This monograph is a detailed introduction to the nascent and ever-evolving fields of metamaterials and nanophotonics, with key techniques and applications needed for a comprehensive understanding of these fields all detailed. These include the 'standard' and high-accuracy 'nonstandard' FDTD techniques, finite-difference frequency-domain mode solvers, the transfer matrix method, analytic calculations for dielectric and plasmonic waveguides, dispersion, Maxwell-Bloch and density functional theory, as well as design methods for constructing metamaterials and nanolasers, and quantum plasmonics. The book is intended for final-year undergraduates, as well as postgraduates or active researchers who wish to understand and enter these fields in a 'user-friendly' manner, and who have a basic understanding of and familiarity with electromagnetic theory.

Τhe incumbent technology for bringing light to the nanoscale, the near-field scanning optical microscope, has notoriously small throughput efficiencies of the order of 104 −105, or less. We report on a broadband, topological, unidirectionally guiding structure, not requiring adiabatic tapering and, in principle, enabling near-perfect (∼100%) optical transmission through an unstructured single arbitrarily subdiffraction slit at its end. Specifically, for a slit width of just λeff/72 (λ0/138) the attained normalized transmission coefficient reaches a value of 1.52, while for a unidirectional-only (nontopological) device the normalized transmission through a λeff/21 (∼λ0/107) slit reaches 1.14; both limited only by inherent material losses, and with zero reflection from the slit. The associated, under ideal (ultralow-loss) conditions, near-perfect optical extraordinary transmission has implications, among diverse areas in wave physics and engineering, for high-efficiency, maximum-throughput nanoscopes and heat-assisted magnetic recording devices.

Topological features, in particular distinct band intersections known as nodal rings, usually requiring three-dimensional structures, have now been demonstrated experimentally in an elegantly simple one-dimensional photonic crystal.

The classical “time-bandwidth” limit for linear time-invariant (LTI) devices in physics and engineering asserts that it is impossible to store broadband propagating waves (large Δω">Δω’s) for long times (large Δt’s). For standing (non-propagating) waves, i.e., vibrations, in particular, this limit takes on a simple form, ΔtΔω=1">ΔtΔω=1, where Δω">Δω is the bandwidth over which localization (energy storage) occurs, and Δt">Δt is the storage time. This is related to a well-known result in dynamics, namely that one can achieve a high Q-factor (narrowband resonance) for low damping, or small Q-factor (broadband resonance) for high damping, but not simultaneously both. It thus remains a fundamental challenge in classical wave physics and vibration engineering to try to find ways to overcome this limit, not least because that would allow for storing broadband waves for long times, or achieving broadband resonance for low damping. Recent theoretical studies have suggested that such a feat might be possible in LTI terminated unidirectional waveguides or LTI topological “rainbow trapping” devices, although an experimental confirmation of either concept is still lacking. In this work, we consider a nonlinear but time-invariant mechanical system and demonstrate experimentally that its time-bandwidth product can exceed the classical time-bandwidth limit, thus achieving values both above and below unity, in an energy-tunable way. Our proposed structure consists of a single-degree-of-freedom nonlinear oscillator, rigidly coupled to a nondispersive waveguide. Upon developing the full theoretical framework for this class of nonlinear systems, we show how one may control the nonlinear flow of energy in the frequency domain, thereby managing to disproportionately decrease (increase) Δt">Δt, the storage time in the resonator, as compared with an increase (decrease) of the system’s bandwidth Δω">Δω. Our results pave the way toward conceiving and harnessing hitherto unattainable broadband and simultaneously low-loss wave-storage devices, both linear and nonlinear, for a host of key applications in wave physics and engineering.

We comprehensively review several general methods and analytical tools used for causality evaluation of photonic materials. Our objective is to call to mind and then formulate, on a mathematically rigorous basis, a set of theorems which can answer the question whether a considered material model is causal or not. For this purpose, a set of various distributional theorems presented in literature is collected as the distributional version of the Titchmarsh theorem, allowing for evaluation of causality in complicated electromagnetic systems. Furthermore, we correct the existing material models with the use of distribution theory in order to obtain their causal formulations. In addition to the well-known Kramers–Krönig (K–K) relations, we overview four further methods which can be used to assess causality of given dispersion relations, when calculations of integrals involved in the K–K relations are challenging or even impossible. Depending on the given problem, optimal approaches allowing us to prove either the causality or lack thereof are pointed out. These methodologies should be useful for scientists and engineers analyzing causality problems in electrodynamics and optics, particularly with regard to photonic materials, when the involved mathematical distributions have to be invoked.