Ray Dynamics Research Articles

Period spacing of gravity modes strongly affected by rotation

Context. As of today, asteroseismology mainly allows us to probe the internal rotation of stars when modes are only weakly affected by rotation using perturbative methods. Such methods cannot be applied to rapidly rotating stars, which exhibit complex oscillation spectra. In this context, the so-called traditional approximation, which neglects the terms associated with the latitudinal component of the rotation vector, describes modes that are strongly affected by rotation. This approximation is sometimes used for interpreting asteroseismic data, however, its domain of validity is not established yet. Aims. We aim at deriving analytical prescriptions for period spacings of low-frequency gravity modes strongly affected by rotation through the full Coriolis acceleration (i.e. without neglecting any component of the rotation vector), which can be used to probe stellar internal structure and rotation. Methods. We approximated the asymptotic theory of gravito-inertial waves in uniformly rotating stars using ray theory described in a previous paper in the low-frequency regime, where waves are trapped near the equatorial plane. We put the equations of ray dynamics into a separable form and used the Einstein-Brillouin-Keller (EBK) quantisation method to compute modes frequencies from rays. Results. Two spectral patterns that depend on stratification and rotation are predicted within this new approximation: one for axisymmetric modes and one for non-axisymmetric modes. Conclusions. The detection of the predicted patterns in observed oscillation spectra would give constraints on internal rotation and chemical stratification of rapidly rotating stars exhibiting gravity modes, such as γ Doradus, SPB, or Be stars. The obtained results have a mathematical form that is similar to that of the traditional approximation, but the new approximation takes the full Coriolis, which allows for propagation near the centre, and centrifugal accelerations into account.

Interaction of Cosmic Rays with Cold Clouds in Galactic Halos

We investigate the effects of cosmic ray (CR) dynamics on cold, dense clouds embedded in a hot, tenuous galactic halo. If the magnetic field does not increase too much inside the cloud, the local reduction in Alfv\'en speed imposes a bottleneck on CRs streaming out from the star-forming galactic disk. The bottleneck flattens the upstream CR gradient in the hot gas, implying that multi-phase structure could have global effects on CR driven winds. A large CR pressure gradient can also develop on the outward-facing edge of the cloud. This pressure gradient has two independent effects. The CRs push the cloud upward, imparting it with momentum. On smaller scales, the CRs pressurize cold gas in the fronts, reducing its density, consistent with the low densities of cold gas inferred in recent COS observations of local $L_{*}$ galaxies. They also heat the material at the cloud edge, broadening the cloud-halo interface and causing an observable change in interface ionic abundances. Due to the much weaker temperature dependence of cosmic ray heating relative to thermal conductive heating, CR mediated fronts have a higher ratio of low to high ions compared to conduction fronts, in better agreement with observations. We investigate these effects separately using 1D simulations and analytic techniques.

Ray chaos in a photonic crystal

The ray dynamics in a photonic crystal was investigated. Chaos occurs for perfectly periodic crystals, the rays dynamics being very sensitive to the initial conditions. Depending on the filling factor, the ray dynamics can exhibit stable paths near (fully) chaotic motion. The degree of chaoticity is quantified through the computation of Lyapunov exponents. As a result, the more diluted is the geometry, the more chaotic is the dynamic. Therefore, despite the perfect periodicity of the geometry, light transport is a diffusive process which can be tuned from normal diffusion (Brownian motion) to anomalous diffusion because of the existence of Lévy flights.

Energy-dependent correlations in the S-matrix of chaotic systems

The M-dimensional unitary matrix S(E), which describes scattering of waves, is a strongly fluctuating function of the energy for complex systems such as ballistic cavities, whose geometry induces chaotic ray dynamics. Its statistical behaviour can be expressed by means of correlation functions of the kind Sij(E+ϵ)Spq†(E−ϵ), which have been much studied within the random matrix approach. In this work, we consider correlations involving an arbitrary number of matrix elements and express them as infinite series in 1/M, whose coefficients are rational functions of ϵ. From a mathematical point of view, this may be seen as a generalization of the Weingarten functions of circular ensembles.

Regular modes in a mixed-dynamics-based optical fiber.

A multimode optical fiber with a truncated transverse cross section acts as a powerful versatile support to investigate the wave features of complex ray dynamics. In this paper, we concentrate on the case of a geometry inducing mixed dynamics. We highlight that regular modes associated with stable periodic orbits present an enhanced spatial intensity localization. We report the statistics of the inverse participation ratio whose features are analogous to those of Anderson localized modes. Our study is supported by both numerical and experimental results on the spatial localization and spectral regularity of the regular modes.

Frobenius–Perron eigenstates in deformed microdisk cavities: non-Hermitian physics and asymmetric backscattering in ray dynamics

In optical microdisk cavities with boundary deformations the backscattering between clockwise and counter-clockwise propagating waves is in general asymmetric. The striking consequence of this asymmetry is that these apparently weakly open systems show pronounced non-Hermitian phenomena. The optical modes appear in non-orthogonal pairs, where both modes copropagate in a preferred sense of rotation, i.e. the modes exhibit a finite chirality. Full asymmetry in the backscattering results in a non-Hermitian degeneracy (exceptional point) where the deviation from closed system evolution is strongest. We study the effects of asymmetric backscattering in ray dynamics. For this purpose, we construct a finite approximation of the Frobenius–Perron operator for deformed microdisk cavities, which describes the dynamics of intensities in phase space. Eigenstates of the Frobenius–Perron operator show nice analogies to optical modes: they come in non-orthogonal copropagating pairs and have a finite chirality. We introduce a new cavity system with a smooth asymmetric boundary deformation where we demonstrate our results and we illustrate the main aspects with the help of a simple analytically solvable 1D model.

Seasonality and Ontogenetic Habitat Partitioning of Cownose Rays in the Northern Gulf of Mexico

The seasonal and spatial heterogeneity of highly mobile mesopredators may play a large structuring role in estuarine dynamics. With a hypothesized relaxation of predation pressure from large sharks, growing populations of cownose rays (Rhinoptera bonasus) have been implicated in negatively affecting shellfish beds across multiple estuaries of the Atlantic coast; however, the pervasiveness of these potential impacts remains poorly understood elsewhere due to a lack of information on cownose ray distribution and seasonality across the species’ range. To better predict cownose ray dynamics in estuaries of the northern Gulf of Mexico, we conducted a multi-scale study using a combination of aerial and gillnet surveys. Cownose ray abundance was highly seasonal along the Mississippi-Alabama shelf, and a significant along-shelf gradient (west-east) in nearshore ray density was observed. This trend was best explained by changes in salinity, with higher abundances best correlated with more estuarine (i.e., lower salinity) conditions in nearshore areas. From north-south across the Alabama shelf, cownose rays displayed strong spatial and seasonal distributional patterns with ontogeny: adults (in particular, females) were primarily restricted to barrier islands and Gulf waters, whereas juveniles and young-of-the-year (YOY) exploited fresher waters of inshore bays protected from large predators. Among inshore locales, cownose ray catch was lowest over oyster habitats and only consisted of YOY rays, suggesting that foraging impacts may be reduced in these structurally complex substrates.

Incorporating movement in the modelling of shark and ray population dynamics: approaches and management implications

The explicit incorporation of movement in the modelling of population dynamics can allow improved management of highly mobile species. Large-scale movements are increasingly being reported for sharks and rays. Hence, in this review we summarise the current understanding of long-scale movement patterns of sharks and rays and then present the different methods used in fisheries science for modelling population movement with an emphasis on sharks and rays. The use of movement data for informing population modelling and deriving management advice remains rare for sharks and rays. In the few cases where population movement was modelled explicitly, movement information has been solely derived from conventional tagging. Though shark and ray movement has been increasingly studied through a range of approaches these different sources of information have not been used in population models. Integrating these multiple sources of movement information could advance our understanding of shark and ray dynamics. This, in turn, would allow the use of more adequate models for assessing stocks and advising management and conservation effort.

Nonlinear resonance-assisted tunneling induced by microcavity deformation.

Noncircular two-dimensional microcavities support directional output and strong confinement of light, making them suitable for various photonics applications. It is now of primary interest to control the interactions among the cavity modes since novel functionality and enhanced light-matter coupling can be realized through intermode interactions. However, the interaction Hamiltonian induced by cavity deformation is basically unknown, limiting practical utilization of intermode interactions. Here we present the first experimental observation of resonance-assisted tunneling in a deformed two-dimensional microcavity. It is this tunneling mechanism that induces strong inter-mode interactions in mixed phase space as their strength can be directly obtained from a separatrix area in the phase space of intracavity ray dynamics. A selection rule for strong interactions is also found in terms of angular quantum numbers. Our findings, applicable to other physical systems in mixed phase space, make the interaction control more accessible.

Inertial wave rays in rotating spherical fluid domains

AbstractThe behaviour of inertial waves in a rotating spherical container, filled with homogeneous fluid, is here investigated by means of a three-dimensional ray tracing algorithm, in a linear, inviscid framework. In particular, the classical, two-dimensional association between regular modes and periodic trajectories is addressed here for the first time in a fully three-dimensional setting. Three-dimensional, repelling periodic trajectories are found and classified on the basis of the associated frequency and spatial structure, although associated frequencies are hardly reconcilable to Bryan’s (Proc. R. Soc. Lond., vol. 45, 1889, pp. 42–45) classical solutions for inertial waves in the sphere. The normalized squared frequency $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\omega ^2 = 1/2$ appears to divide the frequency range into two different trajectory regimes, where critical latitudes play a different role. Chaotic orbits are not found, as expected, while invariant, non-domain-filling orbits (whispering gallery modes) constitute the majority of the trajectories in the sphere. From ray tracing alone, the wavefield is still far from being completely reconstructed, and a study performed in such a simplified setting is clearly far from any realistic application, however, it appears that three-dimensional ray dynamics constitutes a valid approach to infer information on the spectrum and regularity properties of a system, and is then able to bring new insight in a variety of fundamental problems of geophysical and astrophysical relevance, once its power and limitations have been recognized.

Abnormal high-Q modes of coupled stadium-shaped microcavities.

It is well known that the strongly deformed microcavity with fully chaotic ray dynamics cannot support high-Q modes due to its fast chaotic diffusion to the critical line of refractive emission. Here, we investigate how the Q factor is modified when two chaotic cavities are coupled, and show that some modes, whose Q factor is about 10 times higher than that of the corresponding single cavity, can exist. These abnormal high-Q modes are the result of an optimal combination of coupling and cavity geometry. As an example, in the coupled stadium-shaped microcavities, the mode pattern extends over both cavities such that it follows a whispering-gallery-type mode at both ends, whereas a big coupling spot forms at the closest contact of the two microcavities. The pattern of such a "rounded bow tie" mode allows the mode to have a high-Q factor. This mode pattern minimizes the leakage of light at both ends of the microcavities as the pattern at both ends is similar to the whispering gallery mode.

Chaos-assisted tunneling in a deformed microcavity laser

We investigate the impact of local dynamics on chaos-assisted tunneling in a highly deformed microcavity whose classical ray dynamics exhibits a small measure of trapezoidal-shaped orbit (TSO) stability islands in a main chaotic sea. These two classically completely decomposed regions in phase space can support resonance modes of their own respectively. Using numerical ray and wave analyses, we show that the emission characteristics of the TSO resonance mode are determined by local ray dynamics near TSO islands. The emission characteristics of the other high-Q resonance modes, on the other hand, are governed by usual ray-wave correspondence. We experimentally demonstrate that the TSO emission mode can be lased without selective excitations by devising a half-moon shaped highly deformed cavity. And we also show that the emission characteristics of the TSO lasing modes are well explained by numerical ray and wave analyses.

Adiabatic formation of high-Q modes by suppression of chaotic diffusion in deformed microdiscs

Resonant modes with high-Q factors in a two-dimensional deformed microdisc cavity are analyzed by using a dynamical and semiclassical approach. The analysis focuses particularly on the ultra-small cavity regime, where the scale of a resonant free-space wavelength is comparable with that of the microdisc size. Although the deformed microcavity has strongly chaotic internal ray dynamics, modes with high-Q factors in this regime show unexpectedly regular distributions in configuration space and adiabatic features in phase space. By tracing the evolution process of such high-Q modes through the deformation from a circular cavity, it is uncovered that the high-Q modes are formed adiabatically on cantori. Due to the openness of microcavities, such adiabatic formation of high-Q modes around cantori is enabled, in spite of strong chaos in ray dynamics. Since the cantori are in close contact with short periodic orbits, their influence on the modes, such as localization patterns in phase space, can be also clarified. In order to quantitatively analyze the spectral range where high-Q modes appear, the phase space section of the deformed microcavity is partitioned by partial barriers of short periodic orbits, and the semiclassical quantization scheme is applied to the partitioned areas and their action fluxes. The derived spectral ranges for the high-Q modes show a good agreement with a numerically observed spectrum. In the course of semiclassical quantization, it is shown that the chaotic diffusion in the system that we investigate can be resolved by the scale of a quarter effective Planck's constant, and the topological structure of the manifolds in phase space allows for this resolution higher than a Planck constant scale. By analyzing flux Farey trees, the role of short periodic orbits in chaotic diffusion and their connection to cantori are verified.

In–out decomposition of boundary integral equations

We propose a reformulation of the boundary integral equations for the Helmholtz equation in a domain in terms of incoming and outgoing boundary waves. We obtain transfer operator descriptions which are exact and thus incorporate features such as diffraction and evanescent coupling; these effects are absent in the well-known semiclassical transfer operators in the sense of Bogomolny. It has long been established that transfer operators are equivalent to the boundary integral approach within semiclassical approximation. Exact treatments have been restricted to specific boundary conditions (such as Dirichlet or Neumann). The approach we propose is independent of the boundary conditions, and in fact allows one to decouple entirely the problem of propagating waves across the interior from the problem of reflecting waves at the boundary. As an application, we show how the decomposition may be used to calculate Goos–Hänchen shifts of ray dynamics in billiards with variable boundary conditions and for dielectric cavities.

Discrete flow mapping: transport of phase space densities on triangulated surfaces

Energy distributions of high-frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics, vibroacoustics, seismology, electromagnetics and quantum mechanics. Related flow problems based on general conservation laws are used, for example, in weather forecasting or in molecular dynamics simulations. Solutions to these flow equations are often large-scale, complex and high-dimensional, leading to formidable challenges for numerical approximation methods. This paper presents an efficient and widely applicable method, called discrete flow mapping , for solving such problems on triangulated surfaces. An application in structural dynamics, determining the vibroacoustic response of a cast aluminium car body component, is presented.

Intensity Fluctuations of Waves in Random Media: What Is the Semiclassical Limit?

Waves traveling through weakly random media are known to be strongly affected by their corresponding ray dynamics, in particular in forming linear freak waves. The ray intensity distribution, which, e.g., quantifies the probability of freak waves is unknown, however, and a theory of how it is approached in an appropriate semiclassical limit of wave mechanics is lacking. We show that this limit is not the usual limit of small wavelengths, but that of decoherence. Our theory, which can describe the intensity distribution for an arbitrary degree of coherence is relevant to a wide range of physical systems, as decoherence is omnipresent in real systems.

Light Extraction Improvement for LED COB Devices by Introducing a Patterned Leadframe Substrate Configuration

We propose a patterned leadframe substrate (PLS) configuration for light-emitting diode chip-on-board devices (LED COBs) with regular triangular structures on it. The mechanism of this method is analyzed through ray dynamics, which indicate that the light-propagating regimes are considerably different as the structure inclination angle α changes. For typical encapsulant materials (refractive index=1.41), the optimal α is 22.5°~45°. Then the performance of LED COB devices with PLS configurations are verified through 3-D Monte Carlo ray-tracing simulations as well as experimental measurements. Results show that the light-extraction efficiency is significantly improved. A simulated enhancement of 42% and a measured enhancement of 41.07% are observed. These results are in good consistency with the ray dynamic analysis, confirming our predictions about PLS methods. Furthermore, we find that such an LED COB configuration also provides a way to change the angular distribution of intensity from half-peak side angle 101.84° to 141.80°. The findings of our work represent a new concept for LED COB packaging design of great practicality in building lighting systems.

Feeding ecology and trophic position of a Mediterranean endemic ray: consistency between sexes, maturity stages and seasons

The study of trophic ecology of marine predators is crucial to better understand the ecological factors that condition their role within marine ecosystems. Here we investigated the trophic habits and position of a Mediterranean endemic predator, the starry ray, Raja asterias. Specifically, we quantified the diet composition of this endemic ray in a highly exploited area of the NW Mediterranean, and we evaluated the effects of sex, maturity-stage and season on its feeding habits. Our results revealed that the starry ray is a predator of crustaceans (crabs and shrimps), and to a lower extent on teleosts, molluscs and polychaetes. This species has a high trophic position within its food web and feeds mainly on crabs (mainly Liocarcinus depurator and Goneplax rhomboides), independent of their sex, maturity-stage or season. The great importance of crabs in the diet of starry ray may be due to the fact that crabs are the dominant crustaceans in terms of biomass and abundance in the area where starry rays were collected, thus allowing them to exploit the most abundant food resource. Since the starry ray has shown a progressive decline on the catch, further research is needed to analyse the main drivers of starry ray dynamics in the Western Mediterranean Sea. Our results present important new data that will allow us to further explore the population dynamics of starry rays and the role of crustacean availability and fishing activity.

Controlling deformation in a high quality factor silica microsphere toward single directional emission

High-Q deformed silica microsphere cavities are fabricated by short CO(2) laser pulses, where the deformation is well controlled by adjusting the intensity and number of pulses. Using this method, directional emission from whispering-gallery mode (WGM) with a high quality factor of 10(7) in these microspheres is achieved, and a transition from two-directional to single-directional emission is observed. Such concentrated directional emission and high-Q of WGMs show high potential for future studies of the chaotic ray dynamics in deformed microcavity and cavity quantum electrodynamics and optomechanics.

How curvature affects the far-field emission from deformed optical microcavities

We examine the effects of curvature on the far-field emission properties of deformed optical microcavities. These quasi-two-dimensional systems, where light confinement is due to total internal reflection, are characterized by a curved dielectric interface. Deformation causes the curvature to vary along the system boundary, which directly affects the curvature-dependent Goos–Hänchen shift and consequently the ray dynamics in the microcavity. We discuss the resulting modifications in the far-field characteristics as a function of wavenumber and radius of curvature by means of a concrete example.