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Explicit Symmetry Breaking in Electrodynamic Systems and Electromagnetic Radiation

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Explicit Symmetry Breaking in Electrodynamic Systems and Electromagnetic Radiation Explicit Symmetry Breaking in Electrodynamic Systems and Electromagnetic Radiation Explicit Symmetry Breaking in Electrodynamic Systems and Electromagnetic Radiation Dhiraj Sinha Singapore University of Technology and Design, Singapore Gehan A J Amaratunga University of Cambridge, UK Morgan & Claypool Publishers Copyright ª 2016 Morgan & Claypool Publishers All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher, or as expressly permitted by law or under terms agreed with the appropriate rights organization. Multiple copying is permitted in accordance with the terms of licences issued by the Copyright Licensing Agency, the Copyright Clearance Centre and other reproduction rights organisations. Rights & Permissions To obtain permission to re-use copyrighted material from Morgan & Claypool Publishers, please contact [email protected]. ISBN 978-1-6817-4357-8 (ebook) ISBN 978-1-6817-4356-1 (print) ISBN 978-1-6817-4359-2 (mobi) DOI 10.1088/978-1-6817-4357-8 Version: 20160401 IOP Concise Physics ISSN 2053-2571 (online) ISSN 2054-7307 (print) A Morgan & Claypool publication as part of IOP Concise Physics Published by Morgan & Claypool Publishers, 40 Oak Drive, San Rafael, CA, 94903, USA IOP Publishing, Temple Circus, Temple Way, Bristol BS1 6HG, UK To Jeffrey Goldstone the pioneer of spontaneous symmetry breaking The Centipede A centipede was happy quite, Until a frog in fun Said ‘Pray, which leg comes after which?’ This raised her mind to such a pitch She lay distracted in the ditch Considering how to run. —Anon Contents Preface ix Acknowledgements x Author biographies xi 1 Introduction 1-1 References 1-6 2 Symmetries and conservation theorems 2-1 2.1 Symmetry: a brief historical introduction 2-1 2.2 Symmetry in science 2-5 2.3 Symmetries in dynamic systems 2-8 2.3.1 Lagrangian formulation 2-8 2.3.2 Noether theorem 2-10 2.4 From symmetry to gauge theory 2-13 2.4.1 Gauge symmetry 2-14 2.4.2 Gauge theory 2-16 2.4.3 Symmetries in particle physics 2-18 2.5 Conclusion 2-22 References 2-22 3 Spontaneous symmetry breaking 3-1 3.1 Symmetry breaking 3-1 3.2 Historical overview and early evolution 3-3 3.3 Symmetry breaking in particle physics 3-5 3.4 Condensed matter, superfluidity and Bose–Einstein condensate 3-7 3.5 Spontaneously broken global symmetry 3-9 3.6 Higgs mechanism 3-13 References 3-15 4 Explicit symmetry breaking and electromagnetic radiation 4-1 4.1 Explicit symmetry breaking of electrodynamic systems 4-1 4.2 Electromagnetic radiation under non-conserved Noether current 4-5 vii Explicit Symmetry Breaking in Electrodynamic Systems and Electromagnetic Radiation 4.3 Explicit symmetry breaking and free electron lasers 4-8 4.4 Electromagnetic radiation under explicit symmetry breaking of 4-9 filter circuits References 4-12 5 Explicit symmetry breaking and dielectric antennas 5-1 5.1 Phenomenological challenges in the dielectric resonator antenna 5-1 5.2 Symmetry breaking in dielectric resonator antennas 5-3 References 5-7 6 Piezoelectric antennas 6-1 References 6-8 7 Radiation from a superconducting loop 7-1 7.1 Superconducting antennas 7-1 7.2 Experimental setup 7-2 7.3 Results 7-3 7.4 Analysis 7-6 References 7-6 8 Conclusion and future work 8-1 viii Preface It is a little known fact that Sir Joseph John Thomson (1856–1940), who discovered the electron more than a century ago, also made an exciting discovery on the asymmetric pattern of electric lines of field of an accelerated electron which is associated with electromagnetic radiation. Nearly a century later, while wandering on the premises of Pembroke College of Cambridge University, whose walls face the street leading to the site where the electron was discovered; it occurred to one of us (DS) that the asymmetric electric lines of field of an accelerated electron essentially represent broken symmetries of the electric field and radiation is the non-conserved Noether current emerging out of the charge centre. Thus, the idea of explicit symmetry breaking of an electrodynamic system and electromagnetic radiation was born. The book illustrates the theme in detail along theoretical and empirical lines. The concept of symmetry originated in architecture, evolved to take novel meanings in mathematics and currently embodies the central unifying theme in physics through its relationship with conservation laws. Transformation of symme- tries of physical systems, technically referred to as symmetry breaking, has offered new insights in discoveries of physical phenomenon ranging from ferromagnetism and superconductivity in condensed matter physics to the generation of mass in high particle physics through the Higgs mechanism. Despite all these developments, the ideas of symmetry breaking have not been applied in the context of classical electromagnetism and related engineering applications. The key objective of the current work is to unravel the beauty and excitement of this area to scientists and engineers which would have wide ranging ramifications. The book starts with a brief background on the origin of the concept of symmetry and its meaning as applied in the fields of architecture, mathematics and physics. In the next section, the relationship between symmetries and conservation theorems has been introduced with a minimum level of mathematical rigour. This is followed by a gentle introduction to the concept of symmetry transformation or symmetry break- ing. A special emphasis is towards quantum field theory where a slight level of mathematical rigour is introduced for the interested reader. The next section of the book is focussed on symmetries in electromagnetism and explicit symmetry breaking in the context of radiating electrodynamic systems like antennas. Following this, a chapter is dedicated to the operational aspects of dielectric antennas and how the idea of broken symmetries is used to explain its working. A section is on recent work done by our colleagues in Cambridge on radiation from superconducting loops under explicit symmetry breaking. After reading the book, the reader would develop a broad insight about symmetries and symmetry breaking and should be in a position to apply the knowledge in other fields of endeavour where the sky is the limit! ix Acknowledgements The book has grown out of an integrated effort through the contribution of a number of people who played a key role in research leading to the discovery of the explicit symmetry breaking mechanism of radiation at Cambridge. The most important role was played by the Centre for Advanced Photonics and Electronics of the Department of Engineering at Cambridge where most of the initial research was carried out. Nokia Research Centre, Cambridge, led by Dr Tapani Ryhanen, supported initial research on the mechanism of radiation from piezoelectric materials by sponsoring a research project on radio frequency energy harvesting. Martin Alexander from National Physical Laboratory, Teddington, UK, also provided helped in carrying out the tests in an anechoic chamber. He designed careful experiments to explore the exact source of radiation while developing an advanced antenna measurement laboratory dedicated to ultra-small antenna tests at NPL. DS acknowledges special support from Cambridge Commonwealth Trust and Wingate Foundation for the larger part of his graduate work at Cambridge which laid the initial foundation of this work Additional funding was obtained from the East of England Development Agency, UK, and the Cambridge Angels comprising Richard Parmee and Phil O’Donovan who invested in a company named Smantenna Ltd. Antenova, a Cambridge based dielectric antenna company offered help in tests in their Satimo Stargate antenna test chamber besides support in antenna prototyping. Professor Bryn Webber of Cavendish Laboratory and David Tong of Department of Mathematics at Cambridge provided theoretical support in the field of symmetry breaking aspects of the work through extended discussions. Some additional feedback was also provided by Professor Peter Littlewood, who was the head of Cavendish at that time and is currently the Director of Argonne National Laboratory. The work is an outcome of rather long innings of research in a process where innovation and discovery were seamlessly interwoven through a synergy between government funding, private investors and Trusts, along with academics from various departments—something which lies at the heart of the Cambridge phenomenon. Last but not least, the authors would like to extend their warm thanks to Dr Wayne Yuhasz, who offered us the chance of writing the book on behalf of the Institute of Physics. Chris Benson and his team deserve our heartfelt thanks for the painstaking approach in preparing the final draft. x Author biographies Dhiraj Sinha Dhiraj Sinha is currently working as a Research Fellow at Singapore University of Technology and Design. His areas of interest are electromagnetism, antennas, sensors and thermodynamics. He studied electrical engineering at Institute of Engineering and Technology, the University of Lucknow, India, and did his doctorate in the field of MEMS based radio signal sensors at the University of Cambridge. During his post-doctoral work at Department of Engineering, the University of Cambridge and later as the CTO of Smantenna Ltd, he worked on thin film antennas aimed at their integration at the chip level. He has also worked for Oscion, a technology consulting firm aimed at offering technology services to some niche companies. Gehan Amaratunga Professor Gehan Amaratunga FREng., FIET, CEng., obtained his BSc (1979) from Cardiff University and PhD (1983) from Cambridge, both in electrical engineering. He has held the 1966 Professorship in Engineering at the University of Cambridge since 1998. He currently heads the Electronics, Power and Energy Conversion Group, one of four major research groups within the Electrical Engineering Division of the Cambridge Engineering Faculty.
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