Optical properties of sub-wavelength dielectric gratings and their application for surface-enhanced Raman scattering

We fabricated and measured the far-field optical properties of a sub-wavelength Si₃N₄ (silicon nitride) two dimensional grating. Frequency-dependent transmission measurements from a white-light source revealed that both transverse magnetic (TM) and transverse electric (TE) modes were excited on the grating. We determined the dispersion relations of the modes by tilting the sample with respect to the incoming light beam and measuring the frequency shift of the absorption features. By comparing to a simple model, we determined the effective refractive index for the TM and TE modes and the geometrical constants for the grating. This information enables gratings with desired optical properties to be designed and fabricated. The application of the sub-wavelength grating for surface-enhanced Raman scattering (SERS) is demonstrated.     

含色散介质的一维光子晶体微腔的光学特性和模式调节

采用时域有限差分(FDTD)法计算了含色散介质一维光子晶体微腔的透射谱,研究了缺陷模的频移特性。通过与无色散光子晶体微腔透射谱相比较,发现了介质色散导致的缺陷模频移现象,并详细地分析了中心频率、色散强度和衰减系数等色散介质参量和缺陷模频移的依赖关系。模拟结果显示,缺陷模的频移决定于中心频率、色散强度和衰减系数等色散介质参量的大小,通过合理的调节这些参量,可以有效地调节缺陷模的频率。     

Far-field sub-wavelength imaging and focusing using a wire medium based resonant metalens

This is the second article in a series of two dealing with the concept of a ‘resonant metalens’ we introduced recently. This is a new type of lens capable of coding in time and radiating efficiently in the far-field region sub-diffraction information about an object. A proof of the concept of such a lens is performed in the microwave range, using a medium made out of a square lattice of parallel conducting wires with finite length. We investigate a sub-wavelength focusing scheme with time reversal and demonstrate experimentally spots with focal widths of λ/25. Through a cross-correlation based imaging procedure we show an image reconstruction with a resolution of λ/80. Eventually we discuss the limitations of such a lens which reside essentially in losses.     

Surface shear horizontal waves associated with a periodic array of wires deposited on a substrate

The vibrational and electronic spectra of a semi-infinite crystal with a planar surface are modified by the presence of surface inhomogeneities or roughness such as ridges or grooves, quantum wires or tips. We develop a Green's function formalism to investigate the localized and resonant acoustic modes of shear horizontal polarization associated with the surface of a substrate supporting a single and a periodic array of wires. Each material is assumed to be an isotropic elastic medium. The calculation can be applied to an arbitrary choice of the shape and elastic parameters of the wires. The surface modes are obtained as well-defined peaks of the densities of states (DOS). In this paper, we calculate the variation of the density of states associated with the adsorption of a single wire, and the dispersion curves of the surface modes for a periodic array of wires on the flat surface of a substrate. We discuss their behaviors as a function of the elastic parameters and the relationship between resonant modes of the single wire and dispersion curves of the surface modes for a periodic structure. Received 6 December 2000     

Theoretical investigation of hierarchical sub-wavelength photonic structures fabricated using high-order waveguide-mode interference lithograph

This paper presents the theoretical investigation of hierarchical sub-wavelength photonic structures with various periods and numbers of layers, which were fabricated using a high-order waveguide-mode interference field. A 442-nm laser was used to excite high-order waveguide modes in an asymmetric metal-cladding dielectric waveguide structure. The dispersion curve of the waveguide modes was theoretically analyzed, and the distribution of the interference field of high-order waveguide modes was numerically simulated using the finite-element method. The various dependences of the characteristics of hierarchical sub-wavelength photonic structures on the thickness and refractive index of the photoresist and the waveguide mode were investigated in detail. These hierarchical sub-wavelength photonic structures have various periods and numbers of layers and can be fabricated by a simple and low-cost method.     

Polarization sensitive sub-wavelength metallic structures: toward near-field light confinement control

In this paper, we seek to demonstrate spatial near field light confinement with a truly sub-wavelength resolution in the visible range. For that purpose, an opaque metallic screen is pierced with an array of rectangular nano-apertures which support polarization sensitive guided modes. We show that it is possible to switch on and off sub-wavelength apertures about only 200 nanometers away. Theoretical results have been performed (3D-FDTD home-made code) and are in good agreement with the experimental results. These kinds of nano-structures might offer a convenient and versatile way to sub-wavelength light addressing, optical trapping, molecular, or nano-probing, non-linear spectroscopy.     

Anisotropic Spherical Cavity Resonator I. Azimuthally Homogeneous Oscillations

Resonant oscillations are considered in the spherical cavity with the uniform crystal medium and bounded by a non-perfect conductor. The Maxwell equations are reduced to the couple of wave equations each describing the TE and TH modes. We show that the crystal anisotropy affects only the TM modes. The solution of the wave equations satisfies the boundary conditions on the spherical surface that define the spherical characteristics of the resonant oscillations. New types if TM modes appear caused by the anisotropy of the medium. The analytical solution of the dispersion equation is considered in the form of continued fraction. Numerical results are presented demonstrating of natural frequencies of higher mode numbers.     

An anisotropic metamaterial-based rectangular resonant cavity

Resonance properties of a rectangular resonant cavity filled with an anisotropic metamaterial bilayer are investigated. Different from the isotropic case and the one-dimensional resonator, the resonance properties in such a cavity are closely related to the dispersion relation of the anisotropic medium. Three cases including six subcases of different combinations of metamaterials are discussed and it is found that subwavelength resonance modes may occur in all subcases. Particularly, the relation between resonance modes and the transverse cavity width is investigated, and calculated results show that there are infinite subwavelength resonance modes as the transverse cavity width approaches zero. Requirements of the material and geometry parameters to construct a subwavelength resonant cavity are revealed by theoretical analysis, which demonstrates that this kind of subwavelength resonator brings more design flexibility and tolerance. PACS 78.70.Gq; 81.05.Zx; 84.40.Ba     

Terahertz beat frequency generation from two-mode lasing operation of coupled microdisk laser

We propose a coupled microdisk laser as a compact and tunable laser source for the generation of a coherent continuous-wave terahertz radiation by photomixing. Using the Schr?dinger-Bloch model including the nonlinear effect of active medium, we find single-mode and two-mode lasings depending on the pumping strength. We explain the transitions of lasing modes in terms of resonant modes that are the solutions of the Schr?dinger-Bloch model without active medium and nonlinear interaction. In particular, a two-mode lasing is shown to generate a terahertz oscillating frequency originating from the light beating of two nearly degenerated resonant modes with different symmetries.     

Design of metaporous supercells by genetic algorithm for absorption optimization on a wide frequency band

The optimization of acoustic absorption by metaporous materials made of complex unit cells with 2D resonant inclusions is realized using genetic algorithm. A nearly total absorption over a wide frequency band can be obtained for thin structures, even for frequencies below the quarter wavelength resonances i.e., in a sub-wavelength regime. The high absorption performances of this material are due to the interplay of usual visco-thermal losses, local resonances and trapped modes. The density of resonant and trapped modes in this dissipative porous layer, is a key parameter for broadband absorption. The best configurations and critical coupling conditions are found by genetic algorithm optimization. Several types of resonators are included gradually in the studied configurations (split-rings, Helmholtz resonators, back cavities) with increasing complexity. The optimization leads to a metaporous structure with a 2-cm sub-wavelength layer thickness, exhibiting a nearly total absorption between 1800 Hz and 7000 Hz. The influence of the incidence angle on the absorption properties is also shown.     

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.     

Frequency behavior of coherent random lasing in diffusive resonant media

We investigate diffusive propagation of light and consequent random lasing in an amplifying medium comprising resonant spherical scatterers. A Monte-Carlo calculation based on photon propagation via three-dimensional random walks is employed to obtain the dwell-times of light in the system. We compare the inter-scatterer and intra-scatterer dwell-times for representative resonant and non-resonant wavelengths. Our results show that more efficient random lasing, with intense coherent modes, is obtained for a system with intra-scatterer gain. This is also coupled with a larger reduction in frequency fluctuations. We find that such a system can yield almost thresholdless random lasing. Inspired by these results, we discuss a possible practical situation, based on a monodisperse aerosol, wherein frequency controlled coherent random lasing can be obtained. Since our analysis essentially investigates transport of intensity, the results are relevant to coherent random lasers under nonresonant feedback.     

Highly sensitive cladding-etched arc-induced long-period fiber gratings for refractive index sensing

We have investigated the effects of cladding etching in arc-induced long-period fiber gratings. Comparing the position of the resonant wavelengths at each diameter with the corresponding theoretical dispersion curves of effective refractive index, it is found that some of the resonances show a better match with anti-symmetrical cladding modes, while others with symmetrical cladding modes. Etching the cladding diameter to ∼39 μm, results in coupling to a high-order cladding mode that is very sensitive to changes in the ambient refractive index. The resonant peak shifts remarkably (∼230 nm) toward shorter wavelengths as the external refractive index increases. This sensitivity is higher than any previously reported in arc-induced long-period fiber gratings.     

Metal–polymer nano-composite films with ordered vertically aligned metal cylinders for sub-wavelength imaging

We propose a self-assembled and anisotropically metal loaded large area PS-b-P4VP diblock copolymer film as a medium with hyperbolic dispersion for application in superlensing and nanolithography. We obtained domain sizes from 30 to 100 nm with successful demonstration of metal loading inside the nano-templates. The separation between the individual nanorods and their radius was effectively controlled by varying the molecular weights and compositions of the polymers. We apply Maxwell–Garnett homogenization and FDTD simulations to show the sub-wavelength imaging and lithography potential of these hyperbolic metamaterials (HMMs). A proof of principle nanolithography result demonstrates sub-wavelength imaging and lithography using the proposed HMMs.     

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.     

TE0导模干涉刻写周期可调亚波长光栅理论研究

通过棱镜耦合激发非对称金属包覆介质波导结构中的TE₀导波模式, 利用两束TE₀模的干涉从理论上实现了周期可调的亚波长光栅刻写. 分析了TE₀模式的色散关系, 刻写亚波长光栅的周期与激发光源、棱镜折射率、光刻胶薄膜厚度及折射率之间的关系. 用有限元方法数值模拟了金属薄膜、光刻胶薄膜和空气多层结构中TE₀导模的干涉场分布. 研究发现, 激发光源波长越短, TE₀ 模干涉刻写的亚波长光栅周期越小; 光刻胶越厚, 刻写的亚波长光栅周期越小; 高折射率光刻胶有利于更小周期亚波长光栅的刻写. 相较于表面等离子体干涉光刻, 基于TE₀ 模的干涉可在厚光刻胶条件下通过改变激发光源、棱镜折射率、光刻胶材料折射率、特别是光刻胶薄膜的厚度等多种方式实现对亚波长光栅周期的有效调控.     

Low frequency resonant dispersion of sound in bubble media

Presented is a theory of a new type of resonant dispersion of sound in a gas-liquid bubble media based on the use of effective dynamic density. We show that because of spheroidal-translational oscillations of the bubbles the dynamic density of the gas-liquid media has a resonance dependence on the frequency, which is manifested in wave process as a low-frequency resonant dispersion of sound. This dispersion is significantly different from the known high-frequency resonant dispersion, which is due to resonance in the volume oscillations of the bubbles. The results of the experiments confirming the existence of the resonant dispersion of sound at a frequency equal to half the natural frequency of the spheroidal oscillations of bubbles are provided.     

Investigation of transmission resonances on the one-dimensional metallic cylindrical gratings in THz frequency range

In the experiments of THz wave transmitting through the metallic cylindrical gratings fabricated by sub-wavelength brass wires, this paper reports that the discrepancy in the sharp resonances occurred as the grating perpendicular or parallel to the electric vector are observed. A simulation based on the finite difference time domain (FDTD) indicated that the enhanced transmission through the grating is attributed to the combined effects of surface plasmons and cavity modes in the perpendicular condition, while the cavity modes dominate the resonant transmission under the other conditions. Additional experimental data and calculated results show that ～1 enhanced coupling efficiency can be realized in some THz frequency, which could be applied to the design and improvement of various optoelectronic devices, or detection of biological molecule and powder samples, etc.     

Guided Waves in a Multi-Layered Cylindrical Elastic Solid Medium

We investigate the guided waves in a multi-layered cylindrical elastic solid medium. The dispersion function of guided waves is usually complex and the dispersion curves of all modes are not conveniently obtained. Here we present an effective method to obtain the dispersion curves of all modes. First, the dispersion function of the guided waves is transformed into a real function. The dispersion curves are then calculated for all the modes of the guided waves by the bisection method. The modes with the orders n = 0, 1, and 2 are analysed in two- and three-layer media. The existence condition of Stoneley wave is discussed. The modes of the guided waves are also investigated in a two-layer medium, in which the velocity of shear wave in the outer layer is less than that in the inner layer.     

Free vibration characteristics of double-walled carbon nanotubes embedded in an elastic medium

In this Letter, a theoretical analysis of the resonant vibration of double-walled carbon nanotubes (DWCNTs) and the DWCNTs embedded in an elastic medium is presented based on Euler-Bernoulli beam model and Winkler spring model. The vibration modes of DWCNTs are quite different from those of single-walled carbon nanotubes (SWCNTs). The resonant vibrations of DWCNTs are found to have in-phase and anti-phase modes, in which the deflections of the inner and outer nanotubes occur in the same and opposite directions, respectively. For the vibration of DWCNTs with the same harmonic numbers, the resonant frequencies of anti-phase mode are larger than the ones of in-phase mode. Moreover, influence of the surrounding medium on the resonant vibrations is investigated using the Winkler spring model. The results show that surrounding medium makes a strong impact on the vibration frequencies of in-phase mode, but little on those of anti-phase mode.