Photonic realization of the relativistic Dirac oscillator

A photonic realization of the Dirac oscillator (DO), i.e. of the relativistic extension of the quantum harmonic oscillator, is proposed for light propagation in fiber Bragg gratings. Transmission spectra clearly show the existence of electron and positron bound states of the DO, corresponding to resonance modes above and below the Bragg frequency, as well as the asymmetry of the energy spectrum for electron and positron branches

Relationship between mathematical confidence and academic performance, among undergraduate biology students

Background The interconnectivity between the nature and origins of mathematics and science cannot be overstated. However, studies over the past decade have shown that approx. 50% of life science students lack confidence in their mathematical abilities, and as a result, often adopt a rigid attitude to learning mathematics. This is particularly problematic in undergraduate life sciences, when the focus shifts to data handling and calculations. It was hypothesised that this ‘rigidity’ would relate to lower academic performance in biology and mathematics. Aims This study was framed using Bandura (1977) self-efficacy theory and aimed to determine whether low mathematical confidence amongst undergraduate biology students would relate to low academic performance in biology mathematics. Design and methods Students enrolled in an introductory biology course (n=254) at a major research focused university were surveyed as to their attitudes to mathematics, using a modified version of the Fennema-Sherman Attitude Scale (5-point Likert items). Based on their responses to the confidence sub-scale, students were categorised as either possessing ‘low’ (mean Likert score 3.5) confidence, they were then matched to their mean final grades in mathematics and biology, and compared using a student’s independent samples t-test. Results No differences were found between students who possessed ‘low’ or ‘high’ mathematical confidence, in terms of mean final grades in biology. Interestingly, for mathematics, students who were categorised a possessing ‘high’ mathematical confidence, achieved significantly lower grades compared to those students who possessed ‘low’ mathematical confidence. In other words students who were less mathematically confident, achieved significantly higher grades relative to their more mathematically confident peers. Conclusions The recognition that students possess a high degree of additional complexity, with regards to the learning of mathematics and biology, is beneficial to educators. Such that more effective learning and teaching interventions may be developed, to encourage students to develop attitudes to learning that relate to improved educational outcomes

Rotating optical soliton clusters

We introduce the concept of soliton clusters -- multi-soliton bound states in a homogeneous bulk optical medium, and reveal a key physical mechanism for their stabilization associated with a staircase-like phase distribution that induces a net angular momentum and leads to cluster rotation. The ringlike soliton clusters provide a nontrivial generalization of the concepts of two-soliton spiraling, optical vortex solitons, and necklace-type optical beams.Comment: 4 pages, 5 figure

Dispersive properties of quasi-phase-matched optical parametric amplifiers

The dispersive properties of non-degenerate optical parametric amplification in quasi-phase-matched (QPM) nonlinear quadratic crystals with an arbitrary grating profile are theoretically investigated in the no-pump-depletion limit. The spectral group delay curve of the amplifier is shown to be univocally determined by its spectral power gain curve through a Hilbert transform. Such a constraint has important implications on the propagation of spectrally-narrow optical pulses through the amplifier. In particular, it is shown that anomalous transit times, corresponding to superluminal or even negative group velocities, are possible near local minima of the spectral gain curve. A possible experimental observation of such effects using a QPM Lithium-Niobate crystal is suggested.Comment: submitted for publicatio

Induced Coherence and Stable Soliton Spiraling

We develop a theory of soliton spiraling in a bulk nonlinear medium and reveal a new physical mechanism: periodic power exchange via induced coherence, which can lead to stable spiraling and the formation of dynamical two-soliton states. Our theory not only explains earlier observations, but provides a number of predictions which are also verified experimentally. Finally, we show theoretically and experimentally that soliton spiraling can be controled by the degree of mutual initial coherence.Comment: 4 pages, 5 figure

Scattering Theory and PT\mathcal{P}\mathcal{T}-Symmetry

We outline a global approach to scattering theory in one dimension that allows for the description of a large class of scattering systems and their $\mathcal{P}$-, $\mathcal{T}$-, and $\mathcal{P}\mathcal{T}$-symmetries. In particular, we review various relevant concepts such as Jost solutions, transfer and scattering matrices, reciprocity principle, unidirectional reflection and invisibility, and spectral singularities. We discuss in some detail the mathematical conditions that imply or forbid reciprocal transmission, reciprocal reflection, and the presence of spectral singularities and their time-reversal. We also derive generalized unitarity relations for time-reversal-invariant and $\mathcal{P}\mathcal{T}$-symmetric scattering systems, and explore the consequences of breaking them. The results reported here apply to the scattering systems defined by a real or complex local potential as well as those determined by energy-dependent potentials, nonlocal potentials, and general point interactions.Comment: Slightly expanded revised version, 38 page

Microscopic optical buffering in a harmonic potential

In the early days of quantum mechanics, Schrödinger noticed that oscillations of a wave packet in a one-dimensional harmonic potential well are periodic and, in contrast to those in anharmonic potential wells, do not experience distortion over time. This original idea did not find applications up to now since an exact one-dimensional harmonic resonator does not exist in nature and has not been created artificially. However, an optical pulse propagating in a bottle microresonator (a dielectric cylinder with a nanoscale-high bump of the effective radius) can exactly imitate a quantum wave packet in the harmonic potential. Here, we propose a tuneable microresonator that can trap an optical pulse completely, hold it as long as the material losses permit, and release it without distortion. This result suggests the solution of the long standing problem of creating a microscopic optical buffer, the key element of the future optical signal processing devices