Study of spatial-temporal characteristics of optical fiber based on ultrashort-pulse interferometry

We demonstrate a method for reconstruction of the modal intensity distribution of light at the output of an optical fiber. Spatial modes of the optical fiber are separated in time as a result of differences in group velocity and are detected experimentally by observation of the interference of the modal field distribution with the time-gating reference field. The detected interference patterns of the modal fields are analyzed, providing the spatial impulse response of the fiber. We also use interferometric correlation to determine the spatiotemporal characteristics of the fiber modes, such as pulse width, linear chirp, and group velocity, for each mode.     

一种新型无色散慢光光子晶体薄板波导

利用椭圆形孔替代传统光子晶体薄板波导中邻接波导的最内层两排圆孔构成一种新型低损耗光子晶体薄板光波导.该波导的群速度和群速度色散特性强烈依赖于波导中这两排邻接波导的椭圆孔的特性.借助波导导模展开方法,计算得到波导的能带结构和群指数,并分析了它们与椭圆孔的参数关系.通过优化这些椭圆孔的参数,可以增加光子晶体光波导导模在光锥以下的无固有传输损耗带宽,在2—45 nm 的带宽上实现无色散的常数群速度.这些理论结果将为低损耗低色散慢光波导的设计制造提供理论基础. 关键词： 光子晶体薄板波导 群速度 群指数 群速度色散     

Flexural and transversal wave motion in homogeneous isotropic thermoelastic plates by using asymptotic method

The present investigation is concerned with the flexural and transversal wave motion in an infinite, transversely isotropic, thermoelastic plate by asymptotic method. The governing equations for the flexural and transversal motions have been derived from the system of three-dimensional dynamical equations of linear theory of coupled thermoelasticity. The asymptotic operator plate model for free vibrations; both flexural and transversal, in a homogenous thermoelastic plate leads to fifth degree and cubic polynomial secular equations, respectively, that governs frequency and phase velocity of various possible modes of wave propagation at all wavelengths. All the coefficients of differential operator have been expressed as explicit functions of the material parameters. The velocity dispersion equations for the flexural and transversal wave motion have been deduced from the three-dimensional analog of Rayleigh-Lamb frequency equation for thermoelastic plate waves. The approximations for long and short waves and expression for group velocity have also been derived. The thermoelastic Rayleigh-Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations whose equivalence is established with that of asymptotic method. The dispersion curves for phase velocity, group velocity and attenuation coefficient of various flexural and transversal wave modes are shown graphically for aluminum-epoxy material elastic and thermoelastic plates.     

Edge resonance and zero group velocity Lamb modes in a free elastic plate

The local resonances of a free isotropic elastic plate are investigated using laser ultrasonic techniques. Experimental results are interpreted in terms of zero group velocity Lamb modes and edge mode. At a distance from the edge larger than the plate thickness a sharp resonance is observed at the frequency where the group velocity of the first symmetrical Lamb mode vanishes. Close to the edge of the plate, the resonance due to the edge mode dominates. Both zero group velocity and edge resonances appear at the theoretically predicted frequencies. These frequencies do not vary with the distance from the edge of the plate and the transition between the two modes of vibration, at about the plate thickness, is abrupt. Using a laser excitation on the edge, the amplitude profile of the normal displacement at the edge resonance frequency was determined.     

Generalized thermoelastic extensional and flexural wave motions in homogenous isotropic plate by using asymptotic method

In this paper the asymptotic method has been applied to investigate propagation of generalized thermoelastic waves in an infinite homogenous isotropic plate. The governing equations for the extensional, transversal and flexural motions are derived from the system of three-dimensional dynamical equations of linear theories of generalized thermoelasticity. The asymptotic operator plate model for extensional and flexural free vibrations in a homogenous thermoelastic plate leads to sixth and fifth degree polynomial secular equations, respectively. These secular equations govern frequency and phase velocity of various possible modes of wave propagation at all wavelengths. The velocity dispersion equations for extensional and flexural wave motion are deduced from the three-dimensional analog of Rayleigh-Lamb frequency equation for thermoelastic plate. The approximation for long and short waves along with expression for group velocity has also been obtained. The Rayleigh-Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations and its equivalence established with that of asymptotic method. The numeric values for phase velocity, group velocity and attenuation coefficients has also been obtained using MATHCAD software and are shown graphically for extensional and flexural waves in generalized theories of thermoelastic plate for solid helium material.     

Dispersionless slow light by photonic crystal slab waveguide with innermost elliptical air holes

We report a low-loss photonic crystal slab waveguide formed by deforming the innermost circle air holes in the conventional photonic crystal slab waveguide into elliptical ones. We obtain the photonic bands and group index of guided modes in this photonic crystal waveguide by guided-mode expansion method and investigate the dependence of photonic bands and group index of guided modes on the parameters of the innermost elliptical air holes. The group velocity and group velocity dispersion of this waveguide strongly depend on the innermost elliptical air holes. Photonic crystal slab waveguide with the optimum innermost elliptical air holes possesses a wider single mode region below the light line, in which light can easily propagate without intrinsic loss. At the same time, the guided mode supported by this waveguide has nearly constant group velocity and vanishing group velocity dispersion in a 3-5 nm bandwidth.     

Time of flight of excitonic polaritons in CdSe

Time of flight of polaritons is studied in the forbidden, mixed and allowed modes of propagation. With only one adjustable parameter, we obtain a very good agreement between all the experimental data and the usual oscillator model. In the calculation, the excited states of the A exciton and the n = 1 state of the B exciton are taken into account. The longitudinal-transverse splitting energy ?ω_LT is found to be equal to 1.3 meV. We show that very close to resonances, it is not possible to describe the temporal evolution of the pulse by the group velocity of the wave packet. We give an example which shows we have to use the Fourier transform method.     

Bragg空芯光纤中的群速度超光速的理论探讨

运用渐近法计算了多模B ragg光纤的场分布、有效折射率、各模式的色散参量、群速度及TE01模的能量速度。结果表明:各模式色散参量有正有负,但群速度都大于光速,而能量速度不大于光速。     

Materials for freezing light

Recent theoretical investigations have predicted the existence of axially frozen modes that arise when light is incident upon an anisotropic one-dimensional photonic crystal. Such electromagnetic modes are of interest since they suggest a near-zero group velocity with extraordinary amplitudes. This paper addresses the crystal physics associated with realizing such effects and provides specific examples based on antimony sulfoiodide (SbSI) and barium titanate (BaTiO₃) superlattices. Such novel photonic crystal structures could have a profound effect on non-linear optics and optical computing.     

Leaky modes and the first arrivals in cased boreholes with poorly bonded conditions

The generation mechanism of the first arrivals in the cased boreholes for the poorly bonded conditions is investigated. Based on the analyses of the Riemann surface structure of the characteristic function, the dispersion features, excitation spectra and contributions of modes excited in the cased boreholes with different cementing types are studied. The phase velocity dispersion studies of leaky modes show that high-order modes form "plateau" regions with one approximate velocity denoted by v separated by their cutoff frequencies, in which the phase velocity changes little with a considerable frequency range, while the group velocity keeps a relatively constant high value. Usually, the operation frequency range of a specific cementing evaluation acoustic logging tool is covered by such a "plateau" region. Mode excitation and contribution analyses show that the first arrivals in the cased boreholes for the poorly bonded conditions are the contributions from leaky modes, where the traveling velocity of the first arrivals processed by slowness time coherence(STC) method is equal to the approximated velocity v. Analyses on generation of leaky modes in the cased boreholes supplement the understanding of the generation mechanism of the first arrivals.     

Anomalous dispersion relations by symmetry breaking in axially uniform waveguides

We show that modes of axially uniform waveguides of arbitrary cross section can be made to have anomalous dispersion relations resulting from strong repulsion between two modes. When the axial wave vector k is 0, the two modes have different TE/TM symmetry and thus can be brought arbitrarily close to an accidental frequency degeneracy. For nonzero k, the symmetry is broken causing the modes to repel. When the modes are sufficiently close together this repulsion leads to unusual features such as extremely flattened dispersion relations, backward waves, zero group velocity for nonzero k, atypical divergence of the density of states, and nonzero group velocity at k=0.     

Design and fabrication of two-dimensional photonic crystals with predetermined nonlinear optical properties

By probing the resonances between a photonic band and an external laser field and their nonlinear changes in angle-resolved reflectivity, we show experimental evidence that the nonlinear optical changes in a two-dimensional photonic crystal waveguide with a Kerr nonlinearity are critically dependent on the dispersion nature and the group velocity of the photonic bands. The results agree well with the behavior predicted from band structures, indicating that the design of nonlinear optical properties of material systems is realistically possible by band dispersion and group velocity engineering.     

Materials for freezing light

Recent theoretical investigations have predicted the existence of axially frozen modes that arise when light is incident upon an anisotropic one-dimensional photonic crystal. Such electromagnetic modes are of interest since they suggest a near-zero group velocity with extraordinary amplitudes. This paper addresses the crystal physics associated with realizing such effects and provides specific examples based on antimony sulfoiodide (SbSI) and barium titanate (BaTiO₃) superlattices. Such novel photonic crystal structures could have a profound effect on non-linear optics and optical computing.     

Rayleigh wave and detection of low-velocity layers in a stratified half-space

The excitation and propagation of the guided waves in a stratified half-space and a Rayleigh wave exploration method in shallow engineering seismic exploration are studied in this paper. All the modes of the guided waves are calculated by the bisection method in the case where the low velocity layers are contained in a stratified half-space. Cases when the formation shear wave velocity gradually decreases from the top to the bottom layers are also studied. The dispersion curves obtained in actual Rayleigh wave exploration are usually noncontinual zigzag curves, but the dispersion curves given by the elastic theory for given modes of the guided waves are smooth and continual curves. In this paper, the mechanism of zigzag dispersion curves in Rayleigh wave exploration is investigated and analyzed thoroughly. The zigzag dispersion curves can give not only the possible positions of the low-velocity layers but also the other information on the formation structure (fractures, oil, gas, etc.). It is found that the zigzag dispersion curves of the Rayleigh wave are the result of the leap of the modes and the existence of low velocity layers in a stratified half-space. The effects of the compressional wave velocity, shear wave velocity, and density of each layer on zigzag dispersion curves and the relationship of the low velocity layers to zigzag dispersion curves are also investigated in detail. Finally, the exploration depth of the Rayleigh wave is discussed. The exploration depth of the Rayleigh wave is equal to the wavelength multiplied by a coefficient that is variable and usually given by the work experience and the formation properties of the local work area.     

Guided wave dispersion curves for a bar with an arbitrary cross-section,a rod and rail example

Theoretical and experimental issues of acquiring dispersion curves for bars of arbitrary cross-section are discussed. Since a guided wave can propagate over long distances in a structure, guided waves have great potential for being applied to the rapid non-destructive evaluation of large structures such as rails in the railroad industry. Such fundamental data as phase velocity, group velocity, and wave structure for each guided wave mode is presented for structures with complicated cross-sectional geometries as rail. Phase velocity and group velocity dispersion curves are obtained for bars with an arbitrary cross-section using a semi-analytical finite element method. Since a large number of propagating modes with close phase velocities exist, dispersion curves consisting of only dominant modes are obtained by calculating the displacement at a received point for each mode. These theoretical dispersion curves agree in characteristic parts with the experimental dispersion curves obtained by a two-dimensional Fourier transform technique.     

Low group velocity in a photonic crystal coupled-cavity waveguide

A two-dimensional photonic crystal coupled-cavity waveguide is designed and optimized, the transmission spectrum is calculated by using the finite-difference time-domain method, and the group velocity of c/1856 is obtained. To our knowledge, this value of group velocity is the lowest group velocity in a photonic crystal waveguide calculated from its transmission spectrum so far. The result is confirmed by the photonic band structure calculated by using the plane wave expansion method, and it is found that the photonic crystal waveguide modes in a photonic band structure are in accordance with those in the transmission spectrum by using the finite-difference time-domain method. The mechanism of slow light in the coupled-cavity waveguide of photonic crystal is analysed.     

The analysis and interpretation of some special properties of higher order symmetric lamb waves: the case for plates

Results derived from exact linear homogeneous elastodynamic theory are used for two-dimensional unloaded plates in order to understand certain features generated by proper symmetric Lamb modes. It is shown that S1 modes for all elastic materials have a phase velocity defined below the usual critical frequency and which initially exhibits anomalous dispersion (has a negative slope with respect to frequency). Over a certain range, it has a phase velocity that is double valued. In addition, there are an infinite number of proper symmetric Lamb modes that have this characteristic for materials with a Poisson ratio equal to 1/3. It also appears that all A3n modes are anomalous when V(L) < or = 2 V(T). The cause and implication of these effects are examined, including an associated negative group velocity over a small frequency zone for these modes. Further, it is noted that all proper symmetric Lamb modes have a plateau region in phase velocity with respect to wave number. It is shown that this always occurs for a phase velocity corresponding to the longitudinal bulk velocity of the elastic material. These issues are examined along with how one may obtain material parameters and possibly plate thickness from their dispersion curves.     

Statistics of Fourier modes of velocity and vorticity in turbulent flows: intermittency and long-range correlations

We perform a statistical analysis of experimental fully developed turbulence longitudinal velocity data in the Fourier space. We address the controversial issue of statistical intermittency of spatial Fourier modes by acting on the finite spectral resolution. We derive a link between velocity structure functions and the flatness of Fourier modes thanks to cascade models. Similar statistical behaviors are recovered in the analysis of spatial Fourier modes of vorticity obtained in an acoustic scattering experiment. We conclude that vorticity is long-range correlated and found more intermittent than longitudinal velocity.     

Coupling of spontaneous emission from GaN-AlN quantum dots into silver surface plasmons

We have demonstrated the decay of spontaneous emission (SE) from AlN-GaN quantum dots (QDs) into silver surface plasmon (SP) modes in the ultraviolet at approximately 375-380 nm. Using time-resolved photoluminescence (PL), we show that the electron-hole recombination rate in AlN-GaN QDs is enhanced when SE is resonantly coupled to a metal SP mode, corresponding to the dip in the continuous-wave PL spectrum. Exciton recombination by means of silver SP modes is as much as 3-7 times faster than in normal QD SE and depends strongly on emission wavelength and thickness of the silver.     

Transverse electromagnetic modes in aperture waveguides containing a metamaterial with extreme anisotropy

We use metamaterials with extreme anisotropy to solve the fundamental problem of light transport in deep subwavelength apertures. By filling a simply connected aperture with an anisotropic medium, we decouple the cutoff frequency and the group velocity of modes inside apertures. In the limit of extreme anisotropy, all modes become purely transverse electromagnetic modes, free from geometrical dispersion, propagate with a velocity controlled by the transverse permittivity and permeability, and have zero cutoff frequency. We analyze physically realizable cases for a circular aperture and show a metamaterial design using existing materials.