Ray Dynamics Research Articles

Tailoring chaotic motion of microcavity photons in ray and wave dynamics by tuning the curvature of space

Tailoring chaotic motion of microcavity photons in ray and wave dynamics by tuning the curvature of space

Predicting the turbulent transport of cosmic rays via neural networks

A fast artificial neural network is developed for the prediction of cosmic ray transport in turbulent astrophysical magnetic fields. The setup is trained and tested on bespoke datasets that are constructed with the aid of test-particle numerical simulations of relativistic cosmic ray dynamics in synthetic stochastic fields. The neural network uses, as input, particle and field properties and estimates transport coefficients 107 faster than standard numerical simulations with an overall error of ∼5%.

Impact of Cavity Geometry on Microlaser Dynamics.

We experimentally investigate spatiotemporal lasing dynamics in semiconductor microcavities with various geometries, featuring integrable or chaotic ray dynamics. The classical ray dynamics directly impacts the lasing dynamics, which is primarily determined by the local directionality of long-lived ray trajectories. The directionality of optical propagation dictates the characteristic length scales of intensity variations, which play a pivotal role in nonlinear light-matter interactions. While wavelength-scale intensity variations tend to stabilize lasing dynamics, modulation on much longer scales causes spatial filamentation and irregular pulsation. Our results will pave the way to control the lasing dynamics by engineering the cavity geometry and ray dynamical properties.

Highly efficient waveguide-coupled output in asymmetrically deformed square cavity microlasers.

We propose and demonstrate deformed square cavity microlasers for realizing highly efficient output from a connected waveguide. The square cavities are deformed asymmetrically by replacing two adjacent flat sides with circular arcs to manipulate the ray dynamics and couple the light to the connected waveguide. The numerical simulations show that the resonant light can efficiently couple to the fundamental mode of the multi-mode waveguide by carefully designing the deformation parameter utilizing global chaos ray dynamics and internal mode coupling. An enhancement of approximately six times in the output power is realized in the experiment compared to the non-deformed square cavity microlasers, while the lasing thresholds are reduced by about 20%. The measured far-field pattern shows highly unidirectional emission agreeing well with the simulation, which confirms the feasibility of the deformed square cavity microlasers for practical applications.

Wigner distribution function approach to analyze MIMO communication within a waveguide

Multiple-input-multiple-output (MIMO) communication is a technology to create high capacity wireless links. The main aim of this paper is to provide a foundation to mathematically model wireless chip to chip communication within complex enclosures. This paper mainly concentrates on modelling wave propagation between transmit and receive antennas through a phase space approach which exploits the relationship between the field-field correlation function (CF) and the Wigner distribution function (WDF). A reliable model of wireless chip-to-chip (C2C) communication helps mitigate the information bottleneck caused due to the wired connections between chips, thus, help improve the efficiency of electronic devices of the future. Placing complex sources such as printed circuit board (PCB) inside a cavity or enclosure results in multi-path interference and hence makes the prediction of signal propagation more difficult. Thus, the CFs can be propagated based on a ray transport approach that predicts the average radiated density, but not the significant fluctuations that occur about it. Hence, the WDF approach can be extended to problems in finite cavities that incorporates reflections as well. Phase space propagators based on classical multi-reflection ray dynamics can be obtained by considering the high-frequency asymptotics.

Chaotic Resonance Modes in Dielectric Cavities: Product of Conditionally Invariant Measure and Universal Fluctuations.

We conjecture that chaotic resonance modes in scattering systems are a product of a conditionally invariant measure from classical dynamics and universal exponentially distributed fluctuations. Themultifractal structure of the first factor depends strongly on the lifetime of the mode and describes the average of modes with similar lifetime. The conjecture is supported for a dielectric cavity with chaotic ray dynamics at small wavelengths, in particular for experimentally relevant modes with longest lifetime. We explain scarring of the vast majority of modes along segments of rays based on multifractality and universal fluctuations, which is conceptually different from periodic-orbit scarring.

Standard self-confinement and extrinsic turbulence models for cosmic ray transport are fundamentally incompatible with observations

ABSTRACT Models for cosmic ray (CR) dynamics fundamentally depend on the rate of CR scattering from magnetic fluctuations. In the ISM, for CRs with energies ∼MeV-TeV, these fluctuations are usually attributed either to ‘extrinsic turbulence’ (ET) – a cascade from larger scales – or ‘self-confinement’ (SC) – self-generated fluctuations from CR streaming. Using simple analytic arguments and detailed ‘live’ numerical CR transport calculations in galaxy simulations, we show that both of these, in standard form, cannot explain even basic qualitative features of observed CR spectra. For ET, any spectrum that obeys critical balance or features realistic anisotropy, or any spectrum that accounts for finite damping below the dissipation scale, predicts qualitatively incorrect spectral shapes and scalings of B/C and other species. Even if somehow one ignored both anisotropy and damping, observationally required scattering rates disagree with ET predictions by orders of magnitude. For SC, the dependence of driving on CR energy density means that it is nearly impossible to recover observed CR spectral shapes and scalings, and again there is an orders-of-magnitude normalization problem. But more severely, SC solutions with super-Alfvénic streaming are unstable. In live simulations, they revert to either arbitrarily rapid CR escape with zero secondary production, or to bottleneck solutions with far-too-strong CR confinement and secondary production. Resolving these fundamental issues without discarding basic plasma processes requires invoking different drivers for scattering fluctuations. These must act on a broad range of scales with a power spectrum obeying several specific (but plausible) constraints.

Forward modelling and the quest for mode identification in rapidly rotating stars

Asteroseismology has opened a window on the internal physics of thousands of stars, by relating oscillation spectra properties to the internal physics of stars. Mode identification, namely the process of associating a measured oscillation frequency to the corresponding mode geometry and properties, is the cornerstone of this analysis of seismic spectra. In rapidly rotating stars this identification is a challenging task that remains incomplete, as modes assume complex geometries and regular patterns in frequencies get scrambled under the influence of the Coriolis force and centrifugal flattening. In this article, I will first discuss the various classes of mode geometries that emerge in rapidly rotating stars and the related frequency and period patterns, as predicted by ray dynamics, complete (non-)adiabatic calculations, or using the traditional approximation of rotation. These patterns scale with structural quantities and help us derive crucial constraints on the structure and evolution of these stars. I will summarize the amazing progress accomplished over the last few years for the deciphering of gravity-mode pulsator oscillation spectra, and recent developments based on machine-learning classification techniques to distinguish oscillation modes and pattern analysis strategies that let us access the underlying physics of pressure-mode pulsators. These approaches pave the way to ensemble asteroseismology of classical pulsators. Finally, I will highlight how these recent progress can be combined to improve forward seismic modelling. I will focus on the example of Rasalhague, a well-known rapid rotator, to illustrate the process and the needed advances to obtain à-la-carte modelling of such stars.

Ray-tracking methods for characterizing the dynamics of curved detonation

Current analyses of curved detonations are mostly limited to the dynamics along the wall or the symmetry axis due to the lack of efficient approaches for reliably tracking stream tubes with curved shock fronts. To address this lack, the present work proposes a novel curved ray-tracking algorithm with two implementation methods. The curved ray is characterized by a specific arc of constant curvature perpendicularly intersecting both successive fronts. The methods were validated against Whitham's exact geometrical shock dynamics solutions of the self-similar shock diffraction problem. As compared to the typical forward straight-ray method, which is of the first order, the proposed methods demonstrate convergence rates greater by more than one order of magnitude and tend to be of the second order. The convergence analysis enabled to determine the range of time resolution required for the proposed methods to provide reliable results. This range is comparable to the acquisition rate of a modern high-speed camera that is commonly used in detonation visualization experiments. Differences between the proposed curved ray-tracking methods and the typical forward straight-ray method have been further examined by analyzing the ray dynamics during the weakly unstable hydrogen–oxygen–argon detonation diffraction. The ray-tube-based velocity-curvature relationship showed satisfactory agreement with those already well-established in quasi-steady experiments and predicted by the generalized Zeldovich–von Neumann–Doering model. This suggests the limited role of unsteadiness and cellular structure in the macro-scale dynamics of weakly unstable detonations.

Eigenfunction non-orthogonality factors and the shape of CPA-like dips in a single-channel reflection from lossy chaotic cavities

Motivated by the phenomenon of coherent perfect absorption, we study the shape of the deepest dips in the frequency-dependent single-channel reflection of waves from a cavity with spatially uniform losses. We show that it is largely determined by non-orthogonality factors O nn of the eigenmodes associated with the non-selfadjoint effective Hamiltonian. For cavities supporting chaotic ray dynamics we then use random matrix theory to derive, fully non-perturbatively, the explicit distribution of the non-orthogonality factors for systems with both broken and preserved time reversal symmetry. The results imply that O nn are heavy-tail distributed. As a by-product, we derive an explicit non-perturbative expression for the resonance density in a single-channel chaotic systems in a much simpler form than available in the literature.

Sensitive control of broad-area semiconductor lasers by cavity shape

The ray dynamics of optical cavities exhibits bifurcation points: special geometries at which ray trajectories switch abruptly between stable and unstable. A prominent example is the Fabry–Perot cavity with two planar mirrors, which is widely employed for broad-area semiconductor lasers. Such cavities support lasing in a relatively small number of transverse modes, and the laser is highly susceptible to filamentation and irregular pulsations. Here, we demonstrate experimentally that a slight deviation from this bifurcation point (planar cavity) dramatically changes the laser performance. In a near-planar cavity with two concave mirrors, the number of transverse lasing modes increases drastically. While the spatial coherence of the laser emission is reduced, the divergence angle of the output beam remains relatively narrow. Moreover, the spatiotemporal lasing dynamics becomes significantly more stable compared to that in a Fabry–Perot cavity. Our near-planar broad-area semiconductor laser has higher brightness, better directionality, and hence allows shorter integration times than an incandescent lamp while featuring sufficiently low speckle contrast at the same time, making it a vastly superior light source for speckle-free imaging. Furthermore, our method of controlling spatiotemporal dynamics with extreme sensitivity near a bifurcation point may be applied to other types of high-power lasers and nonlinear dynamic systems.

The waveguide invariant: Wavefield structure, ray stability, time spreads and modal dispersion

Prior to the seminal work of Chuprov and Grachev, who introduced the underwater acoustic waveguide invariant, the asymptotic equivalent of the same quantity was recognized as playing an important role in Hamiltonian dynamics. A consequence is that the waveguide invariant controls, to a large extent, underwater acoustic ray dynamics. In this presentation some of the less well known properties of underwater acoustic wavefields, based on both ray- and mode-based descriptors, that are controlled by the waveguide invariant are reviewed. These properties include overall wavefield structure, ray stability, time spreads and modal dispersion. [Work supported by ONR.]

State evolution formula and stability analysis of a paraxial optical system.

By analyzing the phase vector evolution of a paraxial optical system (POS) with a variational background refractive index, we obtain a continuous dynamic equation, called state evolution formula (SEF), which simultaneously gives the phase vector transformation and ray trajectory inside and outside the optical elements. Compared with ray transfer matrix method, this phase-vector equation is universal in treating problems about propagation and stability of paraxial rays, since it extends the linear and discrete matrix equation to a differential equation. It takes a consistent form for both continuous and discontinuous cases without considering the special rays, even the input and output states present a nonlinear relation. Based on the SEF, we further propose a rigorous criterion about whether a continuous and non-periodic POS is stable. This formula provides a reference model for the theoretical analysis of ray dynamics in geometric and physical optical systems.

Oscillations of 2D ESTER models

Context.Recent numerical and theoretical considerations have shown that low-degree acoustic modes in rapidly rotating stars follow an asymptotic formula. In parallel, recent studies have revealed the presence of regular pulsation frequency patterns in rapidly rotatingδScuti stars that seem to match theoretical expectations.Aims.In this context, a key question is whether strong gradients or discontinuities can adversely affect the asymptotic frequency pattern to the point of hindering its identification. Other important questions are how rotational splittings are affected by the 2D rotation profiles expected from baroclinic effects and whether it is possible to probe the rotation profile using these splittings.Methods.In order to address these questions, we numerically calculate stellar pulsation modes in continuous and discontinuous rapidly rotating models produced by the 2D Evolution STEllaire en Rotation (ESTER) code. This code self-consistently calculates the rotation profile based on baroclinic effects and uses a spectral multi-domain approach, thus making it possible to introduce discontinuities at the domain interfaces without loss of numerical accuracy. The pulsation calculations are carried out using an adiabatic version of the Two-dimensional Oscillation Program (TOP) code. The variational principle is then used to confirm the high numerical accuracy of the pulsation frequencies and to derive an integral formula for the generalised rotational splittings. Acoustic glitch theory, combined with ray dynamics, is applied to the discontinuous models in order to interpret their pulsation spectra.Results.Our results show that the generalised rotational splittings are very well approximated by the integral formula, except for modes involved in avoided crossings. This potentially allows the application of inverse theory for probing the rotation profile. We also show that glitch theory applied along the island mode orbit can correctly predict the periodicity of the glitch frequency pattern produced by the discontinuity or Γ1dip related to the He II ionisation zone in some of the models. Furthermore, the asymptotic frequency pattern remains sufficiently well preserved to potentially allow its detection in observed stars.

Tunnelling around bends—Wave scattering in curved shell structures

A ray dynamics describing wave transport on curved and smooth thin shells can be obtained from the underlying wave equations via the Eikonal approximation. We analyse mid-frequency effects near the ring frequency for curved plates consisting of a cylindrical region smoothly connected to two flat plates. Using classical shell theory, we treat a corresponding ray-tracing limit derived in the short wavelength regime for bending, shear and pressure incident waves. A treatment based on real rays gives either total reflection or total transmission; the solution of the full wave equations shows in contrast a smooth transition and exhibits resonant states localised in and around the region of maximal curvature. We show here for the first time, that both the smooth transition from total reflection to total transmission and the occurrence of resonant states can be described in a ray tracing approximation by extending the treatment to complex rays. In this sense, wave transmission across bends is a tunnelling phenomenon similar to the tunnelling effects known in optics and quantum mechanics. Based on simplified graph models, we can make qualitative predictions for resonance positions in parameter and frequency spaces. We are thus able to approximate the scattering matrix for waves incident on the bend accounting for tunnelling mediated by resonant states and uniformly treating the transition between the limits of totally reflected and totally transmitted waves.

Spatial structure of lasing modes in wave-chaotic semiconductor microcavities

We present experimental and numerical studies of broad-area semiconductor lasers with chaotic ray dynamics. The emission intensity distributions at the cavity boundaries are measured and compared to ray tracing simulations and numerical calculations of the passive cavity modes. We study two different cavity geometries, a D-cavity and a stadium, both of which feature fully chaotic ray dynamics. While the far-field distributions exhibit fairly homogeneous emission in all directions, the emission intensity distributions at the cavity boundary are highly inhomogeneous, reflecting the non-uniform intensity distributions inside the cavities. The excellent agreement between experiments and simulations demonstrates that the intensity distributions of wave-chaotic semiconductor lasers are primarily determined by the cavity geometry. This is in contrast to conventional Fabry–Perot broad-area lasers for which the intensity distributions are to a large degree determined by the nonlinear interaction of the lasing modes with the semiconductor gain medium.

Gravitational spin Hall effect of light

The propagation of electromagnetic waves in vacuum is often described within the geometrical optics approximation, which predicts that wave rays follow null geodesics. However, this model is valid only in the limit of infinitely high frequencies. At large but finite frequencies, diffraction can still be negligible, but the ray dynamics becomes affected by the evolution of the wave polarization. Hence, rays can deviate from null geodesics, which is known as the gravitational spin Hall effect of light. In the literature, this effect has been calculated ad hoc for a number of special cases, but no general description has been proposed. Here, we present a covariant Wentzel-Kramers-Brillouin analysis from first principles for the propagation of light in arbitrary curved spacetimes. We obtain polarization-dependent ray equations describing the gravitational spin Hall effect of light. We also present numerical examples of polarization-dependent ray dynamics in the Schwarzschild spacetime, and the magnitude of the effect is briefly discussed. The analysis reported here is analogous to that of the spin Hall effect of light in inhomogeneous media, which has been experimentally verified.

Lasing of scarred mode near above threshold in a semiconductor microcavity laser.

We study a lasing of mode groups in a fully chaotic rounded D-shape InGaAsP semiconductor microcavity laser when an electrode is smaller than a cavity (inward gap). Although there are numerous unstable periodic orbits supporting resonances, a mode group localized on period-5 unstable periodic orbit is more competitive than the others for our laser configuration of the inward gap. By means of theoretical and numerical analyses with ray and wave dynamics, we show that the analyses well agree with our experimental results.

Effect of a strong magnetic field on gravity-mode period spacings in red giant stars

ABSTRACT When a star evolves into a red giant, the enhanced coupling between core-based gravity modes and envelope-based pressure modes forms mixed modes, allowing its deep interior to be probed by asteroseismology. The ability to obtain information about stellar interiors is important for constraining theories of stellar structure and evolution, for which the origin of various discrepancies between prediction and observation is still under debate. Ongoing speculation surrounds the possibility that some red giant stars may harbour strong (dynamically significant) magnetic fields in their cores, but interpretation of the observational data remains controversial. In part, this is tied to shortfalls in our understanding of the effects of strong fields on the seismic properties of gravity modes, which lies beyond the regime of standard perturbative methods. Here, we seek to investigate the effect of a strong magnetic field on the asymptotic period spacings of gravity modes. We use a Hamiltonian ray approach to measure the volume of phase space occupied by mode-forming rays, this being roughly proportional to the average density of modes (number of modes per unit frequency interval). A strong field appears to systematically increase this by about 10 per cent, which predicts a ∼10 per cent smaller period spacing. Evidence of near integrability in the ray dynamics hints that the gravity-mode spectrum may still exhibit pseudo-regularities under a strong field.

Lowest threshold lasing modes localized on marginally unstable periodic orbits in a semiconductor microcavity laser.

The lowest threshold lasing mode in a rounded D-shape microcavity is theoretically analyzed and experimentally demonstrated. To identify the lowest threshold lasing mode, we investigate threshold conditions of different periodic orbits by considering the linear gain condition due to the effective pumping region and total loss consisting of internal and scattering losses in ray dynamics. We compare the ray dynamical result with resonance mode analysis, including gain and loss. We find that the resonance modes localized on the pentagonal marginally unstable periodic orbit have the lowest threshold in our fabrication configuration. Our findings are verified by obtaining the path lengths and far-field patterns of lasing modes.