Abstracts of Invited Lectures

From Micromaser to Microlaser. O. BENSON, H. Walther, Sektion Physik der Universitat Munchen and Max-Planck-Institut fur Quantenoptik, Federal Republic of Germany.
- - - In the lectures the work on the on-atom-maser or micromaser is reviewed. This maser system is the most fundamental where a single atom interacts with a single mode of a cavity. With this setup, the generation process of non-classical light and other quantum phenomena can be investigated in detail. Furthermore, a brief review of the microlaser work will be given where the phenomena of cavity quantum electrodynamics lead to a very low threshold of the laser system.
The simplest and most fundamental system for studying radiation-matter coupling is a single two-level atom interacting with a single mode of an electromagnetic field in a cavity. It received a great deal of attention shortly after the maser was invented, but at that time, the problem was of purely academic interest, since the matrix elements describing the radiation-atom interaction are so small that the field of a single photon is not sufficient to lead to an atom field evolution time shorter than the other characteristic times of the system, such as the excited state lifetime, the time-of-flight of the atom through the cavity and cavity mode damping time. It was therefore not possible to test experimentally the fundamental theories of radiation-matter interaction, which predict among other effects: a) a modification of the spontaneous emission rate of a single atom is a resonant cavity, b) oscillatory energy exchange between a single atom and the cavity mode, and c) the disappearance and quantum revival of Rabi mutation induced in a single atom by a resonant field.
The situation has drastically changed in the last ten years after it became possible to excite large populations of highly excited atomic states characterized by a high principal quantum number n of the valence electron. These states are generally called Rydberg states, since their energy levels can be described by the simple Rydberg formula. Such excited atoms are very suitable for observing quantum effects in radiation-atom coupling for three reasons. First, the states are very strongly coupled to the radiation field (the induced transition rates between neighboring levels scale as n4); second, transitions are in the millimeter wave region so that low-order mode cavities can be made large enough to allow rather long interaction times; finally, Rydberg states have relatively long lifetimes with respect to spontaneous decay.
Recently a number of experiments using low order cavities have also been performed in the visible spectral region. It was even possible to achieve lasing with a single atom. In the lecture, a review on these experiments will be given.

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.

*Operated for the U.S. Department of Energy by Iowa State University under contract no. W-7405-eng-82. This work was supported by the Director for Energy Research, Office of Basic Energy Sciences.

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.

[1] K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Sol. State Commun. 89, 413 (1994).
[2] a) E. Ozbay, E. Michel, G. Tuttle, R. Biswas, M. Sigalas, and K. M. Ho, Appl. Phys. Lett. 64, 2059 (1994).
b) E. Ozbay, E. Michel, G. Tuttle, R. Biswas, K. M. Ho, J. Bostak, and D. M. Bloom, Optics Lett. 19, 1155 (1994)
c) E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, Phys. Rev. B 50, 1945 (1994).

*Operated for the U.S. Department of Energy by Iowa State University under contract no. W-7405-eng-82. This work was supported by the Director for Energy Research, Office of Basic Energy Sciences.

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.

[1] S. John and Tran Quang, Phys. Rev. A 50, 1764 (1994).
[2] S. John and Tran Quang, "Localization of superradiance near a photonic band gap," Phys. Rev. Lett. (in press).
[3] S. John and Tran Quang, "Photon hopping conduction and collectively induced transparency in a photonic band gap," Phys. Rev. A (submitted).
[4] S. John and Tran Quang, "Optical spin-glass state of impurity two-level atoms in a photonic band gap," Phys. Rev. Lett. (submitted).

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].

[1] A. Modinos, Physica A 141, 575 (1987); N. Stefanou, V. Karathanos and A. Modinos, J. Phys.: Condens. Matter 4, 7389 (1992).
[2] V. Karathanos, A. Modinos and N. Stefanou, J. Phys.: Condens. Matter 6, 6257 (1994).
[3] V. Karathanos, N. Stefanou and A. Modinos, J. Mod. Optics, (in press).
[4] N. Stefanou and A. Modinos, J. Phys.: Condens. Matter 5, 8859, (1993).

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.

*Operated for the U.S. Department of Energy by Iowa State University under contract no. W-7405-eng-82. This work was supported by the Director for Energy Research, Office of Basic Energy Sciences.

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.

[1] J. B. Pendry and A. MacKinnon, Phys. Rev. Lett. 89, 2772 (1992).
[2] M. Sigalas, C. M. Soukoulis, E. N. Economou, C. T. Chan, and K. M. Ho, Phys. Rev. B 48, 14221 (1993).
[3] D. R. Smith, S. Schultz, N. Kroll, M. Sigalas, K. M. Ho, and C. M. Soukoulis, Appl. Phys. Lett. 65, 645 (1994).
[4] M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, Phys. Rev. B 49, 11080 (1994) and unpublished.

*Operated for the U.S. Department of Energy by Iowa State University under contract no. W-7405-eng-82. This work was supported by the Director for Energy Research, Office of Basic Energy Sciences.

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.

Last updated: Fri Jun 9 14:01:59 CDT 1995
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