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Helicity and Duality Symmetry in Light Matter Interactions: Theory and Applications

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Helicity and Duality Symmetry in Light Matter Interactions: Theory and Applications Helicity and duality symmetry in light matter interactions: Theory and applications Ivan Fernandez i Corbaton arXiv:1407.4432v3 [physics.optics] 16 Dec 2015 Thesis accepted by Macquarie University for the degree of Doctor of Philosophy Department of Physics and Astronomy Except where acknowledged in the customary manner, the material presented in this thesis is original, to the best of my knowledge, and has not been sub- mitted in whole or part for a degree in any university. Ivan Fernandez i Corbaton i ii Acknowledgments First and foremost I want to thank my wife Magda for agreeing to embark in an adventure that was bound to change both our lives. It indeed has. Her support, in many different ways, has been crucial. I also want to thank my mother, Neus, for her amazing encouragement and support during all the years that I have been studying, working, and again studying in different countries; some of them quite far away from our home town of Almacelles (Catalonia). My brother Darius, and my extended family have also always been supportive of my choices. I particularly want to mention Julia, my goddaughter, to whom I owe a few steak dinners. A debt which I fully intend to settle. I have the fortune to have a few lifelong friends. I would trust and help them with anything. Every time that I see them I can feel my bond with them growing stronger, overcoming the effects of large spatio-temporal distances. I have made new friends in Macquarie University, to whom I wish the best for the future. I will make special mention of Xavier Zambrana-Puyalto, Nora Tischler and Mauro Cirio. I always enjoy talking with them about physics, conversations that have no doubt contributed to my thesis. I also very much enjoy our conversations about (so many!) other matters. I also would like to thank my friend and long time colleague Srikant Jayara- man. I learned a lot from Srikant during the years that we worked together in Qualcomm. Also, Srikant was the one that put the idea of a PhD in my head. Last, but not least by any measure, I thank my advisor A. Prof. Gabriel Molina-Terriza. His guidance, insights, flexibility and wide field of view have made this thesis possible. I want to particularly thank him for taking a risk with me. He took an electrical engineer as his student and approved of him venturing in uncharted territory quite early on. Judging from my short experi- ence, Gabriel seems to me the prototype of an all around physicist, blurring the divide between experimentalists and theorists. I have greatly benefited from his world class knowledge of both disciplines. iii iv ACKNOWLEDGMENTS Agra¨ıments Primer de tot, vull agrair-li a la meva dona Magda que acced´ısa comen¸car una aventura que havia de canviar les nostres vides. Com efectivament ha passat. El seu suport, de molts tipus, ha estat crucial. Tamb´evull donar-li les gr`aciesa la meva mare Neus pel seu suport i en- coratjament durant tots els anys en que he estat estudiant, treballant i es- tudiant altre cop a diferents pa¨ısos;alguns d'ells molt lluny del nostre poble d'Almacelles. El meu germ`aDario i la resta de la meva fam´ıliatamb´ehan estat sempre comprensius envers les meves anades i vingudes. Vull mencionar particularment la meva fillola J´ulia,a qui dec alguns sopars. Un deute el qual tinc la intenci´ode saldar. Tinc la sort de tenir alguns amics de per vida, als quals confiaria qualsevol cosa. Cada cop que els veig sento que la meva connexi´oamb ells es fa m´es forta, superant els efectes deguts a grans dist`anciesespai-temporals. He fet alguns amics nous a Macquarie University, als quals desitjo el mil- lor per al futur. Mencionar´een particular en Xavier Zambrana-Puyalto, la Nora Tischler i en Mauro Cirio. Sempre disfruto parlant amb ells de f´ısica, unes conversacions que han contribu¨ıta la meva tesi. Tamb´edisfruto de les conversacions amb ells sobre (tants!) altres temes. Tamb´evull donar-li les gr`aciesal meu amic, i company de feina durant molt de temps, Srikant Jayaraman. Vaig apendre molt d'en Srikant durant els anys en que v`aremtreballar junts a Qualcomm. A m´esa m´es,ell fou el que em va ficar al cap la idea de fer un doctorat. Per ´ultim,per`ono pas pel que fa a la import`ancia,vull donar les gr`acies al meu director de tesi, el professor associat Gabriel Molina-Terriza. Les seves indicacions, visi´oi flexibilitat han fet possible aquesta tesi. Volia agra¨ır-liespe- cialment haver pres riscos amb mi. Va acceptar com a estudiant un enginyer en telecomunicacions i va deixar que s'endins´esen territori desconegut molt r`apidament.Desde la meva curta experi`encia en f´ısica,en Gabriel em sembla el prototip del f´ısiccomplet, que esborrona la l´ıniaque divideix els experimental- istes dels te`orics.M'he beneficiat enormement del seu coneixement, de nivell mudial, de les dues disciplines. v vi AGRA¨IMENTS Publication list [FCTMT11] Ivan Fernandez-Corbaton, Nora Tischler, and Gabriel Molina- Terriza. Scattering in multilayered structures: Diffraction from a nanohole. Phys. Rev. A, 84:053821, Nov 2011. [FCZPMT12] Ivan Fernandez-Corbaton, Xavier Zambrana-Puyalto, and Gabriel Molina-Terriza. Helicity and angular momentum: A symmetry- based framework for the study of light-matter interactions. Phys. Rev. A, 86(4):042103, October 2012. [FCZPT+13] Ivan Fernandez-Corbaton, Xavier Zambrana-Puyalto, Nora Tis- chler, Xavier Vidal, Mathieu L. Juan, and Gabriel Molina-Terriza. Electro- magnetic duality symmetry and helicity conservation for the macroscopic maxwells equations. Phys. Rev. Lett., 111(6):060401, August 2013. [FCVTMT13] Ivan Fernandez-Corbaton, Xavier Vidal, Nora Tischler, and Gabriel Molina-Terriza. Necessary symmetry conditions for the rotation of light. J. Chem. Phys., 138(21):214311{214311{7, June 2013. [ZPFCJ+13] X. Zambrana-Puyalto, I. Fernandez-Corbaton, M. L. Juan, X. Vi- dal, and G. Molina-Terriza. Duality symmetry and kerker conditions. Opt. Lett., 38(11):1857{1859, June 2013. [FCMT13] Ivan Fernandez-Corbaton and Gabriel Molina-Terriza. Role of dual- ity symmetry in transformation optics. Phys. Rev. B, 88(8):085111, August 2013. [FC13] Ivan Fernandez-Corbaton. Forward and backward helicity scattering coefficients for systems with discrete rotational symmetry. Optics Express, 21(24):29885{29893, December 2013. [FCMT14] Ivan Fernandez-Corbaton and Gabriel Molina-Terriza. Introduc- tion to helicity and electromagnetic duality transformations in optics. Book Chapter, Handbook of Photonics, Wiley, Accepted for publication, 2014. [FCZPMT13] Ivan Fernandez-Corbaton, Xavier Zambrana-Puyalto, and Gabriel Molina-Terriza. On the transformations generated by the electro- vii viii BIBLIOGRAPHY magnetic spin and orbital angular momentum operators. Under review, arXiv e-print 1308.1729, August 2013. [TFCZP+14] Nora Tischler, Ivan Fernandez-Corbaton, Xavier Zambrana- Puyalto, Alexander Minovich, Xavier Vidal, Mathieu L. Juan, and Gabriel Molina-Terriza. Experimental control of optical helicity in nanophotonics. Light Sci Appl, 3(6):e183, June 2014. [TJFC+13] Nora Tischler, Mathieu L. Juan, Ivan Fernandez-Corbaton, Xavier Zambrana-Puyalto, Xavier Vidal, and Gabriel Molina-Terriza. Topologically robust optical position sensing. Under review, 2013. Abstract The understanding of the interaction between electromagnetic radiation and matter has played a crucial role in our technological development. Solar cells, the internet, cell phones, GPS and X-rays are examples of it. In all likelihood this role will continue as we strive to build better solar cells, millimeter sized laboratories and more sensitive medical imaging systems, among other things. Many of these new applications are stretching the capabilities of the tools that we use for studying and engineering the interaction of electromagnetic radiation and matter. This is particularly true at the meso-, nano- and micro- scales. My thesis is an attempt to build a new tool for studying, understanding and engineering the interaction of electromagnetic radiation with material sys- tems. The strategy that I have followed is to approach interaction problems from the point of view of symmetries and conservation laws. The main nov- elty is the systematic use of the electromagnetic duality symmetry and its conserved quantity, the electromagnetic helicity. Their use allows to treat the electromagnetic polarization degrees of freedom in a straightforward way and makes the framework useful in practice. Since the tool is based on symmetries, the results obtained with it are very general. In particular, they are often independent of the electromagnetic size of the scatterers. On the other hand, they are often mostly qualitative. When additional quantitative results are required, more work needs to be done after the symmetry analysis. Nevertheless, one then faces the task armed with a fundamental understanding of the problem. In my thesis, I first develop the theoretical basis and tools for the use of helicity and duality in the study, understanding and engineering of interactions between electromagnetic radiation and material systems. Then, within the general framework of symmetries and conservation laws, I apply the theoreti- cal results to several different problems: Optical activity, zero backscattering, metamaterials for transformation optics and nanophotonics phenomena involv- ing the electromagnetic angular momentum. I will show that the tool provides new insights and design guidelines in all these cases. ix x ABSTRACT Preface I have tried to write my thesis so that it may be useful for as many people as possible. In doing so, I have included material that will appear unnecessary to readers that are familiar with the study of symmetry transformations and Hilbert spaces. Such material is contained mostly in the background chapter (Chap. 1) and the first section of the theory chapter (Sec. 2.1). I hope that those parts will allow the readers that are not familiar with their content to better judge whether the core parts of my thesis, namely the rest of the theory chapter and the application chapters, are of any use to them.
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