Analytical formulation of spatiotemporal modulated graphene-based waveguides using Floquet-Bloch theory.

In this work, an analytical model to study graphene-based spatiotemporal modulated structures is developed and verified through comparison with full wave numerical simulations. Graphene is an ideal material for realizing spatiotemporal modulated structures at high frequencies of THz and optics. In this analysis, the electromagnetic response of studied structures is expressed in terms of weighted Floquet-Bloch modes supported by the structure, while graphene is modeled by a spatiotemporal modulated surface current that imposes certain boundary conditions on the modes. The developed analytical technique is a comprehensive tool and can be used for accurate modeling of different kinds of spatiotemporal devices including lossy, guided, and leaky wave structures. To demonstrate the accuracy of the model, two plasmonic waveguides with space and time modulated graphene conductivity are analyzed and their interband and intraband transition between modes are thoroughly investigated. Using the developed analytical model, spatiotemporal modulation phenomena such as mode conversion, wave amplification and nonreciprocal response are explored and discussed for the studied structures.

Collective cloaking of a cluster of electrostatically defined core-shell quantum dots in graphene.

We study cloaking of aclusterof electrostatically defined core-shell quantum dots in graphene. Guided by the generalized multiparticle Mie theory, the Dirac electron scattering from a cluster of quantum dots is addressed. Indeed distant quantum dots may experience a sort of individual cloaking. But despite the multiple scattering of an incident electron from a set of adjacent quantum dots,collective cloakingmay happen. Via a proper choice of the radii and bias voltages of shells, two most important scattering coefficients and hence the scattering efficiency of the cluster dramatically decrease. Energy-selective electron cloaks are realizable. More importantly, clusters simultaneously transparent to electrons of different energies, are achievable. Being quite sensitive to applied bias voltages, clusters of core-shell quantum dots may be used to develop switches with high on-off ratios.

Electric and Magnetic Hotspots via Hollow InSb Microspheres for Enhanced Terahertz Spectroscopy.

We study electric and magnetic hotspots in the gap between hollow InSb microspheres forming dimers and trimers. The outer radius, core volume fraction, distance, and temperature of the microspheres can be chosen to achieve field enhancement at a certain frequency corresponding to the transition between energy levels of a molecule placed in the gap. For example, utilizing 80 µm radius spheres at a gap of 2 µm held at a temperature of 295 K, allow electric field intensity enhancements of 10-2880 and magnetic field intensity enhancements of 3-61 in the frequency window 0.35-1.50 THz. The core volume fraction and the ambient temperature affect the enhancements, particularly in the frequency window 1.5-2 THz. Electric and magnetic hotspots are promising for THz absorption and circular dichroism spectroscopy.

Magnetic and electric hotspots via fractal clusters of hollow silicon nanoparticles.

We show that fractal clusters of hollow Si nanoparticles provide both magnetic hotspots (MHs) and electric hotspots (EHs). The hollow size tailors the wavelength dependence of the field enhancement. In the wavelength window 400-750 nm, magnetic field intensity enhancements of 10-3790 and electric field intensity enhancements of 10-400 are achievable. Wavelength-tuned MHs and EHs allow better enhancement of Raman optical activity, fluorescence and circular dichroism of molecules, and so on. Si nanoparticles overcome the limitations of metallic ones, which provide only EHs at the price of heat perturbations on a nearby quantum emitter due to metallic ohmic losses.

Casimir rack and pinion as a miniaturized kinetic energy harvester.

We study a nanoscale machine composed of a rack and a pinion with no contact, but intermeshed via the lateral Casimir force. We adopt a simple model for the random velocity of the rack subject to external random forces, namely, a dichotomous noise with zero mean value. We show that the pinion, even when it experiences random thermal torque, can do work against a load. The device thus converts the kinetic energy of the random motions of the rack into useful work.

Three-sphere magnetic swimmer in a shear flow.

We consider a low-Reynolds-number swimmer made from three spheres linked by two slender arms, and explore its motion in a shear flow. This rodlike three-sphere swimmer finally follows the direction dictated by the shear flow. To overcome this shortcoming, we propose a model in which the two outer spheres have permanent magnetic moments along the arms. This magnetic swimmer can be navigated to a desired direction by applying an external static and uniform magnetic field.

Effect of thermal noise on noncontact rack and pinion device.

We study a nanoscale system composed of one corrugated plate (rack) and one corrugated cylinder (pinion) coupled via the lateral Casimir force. We assume that the rack moves uniformly. The axle of the pinion experiences frictional torque and random torque due to a surrounding fluid. We show that even in the presence of thermal noise, the device can work against external loads: The pinion rotates with a nonzero average velocity. The device operation becomes less influenced by the noise as the gap between rack and pinion decreases.

Diffusive transport of light in two-dimensional granular materials.

We study photon diffusion in a two-dimensional random packing of monodisperse disks as a simple model of granular material. We apply ray optics approximation to set up a persistent random walk for the photons. We employ Fresnel's intensity reflectance with its rich dependence on the incidence angle and polarization state of the light. We present an analytic expression for the transport-mean-free path l* in terms of the refractive indices of grains and host medium, grain radius, and packing fraction. We perform numerical simulations to examine our analytical result.

Noncontact rack-pinion-rack device as a differential vibration sensor.

We study a nanoscale system composed of one corrugated cylinder (pinion) placed between two corrugated plates (racks). The pinion and racks have no mechanical contact, but are coupled via the lateral Casimir force-one of the most spectacular consequences of quantum fluctuations of the electromagnetic field. The noncontact design of the device could help with the noteworthy wear problem in nanoscale mechanical systems. We consider the case where both racks undergo harmonic lateral motion. We assume that the amplitude, frequency, and phase of one of the racks are known. We show that probing the pinion motion, one can determine the vibration characteristics of the other rack.

Nonlinear dynamics of a rack-pinion-rack device powered by the Casimir force.

Using the lateral Casimir force-a manifestation of the quantum fluctuations of the electromagnetic field between objects with corrugated surfaces-as the main force transduction mechanism, a nanomechanical device with rich dynamical behaviors is proposed. The device is made of two parallel racks that are moving in the same direction and a pinion in the middle that couples with both racks via the noncontact lateral Casimir force. The built-in frustration in the device causes it to be very sensitive and react dramatically to minute changes in the geometrical parameters and initial conditions of the system. The noncontact nature of the proposed device could help with the ubiquitous wear problem in nanoscale mechanical systems.

Dynamics of noncontact rack-and-pinion device: Periodic back-and-forth motion of the rack.

We study a nanoscale system composed of one corrugated cylinder (pinion) and one corrugated plate (rack). The pinion and rack have no mechanical contact, but are coupled via the lateral Casimir force. We consider the case where the rack position versus time is a periodic triangular signal. We find that the device can rectify the periodic but nonsinusoidal motion of the rack. Using the typical values of parameters, we find that the pinion rotates with an average angular velocity Ω=1∼100 Hz . Experimental observation of the pinion rotation will show that the quantum vacuum can intermesh the noncontact parts of nanomachines.

Optical analog of Matthiessen's rule in a one-dimensional model for diffusive light transport in foams.

We study photon diffusion in a one-dimensional model foam composed of thin films and Plateau borders. Each thin film or Plateau border is characterized by its own intensity transmittance. We relate l(Foam)*, the transport-mean-free path of photons diffusing in the foam, to the foam microstructure. Denoting by l(Film)* (l(PB)*) the transport-mean-free path of photons in a medium composed only of thin films (Plateau borders), we find 1/l(Foam)*=φ(F)/l(Film)*+φ(P)/l(PB)*. Here φ(F) and φ(P)=1-φ(F) are the fraction of films and Plateau borders, respectively.

Three-sphere low-Reynolds-number swimmer near a wall.

We study the influence of a wall on the dynamics of a low-Reynolds-number three-sphere swimmer. A far swimmer whose arm makes an angle theta with the horizon experiences the wall presence as an angle-dependent quadrupole force proportional to (a/L)(2)(L/z)(2)cos theta, where a, L, and z are the radius of spheres, the arm length, and the swimmer distance to the wall, respectively. The wall-induced translational velocity of swimmer is perpendicular to the arms. A far swimmer prefers to orient its arms parallel to the plate. This state is stable. Remarkably, the parallel state is unstable when the swimmer is close to the wall. In this regime, the velocity of swimmer decreases as (z/L)(2). Numerical solution of the equations of motion for arbitrary initial z/L and theta reveals four different phases of locomotion.

Diffusive transport of light in a two-dimensional disordered packing of disks: analytical approach to transport mean free path.

We study photon diffusion in a two-dimensional random packing of monodisperse disks as a simple model of granular media and wet foams. We assume that the intensity reflectance of disks is a constant r . We present an analytic expression for the transport mean free path l;{*} in terms of the velocity of light in the disks and host medium, radius R and packing fraction of the disks, and the intensity reflectance. For glass beads immersed in air or water, we estimate transport mean free paths about half the experimental ones. For air bubbles immersed in water, l;{*}R is a linear function of 1epsilon , where epsilon is the liquid volume fraction of the model wet foam. This throws light on the empirical law of Vera [Appl. Opt. 40, 4210 (2001)] and promotes more realistic models.

Diffusive transport of light in three-dimensional disordered Voronoi structures.

The origin of diffusive transport of light in dry foams is still under debate. In this paper, we consider the random walks of photons as they are reflected or transmitted by liquid films according to the rules of ray optics. The foams are approximately modeled by three-dimensional Voronoi tessellations with varying degree of disorder. We study two cases: A constant intensity reflectance and the reflectance of thin films. Especially in the second case, we find that in the experimentally important regime for the film thicknesses, the transport-mean-free path l;{ *} does not significantly depend on the topological and geometrical disorder of the Voronoi foams including the periodic Kelvin foam. This may indicate that the detailed structure of foams is not crucial for understanding the diffusive transport of light. Furthermore, our theoretical values for l;{ *} fall in the same range as the experimental values observed in dry foams. One can therefore argue that liquid films contribute substantially to the diffusive transport of light in dry foams.

Persistent random walk on a one-dimensional lattice with random asymmetric transmittances.

We study the persistent random walk of photons on a one-dimensional lattice of random asymmetric transmittances. Each site is characterized by its intensity transmittance t (t;{'} not equalt) for photons moving to the right (left) direction. Transmittances at different sites are assumed independent, distributed according to a given probability density F(t,t;{'}) . We use the effective medium approximation and identify two classes of F(t,t;{'}) which lead to the normal diffusion of photons. Monte Carlo simulations confirm our predictions. We mention that the metamaterial introduced by Fedetov [Nano Lett. 7, 1996 (2007)] can be used to realize a lattice of random asymmetric transmittances.

Rectification of the lateral Casimir force in a vibrating noncontact rack and pinion.

The nonlinear dynamics of a cylindrical pinion that is kept at a distance from a vibrating rack is studied, and it is shown that the lateral Casimir force between the two corrugated surfaces can be rectified. The effects of friction and external load are taken into account, and it is shown that the pinion can do work against loads of up to a critical value, which is set by the amplitude of the lateral Casimir force. We present a phase diagram for the rectified motion that could help its experimental investigations, as the system exhibits a chaotic behavior in a large part of the parameter space.

Noncontact racK and pinion powered by the lateral Casimir force.

The lateral Casimir force is employed to propose a design for a potentially wear-proof rack and pinion with no contact, which can be miniaturized to the nanoscale. The robustness of the design is studied by exploring the relation between the pinion velocity and the rack velocity in the different domains of the parameter space. The effects of friction and added external load are also examined. It is shown that the device can hold up extremely high velocities, unlike what the general perception of the Casimir force as a weak interaction might suggest.

Universality in two-dimensional cellular structures evolving by cell division and disappearance.

The dynamics of two-dimensional cellular networks is written in terms of coupled population equations, which describe how the population of s-sided cells is affected by cell division and disappearance. In these equations the effect of the rest of the foam on the disappearing or dividing cell is treated as a local mean field. Under not too restrictive conditions, the equilibrium distribution P(s) of cells satisfies a linear difference equation of order two or higher. The population equations are asymptotically integrable. The asymptotic integrability implies a "universal" distribution P(s) approximately Cs-kZs for large values of s, which is also the Boltzmann distribution associated with the maximum entropy inference. Asymptotic integrability of the population equations is absent in a global mean-field approximation. The importance of short-range topological information to control the evolution of foams is thus confirmed.

Persistent random walk on a site-disordered one-dimensional lattice: photon subdiffusion.

We study the persistent random walk of photons on a one-dimensional lattice of random transmittances. Transmittances at different sites are assumed independent, distributed according to a given probability density f(t). Depending on the behavior of f(t) near t=0, diffusive and subdiffusive transports are predicted by the disorder expansion of the mean square-displacement and the effective medium approximation. Monte Carlo simulations confirm the anomalous diffusion of photons. To observe photon subdiffusion experimentally, we suggest a dielectric film stack for realization of a distribution f(t).