Forbidden Frequency Band Research Articles

Periodic driving shape controls energy transmission.

In the early 2000s, Geniet and Leon [Phys. Rev. Lett. 89, 134102 (2002)0031-900710.1103/PhysRevLett.89.134102] discovered the nonlinear supratransmission (NST) in a medium with a forbidden frequency band gap. It is a process in which nonlinear structures are created by a sinusoidal harmonic boundary condition imposed at a frequency in the band gap. The present study extends this concept and shows that an optimal shape of a periodic nonsinusoidal excitation may induce (or inhibit) energy flow through the lattice below (or above) the NST threshold, demonstrating that nonlinear supratransmission is reliant not only on the driving amplitude but also on its shape. This is evidenced through numerical simulations and mathematical calculations varying the excitation signal shape in the Fermi-Pasta-Ulam case study. Setting the shape parameter to zero recovers the results of the literature in relation to the sinusoidal signal.

Polymeric photonic quasicrystal: octonacci sequence and elasto-optic effect

Here we would like to discuss the light transmission modulation by the one-dimensional polymeric quasi-multilayer which is formed according to substitutional generalized Octonacci with PMMA and PS as the constituent materials. In particular, we will present some theoretical findings using the well-known transfer matrix method. The width of the PBG, the inter-band spacing and the depth of the PBGs can be managed by choosing the appropriate generation number, whereas the number of the major PBGs is the same for all the considered generation numbers. Regarding the position of the PBGs, we found that, with an increase in generation number, the aroused PBGs are shifted symmetrically towards the designed frequency. It also reveals the aroused forbidden frequency band can be manipulated by changing the applied hydrostatic pressure. With an increase in pressure, the frequency spectra are shifted to a higher frequency. In addition to this, we also found that as the thickness of the polymers increases the PBGs are red-shifted. The proposed structure could be another possible system for optical device design specially multi-band tunable optical reflectors.

A new form of forbidden frequency band constraint for dynamic topology optimization

A new form of forbidden frequency band constraint for dynamic topology optimization

The frequency spectrum of rotobreathers with many degrees of freedom

A rotobreather in a lattice of coupled particles with rotational degrees of freedom is a dynamical regime when one particle rotates and the other particles vibrate with amplitudes exponentially decaying with distance from the rotating particle. In addition to rotational, particles can have internal degrees of freedom. Here, the influence of internal degrees of freedom on the possible rotational frequencies of rotobreathers is discussed for two models: a chain of coupled elastic rotators and a molecular crystal of carbon nanotubes (CNTs). It is shown that additional degrees of freedom create forbidden frequency bands for rotobreathers. In the case of a CNT crystal, due to resonances with many internal degrees of freedom, the frequency spectrum of a rotobreather has a complex structure resembling a Cantor set.

Optical Signal Processing for W-Band Radio-Over-Fiber System With Tunable Frequency Response

Tunable frequency response is designed and experimentally demonstrated in this paper. The performance of frequency response in proposed radio-over-fiber (RoF) systems is investigated in terms of theoretical analysis, simulations, and experimental results with various fiber transmission distances. The notch in frequency response can be easily circumvented by changing the oriented angle of polarized lightwave in the proposed direct detection (DD) scheme. For comparison, the conventional Mach-Zehnder modulator (MZM) based DD scheme suffers from fixed frequency notch at certain frequencies, which generates forbidden frequency bands for W-band signal delivery. Our experimental results show that the proposed DD scheme exhibits a stable EVM performance of the 16-QAM signal from 83 GHz to 87 GHz via 25-km standard single-mode fiber (SSMF) and 1-m wireless transmission. On the contrary, the conventional MZM-based DD scheme encounters severe signal degradation at 85 GHz and 86 GHz. In this paper, the proposed scheme is implemented to demonstrate full bandwidth availability within a desirable frequency range by tuning the frequency response. Furthermore, a 10-Gbps 16-QAM signal located at 85 GHz is successfully transmitted by the proposed DD scheme which can provide 10-gigabit data transmission under 5G requirement.

Dispersion engineering of two-dimensional photonic crystals composed of graphene-covered tellurium rods

We investigate theoretically the frequency spectrum of two-dimensional photonic crystals using the well-known Dirichlet-to-Neumann (D-to-N) map method. The PhCs with square and triangular arrangements are built by graphene-covered tellurium rods which are surrounded by ion gel. The resulting frequency spectrum represents two forbidden frequency band, termed Bragg and graphene photonic band gaps. It is demonstrated that these forbidden band gaps can be controlled actively by altering the graphene chemical potential through applying external voltage. A tuning range of 4.81 THz and 5.31 THz was achieved for Bragg photonic band gap in square and triangular lattices, respectively, and a wide tuning range of 13.85 THz and 14.69 THz was achieved for graphene photonic band gap, when the chemical potential varies from μc = 0 to μc = 1.2 eV. These achievements may have future applications in some optical devices such as filters, sensors, nano-composites and energy storage devices in THz spectrum.

Modified plasma waves described by a logarithmic electrodynamics

The propagation of plasma waves in a new nonlinear, logarithmic electrodynamics model is performed. A cold, uniform, collisionless fluid plasma model is applied. Electrostatic waves in magnetized plasma are shown to correspond to modified Trivelpiece-Gould modes, together with changes in the plasma and upper-hybrid frequencies, driven by the logarithmic electrodynamics effects. Electromagnetic waves are described by a generalized Appleton-Hartree dispersion relation. The cases of propagation parallel or perpendicular to the equilibrium magnetic field are analyzed in detail. In particular, generalized ordinary and extraordinary modes are obtained. We determine the changes, due to logarithmic electrodynamics, in the allowable and forbidden frequency bands of the new extraordinary mode. Estimates are provided about the strength of the ambient magnetic field so that the nonlinear electrodynamics effects become decisive.

Analysis of light propagation in quasiregular and hybrid Rudin–Shapiro one-dimensional photonic crystals with superconducting layers

The transmittance spectrum of a one-dimensional hybrid photonic crystal built from the suitable arrangement of periodic and quasiregular Rudin–Shapiro heterolayers that include superconducting slabs is investigated. The four-layer Rudin–Shapiro structure is designed with three lossless dielectric layers and a low-temperature superconductor one. The dielectric function of the superconducting layer is modeled by the two-fluid Gorter–Casimir theory, and the transmittance is calculated with the use of the transfer matrix method. The obtained results reveal the presence of a cut-off frequency fc – a forbidden frequency band for propagation – that can be manipulated by changing the width of the superconducting layer, the temperature and the order of the Rudin–Shapiro sequence. In addition, the spatial distribution of the electric field amplitude for the propagating TM modes is also discussed. It is found that the maximum of localized electric field relative intensity – which reaches a value of several tens – corresponds to the frequency values above to the cut-off frequency, at which, the effective dielectric function of the hybrid unit cell becomes zero. The proposed structure could be another possible system for optical device design for temperature-dependent optical devices such as stop-band filters, or as bolometers.

Band gap control in a line-defect magnonic crystal waveguide

We report on the experimental observation of the spin wave spectrum control in a line-defect magnonic crystal (MC) waveguide. We demonstrate the possibility to control the forbidden frequency band (band gap) for spin waves tuning the line-defect width. In particular, this frequency may be greater or lower than the one of 1D MC waveguide without line-defect. By means of space-resolved Brillouin light scattering technique, we study the localization of magnetization amplitude in the line-defect area. We show that the length of this localization region depends on the line-defect width. These results agree well with theoretical calculations of spin wave spectrum using the proposed model of two coupled magnonic crystal waveguides. The proposed simple geometry of MC with line-defect can be used as a logic and multiplexing block for application in the novel field of magnonic devices.

Zero time tunneling: macroscopic experiments with virtual particles

Feynman introduced virtual particles in his diagrams as intermediate states of an interaction process. They represent necessary intermediate states between observable real states. Such virtual particles were introduced to describe the interaction process be- tween an electron and a positron and for much more complicated interaction processes. Other candidates for virtual particles are evanescent modes in optics and in elastic fields. Evanescent modes have a purely imaginary wave number, they represent the mathemati- cal analogy of the tunneling solutions of the Schrodinger equation. Evanescent modes ex- ist in the forbidden frequency bands of a photonic lattice and in undersized wave guides, for instance. The most prominent example for the occurrence of evanescent modes is the frustrated total internal reflection (FTIR) at double prisms. Evanescent modes and tun- neling lie outside the bounds of the special theory of relativity. They can cause faster than light (FTL) signal velocities. We present examples of the quantum mechanical behavior of evanescent photons and phonons at a macroscopic scale. The evanescent modes of photons are described by virtual particles as predicted by former QED calculations.

Modeling light-sound interaction in nanoscale cavities and waveguides

AbstractThe interaction of light and sound waves at the micro and nanoscale has attracted considerable interest in recent years. The main reason is that this interaction is responsible for a wide variety of intriguing physical phenomena, ranging from the laser-induced cooling of a micromechanical resonator down to its ground state to the management of the speed of guided light pulses by exciting sound waves. A common feature of all these phenomena is the feasibility to tightly confine photons and phonons of similar wavelengths in a very small volume. Amongst the different structures that enable such confinement, optomechanical or phoxonic crystals, which are periodic structures displaying forbidden frequency band gaps for light and sound waves, have revealed themselves as the most appropriate candidates to host nanoscale structures where the light-sound interaction can be boosted. In this review, we describe the theoretical tools that allow the modeling of the interaction between photons and acoustic phonons in nanoscale structures, namely cavities and waveguides, with special emphasis in phoxonic crystal structures. First, we start by summarizing the different optomechanical or phoxonic crystal structures proposed so far and discuss their main advantages and limitations. Then, we describe the different mechanisms that make light interact with sound, and show how to treat them from a theoretical point of view. We then illustrate the different photon-phonon interaction processes with numerical simulations in realistic phoxonic cavities and waveguides. Finally, we introduce some possible applications which can take enormous benefit from the enhanced interaction between light and sound at the nanoscale.

Thermal transport in S-shaped graphene nano-junctions

By using nonequilibrium Green's function method, we study the phonon transport properties in S-shaped graphene nano-junctions (GNJs). Interesting transmission phenomenon is found. The transmission spectrum of low frequency phonon shows forbidden frequency band, by changing the width W2 of the S-shaped GNJs. These low frequency forbidden bands are sensitive to their periodic geometric shape of GNJs. These thermal transport phenomena can be explained by analyzing the phonon transmission coefficient. This paper illustrates the thermal transport mechanisms in the different S-shaped GNJs, and the results could provide significant physical models and theoretical validity in designing the thermal devices based on the GNJs.

Radiation damping optical enhancement in cold atoms

The typically tiny effect of radiation damping on a moving body can be amplified to a favorable extent by exploiting the sharp reflectivity slope at one edge of an optically induced stop-band in atoms loaded into an optical lattice. In this paper, this phenomenon is demonstrated for the periodically trapped and coherently driven cold 87Rb atoms, where radiation damping might be much larger than that anticipated in previous proposals and become comparable with radiation pressure. Such an enhancement could be observed even at speeds of only a few meters per second with less than 1.0% absorption, making radiation damping experimentally accessible. Subjecting an ensemble of cold rubidium atoms to a particular combination of optical beams should enable the study of ‘radiation damping’, a typically minuscule velocity-dependent effect that a light source exerts on a moving body. This is the finding of a theoretical study performed by Jin-Hui Wu at Jilin University, China, in cooperation with researchers from the university of Exeter (UK), the Lens Laboratory and Scuola Normale Superiore (IT). Their proposal is based on exploiting reflections at the boundary between allowed and forbidden frequency bands in the photonic crystal made by periodically distributed cold atoms. This approach should provide a way of amplifying radiation damping to a level suitable for experimental study, making it useful for manipulating cold atoms and potentially other material systems.

Experimental observation on asymmetric energy flux within the forbidden frequency band in the LC transmission line

We study the energy flux in a nonlinear electrical transmission line consisting of two coupled segments which are identical in structure and different in parameters. The asymmetry of energy flux caused by nonlinear wave has been observed experimentally in the forbidden band of the line. The experiment shows whether the energy can flow through the transmission line depends on the amplitude of the boundary driving voltages, which can be well explained in the theoretical framework of nonlinear supratransmission. The numerical simulation based on Kirchhoff’s laws further verifies the existence of the asymmetric energy flux in the forbidden band.

Brillouin light scattering studies of planar metallic magnonic crystals

The application of Brillouin light scattering to the study of the spin-wave spectrum of one- and two-dimensional planar magnonic crystals consisting of arrays of interacting stripes, dots and antidots is reviewed. It is shown that the discrete set of allowed frequencies of an isolated nanoelement becomes a finite-width frequency band for an array of identical interacting elements. It is possible to tune the permitted and forbidden frequency bands, modifying the geometrical or the material magnetic parameters, as well as the external magnetic field. From a technological point of view, the accurate fabrication of planar magnonic crystals and a proper understanding of their magnetic excitation spectrum in the gigahertz range is oriented to the design of filters and waveguides for microwave communication systems.

Study of s-polarized photonic bandgap structure in three component optical fibonacci multilayers composed of nanoscale materials

In this communication dispersion relation, reflection and transmission coefficient for quasiperiodic optical multilayers arranged according to the three-component Fibonacci rule is derived using transfer matrix method. In this work Fibonacci multilayers using three different photonic band gap (PBG) materials is designed and its photonic band gap structure is presented. Also, a detailed calculation for allowed and forbidden frequency bands for s-polarized radiation of light incident on these structures at various angles is presented. It is demonstrated that in case of s-polarized mode of radiation, widening in the band gap and frequency shifts occur as one moves towards the higher frequency region, which shows that such a multilayer can be used as an efficient polarizer. The effect of an imaginary value for the propagation vector Q on the existence of forbidden photonic bands in these lattices is also studied.

Acoustic wave dispersion in a one-dimensional lattice of nonlinear resonant scatterers

Nonlinear effects of acoustic wave propagation and dispersion are observed in a one-dimensional lattice made of Helmholtz resonators connected to a tube. These regularly spaced scatterers exhibit individually a wave frequency dependence, which induces a strong velocity dispersion. In addition, they exhibit a wave amplitude dependence (acoustic nonlinearity), which induces nonlinear effects on the dispersion relation of waves in the lattice. The usually observed forbidden frequency band gaps for the transmission coefficient through the lattice are shown to be amplitude dependent. Experimental results are compared to a developed model taking into account the nonlinear behavior of the Helmholtz resonator.

Properties of Metallic Photonic Band Gap Material with Defect at Microwave Frequencies: Calculation and Experimental Verification

In this paper, the properties of a Metallic Photonic Band Gap Prism (MPBGP) with defects are studied. The MPBGP is made of metallic rods disposed in an isosceles right-angled triangle. The commercial software HFSS based on the finite element method is used to study the behavior of Photonic Band Gap structure by means of three-dimensional dispersion diagrams, iso-frequency curves, radiation patterns and the cartography of electric field. Numerical results showed that the metallic photonic band gap without and with defects behaves like a homogeneous and ultrarefractive medium in the first allowed frequency band. The distribution of defects doesn't modify the propagation of electromagnetic waves through the metallic photonic band gap material, it has properties similar to that of a perfect prism. In the forbidden frequency bands, the anomalous transmission has been obtained by means of surface defects in Metallic structure. This anomalous transmission in forbidden band has also been observed in simulations carried out on a dielectric photonic band gap material made of dielectric rods disposed in an isosceles right-angled triangle. Theoretical results presented in this paper have been successfully validated by measurements carried out in the frequency range [7–16 GHz].

Low-frequency electromagnetic waves in a partially ionized multi-component magnetoplasma

The dispersion properties of low-frequency electromagnetic waves in a partially ionized multi-ion dusty magnetoplasma containing electrons, ions of two different species, charged dust particles and neutrals have been investigated. It has been found that the combined effects of stationary charged dust particles and an additional ion component introduce a new cut-off frequency, and that the polarities of dust particles and the second ion-species significantly modify this new as well as the existing forbidden frequency bands. It has also been observed that the collisions of lighter ion species significantly reduce or completely eliminate both the new and existing forbidden frequency bands, while those of heavier ions reduce or completely eliminate the new forbidden frequency band, but enhance the existing forbidden frequency band.

Magnetodynamics of a multicomponent (dusty) plasma. II. Magnetic drift waves in an inhomogeneous medium

The electromagnetic oscillations near the low-frequency cutoff (the rotation waves) and their stability and nonlinear state, analyzed in the companion paper [G. Ganguli and L. Rudakov, Phys. Plasmas 12, 042110 (2005)] for a homogeneous plasma, are generalized to include inhomogeneity in the equilibrium density and magnetic field. It is shown that in the forbidden frequency band below the cutoff the magnetic drift waves appear, which can exist even in a cold plasma. The magnetic drift wave and nonlinear structures associated with it are analyzed and their relevance to astrophysical plasmas are discussed. It is found that in an inhomogeneous plasma the rotation wave packets can couple to the magnetic drift waves. The behavior of such structures is governed by nonlinear Schrödinger equation. The spatial scale of the nonlinear structures due to the magnetic drift waves in astrophysical plasmas such as dense molecular clouds, which are the regions of star creation, is estimated to be around 10 a.u.