Since the unification of classical electromagnetism by Maxwell’s equations, the boundaries between Mathematics and Physics are slowly fading out thanks to the technological advances in nanoscience, metasurfaces, and optical devices, allowing the numerical and experimental contrast of more defiant and imaginative ideas, from symmetry breaking to singularity defects, and conserved quantities. For example, the use of complex numbers in photonics is usually associated as a mandatory technical step to describe relative phases, imaginary prefactors, or losses, sometimes seen as a challenge to be overcome, rather than a new algebraically closed sandbox where innovative concepts can be tested, even on most familiar equations. In this thesis, a mathematical revision of some fundamental equations in near-field photonics is presented, using an inductive approach at the transition from real to complex numbers, in several scenarios to effectively control new degrees of freedom of light. The first such quantity corresponds to the polarisation of the tails of a waveguided mode - which has recently attracted much attention due to spin-orbit interaction, momentum locking, and conservation rules for effective light control. From the Helmholtz dispersion relation, complex numbers are introduced in the propagation constant (representing lossy waveguides) finding an entanglement between the tails of evanescent modes and the losses of an optical waveguide, with further applications in light nanorouting via Argand angular spectrum selection. Later, this approach is revisit in the context of the interfaces between two materials, to explore the generalised Snell law, with complex-angle wave-vectors demonstrating a theoretical control of phase and amplitude independently by introducing a passive metasurface, allowing a local enhancement in the transmission inside any opaque material. These ideas are later discussed more generally in the context of toroidal dipolar families and open up possibilities for optimising single and periodic arrays of general electromagnetic dipolar sources beyond the multipolar angular spectrum expansion, which finally would be discussed in the context of skyrmions and topological defects.
Imagining the path of light in the nearfield landscape of nanophotonics: Losses, complex wave vectors, and novel dipolar sources
Perea, S. (Author). 1 Dec 2024
Student thesis: Doctoral Thesis › Doctor of Philosophy