Photonic band gap materials: semiconductors of light (Invited)

Sajeev John
Department of Physics, University of Toronto, Toronto, Ontario, Canada

The twentieth century has been the Age of Artificial Materials. One material that stands out in this regard are semiconductors of electricity. The electronics revolution of the 20th century has been made possible through the ability of semiconductors to microscopically manipulate the flow electrons. Along this line of technological progress, many scientists around the world have suggested that the 21st century will be the Age of Photonics, in which artificial materials are synthesized to microscopically mould the flow of laser light. Photonic Band Gap (PBG) materials provide a versatile new platform for this to take place. Unlike semiconductors which facilitate the coherent propagation of electrons, PBG materials execute their novel functions through the coherent trapping or localization of photons. This has important consequences in basic science. It may also be important for optical communications and computing. I review and discuss some of the key developments in the field of PBG materials over the past 15 years and suggest how they may impact us in the near future.

Two-dimensional photonic crystals and photonic crystal slabs (Invited)

Shanhui Fan
Stanford University

There exist important similarities and differences between a pure two-dimensional crystal system where the structure is assumed to be infinite in the third dimension, and a photonic crystal slab system, which consists of two-dimensional index contrast introduced in a high index slab. In this talk, we will highlight these similarities and differences. And we will discuss interesting properties and applications of these systems.

Measurement of the photonic bandgap in a hcp photonic crystal

J. M. Hickmann
University of California at Berkeley (also Universidade Federal de Alagoas, Brazil)
D. Solli, C. McCormick, R. Y. Chiao
University of California at Berkeley

We have measured the photonic bandgap in the transmission of microwaves through a 2D hexagonal closed packed (hcp) photonic crystal slab. The structure was constructed by cementing acrylic rods in a hexagonal closed-packed array to form rectangular stacks. We found a bandgap centered at approximately 11 GHz. Its depth depends on the number of layers, with an exponential decay of transmission on the order of several layers. We have also measured the dependence of transmission on the angle of incidence and polarization of the incoming radiation, finding that the bandgap persists at high angles but is shifted and in certain cases narrowed. This was a first step towards the study of the properties of 2D waveguide structures, based on this kind of crystal.

Potential Applications of Photonic Crystals in Photovoltaic Conversion and Silicon Diode Light Emission

Professor Martin A. Green
Centre for Third Generation Photovoltaics, University of New South Wales

Our recent work with silicon solar cells and light emitting diodes have demonstrated much higher radiative efficiencies than previously thought possible with silicon. This has encouraged exploration of ways in which manipulation of photonic densities of states in these devices might be used to further improve device performance. Increased absorptance for near bandedge light by photonic state manipulation is shown, in principle, to lead to increased performance of both types of device.

Photonic Band Gap Materials: The "Semiconductors" of the future? (Invited)

C. M. Soukoulis
Ames Laboratory and Department of Physics, Iowa State University and Research Center of Crete, University of Crete, Heraklion, Crete, Greece

We review the search of three-dimensional periodic dielectric structures that possess a photonic band gap and in addition, are easily fabricated experimentally. A new dielectric structure[1], constructed with simple layers of dielectric rods is introduced. This new structure has a full three-dimensional photonic band gap of appreciable frequency width. It was first built[2] in the microwave regime by stacking alumina rods, with a photonic band gap around 13 GHz. Crystals with photonic band gaps around 100 GHz and 500 GHz were fabricated using silicon wafers. Recently both the Sandia group and the University of Kyoto group have fabricated this structure at the micron wavelength range. The experimental results are in excellent agreement with theoretical calculations of the transmission coefficient. At midgap, an attenuation of 21 dB per unit cell is obtained. Defect states[3] of "donor" and "acceptor" type can be easily introduced by the addition and removal of dielectric material, respectively. Results for the propagation of the EM energy around an L-shaped[4] photonic crystal waveguide gives a transmission efficient of more than 90%.

In addition, the conditions of obtaining left-handed (LH) behavior in photonic crystals will be examined[5]. Finite difference time domain (FDTD) simulations are used to show that the existence of negative refraction does not necessarily imply LH behavior (i.e. negative index of refraction) for the photonic crystal. The time of evolution of an EM wave as it hits the interface between a positive and negative refractive index material is also examined. It is found that the wave is temporarily trapped on the interface and after a long time moves eventually in the negative direction. This way it is realized how negative refraction can occur on the interface of a material with negative index of refraction without violating causality and the speed of light limit.

[1] Science News 144, 199 (1993) and K. M. Ho et. al. Solid State Comm. 89, 413 (1994).
[2] E. Ozbay et. al. Phys. Rev. B 50, 1945 (1994).
[3] E. Ozbay et. al. Phys. Rev. B 51, 2780 (1995).
[4] M. Sigalas et. al. Microwave Opt. Technol. Lett. 23, 56 (1999); Phys. Rev. B 60, 4426 (1999).
[5] S. Foteinopoulou, E. N. Economou and C. M. Soukoulis, unpublished.

Unconventional photonic band gap systems and their novel properties (Invited)

Che Ting Chan
Physics Department, Hong Kong University of Science and Technology

Conventional classical wave band gap materials are conceived and constructed as a periodic array of scatterers, employing Bragg scattering to create forbidden band gaps. We will show that we can construct other classes of photonic band gap systems in which the spectral gaps are based on different mechanisms. Some of these unconventional systems do not even have orderness or periodicity. Examples are photonic quasi-crystals, metallo-dielectric photonic crystals, fractal-like structures, and spectral gaps from negative index materials. Each of these structures has unique and unusual properties due to their unusual structure, topology and constituent components. For example, the gap in photonic quasi-crystals are nearly isotropic, and the defect properties of these aperiodic systems are more complex and interesting than conventional photonic band gap systems since aperiodic arrangement has many inequivalent sites. We also show that photonic band gaps can be realized in any periodic structure using metal or metal-coated spheres as building blocks. We show by both theory and experiment that a specific class of fractal structures possesses a series of self-similar resonances, giving rise to alternating stop and pass bands and functions like a photonic band gap material, with the special property that it can be very compact so that it can be significantly subwavelength in all three dimensions. In addition, the transmission and reflection can be modulated by an external source. We will also discuss the unusual spectral gaps that may arise when we combine negative (effective) refractive index material with ordinary material.

Discrete gap solitons in photonic structures

Andrey A. Sukhorukov, Yuri S. Kivshar
Australian National University

It was recently demonstrated that optical solitons can be efficiently routed through two-dimensional networks of coupled defects, or cavities, in photonic crystals [1]. The soliton dynamics can be approximately described by the discrete nonlinear Schrodinger (DNLS) equation for the amplitudes of the defect modes. In the general case, it is necessary to take into account long-range interactions [2]. On the other hand, if the defects are weakly coupled, then the nearest-neighbor interactions are dominant. In the latter case, which we consider in our study, the DNLS equation has a standard form. This conventional DNLS equation has been extensively used during the last decade to study the properties of discrete solitons in one-dimensional arrays of optical waveguides [3].

We suggest a new way to engineer the properties of discrete solitons. We demonstrate that, if the parameters of defects vary periodically, then the so-called Rowland ghost gap appears in the linear transmission spectrum, and predict the existence of discrete solitons in this gap. The discrete gap solitons possess the properties of both conventional discrete and Bragg grating solitons. We show that both the soliton velocity and propagation direction can be controlled by varying the input light intensity, and discuss the soliton stability properties.

References:

1. D. N. Christodoulides and N. K. Efremidis, Opt. Lett. 27, 568 (2002).

2. S. F. Mingaleev and Yu. S. Kivshar, Phys. Rev. Lett. 86, 5474 (2001).

3. F. Lederer, S. Darmanyan, and A. Kobyakov, "Discrete solitons," in Spatial Optical Solitons, Vol. 82 of Springer series in optical sciences, S. Trillo and W. E. Torruellas, eds., (Springer-Verlag, New York, 2001), pp. 269-292.

Signal Regeneration in a Parametric Photonic Crystal

Gregory R Collecutt, Peter D Drummond
The University of Queensland

We present a concept for performing 4-R (re-amplification, re-timing, re-shaping, and re-tuning) signal regeneration all-optically within a 1-D parametric band gap wave guide. Performance is investigated by numerical simulation, in which full 4-R signal regeneration is demonstrated.

Soliton-Driven Photonics: A New Dawn (Invited)

A. D. Boardman, L. Valesco
Institute of Materials Research, Joule Physics Laboratory, University of Salford, Salford, M5 4WT, UK

This is tutorial talk that is designed to be a pleasant walk-through history, events and ideas that have brought us to our present state of appreciation of what solitons can do for us. It is an equation-free pictorial journey from Scott-Russell's interaction with his nineteenth century supporters, and detractors to the present day. The talk is designed both to introduce new directions and to give a perspective on how solutions are very much going to be a part of the photonics-driven life we lead in the 21rst century.

Single and two-photon photopolymerization for micro-nano fabrication (Invited)

Satoshi Kawata
Osaka University
Satoru Shoji
Kyushu University

Photopolymer is an attractive material for fabricating functional micro- andÅ@nano-devices. We have proposed a method for fabricating a complexÅ@three-dimensional structure based on two-photon polymerization [1]. TheÅ@resolution of the fabricated structure exceeds theÅ@diffraction limit of theÅ@light upto fifty nanometers [2]. Functions such as luminescence andÅ@elasticity can be implemented in the devices [3,4]. We have also developedÅ@a method for single- or double-exposure fabrication of three-dimensionallyÅ@periodic structures [5]. AÅ@hexagonal rod array which cross the periodicÅ@layers has been made with a three-beam interference plus a double-beamÅ@interference; anÅ@alternatively aligned woodpile structure has been also made with two four-beam interferences [6].

[1] S. Maruo, O. Nakamura, S. Kawata, Opt. Lett. 22, 132 (1997).
[2] T, Tanaka, H-B Sun, S. Kawata, Appl. Phys. Lett. 80, 312 (2002).
[3] S. Kawata, H-B Sun, T. Tanaka, K. takada, Nature 412, 697 (2001).
[4] H-B Sun, K. Takada, S. Kawata, Appl. Phys. Lett. 79, 3173 (2001).
[5] S. Shoji and S. Kawata, Appl. Phys. Lett. 76, 2668 (2000).
[6] S. Shoji and S. Kawata, (submitted).

Nonlinear photonic crystals: Towards all-optical technologies (Invited)

Sergei F. Mingaleev
Theoretical Nano-Photonics, Institut für Theorie der Kondensierten Materie, Department of Physics, University of Karlsruhe, 76128 Karlsruhe, Germany

One of the most promising applications of photonic crystals is a possibility to create compact integrated optical devices, which would be analogous to the integrated circuits in electronics, but operating entirely with light. To accomplish this, it is crucially important to achieve a dynamical tunability of the properties of photonic crystals, and one of the most promising approaches is based on the idea to employ nonlinear photonic crystals, i.e. photonic crystals made from dielectric materials whose refractive index depends on the light intensity. This opens a broad range of novel applications [1] of photonic crystals for all-optical signal processing and switching, which will be discussed in our talk.

[1] Sergei Mingaleev and Yuri Kivshar, "Nonlinear photonic crystals: Towards all-optical technologies", Optics & Photonics News, July 2002, pp. 48-51.

Photonic crystal fibres (Invited)

Martijn de Sterke
University of Sydney
Lindsay Botten
University of Technology Sydney
Boris Kuhlmey
University of Sydney and Institute Fresnel, Faculte des Sciences et Techniques de Saint Jerome, Marseille, France
Daniel Maystre
Institute Fresnel, Faculte des Sciences et Techniques de Saint Jerome, Marseille, France
Ross McPhedran
University of Sydney
Gilles Renversez
Institute Fresnel, Faculte des Sciences et Techniques de Saint Jerome, Marseille, France
Tom White
University of Sydney

One way to think about the modes of an optical fibre is that their presence depends on two conditions being satisfied. The first of these is the presence of a "mirror" which forms a cavity and prevents the light from escaping. The second is that some phase relation is satisfied. In standard optical fibres the mirror is due to total internal reflection at the core-cladding interface. However, it has been known for many years that other reflection mechanisms, such as Bragg reflection, can also be used. This is the reflection mechanism in Bragg fibres which consist of concentric rings of low- and high index glass. However, these fibres suffer from a low refractive index contrast, which limits the confinement. In a more recent invention, photonic crystal fibre, the index contrast is much larger since the structure that gives Bragg reflection consists of periodically positioned air holes that run parallel to the fibre. I will review the physics of these novel fibres and also discuss possible applications.

Design principle for effectively single mode TE Bragg fibres – scalar light?

Ian Bassett
Australian Photonics CRC, University of Sydney
Alexander Argyros
Australian Photonics CRC University of Sydney

Bragg fibres have no true bound modes, but can be designed so that they have just one mode which is orders of magnitude less leaky than any other. The mode so singled out is TE – so that the modal field is invariant under rotation about the fibre axis, like the fibre itself. It is necessary to say what is meant by single mode in this leaky context, because the property is length dependent. If a leaky fibre of given cross section is short enough, many modes suffer little loss, and if it is long enough, no significant power remains in any mode. This suggests defining a fibre to be effectively single moded if its length L lies between two limits, Lsm < L < Lmax where Lmax is the length at which even the least leaky mode is exhausted (say less than 1% left) and Lsm is the length at which the other modes are similarly exhausted. Provided one mode is a lot less leaky than any other, there will be a useful range of lengths at which the fibre is effectively single moded. Given fibre which is single moded in this sense, since fibre and modal field are round, there would be no orientation problem in splicing or making couplers from such fibres. One can imagine making a fibre network in which polarisation plays no role, and in which light might be described as being in effect scalar, free from the problems which polarisation brings in most applications.

Modeling the dynamics of holey fibre drawing

Dr. Bill Slade, Dr. Arnan Mitchell
RMIT School of Electrical and Computer Engineering

The numerical modeling of the flow processes encountered in holey-fibre drawing present a number of challenges. This work attempts to address these challenges to build a reliable model for the incompressible, viscous, non-isothermal flow in the neck-down region of a holey fibre draw. We wish to study the deformation of the holes as a function of flow parameters (namely: surface tension, viscosity, internal hole pressure, temperature, draw speed).

Starting with the incompressible Navier-Stokes and energy equations and expanding on the work of Fitt, et al. [1], it is possible to develop a set of partial differential equations which describe the geometry of a fibre with non-axisymmetrically placed holes. This method is preferred over the use of brute-force finite-difference or finite-element methods because the lineal dimensional ratios in the draw-down region can exceed 100-1000. The amount of discretization needed to resolve the fibre and hole features using traditional finite numerical flow solvers in three dimensions would likely be enormous.

We will present elements of the mathematical foundation for the flow geometry model. Of particular importance are the treatment of the velocity terms in the axisymmetric as well as the non-axisymmetric case. Several critical approximations and scaling tricks are needed to make the problem tractible (even on supercomputing platforms). Candidate numerical methods will be briefly discussed.

Analytical and computational methods for photonic crystal waveguides (Invited)

Lindsay C Botten, Ara A Asatryan, Timothy N Langtry
Department of Mathematical Sciences, University of Technology, Sydney
C Martijn de Sterke, Ross C McPhedran
School of Physics, University of Sydney

An essential component in the design and fabrication of large scale integrated optical circuits is the photonic crystal waveguide. In two-dimensional photonic crystals, waveguides may be introduced by a channel defect, the most common example of which is removal of a line of scatterers that leaves a line shaped void. When the crystal is operated in a band gap, we have a device which can channel light with minimal loss, either in a straight line or around tight bends, when two straight guides are jointed together. Because of their practical importance, there is substantial interest in the theoretical and computational modelling of the properties of waveguides. To date, however, the these studies have been almost exclusively computational in nature. While this modelling accurately predicts various performance characteristics, it does not provide significant insight into the underlying physical processes involved. Coupled mode theories that provide a description of the transmission properties have been developed, although the limits of their applicability are not clear.

Closely related is the issue of coupling radiation into and out of waveguides — a problem that requires a complete knowledge of the modes of the guide. This solution of the full circuit problem —-- involving coupling in, transmission and coupling out --— is of substantial interest and is the subject of this paper. In particular, we outline a rigorous theory which can accurately and efficiently model the process, and which can be extended to handle the interfacing of guides to other devices. We present two theoretical models, one which enables us to characterise simply the dispersion properties of guides, and a second, more elaborate theory, used in the solution of the full circuit problem, which generates a complete set of modes, thus enabling the exact calculation of the energy properties of the structure.

In the first of these, we treat an infinite waveguide as a channel sandwiched between two semi-infinite photonic crystals, each of which are characterised by a reflection scattering matrix (which is a by-product of the calculation of the modes of the crystal). From this, it is straightforward to develop a dispersion equation through consistency relations that yields the propagating modes of the guide. In this treatment, we regard the bulk crystal that surrounds the guide channel as a stack of diffraction gratings, each of which is characterised by its reflection and transmission scattering matrices, and we exploit Bloch’s theorem to generate the modes that subsequently enable us to develop exact expressions for field and energy quantities within both finite and infinite crystals.

For the full circuit problem, we consider an alternative configuration of an infinite array of periodically spaced waveguides, sufficiently separated so that their cross-talk is negligible. Using a scattering matrix treatment and Bloch’s method, we generate a complete set of modes for the structure and reveal an interesting set of modal orthogonality relations which underpin the subsequent energy calculations. From this, we proceed to develop an exact solution of the field problem, analytic expressions for the transmittance and various field quantities, and undertake an asymptotic analysis for the case of long guides. In doing so, we demonstrate an equivalence between this formulation and the theory of Fabry-Perot interferometers. In the case of monomodal propagation, we develop simple quasi-analytic expressions for these quantities involving only two parameters, which generate results of outstanding accuracy.

Nonlinear Magnetooptic Layered Structures (Invited)

A. D. Boardman, M. Xie
University of Salford

Magneto-optics traces its origins back to the Faraday and Cotton-Mouton effects, which permit optical polarisation control and introduce non-reciprocal propagation. The latter is so important that it has led to commercially viable bulk devices like isolators, switches and information storage media. In spite of all this activity, nonlinear magneto-optics is still very much an open field with the potential to produce many new and pivotal devices. In this context, we will discuss the propagation of diffraction-free light beams, called spatial solitons, in nonlinear, planar, layered magnetooptic waveguides. Varying degrees of complex linear magnetooptic layers are used, closely coupled to optically nonlinear layers. The presence of interfaces is shown to be vital because they introduce an impressive degree of dynamical control. Although the deployment of a considerable range of methods is possible, in order to get a feeling for the soliton control, we opt for a split-field method. It is pointed out that magnetooptic systems are very easy to create, in principle, but that low quality manufacturing tolerances can quickly destroy any nonreciprocity. Nevertheless, elegant degrees of sophistication can be mastered and the area looks to be very promising for future all-optical processing.

The sheer number of bulk isolators in use represents a major investment by the photonics industry, so any real progress using integration with diode lasers is welcome. The approach is to use ferromagnetic materials such as iron, nickel and related alloys deposited as thin polycrystalline films onto semiconductors. It is apparent that complex device structures may use periodic magnetic fields and photonic crystals. Indeed, (magneto-) photonic crystals will add a new dimension through microcavity resonance and band-structure control e.g., large group velocity dispersion and super-prism effects. Although the majority of this talk will focus upon a limited set of complex structures and report precursor studies to full integration, it will also report some (magneto-) photonic crystal work. The latter will receive limited attention but, together with some results on vortices in gyrotropic media, will point the way forward. The main aim is to address the 'classic' magnetooptic functionalities of non-reciprocal isolation and circulation.

Bandgap design: 1 dimension and beyond

Graham Town
Department of Electronics, Macquarie University
Rui Hong Chu
School of Electrical Engineering, University of Sydney

Determining the bandgap characteristics of a given periodic or quasi-periodic structure is relatively straightforward. Bandgap design is the inverse problem, in which a specified response is given, and the structure to produce it must be determined.

We review the fundamentals of bandgap design in the context of lossless one-dimensional structures (e.g. Bragg grating filters and optical fibre waveguides) in which the application of inverse scattering and digital filter design techniques are beginning to make a significant impact. We then discuss the possibilities for bandgap design in higher dimensions.

Left-handed metamaterials. An overview.

Ilya Shadrivov
Australian National University

These days, there is a growing interest in the study of a new type of composite materials possessing unusual properties. In such materials, electromagnetic waves are backward or left-handed, and that is why these composites are called left-handed materials (LHM). It has been claimed, that these materials possess both negative dielectric permittivity and magnetic permeability. In the first theoretical study of the LHM [1], a number of remarkable phenomena were predicted. One of them, the negative refraction of the electromagnetic waves at the interface between the LHM and a usual material, has been recently observed experimentally for microwaves. It has been suggested, that a slab of the LHM can act as a perfect lens without diffractional resolution limit. However, it is a controversial topic nowadays. Photonic crystals possess a complicated band gap structure and under particular conditions, the LHM phenomena are shown to take place in photonic crystals. There is a potential to create perfect lenses and many other useful devices for optical applications.

1. V.G. Veselago, Usp. Fiz. Nauk 92, 517 (1968)