Theory of resonance and mode coupling in photonic crystal devices

Transcription

1 Theory of resonance and mode coupling in photonic crystal devices Thomas P. White A thesis submitted for the degree of Doctor of Philosophy Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), School of Physics, The University of Sydney, Sydney, Australia. August 2005

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3 Statement of originality This thesis describes work carried out in the School of Physics at the University of Sydney between April 2002 and August Except where otherwise acknowledged, the work presented is my own, and has not been submitted for a higher degree at any other university or institution. More specifically, my contribution to the work presented in Chapter 2 requires clarification. The formulation and numerical implementation of the Bloch mode method described in this chapter is largely the work of Professor Lindsay Botten and colleagues at the University of Technology, Sydney, and the University of Sydney. However, the numerical examples presented throughout this thesis are my own work and form some of the first research results obtained with the method. My research has thus provided valuable feedback regarding the application of the Bloch mode method to studying photonic crystal devices and this has led to a number of improvements and modifications. The discussions in Sections 2.4 and 2.5 regarding application issues are based on my own experiences of using the method, and hence are my main contribution to this chapter. The remainder of the research presented in Chapters 3 6 is my own work, which has been guided by advice and suggestions from my supervisors, Professors Ross McPhedran, Martijn de Sterke and Lindsay Botten. Thomas White Sydney, Australia August 2005 iii

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5 Acknowledgements While this thesis is a summary of my own research, it has only been possible as a result of contributions, both professional and personal, from many people. To list in detail all of the help, support and encouragement I have received during the last three and a half years would require many pages, so I apologise if I have missed anyone in my brief summary here. First and foremost I am indebted to my supervisors Professors Ross McPhedran and Martijn de Sterke at the University of Sydney, and Professor Lindsay Botten at the University of Technology, Sydney. I cannot imagine a better balance of skills, knowledge and personalities than the combined supervision of these three people has provided. It is always an inspiration to be involved in their discussions and to see the very different, but complementary approaches that each takes when tackling a new problem. With the combination of Ross broad knowledge of all things electromagnetic, Martijn s determination to find simple physical explanations wherever possible, and Lindsay s mathematical wizardry, very few difficult problems remain so for long. I hope I can absorb at least a fraction of each of these skills and put them to good use in the future. On a day to day basis, Ross and Martijn have provided support and advice on all aspects of this work, including meticulous proof-reading of this thesis. In addition, they have encouraged me to apply for several prizes and awards that I would not have considered otherwise. For these things and many others I am deeply grateful. Lindsay has also provided essential assistance along the way whenever I ran into numerical or computational problems or needed a question answered regarding the Bloch mode method. His ability to manipulate matrix equations in his head is rivalled only by his ability to manipulate them in Mathematica, both of which I have taken full advantage of at various times. For their support on various software related matters I want to thank Ara Asatryan and Nicolae Nicorovici for answering all my questions about the intricacies of the grating calculations and the multipole method and also Mike Steel and Christian Grillet for advice on using the RSoft software. I am also indebted to Mike for assistance with calculating the collimation parameters in Chapter 5. As a member of CUDOS since its inception in 2003, and before that, the theoretical physics group, I have had the pleasure of working in two vibrant and friendly research groups. I especially want to thank everyone in CUDOS for providing such a stimulating and inclusive research environment. Good luck! I hope there will be opportunities to v

6 vi work with some of you again in the future. On a more personal note, I could not have completed this work without the support and inspiration of family and friends. I especially want to thank my family Mum, Dad, Evelyn, Daniel (and Kelly and Jack) and Bridget for encouragement and support throughout. Thank you also to the Topps for welcoming me into their family over the last two years, and especially to Steph, who I have the greatest pleasure in acknowledging as one of my best friends as well as my sister-in-law. I cannot go any further without thanking the people I have lived with during the last three years. I especially want to thank Mert, Boris, Fiona, Ross and Laina for all the fun times at 14 Short St. Another group of people who have been a large part of my life for a number of years is the Sydney University Judo Club, who have provided me with a life outside physics, and an outlet for my frustrations during particularly tough weeks. Finally, I don t know how to express my thanks appropriately to my amazing wife Kathryn for her love, support and encouragement, especially when I needed it most during the tough thesis-writing months. I only hope I can be as patient and supportive as her own thesis approaches completion.

7 List of author s publications relevant to this thesis Journal papers [1] L. C. Botten, A. A. Asatryan, T. N. Langtry, T. P. White, C. M. de Sterke, and R. C. McPhedran, Semianalytic treatment for propagation in finite photonic crystal waveguides, Opt. Lett. 28, (2003). [2] T. P. White, L. C. Botten, R. C. McPhedran, and C. M. de Sterke, Ultracompact resonant filters in photonic crystals, Opt. Lett. 28, (2003). [3] L. C. Botten, T. P. White, C. M. de Sterke, R. C. McPhedran, A. A. Asatryan, and T. N. Langtry, Photonic crystal devices modelled as grating stacks: matrix generalizations of thin film optics, Opt. Express 12, (2004). [4] C. M. de Sterke, L. C. Botten, A. A. Asatryan, T. P. White, and R. C. McPhedran, Modes of coupled photonic crystal waveguides, Opt. Lett. 29, (2004). [5] T. P. White, C. M. de Sterke, R. C. McPhedran, T. Huang, and L. C. Botten, Recirculation-enhanced switching in photonic crystal Mach-Zehnder interferometers, Opt. Express 12, (2004). [6] L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, Bloch mode scattering matrix methods for modeling extended photonic crystal structures. Part I: Theory, Phys. Rev. E 70, (2004). [7] T. P. White, L. C. Botten, C. M. de Sterke, R. C. McPhedran, A. A. Asatryan, and T. N. Langtry, Bloch mode scattering matrix methods for modeling extended photonic crystal structures. Part II: Applications, Phys. Rev. E 70, (2004). [8] T. P. White, C. M. de Sterke, R. C. McPhedran, and L. C. Botten, Highly efficient wide-angle coupling into uniform rod-type photonic crystals, Appl. Phys. Lett. 87, (2005). Book chapter [9] L. C. Botten, R. C. McPhedran, C. M. de Sterke, N. A. Nicorovici, A. A. Asatryan, G. H. Smith, T. N. Langtry, T. P. White, D. P. Fussell, and B. T. Kuhlmey, From multipole methods to photonic crystal device modeling, in Electromagnetic theory and applications for photonic crystals, K. Yasomoto, ed. (CRC Taylor and Francis, Boca Raton, 2006). vii A full list of the author s publications is given in Appendix A.

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9 Contents Introduction 1 1 Photonic crystals: properties and applications Introduction One-dimensional photonic crystals Two-dimensional photonic crystals Three-dimensional photonic crystals Band structure and Bloch modes of 2D photonic crystals Band structure calculation TE and TM modes Band structures of square and triangular lattices Photonic crystal slabs The lightline Hole-type photonic crystal slabs Rod-type photonic crystal slabs D vs 3D modelling of PhC slabs Defect states in PhCs: cavities and waveguides Cavities Waveguides Linear waveguide modes Dispersion Integrated waveguide and cavity devices In-band applications Coupling to Bloch modes p and q parameters Negative refraction Auto-collimation Superprism effects Computational methods Discussion and thesis outline ix

10 x CONTENTS 2 Bloch mode scattering matrix method Introduction From a grating to a PhC Grating characterisation Basic PhC lattices Bloch mode calculation Bloch mode partitioning From a PhC segment to a PhC device Propagation in a single PhC medium Interfacing two semi-infinite segments Propagation through three segments Propagation through N segments Numerical aspects Modelling complex structures Lattice orientation Composite devices Discussion Coupled waveguide devices Introduction Photonic crystal and numerical parameters Coupled waveguide modes Coupling of two waveguides Coupling of three waveguides Waveguide coupling at interfaces Waveguide dislocations Fabry-Pérot cavity Folded directional coupler Semianalytic model: coupling analysis Semianalytic model: Bloch mode matrix method Transmission properties High-Q tuning Comparison with side-coupled cavity Discussion Coupled Y-junction Serpentine waveguide Derivation of the dispersion relation Serpentine waveguide properties Symmetry properties of the serpentine waveguide Conclusion

11 CONTENTS xi 4 Recirculating Mach-Zehnder interferometer Introduction Modal analysis Transmission characteristics Photonic crystal recirculating MZI structures Design Tuning ϕ Numerical results Semianalytic Bloch mode matrix derivation Recirculation in coupler-based MZIs Discussion Efficient wide-angle transmission into rod-type photonic crystals Introduction Plane wave coupling to semi-infinite PhCs Single cylinder scattering Grating properties Efficient coupling for auto-collimation Design Results: 2D vs 3D coupling properties Results: collimation Discussion Discussion and conclusions 149 Bibliography 153 A List of author s publications 173

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13 Introduction Since the achievement of low loss optical fibres in the 1970s, optics has had a dramatic impact on the way the world communicates. Today, more than ever, we depend on the ability to transmit and receive large amounts of information within seconds to and from almost anywhere in the world, and demand for higher transmission rates and cheaper systems continues to increase. While existing optical networks still rely extensively on electronic signal processing, this is becoming increasingly difficult as data rates approach the processing limit of high-speed electronic components. Therefore, the next generation of networks will require all-optical devices for switching, regeneration and monitoring of optical signals. Many of these functions have already been demonstrated experimentally, and basic all-optical components are already being incorporated into existing networks. All-optical processing has many additional advantages when compared to electronic processing, not the least being a reduction in operation costs due to reduced power and space requirements, and in some cases the possibility of processing multiple wavelength channels simultaneously without the need for demultiplexing. It has also been suggested that the new systems will be easier to adapt and reconfigure according to demand or network changes. Before these advantages can be realised, however, all-optical devices will have to be proven superior to the existing technology. Three key features that must be demonstrated are: reliability, low fabrication costs, compatibility with existing systems. An obvious way to achieve all three of these features is integration. The concept of a photonic integrated circuit is analogous to the semiconductor integrated circuit; many optical components integrated into a single functional device that can be inserted into an optical system to perform a specific processing task or tasks. While this may be the ultimate goal, many intermediate steps are required before it is reached. Of the many different technologies being proposed as a basis for photonic integrated circuits, photonic crystals are one of the most promising. Photonic crystals are periodically structured optical materials that provide unprecedented control over the 1

14 2 INTRODUCTION propagation of light down to wavelength scales. In addition, they exhibit many unique properties, ranging from unusual dispersion characteristics to photonic bandgaps frequency ranges for which light is unable to propagate. Much of the research into photonic crystals has been directed at understanding the properties of these bandgaps and the effects that occur when a defect state is introduced. While interest in photonic crystals extends to many areas outside optical communications such as quantum electrodynamics, spectroscopy and quantum computing, to name just a few, the focus of this thesis is the understanding and design of components for photonic integrated circuits. The rapidly developing field of photonic crystal research is entering a new and exciting third phase in which we are likely to see the first demonstrations of functional integrated photonic circuits. In the first phase, the potential of photonic crystals was recognised through theoretical observations and predictions, which led to the development of theoretical and experimental techniques for dealing with this new type of structure. The second phase saw the maturing of the field as many of the predicted properties of photonic crystals were demonstrated experimentally, and at the same time, improvement in theoretical and numerical methods provided further insight into the properties, leading to new device concepts and designs. As this phase has progressed to the present day, more and more of the essential building blocks for photonic crystal circuits have been demonstrated, including waveguides, resonant cavities and lasers, to the point where these components are competing with, and in some cases outperforming, more mature technologies. Fabrication techniques have been refined to the stage where they can reliably reproduce theoretical results and designs, even down to relatively fine details, while at the same time, modelling methods are capable of simulating realistic three-dimensional structures on a large scale. This is the situation of the field today as it enters the third phase. The research undertaken for this thesis spans the transition period between the second and third phases. During this time, the field has continued to expand at an almost exponential rate, as it has done for almost twenty years. In the first eight months of 2005, more than 1100 journal papers have been published with the phrase photonic crystal(s) in the topic list, with more than 350 of those appearing in the time it has taken to write this thesis. Keeping abreast of the developments in such a rapidly advancing research field is a challenge, and no single review of the subject can do it justice. Notwithstanding this, in Chapter 1 we attempt to provide an overview of photonic crystals as they relate to optical communications and more specifically the ultimate aim of producing a photonic integrated circuit. In later chapters we make three significant contributions to the field as it enters the third phase. The first contribution is the theoretical demonstration and analysis of a new class of photonic crystal device based on the combination of mode coupling and Fabry-Pérot resonance effects. These structures exhibit characteristics that make them promising candidates as compact, integrated photonic components. The second Thomson ISI Web of Science database:

15 INTRODUCTION 3 contribution is a study of highly-efficient coupling into uniform photonic crystals. The results of this study identify inherent advantages of rod-type photonic crystals over the more common hole-type structures for in-band applications. The third contribution of this thesis is the demonstration of an efficient and powerful theoretical approach to studying photonic crystal devices. Throughout this work, we combine general numerical methods with simple physical models to develop physical insight into the behaviour of photonic crystal structures. We show that this can lead to novel device geometries with highly attractive properties.

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