Controlled modification of the expansion order as a tool in mie computations

In the framework of Mie theory the involved electromagnetic fields are expanded in an infinite series of multipoles. In numerical computations the summation has to be terminated after a finite number of terms (the expansion order N), which unavoidably produces errors. On the other hand, it is known that the contributions of terms of order l with x 相似文献   

Mie resonances and Bragg-like multiple scattering in opacity of two-dimensional photonic crystals

The lowest (main) and high-order Mie resonances and the Bragg-like multiple scattering of electromagnetic (EM) waves are determined as three mechanisms of formation and frequency position of two opaque bands, with narrow peaks in one of the bands in the transmission spectra of 2D photonic crystals composed of dielectric cylinders arranged parallel to the EM wave's electric vector in the square lattice. The main Mie resonance in a single cylinder defines the frequency position of the main gap whose formation results from the Bragg-like scattering. An additional gap with narrow transmission peaks opens in the spectrum of a cylinder layer and becomes pronounced with the number of layers. It is argued that higher-order Mie resonances are responsible for the transmission peaks within the additional band of a perfect crystal. It is shown that 2D photonic crystals with a filling factor ranging from 3% to 20% at a fixed crystal period may be a good zero approximation to study wave transmission through a localizing 2D dense random medium slab.     

Tailoring Optical and Plasmon Resonances in Core-shell and Core-multishell Nanowires for Visible Range Negative Refraction and Plasmonic Light Harvesting:A Review

Semiconductor nanowires(NWs) are sub-wavelength structures which exhibit strong optical(Mie)resonances in the visible range.In addition to such optical resonances,the localized surface plasmon resonances(LSPRs) in metal-semiconductor core-shell(CS) and core-multishell(CMS) NWs can be tailored to achieve novel negative-index metamaterials(N1M),extreme absorbers,invisibility cloaks and sensors.Particularly,in this review,we focus on our recent theoretical studies which highlight the versatility of CS and CMS NWs for:1) the design of negative-index metamaterials in the visible range and2) plasmonic light harvesting in ultrathin photocatalyst layers for water splitting.Utilizing the LSPR in the metal layer and the magnetic dipole(Mie) resonance in the semiconductor shell under transverse electric(TE) polarization,semiconductor-metal-semiconductor CMS NWs can be designed to exhibit spectrally overlapping electric and magnetic resonances in the visible range.NWs exhibiting such double resonances can be considered as meta-atoms and arrayed to form polarization dependent,low-loss NIM.Alternatively,by tuning the LSPR in the TE polarization and the optical resonance in the transverse magnetic(TM) polarization of metal-photocatalyst CS and semiconductor-metal-photocatalyst CMS NWs,the absorption within ultrathin(sub-50 nm) photocatalyst layers can be substantially enhanced.Notably,aluminum and copper based NWs provide absorption enhancement remarkably close to silver and gold based NWs,respectively.Further,such absorption is polarization independent and remains high over a large range of incidence angles and permittivity of the medium.Therefore,due to the tunability of their optical properties,CS and CMS NWs are expected to be vital components for the design of nanophotonic devices.     

Observation of intrinsic size effects in the optical response of individual gold nanoparticles

The photothermal heterodyne imaging method is used to study for the first time the absorption spectra of individual gold nanoparticles with diameters down to 5 nm. Intrinsic size effects that result in a broadening of the surface plasmon resonance are unambiguously observed. Dispersions in the peak energies and homogeneous widths of the single-particle resonances are revealed. The experimental results are analyzed within the frame of Mie theory.     

Temperature and wavelength dependence of gain and threshold current detuning with cavity resonance in vertical-cavity surface-emitting lasers

Heating-induced threshold current detuning with different cavity resonances of AlInGaAs-AlGaAs vertical-cavity surface-emitting lasers (VCSELs) was studied based on gain spectrum analysis and threshold current construction as functions of cavity resonance wavelength and temperature. The quantitative correlations between gain peak, cavity resonance and the minimal threshold current were established. The results showed that the minimal threshold current was in agreement with the gain peak in wavelength only at the temperatures of 300-320 K. Higher temperatures led to a detuning difference between the gain peak and the minimal threshold current relative to the cavity resonance due to band-like nature of the states. In addition, this theoretical analysis about thermal tuning of the cavity resonance pointed out that the wavelength of cavity resonance shifted in an exponential function of temperature. The linear approximation was consistent with the experimental results in the temperature range 300-400 K. A new approach for the gain offsetting is provided so that the minimum in threshold currents can be aligned with the cavity resonance, instead of doing it with the gain peak to achieve the lowest threshold current of the VCSEL at a given temperature.     

Universal scaling of plasmon coupling in metal nanostructures: extension from particle pairs to nanoshells

It has been recently shown that the strength of plasmon coupling between a pair of plasmonic metal nanoparticles falls as a function of the interparticle gap scaled by the particle size with a near-exponential decay trend that is universally independent of nanoparticle size, shape, metal type, or medium dielectric constant. In this letter, we extend this universal scaling behavior to the dielectric core-metal shell nanostructure. By using extended Mie theory simulations of silica core-metal nanoshells, we show that when the shift of the nanoshell plasmon resonance wavelength scaled by the solid nanosphere resonance wavelength is plotted against the shell thickness scaled by the core radius, nanoshells with different dimensions (radii) exhibit the same near-exponential decay. Thus, the nanoshell system becomes physically analogous to the particle-pair system, i.e., the nanoshell plasmon resonance results from the coupling of the inner shell surface (cavity) and the outer shell surface (sphere) plasmons over a separation distance essentially given by the metal shell thickness, which is consistent with the plasmon hybridization model of Prodan, Halas, and Nordlander. By using the universal scaling behavior in the nanoshell system, we propose a simple expression for predicting the dipolar plasmon resonance of a silica-gold nanoshell of given dimensions.     

Determination of the natural frequency of a cantilevered ZnO nanowire resonantly excited by a sinusoidal electric field

The electric-field-induced mechanical resonance of an individual nanotube (NT) or nanowire (NW) has been utilized as a versatile technique for in situ measurement of the Young's modulus of the NT/NW in electron microscopes. The key step of this technique is to determine the fundamental natural frequency of the NT/NW. However, the emergence of super-?and/or sub-harmonic resonances might make the determination uncertain. This paper investigates the resonance behaviour of ZnO NWs in a nanotip-nanowire system in order to clarify this obscurity. It is found that forced and parametric resonance are two basic modes of the observed multi-frequency resonances and that each mode exhibits a distinct characteristic. By controlling the driving force exerted on the NW to be either lateral or axial, the two otherwise entangled modes are clearly separated. Based on this resonance mode separation, a criterion for identifying the natural frequency of ZnO NWs is proposed.     

两端固定输流管道的稳定性和参数共振

研究了两端固定输流管道在脉动内流作用下的参数共振问题。用平均法导出了管道失稳判据和三种参数共振区域的边界曲线方程，讨论了系统参数对失稳区域的影响。用数值方法给出了各种参数共振的响应曲线，分析了其存在区域以及响应频率与脉动流频率之间的关系。研究结果表明，组合共振区域内可发生拟周期运动和组合周期运动；组合共振曲线能延伸到第二振型次谐波共振区域；第一振型次谐波共振曲线能覆盖整个组合共振区域，而且能延伸到第二振型次谐波共振区域。因此，此系统存在同一个脉动频率与多种运动相对应的参数区域。     

Properties of TM resonances on metallic slit gratings

Electromagnetic resonances on metallic slit gratings induced by TM polarized incident light have been investigated and physically interpreted. We have developed an electromagnetic model imposing surface impedance boundary conditions on the metallic grating surface from which we derive simple formulas explaining all physical properties of these resonances. It is demonstrated that Fabry-Perot (or cavity) resonances are generated by the zeroth slit mode yielding extraordinary transmission. For very narrow slits, the resonant H-field is squeezed to the slit walls and causes enhanced power losses. The excitation of surface plasmon polaritons (SPPs), however, is generated by two mode coupling. SPPs are linked to sharp absorption peaks and dips in transmittance. It is shown that these phenomena are primarily caused by the interaction of the electromagnetic fields with the finite conducting slit walls. These findings have been confirmed by measured transmittance data of gold gratings with periods of 0.5 μm, 1 μm, and 2 μm.     

Equivalent-circuit model for the thickness-shear mode resonator with a viscoelastic film near film resonance

We derive a lumped-element, equivalent-circuit model for the thickness-shear mode (TSM) resonator with a viscoelastic film. This modified Butterworth-Van Dyke model includes in the motional branch a series LCR resonator, representing the quartz resonance, and a parallel LCR resonator, representing the film resonance. This model is valid in the vicinity of film resonance, which occurs when the acoustic phase shift across the film is an odd multiple of pi/2 rad. For low-loss films, this model accurately predicts the frequency changes and damping that arise at resonance and is a reasonable approximation away from resonance. Elements of the parallel LCR resonator are explicitly related to film properties and can be interpreted in terms of elastic energy storage and viscous power dissipation. The model leads to a simple graphical interpretation of the coupling between the quartz and film resonances and facilitates understanding of the resulting responses. These responses are compared with predictions from the transmission-line and Sauerbrey models.     

两端固定输流管道参数共振的实验研究

用实验方法研究了两端固定输流管道在脉动内流作用下的参数共振问题。所设计的实验系统合理有效,基本符合进行参数共振实验的设计目的。对三种合成管道在几个不同的平均流速和脉动流作用下做了多次重复实验获得了第一振型1/2次谐波参数共振相关实验数据,实验结果与理论结果在定性上一致。本文还对可能引起定量误差的原因做了较详细的分析。通过实验观察,得到以下结论：（1）当平均流速达到一定值时,两端固定管道在一定的脉动流振幅和脉动频率下会产生第一振型1/2次谐波参数共振。脉动流振幅越大,发生参数共振的频率范围也越大。当脉动流振幅小于一定值时,不再发生参数共振。（2）平均流速越大,发生参数共振所需要的脉动流频率就越小。平均流速大小对于能否出现1/2次谐波参数共振、共振区域大小、形状以及位置都有很重要的影响。在其它条件一定的情况下,低频脉动时平均流速越大管道越容易失稳。以上观察到的现象与理论分析中得到的结果是一致的。     

Plasmon Resonances of Nanoshells of Spheroidal Shape

Plasmon resonances are computed for nanoshells of prolate and oblate spheroidal shape. Both longitudinal and transverse resonances are investigated as a function of aspect ratio and shell thickness. Formulas for the surface charge density on the outside and inside shell surfaces are derived.     

Tunable ultranarrow linewidth of a cavity induced by interacting dark resonances

A scheme for obtaining a tunable ultranarrow linewidth of a cavity due to an embedded four-level atomic medium with double-dark resonances is proposed. It is shown that the steep dispersion induced by double-dark resonances in the transparency window leads to the ultranarrow transmission peak. Compared with the case of a single-dark resonance system, the linewidth can be narrowed even by one order under proper conditions. Furthermore, the position of the ultranarrow peak can be engineered by varying the detuning of the control field.     

Numerical characterization of whispering-gallery mode optical microcavities

We characterize planar microcavities in whispering-gallery mode optical resonances. The microcavity consists of a waveguide and a microdisk, and a nanoscale gap separates the waveguide and the microdisk. The devices can be fabricated on Si-based thin films by using conventional microelectronics techniques. To characterize these types of cavity, we study a broad range of resonator configuration parameters including the size of the microdisk, the width of the gap, and the waveguide dimensions. The finite-element method is used for solving Maxwell's equations. The electric fields and the energy density distributions are obtained and compared between the on-resonance and off-resonance situations. A brilliant ring with a strong electric field and a high-energy density is found inside the periphery of the microdisk under first-order resonance. While under second-order resonance, there are two bright rings, and the light intensity in the inner ring is stronger than that in the outer ring. The resonant frequencies and their free spectral ranges are predominantly determined by the size of the microdisk. The gap effect on the resonant frequencies is observable, although it is minor. The gap strongly affects the full width at half-maximum (FWHM), finesse, and quality factor of the resonances. With an increase in the gap width from 100 to 300 nm, both the Q value and finesse increase substantially, while the FWHM decreases. The waveguide width has a visible influence on the Q value, FWHM, and finesse as well.     

A New Closed-Form Solution to Light Scattering by Spherical Nanoshells

Light or electromagnetic wave scattered by a single sphere or a coated sphere has been considered as a classic Mie theory. There have been some further extensions that were made further based on the Mie theory. Recently, a closed-form analytical model of the scattering cross section of a single nanoshell has been considered. The present paper is documented further, based on the work in 2006 by Alam and Massoud, to derive another different closed-form solution to the problem of light scattered by the nanoshells using polynomials of up to order 6. Validation is made by comparing the present closed-form solution to the exact Mie scattering solution and also to the other closed-form solution by Alam and Massoud. This study is found to be, however, more generalized and also more accurate for the coated spheres of either tiny/small or medium sizes than that of Alam and Massoud. Therefore, the derived formulas can be used for accurately characterizing both surface plasmon resonances of nanoparticles (of small sizes) or nanoantenna near-field properties (of medium sizes comparable with half wavelength).     

Observation of Supercavity Modes in Subwavelength Dielectric Resonators

Electromagnetic response of dielectric resonators with high refractive index is governed by optically induced electric and magnetic Mie resonances facilitating confinement of light with the amplitude enhancement. Traditionally, strong subwavelength trapping of light was associated only with plasmonic or epsilon‐near‐zero structures, which however suffer from material losses. Recently, an alternative localization mechanism was proposed allowing the trapping of light in individual subwavelength optical resonators with a high quality factor in the regime of a supercavity mode. Here, the experimental observation of the supercavity modes in subwavelength ceramic resonators in the radio‐frequency range is presented. It is experimentally demonstrated that the regime of supercavity modes can be achieved via precise tuning of the resonator's dimensions. A huge growth of the unloaded quality factor is achieved with experimental values up to 1.25 × 10⁴, limited only by material losses of ceramics. It is revealed that the supercavity modes can be excited efficiently both in the near‐ and far‐field. In both cases, the supercavity mode manifests itself explicitly as a Fano resonance with characteristic peculiarities of spectral shape and radiation pattern. A comparison of supercavities made of diversified materials for the visible, infrared, THz, and radio‐frequency regimes is provided.     

Microwave-Dimensional Measurements of Cylindrical Resonators for Primary Acoustic Thermometry

Acoustic gas thermometry relies on the fundamental relationship between the speed of sound in a monatomic gas and its thermodynamic temperature. The speed of sound is calculated from the resonance frequencies of a cavity whose dimensions or thermal expansivity must be measured with high accuracy. For quasi-spherical cavities, the use of microwave resonances is a successful and proven dimensional measurement technique. The simplicity and economy of cylindrical resonators makes them an attractive alternative to quasi-spherical resonators, particularly for high-temperature thermometry. This article summarizes the basic theory of cylindrical microwave resonators, and describes methods for obtaining cavity dimensions from the mode frequencies. The perturbing effects of cavity shape deformations, the wall to end-plate junction, coupling probes and non-conducting surface layers are discussed. The results of an experiment with a simple aluminum cavity are presented, which demonstrate the superior performance of the TE0 \(pq\) modes over the more commonly used TM0 \(pq\) modes.     

Edge States and Topological Phase Transitions in Chains of Dielectric Nanoparticles

Recently introduced field of topological photonics aims to explore the concepts of topological insulators for novel phenomena in optics. Here polymeric chains of subwavelength silicon nanodisks are studied and it is demonstrated that these chains can support two types of topological edge modes based on magnetic and electric Mie resonances, and their topological properties are fully dictated by the spatial arrangement of the nanoparticles in the chain. It is observed experimentally and described how theoretically topological phase transitions at the nanoscale define a change from trivial to nontrivial topological states when the edge mode is excited.     

Thermo-optical model of repetitively pumped solid-state lasers

A thermo-optical model describing the cavity stability and TEM00-mode volume of a repetitively pumped solid-state laser is developed and verified experimentally. The model predicts a maximum theoretical TEM00 Gaussian-mode radius in the laser rod. This maximum mode radius is caused by a bifocusing of the cavity mode and is present even in gain-polarized materials that nominally suppress the effect of birefringence on beam polarization. The mode limitation effect is not eliminated by conventional optics and is reduced only marginally by the often-described technique of placing a second identical laser head in the cavity. A maximum mode radius implies a fundamental limit on the TEM00-mode energy that can be extracted from a given laser cavity.     

Enhanced transmission due to nonplasmon resonances in one- and two-dimensional gratings

Enhanced transmission through subwavelength slit gratings and hole arrays is studied in view of its application in the far-infrared and microwave domains. Because for perfectly conducting gratings, plasmon resonances are not expected to produce an enhanced transmission, other kinds of resonance, such as Fabry-Perot, waveguide-mode, and cavity-mode resonances, are studied. The possibility of reaching 100% transmittivity for some particular wavelengths is established when two superimposed identical gratings are used while each of them transmits approximately 1% off resonance. A similar transmission is obtained with hole arrays. The study of the field map inside the groove region allows our establishing the nature of the resonance, that is involved. Comparison of the bandwidth with respect to the wavelength or incidence given by various kinds of resonance is presented.