q-Breathers and the Fermi-Pasta-Ulam problem

The Fermi-Pasta-Ulam (FPU) paradox consists of the non-equipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number q. We continue normal modes from the harmonic limit into the FPU parameter regime and obtain persistence of these periodic orbits, termed here q-breathers (QB). They are characterized by time periodicity, exponential localization in the q-space of normal modes and linear stability up to a size-dependent threshold amplitude. Trajectories computed in the original FPU setting are perturbations around these exact QB solutions. The QB concept is applicable to other nonlinear lattices as well.     

Manipulating electromagnetic resonances in meta-molecules with double split ring resonators

We proposed meta-molecules structure composed of stacked double split ring resonators (DSRRs) and studied its electromagnetic resonances in the optical frequency range. We demonstrated that, for the first order plasmonic modes, the coupling between the outer and the inner SRRs in plane strongly influences on the resonant frequency splitting of the stacked DSRRs. And their resonant dips change with the arrangement of SRRs. However, the resonant frequencies for the high order plasmonic modes always remain immobile as the configuration varies. Our investigation offers an effective way to manipulate the resonant behavior in metamaterials.     

q-Breathers in finite two- and three-dimensional nonlinear acoustic lattices

In their celebrated experiment, Fermi, Pasta, and Ulam (FPU) [Los Alamos Report No. LA-1940, 1955] observed that in simple one-dimensional nonlinear atomic chains the energy must not always be equally shared among the modes. Recently, it was shown that exact and stable time-periodic orbits, coined q-breathers (QBs), localize the mode energy in normal mode space in an exponential way, and account for many aspects of the FPU problem. Here we take the problem into more physically important cases of two- and three-dimensional acoustic lattices to find existence and principally different features of QBs. By use of perturbation theory and numerical calculations we obtain that the localization and stability of QBs are enhanced with increasing system size in higher lattice dimensions opposite to their one-dimensional analogues.     

Resonances of Spin-1/2 Fermions in Eddington-Inspired Born-Infeld Gravity

We investigate the fermionic resonances for both chiralities in five-dimensional Eddington-inspired BornInfeld(EiBI)theory.In order to localize fermion on the brane,it needs to be considered the Yukawa coupling between the fermion and the background scalar field.In our models,since the background scalar field has kink,double kink,or anti-kink solution,the system has rich resonant Kaluza-Klein(KK)modes structure.The massive KK fermionic modes feel a volcano potential,which result in a fermionic zero mode and a set of continuous massive KK modes.The inner structure of the branes and a free parameter in background scalar field influence the resonant behaviors of the massive KK fermions.     

Experimental observation of strong photon localization in disordered photonic crystal waveguides

We demonstrate experimentally that structural perturbations imposed on highly dispersive photonic crystal-based waveguides give rise to spectral features that bear signatures of Anderson localization. Sharp resonances with effective Q's of over 30 000 are found in scattering spectra of disordered waveguides. The resonances are observed in a approximately 20-nm bandwidth centered at the cutoff of slowly guided Bloch modes. The origin of the spectral features can be explained by the interference of coherently scattered electromagnetic waves which results in the formation of a narrow impurity (or localization) band populated with spectrally distinct quasistates. Standard photon localization criteria are fulfilled in the localization band.     

Tuning properties of long period gratings in photonic bandgap fibers

We investigate the thermal tuning properties of long period gratings (LPGs) in a fluid-filled photonic bandgap fiber (PBGF). The combination of strong, resonant waveguide dispersion, characteristic of all PBGF modes, and the large thermo-optic coefficients of fluids yields highly tunable grating resonances. We measure grating resonances in three transmission bands with large tuning coefficients of up to -1.58 nm/degrees C, which match numerical results. We derive an analytic model for the PBGF LPG tuning coefficient to show how it depends on both the shift of the transmission bands and the dispersion of the coupled modes.     

Non resonant transmission modelling with statistical modal energy distribution analysis

Statistical modal Energy distribution Analysis (SmEdA) can be used as an alternative to Statistical Energy Analysis for describing subsystems with low modal overlap. In its original form, SmEdA predicts the power flow exchanged between the resonant modes of different subsystems. In the case of sound transmission through a thin structure, it is well-known that the non resonant response of the structure plays a significant role in transmission below the critical frequency. In this paper, we present an extension of SmEdA that takes into account the contributions of the non resonant modes of a thin structure. The dual modal formulation (DMF) is used to describe the behaviour of two acoustic cavities separated by a thin structure, with prior knowledge of the modal basis of each subsystem. Condensation in the DMF equations is achieved on the amplitudes of the non resonant modes and a new coupling scheme between the resonant modes of the three subsystems is obtained after several simplifications. We show that the contribution of the non resonant panel mode results in coupling the cavity modes of stiffness type, characterised by the mode shapes of both the cavities and the structure. Comparisons with reference results demonstrate that the present approach can take into account the non resonant contributions of the structure in the evaluation of the transmission loss.     

On the internal nonlinear resonant three-mode interaction of charged drop oscillations

The difference between internal nonlinear three-mode degenerate and Raman resonances is found for the first time: in the former case, the energy spent on the initial deformation of a drop is only transferred from lower to higher modes; in the latter case, it is transferred in both directions. It turns out that degenerate resonances are slightly sensitive to the physical quantities that are responsible for the exact positions of the resonances (i.e., to the amount of electric charge). A deviation from the resonant value only changes the fraction of the energy the modes exchange and the time of resonant energy exchange: the interaction itself remains resonant.     

局域共振复合单元声子晶体结构的低频带隙特性研究

本文提出了一种新型局域共振复合单元声子晶体结构, 并结合有限元方法对结构的带隙机理及低频共振带隙特性进行了分析和研究. 共振带隙产生的频率位置由所对应的局域共振模态的固有频率决定, 并且带隙宽度与局域共振模态的品质因子及其与基体之间的耦合作用强度有关. 采用局域共振复合单元结构可以实现声子晶体的多重共振, 在低频范围能打开多条共振带隙, 但受到共振单元排列方式的的影响. 由于纵向和横向局域共振模态的简并, 复合单元结构能在200 Hz以下的低频范围打开超过60%宽度的共振带隙, 最低带隙频率低至18 Hz. 这为声子晶体结构获得低频、超低频带隙提供了一种有效的方法. 关键词： 局域共振 低频带隙 复合单元 声子晶体     

Extraordinary Resonant Scattering in Imperfect Acoustic Cloak

We present a systematic study on the extraordinary resonant scattering in imperfect acoustic cloak by means of acoustic scattering theory. Analysis results demonstrate that the resonances are inevitable due to the perturbation to the ideal clo~k, and specific resonance modes are excited by specific order waves. The strength of resonance is determined by the magnitude of perturbation and each order wave＇s sensitivity to the perturbation. Further studies reveal the unique scattering characters of different resonance modes.     

Time scale to ergodicity in the Fermi-Pasta-Ulam system

We study the approach to near-equipartition in the N-dimensional Fermi-Pasta-Ulam Hamiltonian with quartic (hard spring) nonlinearity. We investigate numerically the time evolution of orbits with initial energy in some few low-frequency linear modes. Our results indicate a transition where, above a critical energy which is independent of N, one can reach equipartition if one waits for a time proportional to N(2). Below this critical energy the time to equipartition is exponentially long. We develop a theory to determine the time evolution and the excitation of the nonlinear modes based on a resonant normal form treatment of the resonances among the oscillators. Our theory predicts the critical energy for equipartition, the time scale to equipartition, and the form of the nonlinear modes below equipartition, in qualitative agreement with the numerical results. (c) 1995 American Institute of Physics.     

Electric and magnetic excitations in anisotropic broadside-coupled triangular-split-ring resonators

The electric and magnetic resonances of anisotropic broadside-coupled triangular-split-ring resonators are studied for different incident wave excitations. It is shown that the higher order modes exist in both electric and magnetic resonances. It is observed that the incident electric field couples to the magnetic resonance of the designed structure under different excitations. Multiple resonance features due to the anisotropy of the structure are found in the case of different excitations and the nature of these resonances can be regulated as either an electric or a magnetic mode for different frequencies. In this way, a resonant effective permittivity or permeability can be obtained. Hence, controllable properties of the constitutive material parameters (i.e. electric or magnetic resonances, negative values, etc.) can be determined by changing the incident wave excitation.     

Resonances of the Faraday Effect in Nanostructured Iron Garnet Films

Magnetic nanostructures make it possible to enhance magneto-optical effects by many times owing to the excitation of optical resonances. A new type of magnetic structure is proposed, which is a two-dimensional all-dielectric bismuth-substituted iron garnet grating. Enhancement of the Faraday effect in such a structure caused by the excitation of waveguide modes is described analytically, and the conditions for the resonant enhancement are revealed. The resonant enhancement of the Faraday effect in all-dielectric magnetic nanostructures has been experimentally demonstrated for the first time.

     

Thermopower for a molecule with vibrational degrees of freedom

We study a simple model to describe resonant tunneling through an organic molecule between two conducting leads, taking into account the vibrational modes of the molecule. We solve the model approximately analytically in the weak coupling limit and give explicit expressions for the thermopower and Seebeck coefficient. The behavior of these two quantities is studied as function of model parameters and temperature. For a certain regime of parameters a rather peculiar variation of the thermopower and Seebeck coefficient is observed.     

Elastic resonances of a periodic array of fluid-filled cylindrical cavities embedded in an elastic matrix

The resonant scattering by a periodic infinite array of fluid-filled cylindrical cavities in an elastic matrix is studied. The exact reflection and transmission coefficients of the array are calculated by means of a multiple scattering formalism taking into account all the interactions between the cavities. Numerical results are next given for low frequencies for which only the longitudinal and transverse zero modes propagate. A first study based on the analysis of the transmission coefficients clearly shows that the resonances of the array can be classified into two sets: those close to the resonances of a single cavity and those due to a resonant coupling between a cavity and its nearer neighbors. The resonant coupling is due to the interaction between the whispering-gallery surface waves propagating around each cavity. In the case of cavities with very close spacing, it is observed that the dispersion curves of the waves propagating along the array can also be classified into two sets: those with a positive group velocity have cut-off frequencies that correspond to the resonances of a single cavity, those with a negative group velocity have cut-off frequencies that correspond to the resonances resulting from the strong coupling. A new method for the analysis of the resonances is presented. It is based on the properties of the scattering matrix and consists in studying the resonant eigenvalues of the scattering matrix of the array once the background is removed. For the detection of very fine resonances, as well as in the separation of several resonances very close to each other, this method proves to be more efficient than one based on the analysis of the reflection and transmission coefficients.     

Modification of laser gain properties through local-field effects and nanostructuring

We have recently developed a simple phenomenological model that allows one to account for the modifications of the gain characteristics of nanocomposite optical materials with specific geometries. Here we give a generalized formulation of our model to show that it can be applied to a broad variety of composite geometries. We demonstrate the application of our model using the Maxwell Garnett composite geometry with the resonant molecules in its host, which represent a practically important case that has not been treated earlier. We also give numerical examples for the Maxwell Garnett composite geometry with the resonances in either host or inclusions, and find the conditions under which it is possible to achieve an enhancement or suppression of the small-signal gain coefficient compared to its value in a bulk material. Using our simple model, one can identify the set of parameters, exhibiting the desired changes to the gain characteristics, prior to or instead of performing a more precise computationally intensive analysis.     

The Fermi-Pasta-Ulam problem: Periodic orbits, normal forms and resonance overlap criteria

Fermi, Pasta and Ulam observed that the excitation of a low frequency normal mode in a nonlinear acoustic chain leads to localization in normal mode space on large time scales. Fast equipartition (and thus complete delocalization) in the Fermi-Pasta-Ulam chain is restored if relevant intensive control parameters exceed certain threshold values. We compare recent results on periodic orbits (in the localization regime) and resonant normal forms (in a weak delocalization regime), and relate them to various resonance overlap criteria. We show that the approaches quantitatively agree in their estimate of the localization-delocalization threshold. A key ingredient for this transition are resonances of overtones.     

Gravity localization in sine-Gordon braneworlds

In this work we study two types of five-dimensional braneworld models given by sine-Gordon potentials. In both scenarios, the thick brane is generated by a real scalar field coupled to gravity. We focus our investigation on the localization of graviton field and the behaviour of the massive spectrum. In particular, we analyse the localization of massive modes by means of a relative probability method in a Quantum Mechanics context. Initially, considering a scalar field sine-Gordon potential, we find a localized state to the graviton at zero mode. However, when we consider a double sine-Gordon potential, the brane structure is changed allowing the existence of massive resonant states. The new results show how the existence of an internal structure can aid in the emergence of massive resonant modes on the brane.     

Cavity-mode selection in spontaneous emission from oriented molecules in a microparticle

We observe preferential cavity-mode selection in spontaneous emission by oriented molecules at the surface of a microparticle. Polarization-analyzed images of a levitated microdroplet containing surface active molecules reveal a well-defined system in terms of molecular position and orientation. The measured fluorescence spectrum is compared with that of a semiclassical emission-rate-enhancement model that treats the coupling between an excited state and Mie resonances as an oscillating dipole interacting with its self-scattered field. By comparing results obtained with this theory with the relative strengths of TE to TM modes measured in the emission spectrum, we show that one can elucidate the heterogeneity of a particle from this resonant structure and determine the orientation of the emission moments relative to the phase boundary.