Quartic Dispersion Research Articles

Evolutionary pulsational mode dynamics in nonthermal turbulent viscous astrofluids

The pulsational mode of gravitational collapse in a partially ionized self-gravitating inhomogeneous viscous nonthermal nonextensive astrofluid in the presence of turbulence pressure is illustratively analyzed. The constitutive thermal species, lighter electrons and ions, are thermostatistically treated with the nonthermal $\kappa$ -distribution laws. The inertial species, such as identical heavier neutral and charged dust microspheres, are modelled in the turbulent fluid framework. All the possible linear processes responsible for dust-dust collisions are accounted. The Larson logatropic equations of state relating the dust thermal (linear) and turbulence (nonlinear) pressures with dust densities are included. A regular linear normal perturbation analysis (local) over the complex astrocloud ensues in a generalized quartic dispersion relation with unique nature of plasma-dependent multi-parametric coefficients. A numerical standpoint is provided to showcase the basic mode features in a judicious astronomical paradigm. It is shown that both the kinematic viscosity of the dust fluids and nonthermality parameter (kappa, the power-law tail index) of the thermal species act as stabilizing (damping) agent against the gravity; and so forth. The underlying evolutionary microphysics is explored. The significance of redistributing astrofluid material via waveinduced accretion in dynamic nonhomologic structureless cloud collapse leading to hierarchical astrostructure formation is actualized.

Pulsational mode behaviour in complex non-extensive non-thermal viscous astrophysical fluids

A semi-analytic evolutionary model is classically constructed to see the pulsational mode dynamics of gravitational collapse in a hydrostatically bounded complex non-thermal astrocloud on the Jeans scales of space and time. The multi-fluidic model consists of non-extensive electrons and ions, and massive dust grains along with partial ionization in flat space-time. A linear Fourier-based normal mode analysis around the defined static (homogeneous) equilibrium reduces the basic cloud equations into a quartic (biquadratic) dispersion relation with a unique set of multi-parametric coefficients. It is interestingly found that non-thermal associations in the cloud pave the way for faster normal mode propagation. The neutral dust viscosity plays a decisive role towards a transition of the pulsational mode from a non-dispersive to a dispersive form. It is also observed that the viscosity has a stabilizing influence on the cloud. The dust-charge variation is noted to play an insignificant role on the stability. The results may be significant in understanding the dynamic non-homological cloud collapse leading to a hierarchical initiation of a bounded structure formation in diverse astro-cosmic anti-equilibrium environs.

Stability of gravito-coupled complex gyratory astrofluids

We analyze the gravitational instability of complex rotating astrofluids in the presence of dynamic role of dark matter in a homogeneous hydrostatic equilibrium framework. The effects of the lowest-order fluid viscoelasticity, Coriolis force, fluid turbulence and inter-layer frictional coupling dynamics are concurrently considered in spatially-flat geometry. The Coriolis rotation is relative to the center of the entire fluid mass distribution, contributed by both the gyratory bright (visible) and dark (invisible) sectors, conjugated via the mutual gravitational interaction. The turbulence effects are included via the modified Larson equation of state. We use a regular Fourier-based linear perturbation analysis over the rotating fluid field equations to obtain a unique form of quartic dispersion relation with variable coefficients. We numerically carry out the dispersion analysis in two extreme limits: hydrodynamic (low-frequency) and kinetic (high-frequency) regimes. It is demonstrated that, in the former regime, the gas as well as dark matter rotations have stabilizing effects on the Jeans instability of the bi-fluidic admixture. In contrast, in the latter, the rotations play destabilizing roles on the instability. An interesting feature noted here is that the magnitude of the group velocity of the fluctuations throughout increases with both the gas and dark matter rotation frequencies, and vice-versa. We, finally, hope that the obtained results could be helpful in understanding the top-down kinetic mechanisms of bounded structure formation via gravitational collapse dynamics.

Quartic Dispersion, Strong Singularity, Magnetic Instability, and Unique Thermoelectric Properties in Two-Dimensional Hexagonal Lattices of Group-VA Elements.

The critical points and the corresponding singularities in the density of states of crystals were first classified by Van Hove with respect to their dimensionality and energy-momentum dispersions. Here, different from saddle-point Van Hove singularities, the occurrence of a continuum of critical points, which give rise to strong singularities in two-dimensional elemental hexagonal lattices, is shown using a minimal tight-binding formalism. The model predicts quartic energy-momentum dispersions despite quadratic or linear ones, which is also the origin of the strong singularity. Starting with this model and using first-principles density functional theory calculations, a family of novel two-dimensional materials that actually display such singularities are identified and their extraordinary features are investigated. The strong singularity gives rise to ferromagnetic instability with an inverse-square-root temperature dependence and the quartic dispersion is responsible for a steplike transmission spectrum, which is a characteristic feature of one-dimensional systems. Because of the abrupt change in transmission at the band edge, these materials have temperature-independent thermopower and enhanced thermoelectric efficiencies. Nitrogene has exceptionally high thermoelectric efficiencies at temperatures down to 50 K, which could make low-temperature thermoelectric applications possible.

Experimental Verification of Degenerate Band Edge Dispersion in Silicon Photonic Integrated Circuits

On resonance, periodic dielectric media of finite length exhibit large and distributed internal electric field distributions. The large and distributed fields have been exploited for applications in light emission, optical switching, and nonlinear optics. Resonance quality factors scale as the number of periods cubed near a regular band edge with quadratic dispersion. For chip-scale integrated photonics, significant footprint reduction is possible by exploiting the quartic dispersion of a degenerate band edge with quality factors that scale to the fifth power of the number of periods. Band diagrams with quartic dispersion are extracted from transmission measurements of fabricated devices realized in silicon photonics. Transmission measurements show Fano resonances with a sharp transmission peak-to-bandgap extinction ratio of 20 dB and quality factors of 27 000.

Three-dimensional Gross–Pitaevskii solitary waves in optical lattices: Stabilization using the artificial quartic kinetic energy induced by lattice shaking

In this Letter, we show that a three-dimensional Bose–Einstein solitary wave can become stable if the dispersion law is changed from quadratic to quartic. We suggest a way to realize the quartic dispersion, using shaken optical lattices. Estimates show that the resulting solitary waves can occupy as little as ∼1/20-th of the Brillouin zone in each of the three directions and contain as many as N=103 atoms, thus representing a fully mobile macroscopic three-dimensional object.

A two-dimensional algebraic quantum liquid produced by an atomic simulator of the quantum Lifshitz model.

Bosons have a natural instinct to condense at zero temperature. It is a long-standing challenge to create a high-dimensional quantum liquid that does not exhibit long-range order at the ground state, as either extreme experimental parameters or sophisticated designs of microscopic Hamiltonians are required for suppressing the condensation. Here we show that synthetic gauge fields for ultracold atoms, using either the Raman scheme or shaken lattices, provide physicists a simple and practical scheme to produce a two-dimensional algebraic quantum liquid at the ground state. This quantum liquid arises at a critical Lifshitz point, where a two-dimensional quartic dispersion emerges in the momentum space, and many fundamental properties of two-dimensional bosons are changed in its proximity. Such an ideal simulator of the quantum Lifshitz model allows experimentalists to directly visualize and explore the deconfinement transition of topological excitations, an intriguing phenomenon that is difficult to access in other systems.

Strong correlation effects in a two-dimensional Bose gas with quartic dispersion

Motivated by the fundamental question of the fate of interacting bosons in flat bands, we consider a two-dimensional Bose gas at zero temperature with an underlying quartic single-particle dispersion in one spatial direction. This type of band structure can be realized using the NIST scheme of spin-orbit coupling [Y.-J. Lin, K. Jim\'{e}nez-Garcia, and I. B. Spielman, Nature $\textbf{471}$, 83 (2011)], in the regime where the lower band dispersion has the form $\varepsilon_{\textbf{k}} \sim k_{x}^{4}/4+k_{y}^{2}+\ldots$, or using the shaken lattice scheme of Parker $\textit{et al.}$ [C. V. Parker, L.-C. Ha and C. Chin, Nature Physics $\textbf{9}$, 769 (2013)]. We numerically compare the ground state energies of the mean-field Bose-Einstein condensate (BEC) and various trial wave-functions, where bosons avoid each other at short distances. We discover that, at low densities, several types of strongly correlated states have an energy per particle ($\epsilon$), which scales with density ($n$) as $\epsilon \sim n^{4/3}$, in contrast to $\epsilon \sim n$ for the weakly interacting Bose gas. These competing states include a Wigner crystal, quasi-condensates described in terms properly symmetrized fermionic states, and variational wave-functions of Jastrow type. We find that one of the latter has the lowest energy among the states we consider. This Jastrow-type state has a strongly reduced, but finite condensate fraction, and true off-diagonal long range order, which suggests that the ground state of interacting bosons with quartic dispersion is a strongly-correlated condensate reminiscent of superfluid Helium-4. Our results show that even for weakly-interacting bosons in higher dimensions, one can explore the crossover from a weakly-coupled BEC to a strongly-correlated condensate by simply tuning the single particle dispersion or density.

Finsler-like structures from Lorentz-breaking classical particles

A method is presented for deducing classical point-particle Lagrange functions corresponding to a class of quartic dispersion relations. Applying this to particles violating Lorentz symmetry in the minimal Standard-Model Extension leads to a variety of novel lagrangians in flat spacetime. Morphisms in these classical systems are studied that echo invariance under field redefinitions in the quantized theory. The Lagrange functions found offer new possibilities for understanding Lorentz-breaking effects by exploring parallels with Finsler-like geometries.

PLANE-WAVE PROPAGATION IN ELECTROMAGNETIC PQ MEDIUM

Two basic classes of electromagnetic medium, recently defined as P and Q medium, are generalized to define the class of PQ media. Plane wave propagation in the general PQ medium is studied and the quartic dispersion equation is derived in analytic form applying four-dimensional dyadic formalism. The result is verified by considering various special cases of PQ media for which the dispersion equation is either decomposed to two quadratic equations or is identically satisfied (media with no dispersion equation). As a numerical example, the dispersion surface of a PQ medium with non-decomposable dispersion equation is considered.

Low-amplitude instability as a premise for the spontaneous symmetry breaking in the new integrable semidiscrete nonlinear system

The new integrable semidiscrete multicomponent nonlinear system characterized by two coupling parameters is presented. Relying upon the lowest local conservation laws the concise form of the system is given and its selfconsistent symmetric parametrization in terms of four independent field variables is found. The comprehensive analysis of quartic dispersion equation for the system low-amplitude excitations is made. The criteria distinguishing the domains of stability and instability of low-amplitude excitations are formulated and a collection of qualitatively distinct realizations of a dispersion law are graphically presented. The loop-like structure of a low-amplitude dispersion law of reduced system emerging within certain windows of adjustable coupling parameter turns out to resemble the loop-like structure of a dispersion law typical of beam-plasma oscillations. Basing on the peculiarities of low-amplitude dispersion law as the function of adjustable coupling parameter it is possible to predict the windows of spontaneous symmetry breaking even without an explicit knowledge of the system Lagrangian function. Having been rewritten in terms of properly chosen modified field variables the reduced four wave integrable system can be qualified as consisting of two coupled nonlinear lattice subsystems, namely the self-dual ladder network and the vibrational ones.

An efficient broad-band mid-wave IR fiber optic light source: design and performance simulation

Design of a mid-wave IR (MWIR) broad-band fiber-based light source exploiting degenerate four-wave mixing (D-FWM) in a meter long suitably designed highly nonlinear (NL) chalcogenide microstructured optical fiber (MOF) is reported. This superior FWM bandwidth (BW) was obtained through precise tailoring of the fiber's dispersion profile so as to realize positive quartic dispersion at the pump wavelength. We consider an Erbium (Er(3+)) - doped continuous wave (CW) ZBLAN fiber laser emitting at 2.8 μm as the pump source with an average power of 5 W. Amplification factor as high as 25 dB is achievable in the 3 - 3.9 μm spectral range with average power conversion efficiency > 32%.

Role of the van Hove singularity in the quantum criticality of the Hubbard model

A quantum critical point (QCP), separating the non-Fermi liquid region from the Fermi liquid, exists in the phase diagram of the 2D Hubbard model [Vidhyadhiraja et. al, Phys. Rev. Lett. 102, 206407 (2009)]. Due to the vanishing of the critical temperature associated with a phase separation transition, the QCP is characterized by a vanishing quasiparticle weight. Near the QCP, the pairing is enhanced since the real part of the bare d-wave p-p susceptibility exhibits algebraic divergence with decreasing temperature, replacing the logarithmic divergence found in a Fermi liquid [Yang et. al, Phys. Rev. Lett. 106, 047004 (2011)]. In this paper we explore the single-particle and transport properties near the QCP. We focus mainly on a van Hove singularity (vHS) coming from the relatively flat dispersion that crosses the Fermi level near the quantum critical filling. The flat part of the dispersion orthogonal to the antinodal direction remains pinned near the Fermi level for a range of doping that increases when we include a negative next-near-neighbor hopping t' in the model. For comparison, we calculate the bare d-wave pairing susceptibility for non-interacting models with the usual two-dimensional tight binding dispersion and a hypothetical quartic dispersion. We find that neither model yields a vHS that completely describes the critical algebraic behavior of the bare d-wave pairing susceptibility. The resistivity, thermal conductivity, thermopower, and the Wiedemann-Franz Law are examined in the Fermi liquid, marginal Fermi liquid, and pseudo-gap doping regions. A negative next-near-neighbor hopping t' increases the doping region with marginal Fermi liquid character. Both T and negative t' are relevant variables for the QCP, and both the transport and the motion of the vHS with filling suggest that they are qualitatively similar in their effect.

Black/white hole radiation from dispersive theories

We study the fluxes emitted by black holes when using dispersive field theories. We work with stationary one-dimensional backgrounds which are asymptotically flat on both sides of the horizon. The asymptotic fluxes are governed by a $3\ifmmode\times\else\texttimes\fi{}3$ Bogoliubov transformation. The fluxes emitted by the corresponding white holes are regular and governed by the inverse transformation. We numerically compute the spectral properties of these fluxes for both sub- and superluminal quartic dispersion. The leading deviations with respect to the dispersionless flux are computed and shown to be governed by a critical frequency above which there is no radiation. Unlike the UV scale governing dispersion, its value critically depends on the asymptotic properties of the background. We also study the flux outside the robust regime. In particular we show that its low-frequency part remains almost thermal but with a temperature which significantly differs from the standard one. Applications to four-dimensional black holes and Bose-Einstein condensates are in preparation.

Numerical study of photonic crystals with a split band edge: Polarization dependence and sensitivity analysis

We examine photonic crystals (PhC) made of periodic stacks of anisotropic dielectric layers with a split band edge (SBE) on the band diagram. Just below the band edge frequency, the dispersion relation $\ensuremath{\omega}(k)$ of SBE PhCs can be approximated as a linear combination of a quadratic term and a quartic term. This is in contrast to regular (conventional) band edge PhCs, which produce a quadratic dispersion relation, and to degenerate band edge (DBE) PhCs, which produce a quartic dispersion relation. Finite-size DBE PhCs and SBE PhCs are of interest because they both can support slow-wave Fabry-Perot resonances with very good transmittance. One of the most significant differences between DBE and SBE is that the transmittance of the former depends on the incident wave polarization whereas in the latter it does not. In this work, we investigate the transmittance behavior of SBE PhCs and perform a sensitivity analysis of their responses against geometrical and/or material perturbations. Dielectric losses, thickness perturbations, and misalignment angle perturbations are considered. The analysis uses a full-wave numerical technique for transient Maxwell's equations in inhomogeneous anisotropic media based on a complex-envelope alternating-direction-implicit finite-difference time-domain. A comparison is also made between the sensitivity of the SBE PhCs response versus that of DBE PhCs.

Multi-order dispersion engineering for optimal four-wave mixing

Four-wave mixing in high refractive index materials, such as chalcogenide glass or semiconductors, is promising because of their large cubic nonlinearity. However, these materials tend to have normal dispersion at telecom wavelengths, preventing phase matched operation. Recent work has shown that the waveguide dispersion in strongly confining guided-wave structures can lead to anomalous dispersion, but the resulting four-wave mixing has limited bandwidth because of negative quartic dispersion. Here we first show that the negative quartic dispersion is an inevitable consequence of this dispersion engineering procedure. However, we also demonstrate that a slight change in the procedure leads to positive quartic dispersion, resulting in a superior bandwidth. We give an example in which the four-wave mixing bandwidth is doubled in this way.

Photonic crystals with a degenerate band edge: Field enhancement effects and sensitivity analysis

Photonic crystals (PhCs) with a degenerate band edge (DBE) are dispersion-tailored materials composed of a periodic arrangement of misaligned anisotropic dielectric layers and an isotropic dielectric layer. DBE PhCs yield an (approximately) quartic dispersion relation just below the DBE frequency rather than the conventional quadratic dispersion relation present below a regular band edge (RBE). We present a sensitivity analysis of the performance of DBE PhCs under various perturbations. This analysis is made possible by means of an unconditionally stable finite-difference time-domain scheme to solve Maxwell's equations in anisotropic media based on a complex-envelope alternating-direction-implicit algorithm. Numerical simulations are performed to examine the gigantic field intensity enhancement at Fabry-Perot resonances associated with finite-stack DBE PhCs. Numerical simulations are also used to investigate the sensitivity of field enhancement effects against the bandwidth of the excitation. The effects of layer thickness perturbations, grounding, and dielectric losses on the electromagnetic response of DBE PhCs are also examined. The numerical results are used to compare Fabry-Perot RBE resonances against Fabry-Perot DBE resonances.

Theoretical analysis of the self-frequency shift near zero-dispersion points: Soliton spectral tunneling

Soliton dynamics under the action of higher-order dispersion and the Raman effect is analyzed. Though we consider a wide variety of parameters, a particularly interesting phenomenon occurs when the presence of cubic and quartic dispersion results in two regions of anomalous group velocity dispersion (GVD) separated by a region of normal dispersion. In this case a sharp switching of the soliton frequency from one anomalous GVD region to the other may exist. During such a transformation, the center of the soliton spectrum passes through the normal GVD region. We show that this switching occurs due to the phase matching between the soliton and the resonance frequency in the two anomalous GVD regions.

Numerical simulation for characterizing femtosecond optical pulses with the SPIDER algorithm

In this article based on the spectral phase interferometry for direct electric-field reconstruction (SPIDER), the femtosecond pulses with various phase characters are numerically simulated. The spectral phases and amplitudes of the transform-limited pulse, the linear chirped pulse, the cubic dispersion pulse, the quartic dispersion pulse, the self-phase modulation pulse and the pulses with the combination of different chirped characters are retrieved. These characterized pulses are applicable to the real-time measurement as samples for diagnosing the chirped characters of pulses quickly.

Programmable dispersion compensation and pulse shaping in a 26-fs chirped-pulse amplifier

We have constructed a 26-fs chirped-pulse amplifier that incorporates a programmable liquid-crystal spatial light modulator in the pulse stretcher. The modulator serves a dual purpose. First, we apply frequency-dependent phase shifts to compensate for cubic, quartic, and nonlinear phase dispersion in the amplifier, which results in a reduction in pulse duration from 32 to 26 fs, in agreement with the transform limit of the amplified pulse spectrum. Second, we are able to produce high-fidelity compressed amplified shaped pulses by applying phase masks directly within the stretcher. Shaped pulse energies of greater than 1 mJ are routinely obtained.