Dynamic homogenisation of Maxwell’s equations with applications to photonic crystals and localised waveforms on gratings

A two-scale asymptotic theory is developed to generate continuum equations that model the macroscopic be- haviour of electromagnetic waves in periodic photonic structures when the wavelength is not necessarily long relative to the periodic cell dimensions; potentially highly-oscillatory short-scale detail is encapsulated through integrated quantities. The resulting equations include tensors that represent effective refractive indices near band edge frequencies along all principal axes directions, and these govern scalar functions providing long-scale mod- ulation of short-scale Bloch eigenstates, which can be used to predict the propagation of waves at frequencies outside of the long wavelength regime; these results are outside of the remit of typical homogenisation schemes. The theory we develop is applied to two topical examples, the first being the case of aligned dielectric cylin- ders, which has great importance in modelling photonic crystal fibres. Results of the asymptotic theory are veri- fied against numerical simulations by comparing photonic band diagrams and evanescent decay rates for guided modes. The second example is the propagation of electromagnetic waves localised within a planar array of di- electric spheres; at certain frequencies strongly directional propagation is observed, commonly described as dy- namic anisotropy. Computationally this is a challenging three-dimensional calculation, which we perform, and then demonstrate that the asymptotic theory captures the effect, giving highly accurate qualitative and quantitative comparisons as well as providing interpretation for the underlying change from elliptic to hyperbolic behaviour

Scintillation Reduction for Laser Beams Propagating Through Turbulent Atmosphere

We numerically examine the spatial evolution of the structure of coherent and partially coherent laser beams, including the optical vortices, propagating in turbulent atmospheres. The influence of beam fragmentation and wandering relative to the axis of propagation (z-axis) on the value of the scintillation index (SI) of the signal at the detector is analyzed. These studies were performed for different dimensions of the detector, distances of propagation, and strengths of the atmospheric turbulence. Methods for significantly reducing the scintillation index are described. These methods utilize averaging of the signal at the detector over a set of partially coherent beams (PCBs). It is demonstrated that the most effective approach is using a set of PCBs with definite initial directions of propagation relative to the z-axis. This approach results in a significant compensation of the beam wandering which in many cases is the main contributor to the SI. A novel method is to generate the PCBs by combining two laser beams - Gaussian and vortex beams, with different frequencies (the difference between these two frequencies being significantly smaller than the frequencies themselves). In this case, the effective suppression of the SI does not require high-frequency modulators. This result is important for achieving gigabit data-rates in long-distance laser communication through turbulent atmospheres.Comment: 35 pages, 29 figure

Interferometers as Probes of Planckian Quantum Geometry

A theory of position of massive bodies is proposed that results in an observable quantum behavior of geometry at the Planck scale, $t_P$. Departures from classical world lines in flat spacetime are described by Planckian noncommuting operators for position in different directions, as defined by interactions with null waves. The resulting evolution of position wavefunctions in two dimensions displays a new kind of directionally-coherent quantum noise of transverse position. The amplitude of the effect in physical units is predicted with no parameters, by equating the number of degrees of freedom of position wavefunctions on a 2D spacelike surface with the entropy density of a black hole event horizon of the same area. In a region of size $L$, the effect resembles spatially and directionally coherent random transverse shear deformations on timescale $\approx L/c$ with typical amplitude $\approx \sqrt{ct_PL}$. This quantum-geometrical "holographic noise" in position is not describable as fluctuations of a quantized metric, or as any kind of fluctuation, dispersion or propagation effect in quantum fields. In a Michelson interferometer the effect appears as noise that resembles a random Planckian walk of the beamsplitter for durations up to the light crossing time. Signal spectra and correlation functions in interferometers are derived, and predicted to be comparable with the sensitivities of current and planned experiments. It is proposed that nearly co-located Michelson interferometers of laboratory scale, cross-correlated at high frequency, can test the Planckian noise prediction with current technology.Comment: 23 pages, 6 figures, Latex. To appear in Physical Review

Design of wideband vibration-based electromagnetic generator by means of dual-resonator

This paper describes the design of a wideband electromagnetic energy harvester that utilizes a novel dual-resonator method to improve the operational frequency range of the vibration-based generator. The device consists of two separate resonator systems (coil and magnet), which each comply with their respective resonance frequencies. This is because both resonators are designed in such a way that both magnet and coil components will oscillate at an additive phase angle, and hence create greater relative motion between the two dominating resonance frequencies, which realizes the wideband generator. Each resonator system consists of a distinctive cantilever beam, one attached with four magnets and steel keepers, the other attached with a copper coil and stainless steel holder as the free end mass. Both cantilevers are clamped and fitted to a common base that is subjected to a vibration source. Basic analytical models are derived and a numerical model is implemented in MATLAB-Simulink. Electromagnetic, structural modal and static mechanical analysis for the design of the prototype are completed using ANSYS finite element tools. For a 0.8 m s−2 acceleration, the open-loop voltage obtained from the experiment shows a good correlation with those from the simulation. Peak induced voltage is measured to be 259.5Vrms as compared to 240.9Vrms from the simulator at 21.3 Hz, which implies an error range of 7.7%. The results also indicate that there is a maximum of 58.22% improvement in the induced voltage within the intermediate region which occurs at the intersection point between the output response plots of two single resonator generators

The applicability of physical optics in the millimetre and sub-millimetre spectral region. Part II: Application to a three-component model of ice cloud and its evaluation against the bulk single-scattering properties of various other aggregate models

The bulk single-scattering properties of various randomly oriented aggregate ice crystal models are com- pared and contrasted at a number of frequencies between 89 and 874 GHz. The model ice particles consist of the ten-branched plate aggregate, five-branched plate aggregate, eight-branched hexagonal aggregate, Voronoi ice aggregate, six-branched hollow bullet rosette, hexagonal column of aspect ratio unity, and the ten-branched hexagonal aggregate. The bulk single-scattering properties of the latter two ice particle models have been calculated using the light scattering methods described in Part I, which represent the two most extreme members of an ensemble model of cirrus ice crystals. In Part I, it was shown that the method of physical optics could be combined with the T-matrix at a size parameter of about 18 to compute the bulk integral ice optical properties and the phase function in the microwave to sufficient ac- curacy to be of practical value. Here, the bulk single-scattering properties predicted by the two ensemble model members and the Voronoi model are shown to generally bound those of all other models at fre- quencies between 89 and 874 GHz, thus representing a three-component model of ice cloud that can be generally applied to the microwave, rather than using many differing ice particle models. Moreover, the Voronoi model and hollow bullet rosette scatter similarly to each other in the microwave. Furthermore, from the various comparisons, the importance of assumed shapes of the particle size distribution as well as cm-sized ice aggregates is demonstrated.Peer reviewedFinal Accepted Versio