arXiv subjects

J. Duan

Publications and source records attributed to J. Duan.

11 recordsLinked to original sources

arXiv2023

Multiple and spectrally robust photonic magic angles in reconfigurable α-MoO3 trilayers

The assembling of twisted stacks of van der Waals (vdW) materials had led to the discovery of a profusion of remarkable physical phenomena in recent years, as it provides a means to accurately control and harness electronic band structures. This has given birth to the so-called field of twistronics. An analogous concept has been developed for highly confined polaritons, or nanolight, in twisted bilayers of strongly anisotropic vdW materials, extending the field to the twistoptics realm. In this case, the emergence of a topological transition of the polaritonic dispersion at a given twist angle (photonic magic angle) results in the propagation of nanolight along one specific direction (canalization regime), holding promises for unprecedented control of the flow of energy at the nanoscale. However, there is a fundamental limitation in twistoptics that critically impedes such control: there is only one photonic magic angle (and thus canalization direction) in a twisted bilayer and it is fixed for each incident frequency. Here, we overcome this limitation by demonstrating the existence of multiple spectrally robust photonic magic angles in reconfigurable twisted vdW trilayers. As a result, we show that canalization of nanolight can be programmed at will along any desired in-plane direction in a single device, and, importantly, within broad spectral ranges of up to 70 cm-1. Our findings lay the foundation for robust and widely tunable twistoptics, opening the door for applications in nanophotonics where on-demand control of energy at the nanoscale is crucial, such as thermal management, nanoimaging or entanglement of quantum emitters.

physics.optics↗

arXiv2022

Twist-tunable Polaritonic Nanoresonators in a van der Waals Crystal

Optical nanoresonators are fundamental building blocks in a number of nanotechnology applications (e.g. in spectroscopy) due to their ability to efficiently confine light at the nanoscale. Recently, nanoresonators based on the excitation of phonon polaritons (PhPs) $-$ light coupled to lattice vibrations $-$ in polar crystals (e.g. SiC, or h-BN) have attracted much attention due to their strong field confinement, high-quality factors, and potential to enhance the photonic density of states at mid-infrared (IR) frequencies. Here, we go one step further by introducing PhPs nanoresonators that not only exhibit these extraordinary properties but also incorporate a new degree of freedom $-$ twist tuning, i.e. the possibility to be spectrally controlled by a simple rotation. To that end, we both take advantage of the low-loss in-plane hyperbolic propagation of PhPs in the van der Waals crystal $α$-MoO$_3$, and realize dielectric engineering of a pristine $α$-MoO$_3$ slab placed on top of metal ribbon grating, which preserves the high-quality of the polaritonic resonances. By simple rotating the $α$-MoO$_3$ slab in the plane (from 0 to 45$^{\circ}$), we demonstrate via far- and near-field measurements that the narrow polaritonic resonances (with quality factors Q up to 200) can be tuned in a broad range (up to 32 cm$^{-1}$, i.e up 6 ~ times its full width at half maximum, FWHM ~ 5 cm$^{-1}$). Our results open the door to the development of tunable low-loss nanotechnologies at IR frequencies with application in sensing, emission or photodetection.

physics.optics↗

arXiv2021

Planar nano-optics in anisotropic media: anomalous refraction and diffraction-free lensing of highly confined polaritons

As one of the most fundamental optical phenomena, refraction between isotropic media is characterized by light bending towards the normal to the boundary when passing from a low- to a high-refractive-index medium. However, in anisotropic media, refraction is a much more exotic phenomenon. The most general case of refraction between two anisotropic media remains unexplored, particularly in natural media and at the nanoscale. Here, we visualize and comprehensively study refraction of electromagnetic waves between two strongly anisotropic (hyperbolic) media, and, importantly, we do it with the use of polaritons confined to the nanoscale in a low-loss natural medium, alpha-MoO3. Our images show refraction of polaritons under the general case in which both the direction of propagation and the wavevector are not collinear. As they traverse planar nanoprisms tailored in alpha-MoO3, refracted polaritons exhibit non-intuitive directions of propagation, enabling us to unveil an exotic optical effect: bending-free refraction. Furthermore, we succeed in developing the first in-plane refractive hyperlens, which yields foci as small as lamdap/6, being lamdap the polariton wavelength (lamda0/50 with respect to the wavelength of light in free space). Our results set the grounds for planar nano-optics in strongly anisotropic media, with potential for unprecedented control of the flow of energy at the nanoscale.

physics.optics↗

arXiv2021

Giant optical anisotropy in transition metal dichalcogenides for next-generation photonics

Large optical anisotropy observed in a broad spectral range is of paramount importance for efficient light manipulation in countless devices. Although a giant anisotropy was recently observed in the mid-infrared wavelength range, for visible and near-infrared spectral intervals, the problem remains acute with the highest reported birefringence values of 0.8 in BaTiS3 and h-BN crystals. This inspired an intensive search for giant optical anisotropy among natural and artificial materials. Here, we demonstrate that layered transition metal dichalcogenides (TMDCs) provide an answer to this quest owing to their fundamental differences between intralayer strong covalent bonding and weak interlayer van der Walls interaction. To do this, we carried out a correlative far- and near-field characterization validated by first-principle calculations that reveals an unprecedented birefringence of 1.5 in the infrared and 3 in the visible light for MoS2. Our findings demonstrate that this outstanding anisotropy allows for tackling the diffraction limit enabling an avenue for on-chip next-generation photonics.

physics.app-ph↗

arXiv2013

Propagation of nuclear data uncertainties for ELECTRA burn-up calculations

The European Lead-Cooled Training Reactor (ELECTRA) has been proposed as a training reactor for fast systems within the Swedish nuclear program. It is a low-power fast reactor cooled by pure liquid lead. In this work, we propagate the uncertainties in Pu-239 transport data to uncertainties in the fuel inventory of ELECTRA during the reactor life using the Total Monte Carlo approach (TMC). Within the TENDL project the nuclear models input parameters were randomized within their uncertainties and 740 Pu-239 nuclear data libraries were generated. These libraries are used as inputs to reactor codes, in our case SERPENT, to perform uncertainty analysis of nuclear reactor inventory during burn-up. The uncertainty in the inventory determines uncertainties in: the long-term radio-toxicity, the decay heat, the evolution of reactivity parameters, gas pressure and volatile fission product content. In this work, a methodology called fast TMC is utilized, which reduces the overall calculation time. The uncertainty in the long-term radiotoxicity, decay heat, gas pressure and volatile fission products were found to be insignificant. However, the uncertainty of some minor actinides were observed to be rather large and therefore their impact on multiple recycling should be investigated further. It was also found that, criticality benchmarks can be used to reduce inventory uncertainties due to nuclear data. Further studies are needed to include fission yield uncertainties, more isotopes, and a larger set of benchmarks.

nucl-th↗

arXiv2011

A sufficient condition on monotonic increase of the number of nonzero entry in the optimizer of L1 norm penalized least-square problem

The $\ell$-1 norm based optimization is widely used in signal processing, especially in recent compressed sensing theory. This paper studies the solution path of the $\ell$-1 norm penalized least-square problem, whose constrained form is known as Least Absolute Shrinkage and Selection Operator (LASSO). A solution path is the set of all the optimizers with respect to the evolution of the hyperparameter (Lagrange multiplier). The study of the solution path is of great significance in viewing and understanding the profile of the tradeoff between the approximation and regularization terms. If the solution path of a given problem is known, it can help us to find the optimal hyperparameter under a given criterion such as the Akaike Information Criterion. In this paper we present a sufficient condition on $\ell$-1 norm penalized least-square problem. Under this sufficient condition, the number of nonzero entries in the optimizer or solution vector increases monotonically when the hyperparameter decreases. We also generalize the result to the often used total variation case, where the $\ell$-1 norm is taken over the first order derivative of the solution vector. We prove that the proposed condition has intrinsic connections with the condition given by Donoho, et al \cite{Donoho08} and the positive cone condition by Efron {\it el al} \cite{Efron04}. However, the proposed condition does not need to assume the sparsity level of the signal as required by Donoho et al's condition, and is easier to verify than Efron, et al's positive cone condition when being used for practical applications.

stat.ML↗

arXiv2004

Fractional Fokker--Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises

The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. In this paper, we derive a Fractional Fokker--Planck equation for the probability distribution of particles whose motion is governed by a {\em nonlinear} Langevin-type equation, which is driven by a non-Gaussian Levy-stable noise. We obtain in fact a more general result for Markovian processes generated by stochastic differential equations.}

math.AP↗

arXiv2004

Stochastic Dynamics of a Coupled Atmosphere--Ocean Model

The investigation of the coupled atmosphere-ocean system is not only scientifically challenging but also practically important. We consider a coupled atmosphere-ocean model, which involves hydrodynamics, thermodynamics, and random atmospheric dynamics due to short time influences at the air-sea interface. We reformulate this model as a random dynamical system. First, we have shown that the asymptotic dynamics of the coupled atmosphere-ocean model is described by a random climatic attractor. Second, we have estimated the atmospheric temperature evolution under oceanic feedback, in terms of the freshwater flux, heat flux and the external fluctuation at the air-sea interface, as well as the earth's longwave radiation coefficient and the shortwave solar radiation profile. Third, we have demonstrated that this system has finite degree of freedom by presenting a finite set of determining functionals in probability. Finally, we have proved that the coupled atmosphere-ocean model is ergodic under suitable conditions for physical parameters and randomness, and thus for any observable of the coupled atmosphere-ocean flows, its time average approximates the statistical ensemble average, as long as the time interval is sufficiently long.

math.DS↗

arXiv2000

Fractional Fokker-Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises

The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. However, there are both theoretical and empirical reasons to consider similar equations driven by strongly non-Gaussian noises. In particular, they yield strongly non-Gaussian anomalous diffusion which seems to be relevant in different domains of Physics. We therefore derive in this paper a Fractional Fokker-Planck equation for the probability distribution of particles whose motion is governed by a nonlinear Langevin-type equation, which is driven by a Levy-stable noise rather than a Gaussian. We obtain in fact a general result for a Markovian forcing. We also discuss the existence and uniqueness of the solution of the Fractional Fokker-Planck equation

chao-dyn↗

arXiv1999

Generalized Stable Multivariate Distribution and Anisotropic Dilations

After having closely re-examined the notion of a Lévy's stable vector, it is shown that the notion of a stable multivariate distribution is more general than previously defined. Indeed, a more intrinsic vector definition is obtained with the help of non isotropic dilations and a related notion of generalized scale. In this framework, the components of a stable vector may not only have distinct Levy's stability indices $α$'s, but the latter may depend on its norm. Indeed, we demonstrate that the Levy's stability index of a vector rather correspond to a linear application than to a scalar, and we show that the former should satisfy a simple spectral property.

chao-dyn↗

arXiv1996

Limit Set of Trajectories of the Coupled Viscous Burgers' Equations

In this letter, a coupled system of viscous Burgers' equations with zero Dirichlet boundary conditions and appropriate initial data is considered. For the well-known single viscous Burgers' equation with zero Dirichlet boundary conditions, the zero equilibrium is the unique global exponential point attractor. A similar property is shown for the coupled Burgers' equations, i.e., trajectories starting with initial data which is not too large approach the zero equilibrium as time goes to infinity. This ``approaching" or convergence is not necessarily exponentially fast, unlike the single viscous Burgers' equation.

chao-dyn↗