Electromagnetic Eigenvalue Problems and Nonhermitian Effects in Linear and Saturable Scattering

Abstract

In this thesis we address a series of new problems in non-hermitian optical scattering with increasing degrees of complexity. We develop the theory of reflectionless scattering modes, introducing a novel and broad class of impedance-matched eigenproblems: for a given structure, find the incident wavefronts and frequencies which are not partially reflected, but are instead transmitted through the scatterer, or dissipated within it. We analyze the relevant symmetry properties, and find that they support exceptional points (EPs) which can be directly probed with steady-state excitation. We study degenerate coherent perfect absorption (CPA EP), which is a specific example of the new kind of EP mentioned above. We show that the CPA EP is chiral in a ring resonator, and use this to design a resonator which predominantly absorbs or reflects light, depending on the direction of incidence. We extend CPA from cavities with a linear dielectric response to include the saturating nonlinearity and dispersion of a two-level absorbing medium. We show that the SALT algorithm in the single-mode regime can also be used to find the saturable CPA modes through a simple mapping. We also clarify the bad-cavity limit of dispersive but linear CPA, identifying new modes that are hybrids of the cavity and atomic degrees of freedom. We present and solve the general problem of scattering from an arbitrary cavity with a saturable two-level amplifying or absorbing medium, generalizing the known phenomenology of bistability that has mainly been studied in structures with little or no spatial complexity. We carefully analyze the validity of approximations used for isolated resonances, and find that the previously used inverse single-pole approximation requires some modification for the case of scattering.

PhD Theis, 226 pages, 28 figures

References in corpus (23)

• The physics of exceptional points
• Topological nature of bound states in the radiation continuum
• Coherent Perfect Absorbers: Time-reversed Lasers
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Visualization of Branch Points in PT-Symmetric Waveguides
• Light fields in complex media: mesoscopic scattering meets wave control
• Approaching Unit Visibility for Control of a Superconducting Qubit with Dispersive Readout
• Reversing the Pump-Dependence of a Laser at an Exceptional Point
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Supporting Online Material for "Strong Interactions in Multimode Random Lasers"
• Strong Interactions in Multimode Random Lasers
• Self-consistent multi-mode lasing theory for complex or random lasing media
• Invisibility and PT-symmetry
• Perfect Single-Sided Radiation and Absorption without Mirrors
• $\mathcal{P}\mathcal{T}$-symmetric microring laser-absorber
• Theory of the spatial structure of non-linear lasing modes
• Fast Excitation and Photon Emission of a Single-Atom-Cavity System
• Quantitative Verification of Ab Initio Self-consistent Laser Theory
• Unidirectional reflectionlessness and invisibility in the TE and TM modes of a PT-symmetric slab system
• Ab-initio multimode linewidth theory for arbitrary inhomogeneous laser cavities
• Unidirectional Invisibility and PT-Symmetry with Graphene
• Induced transparency: interference or polarization?
• Nonlocal effects in plasmonic metasurfaces with almost touching surfaces