Spectral properties of a two-dimensional resonant metal-dielectric photonic crystal

We have studied the transmission spectra of resonant two-dimensional photonic crystals of two types, one of which consists of nanocomposite cylinders that form a square lattice in vacuum and the other of which consists of cylindrical holes that form a square lattice in nanocomposite matrix. The nanocomposite consists of metallic nanospheres that are dispersed in a transparent matrix and is characterized by an effective resonant dielectric permittivity. We show that, depending on the position of the resonant frequency of the nanocomposite with respect to the boundaries of the band gap, there arises either an additional transmission band in the transmission spectrum in the band gap or an additional band gap in the continuous spectrum of the photonic crystal. As the structural and geometric parameters of the system change, both the additional transmission band and the additional band gap are considerably modified. We analyze particular features of the spatial distribution of the electromagnetic field intensity in crystals. The considered effects can be used to extend the possibilities of creating new photonic crystals with specified properties.     

Traveling of light through a 1D photonic crystal containing a defect layer with resonant dispersion

Spectral properties of a 1D photonic crystal that is comprised of two multilayered dielectric mirrors and a nanocomposite layer between them as a structural defect are studied. The nanocomposite consists of silver nanoballs dispersed in a transparent matrix and is characterized by an effective resonant permittivity. The spectral manifestation of the defect mode splitting for the s-polarized waves is studied as a function of the angle of incidence and concentration of nanoballs. Specific features of the transmission spectra for the s- and p-polarized waves are established for the angle of incidence equal to the Brewster angle of the seeding photonic crystal. It is shown, in particular, that, in the region of the continuous transmission spectrum of the spolarized waves, there arises an additional bandgap caused by mixing of the resonant mode with photonic modes.     

Spectral properties of a one-dimensional photonic crystal with a resonant defect nanocomposite layer

The spectral properties of a one-dimensional photonic crystal with a defect nanocomposite layer that consists of metallic nanoballs distributed in a transparent matrix and is characterized by an effective resonance permittivity are studied. The problem of calculating the transmission, reflection, and absorption spectra of p-polarized waves in such structures is solved for oblique incidence of light, and the spectral manifestation of defect-mode splitting as a function of the volume fraction of nanoballs and the structural parameters is studied. The splitting is found to depend substantially on the nanoball concentration in the defect, the defect layer thickness, and the angle of incidence. The angle of incidence is found at which the resonance frequency of the nanocomposite is located near the edge of the bandgap or falls in the frequency region of a continuous spectrum. The resonance situation appearing in this case results in an additional transmission band or an additional bandgap in the transmission spectrum.     

Specific features of the spectral properties of a cholesteric liquid crystal with a resonance defective nanocomposite layer

This paper reports on studying the spectral properties of a cholesteric liquid crystal with a defective layer of a nanocomposite consisting of metallic nanoballs dispersed in a transparent matrix and characterized by an effective resonance dielectric permittivity. The transmission, reflection, and absorption spectra of waves of both circular polarizations have been calculated, and the spectral splitting of the defective mode when its frequency coincides with the resonance frequency of the nanocomposite has been studied. An essential dependence of the splitting on the nanoball concentration in the defect has been established. It has been shown that, depending on the position of the resonance frequency with respect to the boundaries of the cholesteric band gap, an additional passband appears in the transmission spectrum, which corresponds to waves of the diffracting circular polarization, or an additional band gap for waves of both circular polarizations, which are substantially modified with variations of both the incidence angle of light and the cholesteric helix pitch.     

Optical Tamm states at the interface between a photonic crystal and a nanocomposite with resonance dispersion

Optical Tamm states localized at the edges of a photonic crystal bounded from one or both sides by a nanocomposite have been studied. The nanocomposite consists of metallic nanoinclusions, which have a spherical or orientationally ordered spheroidal shape and are dispersed in a transparent matrix, and is characterized by the resonant effective permittivity. The transmission, reflection, and absorption spectra have been calculated for waves with longitudinal and transverse polarizations in such structures at the normal incidence of light. The spectral manifestation of Tamm states that is due to the existence of negative values of the real part of the effective permittivity has been analyzed for the visible spectral range. It has been established that the characteristics of Tamm states localized at the edge of the photonic crystal depend strongly both on the concentration of nanoballs in the nanocomposite film and on its thickness. Modes formed by two coupled Tamm plasmon polaritons localized at the edges of the photonic crystal adjacent to two nanocomposite layers have been examined. It has been shown that, in the case of the anisotropic nanocomposite layer adjacent to the photonic crystal, each of two orthogonal polarizations of the incident wave corresponds to a specific frequency of the Tamm state localized at the edge; owing to this property, the transmission spectra of such a structure are polarization sensitive.     

Influence of the dielectric background on the quality factors of metallo-dielectric photonic crystals

The effect of varying the dielectric background on the quality factor of two-dimensional metallo-dielectric photonic crystals is theoretically studied. The studied metallo-dielectric photonic crystal consists of a square lattice of circular metallic rods embedded into a dielectric background with a defect rod on the center that creates resonant modes within the photonic band gap. The metal is modeled with the Drude dispersion relation. A combination of the finite-difference time-domain method together with a frequency filtering technique is used to estimate accurately the resonant frequencies and their quality factors. The results show that the quality factors increase with increasing background dielectric constant. If a dielectric background material such as Silicon is used instead of air, an enhancement in the quality factor of up to eight times can be achieved, depending on the resonant mode. We also show that, depending on the modes, there exists an optimal size for the defect rod that gives the maximum quality factor.     

Anharmonic effects on lattice resonant modes of impure metallic crystals

The effect of lattice anharmonicity on the resonant modes of dilute impurities for Au-Cu, Au-Ag and W-Cr metallic systems are studied from the poles of the double time temperature dependent impure Green’s function of these crystals. The third order force constants used in the present work are derived assuming the systems to obey the Lennard-Jones potential. The inclusion of lattice anharmonicity has been found to increase the resonant frequency which depends upon the mass defect, force constant change parameter and the impurity concentration terms. Some interesting features about the phase shift and the change in width of the vibrational spectrum are reported at room temperature for the isotopic defects and the defects interacting with host atoms. The results are found to be in qualitative agreement with the experiments on the systems considered.     

用紧束缚方法描述光子晶体缺陷耦合的共振频率移动

通常采用含两个耦合参数的紧束缚近似，就能很好地描述光子晶体缺陷因耦合而导致的共振频率分裂.然而，缺陷耦合造成的共振频率移动，即包含奇数个缺陷的耦合系统的中央共振频率位置与原来单缺陷时的共振频率位置存在差异，则只有采用含三个耦合参数的严格紧束缚方法才能正确描述.根据耦合参数与共振频率的关系，利用三缺陷耦合系统的模拟计算结果确定了三个耦合参数的具体值，从而在理论上能够预言由任意个缺陷构成的耦合系统的共振频率的移动和分裂.理论预言与基于有限时域差分法的数值计算完全相符.     

Specific features of the emission of chiral photonic crystals with an anisotropic defect: I. Thickness effects

The specific features of defect modes of chiral photonic crystals with an anisotropic defect have been investigated. Peculiarities of the spectra of polarization observables of the system under consideration are analyzed at different thicknesses of the defect layer. It is shown that single refraction occurs in a defect mode, even though the system is anisotropic and inhomogeneous. We also investigated the specific features of the spectra of the photon density of states, light intensity at the defect center, and the Q factor of defect modes at different thicknesses of the defect layer and chiral photonic crystals. It is shown that the lasing wavelength of chiral photonic crystals with an anisotropic defect enriched in laser dyes (resonant atoms) can be controlled in a different way: by varying the defect layer thickness. It is shown that this system can operate as a narrow-band filter (mirror) with a controlled frequency width and location of the total transmission (reflection) range on the frequency scale.     

Resonant modes and inter-well coupling in photonic quantum well with negative index materials

The transfer matrix method was used to study the resonant modes in photonic quantum well by stacking different photonic crystals consisting of positive index materials and negative index materials. The eigenfrequency equation for the resonant modes is derived. It is found that these resonant modes are omnidirectional, and the number of resonant modes is equal to the period number of photonic quantum wells. Moreover, the resonant modes become N-fold splitting in the N photonic quantum wells. The splitting intervals increase with the deceasing of photonic barrier thickness due to the coupling among the wells.     

A computational study of the optical response of strongly coupled metal nanoparticle chains

We study the optical response of strongly coupled metal nanoparticle chains using rigorous multiple scattering calculations. The collective resonant frequency of silver nanosphere chains and the coupling between chains are considered. The coupling between silver nanoparticle chains are understood by the transmission and reflection calculations of 2D periodic arrays of nanospheres. The results are in agreement with recent experiments. The splitting of plasmon resonance modes for different polarizations of the incident light are explored. Our results show that the transverse mode resonant wavelength is very sensitive to the inter-chain distance. Results on the effect of disorder are also presented.     

Quantized longitudinal exciton-polaritons in periodic metal–semiconductor nanostructures

We theoretically investigate the optical properties of one-dimensional photonic crystals composed of two alternating layers, namely a semiconductor film and a metallic one. The nonlocal optical response of the semiconductor is here described by using a resonant excitonic dielectric function, whereas the local response function of the metal film is modeled with Drude formula. We calculate optical spectra of the metal–semiconductor 1D photonic crystal for both s- and p-polarization geometries. In both cases the spectra exhibit a rich resonance structure due to the coupling of size-quantized excitons inside the semiconductor film with light. We show the difference between s- and p-polarization reflectivity as the angle of incidence is increased. In the p-polarization geometry, besides transverse exciton-polariton modes, longitudinal polarization waves are excited producing additional spectral resonances. The spectra become radically different when the frequency corresponding to the minimum of the first photonic pass-band is close to the exciton resonance, since such a frequency is distinct for s- and p-polarized modes. We also show how reflectivity spectra for both polarizations are modified with varying the metal filling fraction which controls the width of the gap below the lowest frequency band.     

含具有双增益线原子的光子晶体中的光传播

讨论了缺陷层包含具有双增益线的原子的一维光子晶体中的色散效应及透射谱，双增益线间出现了反常色散区，由于入射光与双增益线的相互作用使得光子带隙中出现了两个透射率远大于1的透射峰；透射峰随着缺陷位置和体系结构参数的变化而产生变化；左透射峰和右透射峰很窄的频率范围内分别出现了斜率极大的反常色散和正常色散，产生了负的群速度和极慢光速的光传播行为。     

Angular reflectance of suspended gold, aluminum and silver nanospheres on a gold film: Effects of concentration and size distribution

In this article, we describe a parametric study of the effects of the size distribution (SD) and the concentration of nanospheres in ethanol on the angular reflectance. Calculations are based on an effective medium approach in which the effective dielectric constant of the mixture is obtained using the Maxwell–Garnett formula. The detectable size limits of gold, aluminum, and silver nanospheres on a 50-nm-thick gold film are calculated to investigate the sensitivity of the reflectance to the SD and the concentration of the nanospheres. The following assumptions are made: (1) the total number of particles in the unit volume of suspension is constant, (2) the nanospheres in the suspension on a gold film have a SD with three different concentrations, and (3) there is no agglomeration and the particles have a log-normal SD, where the effective diameter, d _eff and the effective variance, ν _eff are given. The dependence of the reflectance on the d _eff, ν _eff, and the width of the SD are also investigated numerically. The angular variation of the reflectance as a function of the incident angle shows a strong dependence on the effective size of the metallic nanospheres. The results confirm that the size of the nanospheres (d _eff <100 nm) can be detected by reflected light from the bottom surface of a gold film with a reasonable sensitivity if a proper angle of incidence is chosen based on the type of metallic particles on a gold thin film at λ = 632 nm. We show that the optimum incident angle to characterize the size of nanospheres on a gold film is between 70° and 75° for a given concentration with a particular SD.     

Band gap structures for viscoelastic phononic crystals based on numerical and experimental investigation

Many materials used as phononic crystals (PCs) are viscoelastic one. It is believed that viscosity results in damping to attenuate wave propagation, which may help to tune the defect modes or band gaps of viscoelastic phononic crystals. To investigate above phenomenon, firstly, we have extended the application of boundary element method (BEM) to the study of viscoelastic phononic crystals with and without a point defect. A new developed BEM within the framework of Bloch theory can easily deal with viscoelastic phononic crystals with arbitrary shapes of the scatterers. Experimental methods have been put forward based on the self-made viscoelastic phononic crystals. Verified by the experimental results, systematic comprehensive parametric studies on the band structure of viscoelastic phononic crystals with varying factors (final–initial value ratio, relaxation time, volume fraction of scatterers, shapes of scatterers) have been discussed by the numerical simulation. To further address the possibility to change the defect modes, the band structure of viscoelastic phononic crystals with a point defect has been studied based on the numerical and experimental methods. From present research work, it can be found that by adjusting the two viscous parameters combined with considering the effect of volume fraction and shapes, a wider and lower initial forbidden frequency or lower and higher quality factor resonant frequency can be obtained.     

Graphene based photonic crystal optical filter: Design and exploration of the tunability

Optical characteristics of two new graphene based photonic crystals are studied in detail. A structure containing alternating layers of graphene and SiO₂ slabs is considered as the ideal crystal. The dependency of the photonic band gaps (PBGs) to the dielectric layer thickness and the period number is explored at first step. Potential of the proposed crystal to be used as an optical filter is then investigated. Adding a nonlinear electro-optic polymer as a defect layer, the alterations of the optical features are inspected. Results show that the defect layer insertion causes a resonant mode inside the PBGs. However, the location of the defect layer inside the crystal is very effective on both the frequency and width of the resonant mode. Tunability of the optical features is probed by taking into account of the dependencies to the wave incident angle, graphene chemical potential and the applied external voltage to the defect layer.     

Investigation of one-dimensional photonic crystals composed of dispersive materials

One-dimensional photonic crystals (1DPCs) composed of dispersive materials (including negative refractive index materials, negative μ materials, and negative ? materials) are proposed. The dependence of the band gaps on the angle of incidence and thickness scale are investigated by using the transfer matrix method. Simulation results show that the band gaps of these dispersive material 1DPC are insensitive to the thickness scale. The defect modes of these doped 1DPCs behave specially when the thickness of the defect layer, the angle of incidence and the thickness scale of PC change.     

The effect of magnetic stress and stiffness modulus on resonant characteristics of Ni-Mn-Ga ferromagnetic shape memory alloy actuators

The prospect of using ferromagnetic shape memory alloys (FSMAs) is promising for a resonant actuator that requires large strain output and a drive frequency below 1 kHz. In this investigation, three FSMA actuators, equipped with tetragonal off-stoichiometric Ni₂MnGa single crystals, were developed to study their frequency response and resonant characteristics. The first actuator, labeled as A1, was constructed with low-k bias springs and one Ni-Mn-Ga single crystal. The second actuator, labeled as A2, was constructed with high-k bias springs and one Ni-Mn-Ga crystal. The third actuator, labeled as A3, was constructed with high-k bias springs and two Ni-Mn-Ga crystals connected in parallel. The three actuators were magnetically driven over the frequency range of 10 Hz-1 kHz under 2 and 3.5 kOe magnetic-field amplitudes. The field amplitude of 2 kOe is insufficient to generate significant strain output from all three actuators; the maximum magnetic-field-induced strain (MFIS) at resonance is 2%. The resonant MFIS output improves to 5% under 3.5-kOe amplitude. The frequency responses of all three actuators show a strong effect of the spring k constant and the Ni-Mn-Ga modulus stiffness on the resonant frequencies. The resonant frequency of the Ni-Mn-Ga actuator was raised from 450 to 650 Hz by increasing bias spring k constant and/or the number of Ni-Mn-Ga crystals. The higher number of the Ni-Mn-Ga crystals not only increases the magnetic force output but also raises the total stiffness of the actuator resulting in a higher resonant frequency. The effective modulus of the Ni-Mn-Ga is calculated from the measured resonant frequencies using the mass-spring equation; the calculated modulus values for the three actuators fall in the range of 50-60 MPa. The calculated effective modulus appears to be close to the average modulus value between the low twinning modulus and high elastic modulus of the untwined Ni-Mn-Ga crystal.     

A graphene quantum dot realized by an armchair graphene nanoribbon with line defect

The electron transport in a semiconducting armchair graphene nanoribbon with line defect is theoretically investigated, by coupling it to two normal metallic leads. It is found that the line defect induces a new localized quantum state near the Dirac point, and that the coupling between this state and the leads provides a channel for the resonant tunneling. This means that such a finite‐size nanoribbon can be viewed as a quantum dot. When two line defects are present simultaneously, a coupled quantum dot forms, leading to the splitting of the conductance peaks. With these results, we propose such a structure to be a promising candidate of an electron transistor. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)