Mark R Dennis

Mark R Dennis
University of Birmingham · School of Physics and Astronomy

MSci, PhD

About

191
Publications
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9,174
Citations

Publications

Publications (191)
Article
Full-text available
Natural and artificially created light fields in three-dimensional space contain lines of zero intensity, known as optical vortices. Here, we describe a scheme to create optical beams with isolated optical vortex loops in the forms of knots and links using algebraic topology. The required complex fields with fibred knots and links are constructed f...
Article
Full-text available
The past decade has seen an intensive effort to achieve optical imaging resolution beyond the diffraction limit. Apart from the Pendry-Veselago negative index superlens, implementation of which in optics faces challenges of losses and as yet unattainable fabrication finesse, other super-resolution approaches necessitate the lens either to be in the...
Article
Full-text available
Tangles of string typically become knotted, from macroscopic twine down to long-chain macromolecules such as DNA. Here we demonstrate that knotting also occurs in quantum wavefunctions, where the tangled filaments are vortices (nodal lines/phase singularities). The probability that a vortex loop is knotted is found to increase with its length, and...
Article
Full-text available
Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or disappear rapidly under manipulation and interaction. Knotting has been previously identified in protein back...
Article
Full-text available
We show how careful control of the incident polarization of a light beam close to the Brewster angle gives a giant transverse spatial shift on reflection. This resolves the long-standing puzzle of why such beam shifts transverse to the incident plane (Imbert-Fedorov shifts) tend to be an order of magnitude smaller than the related Goos-Hänchen shif...
Article
Full-text available
Analogies between non-trivial topologies of matter and light have inspired numerous studies, including defect formation in structured light and topological photonic band structures. Three-dimensional topological objects of localised particle-like nature attract broad interest across discipline boundaries from elementary particle physics and cosmolo...
Article
Full-text available
Three-dimensional (3D) topological states resemble truly localised, particle-like objects in physical space. Among the richest such structures are 3D skyrmions and hopfions, that realise integer topological numbers in their configuration via homotopic mappings from real space to the hypersphere (sphere in 4D space) or the 2D sphere. They have recei...
Preprint
Analogies between non-trivial topologies of matter and light have inspired numerous studies, including defect formation in structured light and topological photonic band-structures. Three-dimensional topological objects of localized particle-like nature attract broad interest across discipline boundaries from elementary particle physics and cosmolo...
Preprint
Full-text available
We consider the probability of knotting in equilateral random polygons in Euclidean 3-dimensional space, which model, for instance, random polymers. Results from an extensive Monte Carlo dataset of random polygons indicate a universal scaling formula for the knotting probability with the number of edges. This scaling formula involves an exponential...
Preprint
Full-text available
Three-dimensional (3D) topological states resemble truly localised, particle-like objects in physical space. Among the richest such structures are 3D skyrmions and hopfions that realise integer topological numbers in their configuration via homotopic mappings from real space to the hypersphere (sphere in 4D space) or the 2D sphere. They have receiv...
Preprint
The Ince-Gauss modes of a cavity with aberrated mirrors are shown to constitute a system that is mathematically analogous to the Bose-Hubbard dimer (Bosonic Josephson junction). The latter involves interacting quantum particles while the former involves purely linear optics. The roles of particle interactions and hopping are played by spherical abe...
Article
All light has structure, but only recently has it been possible to control it in all its degrees of freedom and dimensions, fuelling fundamental advances and applications alike. Here we review the recent advances in ‘pushing the limits’ with structured light, from traditional two-dimensional transverse fields towards four-dimensional spatiotemporal...
Article
Full-text available
We consider complex three-dimensional polarizations in the interference of several vector wave fields with different commensurable frequencies and polarizations. We show that the resulting polarizations can form knots, and interfering three waves is sufficient to generate a variety of Lissajous, torus, and other knot types. We describe the spin ang...
Article
Caustics show up in contexts ranging from rainbows and water surfaces to light refracted through drinking glasses, but, despite their attractive propagation features, have rarely been artificially generated or exploited as basic entities for structured-light fabrication. We recently developed a general approach to design, customize and fabricate st...
Preprint
Full-text available
We consider complex 3D polarizations in the interference of several vector wave fields with different commensurable frequencies and polarizations. We show that resulting polarizations can form knots, and interfering three waves is sufficient to generate a variety of Lissajous, torus, and other knot types. We describe spin angular momentum, generali...
Article
Full-text available
Structured light has revolutionized optical particle manipulation, nano-scaled material processing, and high-resolution imaging. In particular, propagation-invariant light fields such as Bessel, Airy, or Mathieu beams show high robustness and have a self-healing nature. To generalize such beneficial features, these light fields can be understood in...
Conference Paper
We present a method to shape transverse high-intensity caustics with arbitrary trajectories into propagation-invariant light and demonstrate a variety of 2D beams, ranging from simple geometric forms to complex patterns.
Conference Paper
The modes of an aberrated cavity are shown to be analogous to a Bose-Hubbard dimer with the net orbital angular momentum and the Ince-Gauss modes taking the roles of particle number and eigenstates, respectively.
Preprint
Full-text available
Structured light has revolutionized optical particle manipulation and nano-scale material processing. In particular, propagation-invariant structured light fields, such as Bessel beams, have enabled applications that require robust intensity distributions. Their self-healing nature facilitates imaging with enhanced resolution e.g. in light-sheet mi...
Article
Geometric phases are a universal concept that underpins numerous phenomena involving multi-component wave fields. These polarization-dependent phases are inherent in interference effects, spin-orbit interaction phenomena, and topological properties of vector wave fields. Geometric phases have been thoroughly studied in two-component fields, such as...
Preprint
Based on the operator formalism that arises from the underlying SU(2) group structure, a formula is derived that provides a description of the generalized Hermite-Laguerre Gauss modes in terms of a Jones vector, traditionally used to describe polarization. This identity highlights the relation between these generalized Gaussian beams, the elliptica...
Preprint
We probe the character of knotting in open, confined polymers, assigning knot types to open curves by identifying their projections as virtual knots. In this sense, virtual knots are transitional, lying in between classical knot types, which are useful to classify the ambiguous nature of knotting in open curves. Modelling confined polymers using bo...
Article
Full-text available
Reconfigurable, ordered matter offers great potential for future low-power computer memory by storing information in energetically stable configurations. Among these, skyrmions—which are topologically protected, robust excitations that have been demonstrated in chiral magnets1–4 and in liquid crystals5–7—are driving much excitement about potential...
Article
Full-text available
Flying doughnuts (FDs) are exact propagating solutions of Maxwell equations in the form of single-cycle, space-time non-separable toroidal pulses. Here we review their properties and reveal the existence of a complex and robust fine topological structure. In particular, the electric and magnetic fields of the FD pulse vanish across a number of plan...
Article
Full-text available
Superoscillations are band-limited functions with the counterintuitive property that they can vary arbitrarily faster than their fastest Fourier component, over arbitrarily long intervals. Modern studies originated in quantum theory, but there were anticipations in radar and optics. The mathematical understanding—still being explored—recognises tha...
Preprint
Geometric phase is a universal concept that underpins numerous phenomena involving multi-component wave fields. These polarization-dependent phases are inherent in interference effects, spin-orbit interaction phenomena, and topological properties of vector wave fields. Geometric phases are thoroughly studied in two-component fields, such as two-lev...
Article
Full-text available
Gaussian mode families, including Laguerre–Gaussian, Hermite–Gaussian and generalized Hermite–Laguerre–Gaussian beams, can be described via a geometric optics construction. Ray families crossing the focal plane are represented as one-parameter families of ellipses, parametrized by curves on an analog Poincaré sphere for rays. We derive the optical...
Article
As the size of an optical vortex knot, imprinted in a coherent light beam, is decreased, nonparaxial effects alter the structure of the knotted optical singularity. For knot structures approaching the scale of wavelength, longitudinal polarization effects become non-negligible, and the electric and magnetic fields differ, leading to intertwined kno...
Article
Full-text available
Knots are topological structures describing how a looped thread can be arranged in space. Although most familiar as knotted material filaments, it is also possible to create knots in singular structures within three-dimensional physical fields such as fluid vortices¹ and the nulls of optical fields2–4. Here we produce, in the transverse polarizatio...
Preprint
As the size of an optical vortex knot, imprinted in a coherent light beam, is decreased, nonparaxial effects alter the structure of the knotted optical singularity. For knot structures approaching the scale of wavelength, longitudinal polarization effects become non-negligible and the electric and magnetic fields differ, leading to intertwined knot...
Article
A simple noninterferometric approach for probing the geometric phase of a structured Gaussian beam is proposed. Both the Gouy and Pancharatnam-Berry phases can be determined from the intensity distribution following a mode transformation if a part of the beam is covered at the initial plane. Moreover, the trajectories described by the centroid of t...
Preprint
Full-text available
Skyrmions are particle-like topological excitations, studied in various condensed matter systems and models of high-energy physics (HEP). They occur as stable spin textures in certain planar magnetic materials and as configurations in chiral nematic liquid crystals, having been originally proposed as model of atomic nuclei. Since magnetic Skyrmions...
Preprint
A simple non-interferometric approach for probing the geometric phase of a structured Gaussian beam is proposed. Both the Gouy and Pancharatnam-Berry phases can be determined from the intensity distribution following a mode transformation if a part of the beam is covered at the initial plane. Moreover, the trajectories described by the centroid of...
Conference Paper
A simple, non-interferometric method for measuring geometric phases of structured-Gaussian beams is presented. By studying the intensity distribution of an occluded beam, the Gouy and Pancharatnam-Berry phases can be determined.
Article
Full-text available
Motivated by recent interest in relativistic electron vortex states, we revisit the spin and orbital angular momentum properties of Dirac electrons. These are uniquely determined by the choice of the position operator for a relativistic electron. We overview two main approaches discussed in the literature: (i) the projection of operators onto the p...
Article
Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the cu...
Article
For centuries, singularities in wave fields have been a mainstay of interest in multiple areas of physics, ranging from plasma physics, fluid dynamics and atmospheric physics to optics and photonics. Singular Optics encompasses studies of structured light with localized and extended singularities, such as optical vortices in scalar optical fields a...
Article
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We describe a procedure that creates an explicit complex-valued polynomial function of three-dimensional space, whose nodal lines are the three-twist knot $5_2$. The construction generalizes a similar approach for lemniscate knots: a braid representation is engineered from finite Fourier series and then considered as the nodal set of a certain comp...
Article
Full-text available
A general family of structured Gaussian beams naturally emerges from a consideration of families of rays. These ray families, with the property that their transverse profile is invariant upon propagation (except for cycling of the rays and a global rescaling), have two parameters, the first giving a position on an ellipse naturally represented by a...
Article
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We describe an algorithm that for every given braid [Formula: see text] explicitly constructs a function [Formula: see text] such that [Formula: see text] is a polynomial in [Formula: see text], [Formula: see text] and [Formula: see text] and the zero level set of [Formula: see text] on the unit three-sphere is the closure of [Formula: see text]. T...
Article
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We study an ensemble of random waves subject to the Aharonov-Bohm effect. The introduction of a point with a magnetic flux of arbitrary strength into a random wave ensemble gives a family of wavefunctions whose distribution of vortices (complex zeros) are responsible for the topological phase associated with the Aharonov-Bohm effect. Analytical exp...
Article
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The connection between Poincaré spheres for polarization and Gaussian beams is explored, focusing on the interpretation of elliptic polarization in terms of the isotropic two-dimensional harmonic oscillator in Hamiltonian mechanics, its canonical quantization and semiclassical interpretation. This leads to the interpretation of structured Gaussian...
Article
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We give an explicit construction of complex maps whose nodal line have the form of lemniscate knots. We review the properties of lemniscate knots, defined as closures of braids where all strands follow the same transverse (1, $\ell$) Lissajous figure, and are therefore a subfamily of spiral knots generalising the torus knots. We then prove that suc...
Article
Full-text available
We present a general construction of divergence-free knotted vector fields from complex scalar fields, whose closed field lines encode many kinds of knots and links, including torus knots, their cables, the figure-8 knot and its generalizations. As finite-energy physical fields they represent initial states for fields such as the magnetic field in...
Data
A figure-eight vortex knot in a random eigenfunction of the threedimensional harmonic oscillator, viewed from different directions.
Data
The knot 10_99 formed from vortices in a random eigenfunction of the the 3-sphere, viewed from different directions.
Data
Two mirrored trefoil vortex knots in a random eigenfunction of the threedimensional harmonic oscillator, viewed from different directions.
Data
Supplementary Figures 1-6, Supplementary Notes 1-4 and Supplementary References
Article
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Radiation pressure is associated with the momentum of light, and it plays a crucial role in a variety of physical systems. It is usually assumed that both the optical momentum and the radiation-pressure force are naturally aligned with the propagation direction of light, given by its wavevector. Here we report the direct observation of an extraordi...
Research
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Experimental measurent of the mechanical effect of extraordinary optical momentum, with supporting calculations and theoretical analysis.
Research
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Experimental measurement of the mechanical effect of extraordinary optical momentum, with supporting calculations and theoretical analysis.
Article
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Radiation pressure has been known since Kepler's observation that a comet's tail is always oriented away from the sun, and in the past centuries this phenomenon stimulated remarkable discoveries in electromagnetism, quantum physics and relativity [1-3]. In modern terms, the pressure of light is associated with the momentum of photons, which plays a...
Article
Full-text available
Whereas nodal points having zero amplitude are well-known wave phenomena, destructive interference across a continuous area is rare. In fact, these strange states seem to defy nature’s “abhorrence of nothingness.” Philosophizing aside, we report general schemes for constructing a nodal area in a spatially coherent beam of light by use of a lossless...
Article
Full-text available
A set of pupil apodization functions for use with a vortex coronagraph on telescopes with obscured apertures is presented. We show analytically that pupil amplitudes given by real-valued Zernike polynomials offer ideal on-axis starlight cancellation when applied to unobscured circular apertures. The charge of the vortex phase element must be a nonz...
Article
Full-text available
The similarities and differences of spatial shifts to the centroids of reflected beams, and their (optical vortex) structure are discussed and reviewed. The differences between vortex-induced shifts to a beam centroid on reflection, and to the distribution of the vortices themselves is discussed. We conclude by discussing the shifts of a reflected...
Article
Full-text available
The short- and long-scale behaviour of tangled wave vortices (nodal lines) in random three-dimensional wave fields is studied via computer experiment. The zero lines are tracked in numerical simulations of periodic superpositions of three-dimensional complex plane waves. The probability distribution of local geometric quantities such as curvature a...
Article
Full-text available
Almost 30 years ago, Durnin discovered that an optical beam with a transverse intensity profile in the form of a Bessel function of the first order is immune to the effects of diffraction. Unlike most laser beams, which spread upon propagation, the transverse distribution of these Bessel beams remains constant. Electrons also obey a wave equation (...