Helicity and duality symmetry in light matter interactions: theory and applications

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 microscales. My thesis is an attempt to build a new tool for studying, understanding and engineering the interaction of electromagnetic radiation with material systems. The strategy that I have followed is to approach interaction problems from the point of view of symmetries and conservation laws. The main novelty 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 theoretical results to several different problems: Optical activity, zero backscattering, metamaterials for transformation optics and nanophotonics phenomena involving the electromagnetic angular momentum. I will show that the tool provides new insights and design guidelines in all these cases.