffraction in crystals,
distributed feedback lasers, grating spectrometers, multilayer coatings,
and credit card holograms. In only a few cases, however, do these
stop-bands become so strong and numerous that propagation is forbidden in
all directions within limited bands of frequency - the *band-gaps*.
The best known example is the electronic band gap in semiconductor
crystals; and, of course, the most recent is the photonic band-gap, whose
eventual realization at infrared and visible wavelengths may revolutionize
optoelectronics.

**Waves in Random Media: Speed(s) and Other Theoretical
Matters**. P. SHENG, *Hong Kong University of Science and
Technology, Clear Water Bay, Kowloon, Hong Kong, and Exxon Research and
Engineering Co., Route 22 East, Clinton Twp., Annandale, New Jersey
08810*.

- - - How to define the wave speed in a random medium
where there is strong scattering ? This question has puzzled
generations of physicists and mathematicians, and provides the primary
motivation for this lecture. Starting from the basics, I will try to
make understandable the formalism of wave scattering, the coherent
potential approximation, and diffusive wave transport. The lecture will
bring the students up to date on the recent work of the Amsterdam group
on energy velocity, and will end with a new proposal.

**Design Considerations for a 2-D Photonic Band Gap Accelerator
Cavity**. D. R. SMITH, N. Kroll, S. Schultz, *Department of
Physics, University of California, San Diego, 9500 Gilman Drive, La
Jolla, CA 92093-0319*.

- - - We discuss recent progress in our
effort to develop a high gradient accelerator cavity based on Photonic
Band Gap (PBG) concepts. Our proposed cavity consists of a
two-dimensional (2-D) photonic lattice, composed of either dielectric or
metal scatterers, bounded in the third dimension by flat conducting (or
superconducting) plates. A defect introduced to the lattice, usually a
removed scatterer, produces a defect mode with fields concentrated at
the defect site and decaying exponentially in all directions away from
the defect site. The defect mode is designed to resonant at frequencies
in the 2-20 GHz range, where metals can still be used to confine the
Energy with minimal loss. We present in this paper some of the
technical considerations which have arisen relevant to this application,
and to PBG structures in general. In particular, we focus on
measurements and calculations carried out for a 2-D metal PBG cavity.

**Photonic Band Gap Structures: Studies of the Transmission
Coefficient**. M. M. Sigalas, C. M. SOUKOULIS, C. T. Chan, K. M. Ho,
*Ames Laboratory* and Department of Physics and Astronomy, Iowa State
University, Ames, IA 50011*.

- - - Using the transfer-matrix technique
for the propagation of EM in dielectric structures, introduced by Pendry
and Mackinnon [1] and discussed thoroughly by J. Pendry in our NATO ASI, we
present results for the transmission and reflection coefficient versus
frequency of the incident wave for different periodic and/or random
arrangement of 2D and 3D dielectric structures. This technique treats
dielectric arrangements, even when the dielectric constant is either
frequency dependent or has a non zero imaginary part. In particular, we
present transmission coefficient T studies for 2D arrays of cylindrical
dielectric [2] or metallic [3] scatterers, as well as cases where single or
multiple defects are introduced. In 3D, we present results [4] of T for
the "3-cylinder" structure of Yablonovitch, for the new layer-by-layer
structure of Iowa State University and for new very interesting metallic
structures. For all the cases studied, the results compared well with
experiment.

**Air-Bridge Microcavities**. P. R. VILLENEUVE, S. Fan, J. D.
Joannopoulos, K.-Y. Lim, G. S. Petrich. L. A. Kolodziejski, R. Reif,
*Massachusetts Institute of Technology, Cambridge, Massachusetts*.

- - - Photonic crystals have emerged as a new class of materials for the
fabrication of optoelectronic devices. We introduce and analyze a new type
of high-Q microcavity which allows for efficient coupling into other
components of optoelectronic circuits. It consists of a channel waveguide
and a one-dimensional photonic crystal; a band gap for the guided modes is
opened and a sharp resonant state is created by adding a single defect in
the periodic system. An analysis of the eigenstates shows that strong
field confinement of the defect state can be achieved with a modal volume
less than half of a cubic half-wavelength. We also present a feasibility
study for the fabrication of suspended structures with micro-sized features
using semiconductor materials. These microcavities offer exciting
possibilities for the fabrication of high density and high speed optical
interconnects and ultra-low threshold single-mode microlasers.

**Progress Toward Photonic Crystals at Optical Wavelength**. V.
Arbet, E. YABLONOVITCH, *University of California, Los Angeles, CA*,
A. Scherer, *California Institute of Technology, Pasadena, CA*.

- - -
We will review the challenges of fabricating 3-dimensional photonic
crystals at optical wavelengths, including the problems of
nano-fabrication, testing, and fulfilling the requirements for functional
opto-electronic devices. We will give a progress report toward meeting
these goals. Then, we will discuss the quantum optical properties of
photonic crystal micro-cavities, including especially the anticipated
applications of these tiny light-emitting structures, and how to place them
in context with other types of novel light emitting structures such as
Vertical Cavity Surface Emitting Lasers (VCSEL's). Finally, we will
mention some new forms of optical band structure such as triangular arrays
of VCSEL's which form a new type 2-dimensional band structure. Such
2-dimensional arrays may be useful for new types of nonlinear image
processing.

**Metallic Wire Band Structure at Micro-Wave Frequencies**. D.
Sievenpiper, C. Lam, M. Goertemiller, E. YABLONOVITCH, *University of
California, Los Angeles, CA*.

- - - Metallic materials, rather than
dielectrics, are particularly appropriate for making artificial band
structures in the important microwave frequency band. Such hexagonal
(graphite structure) wire mesh arrays are already evident in the window
screen of microwave ovens. The 3-dimensional version of such a hexagonal
array is a diamond structure wire mesh. By incorporating resistive and
capacitive defect arrays in such structures, a number of useful microwave
functions can be engineered. Such functions include omni-directional
spectral filters for radome covers, conformal antennas for cellular
telephony, multiple frequency arrays of narrow band filters for radio
communication, and quasi-optical arrays of transistors for high-power
microwave arrays. We will show some examples of the transition from
discrete arrays of defects such as the electromagnetic analog of benzene
molecular structure to a full tight-binding impurity band structure.