Realising Type II Weyl Points in an Optical Lattice

The recent discovery of the Lorentz symmetry-violating 'Type II' Weyl semimetal phase has renewed interest in the study of Weyl physics in condensed matter systems. However, tuning the exceptional properties of this novel state has remained a challenge. Optical lattices, created using standing laser beams, provide a convenient platform to tune tunnelling parameters continuously in time. In this paper, we propose a generalised two level system exhibiting type II Weyl points that can be realised using ultra-cold atoms in an optical lattice. The system is engineered using a three-dimensional lattice with complex $\pi$ phase tunnelling amplitudes. Various unique properties of the type II Weyl semimetal such as open Fermi surface, anomalous chirality and topological Fermi arcs can be probed using the proposed optical lattice scheme.Comment: 5 pages, 4 figure

Bandwidth bounds for wide-field-of-view dispersion-engineered achromatic metalenses

Optical systems with wide field-of-views (FOV) are crucial for many applications such as high performance imaging, optical projection, augmented/virtual reality, and miniaturized medical imaging tools. Typically, aberration-free imaging with a wide FOV is achieved by stacking multiple refractive lenses (as in a "fisheye" lens), adding to the size and weight of the optical system. Single metalenses designed to have a wide FOV have the potential to replace these bulky imaging systems and, moreover, they may be dispersion engineered for spectrally broadband operation. In this paper, we derive a fundamental bound on the spectral bandwidth of dispersion-engineered wide-FOV achromatic metalenses. We show that for metalenses with a relatively large numerical aperture (NA), there is a tradeoff between the maximum achievable bandwidth and the FOV; interestingly, however, the bandwidth reduction saturates beyond a certain FOV that depends on the NA of the metalens. These findings may provide important information and insights for the design of future wide-FOV achromatic flat lenses.Comment: 8 pages, 3 figure

Basic properties of incomplete Macdonald function with applications

The incomplete version of the Macdonald function has various appellations in literature and earns a well-deserved reputation of being a computational challenge. This paper ties together the previously disjoint literature and presents the basic properties of the incomplete Macdonald function, such as recurrence and differential relations, series and asymptotic expansions. This paper also shows that the incomplete Macdonald function, as a simple closed-form expression, is a particular solution to a parabolic partial differential equation, which arises naturally in a wide variety of transient and diffusion-related phenomena

Unidirectional and diffractionless surface plasmon-polaritons on three-dimensional nonreciprocal plasmonic platforms

Light-matter interactions in conventional nanophotonic structures typically lack directionality. Furthermore, surface waves supported by conventional material substrates do not usually have a preferential direction of propagation, and their wavefront tends to spread as it propagates along the surface, unless the surface or the excitation are properly engineered and structured. In this article, we theoretically demonstrate the possibility of realizing \emph{unidirectional and diffractionless surface-plasmon-polariton modes} on a nonreciprocal platform, namely, a gyrotropic magnetized plasma. Based on a rigorous Green function approach, we provide a comprehensive and systematic analysis of all the available physical mechanisms that may bestow the system with directionality, both in the sense of one-way excitation of surface waves, and in the sense of directive diffractionless propagation along the surface. The considered mechanisms include (i) the effect of strong and weak forms of nonreciprocity, (ii) the elliptic-like or hyperbolic-like topology of the modal dispersion surfaces, and (iii) the source polarization state, with the associated possibility of chiral surface-wave excitation governed by angular-momentum matching. We find that three-dimensional gyrotropic plasmonic platforms support a previously-unnoticed wave-propagation regime that exhibit several of these physical mechanisms simultaneously, allowing us to theoretically demonstrate, for the first time, unidirectional surface-plasmon-polariton modes that propagate as a single ultra-narrow diffractionless beam. We also assess the impact of dissipation and nonlocal effects. Our theoretical findings may enable a new generation of plasmonic structures and devices with highly directional response

Dispersion degrees of freedom in metamaterials and metasurfaces

146 pagesUnderstanding the intricacies of the interaction of light and matter is crucial to our perception of the world around us and for creating devices that harness light for technological applications. Many conventional devices such as telescopes, microscopes, cameras, and even reading glasses were based on early insights into the principles of refraction and reflection of light, whereas modern devices such as flat lenses, nano-antennas, and photonic waveguides are based on more complex degrees of freedom afforded by the ability to engineer light-matter interactions at wavelength and sub-wavelength scales. This dissertation investigates key novel degrees of freedom in electromagnetics and photonics, such as topology and nonlocality, which emerge from non-trivial features of the optical response of a material/structure in frequency-momentum domain, and are therefore inextricably linked to the temporal and spatial \textit{dispersion} properties of light in matter. Engineered (meta)materials and metasurfaces have enabled, over the past two decade, a new level of flexibility to realize of a broad range of anomalous optical properties. Most of my work on novel dispersion degrees of freedom has indeed focused on metamaterial platforms, as they provide a fertile playground for these investigations. In particular, in the first two chapters of this dissertation, I discuss topological, nonreciprocal, and chiral plasmonic metamaterials, with a focus on one-way edge (surface) modes, their momentum-space properties, and whether their dispersion diagram is truly unidirectional. I also show how the presence of losses alter momentum-space modal degeneracies and may lead to topological transitions. In the next two chapters, I discuss the relevance of engineering the frequency-dependent and momentum-dependent response of another important class of metamaterial systems, namely, metasurfaces for imaging applications. For instance, a broadband achromatic metalens can be designed by suitably engineering its frequency dispersion, whereas a metasurface with tailored spatial dispersion (nonlocality) can realize momentum-dependent optical functions, such as space-compression effects. Specifically, in this dissertation I discuss the basic principles of these devices and demonstrate their fundamental limitations arising from delay-bandwidth constraints, with respect to relevant performance metrics, particularly bandwidth. The results presented in this dissertation may lead to a better understanding of the intriguing physical effects, practical potential, and fundamental limitations of novel dispersion degrees of freedom in metamaterials and metasurfaces. This may help guide the design of a new generation of electromagnetic and photonic devices for advanced scientific and technological applications

A study of natural convection from a vertical cylinder with variable surface temperature

Convective heat and mass transfer is one of the most important topics of study in physics and engineering. Specifically, natural or free convection mode of heat transfer, driven by fluid density variation in the presence of an external force field such as gravitational or magnetic, dominates numerous natural and industrial heat transfer phenomena. This report serves to present the results of a research undertaken to theoretically study the natural convection flow around of a heated vertical cylinder. Recognising the various technological applications, the surface temperature of the cylinder in this study was defined to be proportional to a power function of the distance from the base of the cylinder ($x^n$). The governing equations for the problem were derived from the Navier-Stokes and energy balance equation and simplified using the Boussinesq and boundary layer approximations. These partial differential equations were then numerically solved by implementing a finite difference scheme based on the Keller box discretisation. The program code was written in Mathematica, and results were calculated for various values of $Pr$ (Prandtl number) and $n$ (surface temperature power). The results were analysed and some recommendations made based on the experience.Bachelor of Engineering (Mechanical Engineering

Nonreciprocal and Topological Plasmonics

Metals, semiconductors, metamaterials, and various two-dimensional materials with plasmonic dispersion exhibit numerous exotic physical effects in the presence of an external bias, for example an external static magnetic field or electric current. These physical phenomena range from Faraday rotation of light propagating in the bulk to strong confinement and directionality of guided modes on the surface and are a consequence of the breaking of Lorentz reciprocity in these systems. The recent introduction of relevant concepts of topological physics, translated from condensed-matter systems to photonics, has not only given a new perspective on some of these topics by relating certain bulk properties of plasmonic media to the surface phenomena, but has also led to the discovery of new regimes of truly unidirectional, backscattering-immune, surface-wave propagation. In this article, we briefly review the concepts of nonreciprocity and topology and describe their manifestation in plasmonic materials. Furthermore, we use these concepts to classify and discuss the different classes of guided surface modes existing on the interfaces of various plasmonic systems

Frequency-selective propagation of localized spoof surface plasmons in a graded plasmonic resonator chain

Localized spoof surface plasmon polaritons (spoof-SPPs) in a graded spoof-plasmonic resonator chain with linearly increasing spacing are experimentally investigated at microwave frequencies. Transmission measurements and direct near-field mappings on this graded chain show that the propagation of localized spoof-SPPs can be cutoff at different positions along the graded chain under different frequencies due to the graded coupling between adjacent resonators. This mechanism can be used to guide localized spoof-SPPs in the graded chain to specific positions depending on the frequency and thereby implement a device that can work as a selective switch in integrated plasmonic circuits.MOE (Min. of Education, S’pore)Published versio