Graphene Optics: Electromagnetic Solution of Canonical Problems

RICARDO A. DEPINE

Morgan & Claypool publication as part of IOP Concise Physics

Lugar: Bristol; Año: 2016 p. 134

978-1-6817-4308-0

This book was written in the same way I would teach a course at graduateor advanced undergraduate level on rigorous macroscopic description of theinteraction between electromagnetic radiation and structures containing graphenesheets, and assuming a course in electrodynamics developed from Maxwell?sequations as a prerequisite. To comply with the purpose of the IOP Concise Physics collection?keeping the text short while providing an introduction to thetopic?I have chosen to present only canonical problems with translational invariant geometries, in which the solution of the original vectorial problem can be reduced to the treatment of two scalar problems, corresponding to two basic polarization modes. This choice excludes other significant problems, such as the Mie-like solution for the scattering of electromagnetic radiation by a graphene sphere, which can be considered the paradigm of a 3D graphene particle, but includes the analogous solution for the scattering of electromagnetic radiation by a graphene wire of circular section, which can be considered the paradigm of a 2D graphene particle. The first chapter provides a summary of the topics of macroscopic electromagnetism which are essential to understand the approach used to model the electromagnetic response of graphene, such as the distinction between free versus bound charges and currents, the formulation of constitutive relations in the frequency domain, the constitutive properties of graphene described by the Kubo model for the graphene surface conductivity and the boundary conditions in the presence of graphene layers. The electromagnetic analysis of graphene structures associated with different degrees of symmetry is given in subsequent chapters, starting from geometries exhibiting two-dimensional continuous translational symmetry, such as the single flat and homogeneously doped sheet (the Fresnel problem, chapter 2) and the graphene planar waveguide (chapter 3), and then moving on to geometries with two-dimensional continuous translational symmetry along the graphene sheets and one-dimensional discrete translational symmetry along the normal direction (1D photonic crystals, section 3.4), before continuing with geometries with one-dimensional continuous translational symmetry along one tangent direction on the graphene sheet and one-dimensional discrete translational symmetry along the other (perpendicular) tangent direction on the graphene sheet (graphene gratings, chapter 4), before finally arriving at structures that keep theone-dimensional continuous translational symmetry along the wire axis, but do not have any translational symmetry in the plane perpendicular to this axis (graphene covered wires, chapter 5). Taking into account the fact that since the advent of photonic metamaterials exhibiting magnetism at high frequencies, manywell-established optic laws for conventional (nonmagnetic) materials now have anexception, the theoretical expressions in this book are given for materials withnon-unity magnetic permeability. However, for reasons of concision, very interesting phenomena, such as negative refraction and propagation in zero index or backward surface waves, have not been investigated in the examples. I really enjoy computational physics and I always try to include computationalproblems in my courses. In order to study the nature of the Universe, aphysicist needs numerical answers and although in the past it was not easy fornon-programmers to get into some type of computing environment, nowadays wehave excellent tools, such as the Python language, which makes numericalcalculations accessible to any science student, even those who have not attended a computer science class. Therefore, many figures in the book are accompanied byPython scripts, which I hope will generate discussions about physics, rather than programming. I hope the book will be useful for advanced undergraduate students, postgraduate students and postdocs interested in the rigorous macroscopic description of the interaction between electromagnetic radiation and two-dimensional materials. Comments and suggestions will be very much appreciated.