Component Of Wave Vector Research Articles

Coupled-mode theory and Fano resonances in guided-mode resonant gratings: the conical diffraction mounting.

We study resonances of guided-mode resonant gratings in conical mounting. By developing 2D time-dependent coupled-mode theory we obtain simple approximations of the transmission and reflection coefficients. Being functions of the incident light's frequency and in-plane wave vector components, the obtained approximations can be considered as multi-variable generalizations of the Fano line shape. We show that the approximations are in good agreement with the rigorously calculated transmission and reflection spectra. We use the developed theory to investigate angular tolerances of the considered structures and to obtain mode excitation conditions. In particular, we obtain the cross-polarization mode excitation conditions in the case of conical mounting.

Damage detection in composite panels based on mode-converted Lamb waves sensed using 3D laser scanning vibrometer

This paper introduces damage identification approach based on guided ultrasonic waves and 3D laser Doppler vibrometry. The method is based on the fact that the symmetric and antisymmetric Lamb wave modes differ in amplitude of the in-plane and out-of-plane vibrations. Moreover, the modes differ also in group velocities and normally they are well separated in time. For a given time window both modes can occur simultaneously only close to the wave source or to a defect that leads to mode conversion. By making the comparison between the in-plane and out-of-plane wave vector components the detection of mode conversion is possible, allowing for superior and reliable damage detection. Experimental verification of the proposed damage identification procedure is performed on fuel tank elements of Reusable Launch Vehicles designed for space exploration. Lamb waves are excited using low-profile, surface-bonded piezoceramic transducers and 3D scanning laser Doppler vibrometer is used to characterize the Lamb wave propagation field. The paper presents theoretical background of the proposed damage identification technique as well as experimental arrangements and results.

Generation of auroral kilometric radiation in inhomogeneous magnetospheric plasma

The generation of auroral kilometric radiation in a narrow 3D plasma cavity, in which a weakly relativistic electron flow is propagated along the magnetic field against a low-density cold background plasma, is studied. The time dynamics of the propagation and intensification of waves are analyzed using geometric optics equations. The waves have different wave vector components and start from the cavity center at an altitude of about the Earth’s radius at plasma parameters typical for the auroral zone at this altitude. It is shown that the global inhomogeneity of the Earth’s magnetic field is of key importance in shaping the auroral kilometric radiation spectra.

The mechanisms and research progress of laser fabrication technologies beyond diffraction limit

Laser is recognized as one of the top technological achievements of 20th century and plays an important role in many fields, such as medicine, industry, entertainment and so on. Laser processing technology is one of the earliest and most developed applications of laser. With the rapid development of nanoscience and nanotechnology and micro/nano electronic devices, the micro/nanofabrication technologies become increasingly demanding in manufacturing industries. In order to realize low-cost, large-area and especially high-precision micro-nanofabrication, it has great scientific significance and application value to study and develop the laser fabrication technologies that can break the diffraction limit. In this article, the super resolution laser fabrication technologies are classified into two groups, far-filed laser direct writing technologies and near-field laser fabrication technologies. Firstly, the mechanisms and progress of several far-field laser direct writing technologies beyond the diffraction limit are summarized, which are attributed to the lasermatter nonlinear interaction. The super-diffraction laser ablation was achieved for the temperature-dependent reaction of materials with the Gaussian distribution laser, and the super-diffraction laser-induced oxidation in Metal-Transparent Metallic Oxide grayscale photomasks was realized by the laser-induced Cabrera-Mott oxidation process. Besides, the multi-photon polymerization techniques including degenerate/non-degenerate two-photon polymerization are introduced and the resolution beyond the diffraction limit was achieved based on the third-order nonlinear optical process. Moreover, the latest stimulated emission depletion technique used in the laser super-resolution fabrication is also introduced. Secondly, the mechanisms and recent advances of novel super diffraction near-field laser fabrication technologies based on the evanescent waves or surface plasmon polaritons are recommended. Scanning near-field lithography used a near-field scanning optical microscope coupled with a laser to create nanoscale structures with a resolution beyond 100 nm. Besides, near-field optical lithography beyond the diffraction limit could also be achieved through super resolution near-field structures, such as a bow-tie nanostructure. The interference by the surface plasmon polariton waves could lead to the fabrication of super diffraction interference fringe structures with a period smaller than 100 nm. Moreover, a femtosecond laser beam could also excite and interfere with surface plasmon polaritons to form laser-induced periodic surface structures. Furthermore, the super-resolution superlens and hyperlens imaging lithography are introduced. Evanescent waves could be amplified by using the superlens of metal film to improve the optical lithography resolution beyond the diffraction resolution. The unique anisotropic dispersion of hyperlens could provide the high wave vector component without the resonance relationship, which could also realize the super resolution imaging. Finally, prospective research and development tend of super diffraction laser fabrication technologies are presented. It is necessary to expand the range of materials which can be fabricated by laser beyond the diffraction limit, especially 2D materials.

Generation of auroral kilometric radiation by a finite-size source in a dipole magnetic field

Generation, amplification, and propagation of auroral kilometric radiation in a narrow three-dimensional plasma cavity in which a weakly relativistic electron beam propagates is studied in the geometrical optics approximation. It is shown that the waves that start with a group velocity directed earthward and have optimal relation between the wave vector components determining the linear growth rate and the wave residence time inside the amplification region undergo the largest amplification. Taking into account the longitudinal velocity of fast electrons results in the shift of the instability domain toward wave vectors directed to the Earth and leads to a change in the dispersion relation, due to which favorable conditions are created for the generation of waves with frequencies above the cutoff frequency for the cold background plasma at the wave generation altitude. The amplification factor for these waves is lower than for waves that have the same wave vectors but are excited by the electron beams with lower velocities along the magnetic field. For waves excited at frequencies below the cutoff frequency of the background plasma at the generation altitude, the amplification factor increases with increasing longitudinal electron velocity, because these waves reside for a longer time in the amplification region.

Resonant tunneling of a wave through a structure that contains a layer with a negative refractive index

We have investigated the transmission ability of a layered structure the central layer of which is made of a “left-handed” material (its refractive index is negative) and is separated by two air slabs from a “right-handed” dielectric medium that surrounds the structure. We consider tunneling of energy fluxes through the structure and determine conditions for the complete (reflectionless) transmission of the power of the incident wave through it. We show that this effect is resonant and is observed when the tangential component of the wave vector of the incident wave coincides with the longitudinal wave vector of one of waveguiding eigenmodes of the left-handed layer.

Optical phase conjugation assisted scattering lens: variable focusing and 3D patterning.

Variable light focusing is the ability to flexibly select the focal distance of a lens. This feature presents technical challenges, but is significant for optical interrogation of three-dimensional objects. Numerous lens designs have been proposed to provide flexible light focusing, including zoom, fluid, and liquid-crystal lenses. Although these lenses are useful for macroscale applications, they have limited utility in micron-scale applications due to restricted modulation range and exacting requirements for fabrication and control. Here, we present a holographic focusing method that enables variable light focusing without any physical modification to the lens element. In this method, a scattering layer couples low-angle (transverse wave vector) components into a full angular spectrum, and a digital optical phase conjugation (DOPC) system characterizes and plays back the wavefront that focuses through the scattering layer. We demonstrate micron-scale light focusing and patterning over a wide range of focal distances of 22–51 mm. The interferometric nature of the focusing scheme also enables an aberration-free scattering lens. The proposed method provides a unique variable focusing capability for imaging thick specimens or selective photoactivation of neuronal networks.

Characteristics of acoustic gravity waves obtained from Dynasonde data

AbstractTraveling ionospheric disturbances (TIDs) are ubiquitous in the thermosphere‐ionosphere and are often assumed to be caused by acoustic gravity waves (AGWs). This study performs an analysis of the TID and AGW activity above Wallops Island, VA, during October 2013. The variations in electron density and ionospheric tilts obtained with the Dynasonde technique are used as primary indicators of wave activity. The temporal and spectral characteristics of the data are discussed in detail, using also results of the Whole Atmosphere Model (WAM) and the Global Ionosphere Plasmasphere Model (GIP). The full set of propagation parameters (frequency, and the vertical, zonal and meridional wave vector components) of the TIDs is determined over the 160–220 km height range. A test of the self‐consistency of these results within the confines of the theoretical AGW dispersion relation is devised. This is applied to a sample data set of 24 October 2013. A remarkable agreement has been achieved for wave periods between 52 and 21 min, for which we can rigorously claim the TIDs are caused by underlying acoustic gravity waves. The Wallops Island Dynasonde can operate for extended periods at a 2 min cadence, allowing determination of the statistical distributions of propagation parameters. A dominant population of TIDs is identified in the frequency band below 1 mHz, and for it, the distributions of the horizontal wavelengths, vertical wavelengths, and horizontal phase speeds are obtained.

Transverse characterization of focused Bessel beams with angular momentum applied to study degree of coherence

The transverse focusing properties at the ‘pseudo-focal’ plane of coherent Bessel beams with angular momentum are analyzed in detail. The transverse magnification of the central dark region of Bessel beams at this pseudo-focal plane is derived for the first time by calculating the ratio of the magnitude of the transverse components of the corresponding wave vectors before and after the focusing lens. We test our results experimentally with coherent laser Bessel beams and excellent agreement is observed. Then, an LED light source is used to generate Bessel beams. By modifying the coherence of the LED light source, we observe that by reducing coherence a smaller and shallower central dark region of Bessel beams with angular momentum is produced at the pseudo-focal plane. This technique can be used as a method to characterize the degree of coherence of vortex beams.

Anti-plane shear waves in periodic elastic composites: band structure and anomalous wave refraction

For anti-plane shear waves in periodic elastic composites, it is shown thatnegative energy refraction can be accompanied by positive phase-velocity refractionandpositive energy refraction can be accompanied by negative phase-velocity refraction, and that this can happen over a broad range of frequencies. Hence, in general, negative refraction does not necessarily require antiparallel group and phase-velocity vectors. Details are given for layered composites and the results are extended to, and illustrated for, two-dimensional periodic composites, revealing a wealth of information about the refractive characteristics of this class of composites. The composite's unit cell may consist of any number of constituents of anyvariable mass density and elastic modulus, admitting large discontinuities. A powerful variational-based solution method is used that applies to one-, two- and three-dimensional composites, irrespective of their constituents being homogeneous or heterogeneous. The calculations are direct, accurate and efficient, yielding the band structure, group-velocity, energy-flux and phase-velocity vectors as functions of the frequency and wavevector components, over an entire frequency band.

Probing Vertical and Horizontal Plasmonic Resonant States in the Photoluminescence of Gold Nanodisks

Localized surface plasmon resonance (LSPR) on gold nanoparticles and nanostructures shows its capability to modulate the spontaneous emission rate for photoluminescence. However, beyond the quasi-static limit with oblique incidence conditions, probing a retardation-based plasmonic resonant state excited by the horizontal incident wave-vector component has not been reported yet in the plasmon-mediated photoluminescence of gold nanostructures. In this paper, we investigated the photoluminescence of individual and coupled gold nanodisks with increasing size, and the peaks in the size-dependent photoluminescence spectra are shown to originate from the preferential excitation of vertical (LSPR) and horizontal (retardation-based) plasmonic resonant states. We have also proposed a three-step model to well describe the contribution of vertical and horizontal plasmonic resonant states in the photoluminescence of gold nanodisks. Our study makes a new contribution to the understanding of photoluminescence from gold nanostructures, and it paves the way toward the applications of plasmon-mediated luminescence and biological studies.

Refraction characteristics of phononic crystals

Some of the most interesting refraction properties of phononic crystals are revealed by examining the anti-plane shear waves in doubly periodic elastic composites with unit cells containing rectangular and/or elliptical multi-inclusions. The corresponding band structure, group velocity, and energy–flux vector are calculated using a powerful mixed variational method that accurately and efficiently yields all the field quantities over multiple frequency pass-bands. The background matrix and the inclusions can be anisotropic, each having distinct elastic moduli and mass densities. Equifrequency contours and energy–flux vectors are readily calculated as functions of the wave-vector components. By superimposing the energy–flux vectors on equifrequency contours in the plane of the wave-vector components, and supplementing this with a three-dimensional graph of the corresponding frequency surface, a wealth of information is extracted essentially at a glance. This way it is shown that a composite with even a simple square unit cell containing a central circular inclusion can display negative or positive energy and phase velocity refractions, or simply performs a harmonic vibration (standing wave), depending on the frequency and the wave-vector. Moreover, that the same composite when interfaced with a suitable homogeneous solid can display: (1) negative refraction with negative phase velocity refraction; (2) negative refraction with positive phase velocity refraction; (3) positive refraction with negative phase velocity refraction; (4) positive refraction with positive phase velocity refraction; or even (5) complete reflection with no energy transmission, depending on the frequency, and direction and the wavelength of the plane-wave that is incident from the homogeneous solid to the interface. For elliptical and rectangular inclusion geometries, analytical expressions are given for the key calculation quantities. Expressions for displacement, velocity, linear momentum, strain, and stress components, as well as the energy–flux and group velocity components are given in series form. The general results are illustrated for rectangular unit cells, one with two and the other with four inclusions, although any number of inclusions can be considered. The energy–flux and the accompanying phase velocity refractions at an interface with a homogeneous solid are demonstrated. Finally, by comparing the results of the present solution method with those obtained using the Rayleigh quotient and, for the layered case, with the exact solutions, the remarkable accuracy and the convergence rate of the present solution method are demonstrated. Anomalous refractive characteristics of phononic crystals are revealed using anti-plane shear waves in doubly periodic elastic composites. It is shown that negative or positive refraction can be accompanied by negative or positive phase velocity refraction, and/or the crystal can have complete refraction with no energy transmission, all depending on the wavelength and frequency of the plane wave that is incident from a homogeneous solid to its interface with the composite. A powerful computational tool is proposed which applies to one-, two-, three-dimensional phononic crystals yielding results with great accuracy.

Influence of Ti doping on the incommensurate charge density wave in1T−TaS2

We report temperature-dependent transport and x-ray diffraction measurements of the influence of Ti hole doping on the charge density wave (CDW) in $1T\text{\ensuremath{-}}{\mathrm{Ta}}_{1\ensuremath{-}x}{\mathrm{Ti}}_{x}{\mathrm{S}}_{2}$. Confirming past studies, we find that even trace impurities eliminate the low-temperature commensurate (C) phase in this system. Surprisingly, the magnitude of the in-plane component of the CDW wave vector in the nearly commensurate (NC) phase does not change significantly with Ti concentration, as might be expected from a changing Fermi surface volume. Instead, the angle of the CDW in the basal plane rotates, from $11.9{}^{\ensuremath{\circ}}$ at $x=0$ to $16.4{}^{\ensuremath{\circ}}$ at $x=0.12$. Ti substitution also leads to an extended region of coexistence between incommensurate (IC) and NC phases, indicating heterogeneous nucleation near the transition. Finally, we explain a resistive anomaly originally observed by Di Salvo [F. J. Di Salvo et al., Phys. Rev. B 12, 2220 (1975)] as arising from pinning of the CDW on the crystal lattice. Our study highlights the importance of commensuration effects in the NC phase, particularly at $x\ensuremath{\sim}0.08$.

Piezoelectric scattering limited mobility as controlled by the transverse component of the phonon wave vector in quantum layers at low temperatures

Theory of the momentum relaxation time of the carriers and of their ohmic mobility in a quantum well in a non-degenerate compound semiconductor has been developed for interaction with piezoelectric phonons at low temperatures. The calculations have been made without taking recourse either to the Kawaji's traditional model of interaction with only the in-plane component of the phonon wave vector or to the equipartition approximation for the phonon population. The numerical results obtained for inversion layers in GaAs and CdS describe how significantly does the consideration of the transverse component of the phonon wave vector in the light of the Ridley's momentum conservation approximation or of the true phonon distribution bring in significant changes in the transport characteristics compared to what the traditional approximations predict.

Studies of the influence of deep subwavelength surface roughness on fields of plasmonic thin film based on Lippmann–Schwinger equation in the spectral domain

In this paper, we consider a line source over a plasmonic thin film with surface roughness. Using layered medium Green’s functions, we derive the Lippmann–Schwinger equation in the spectral domain with scattering potentials for the case of surface roughness over a layered medium. Because of deep subwavelength surface roughness, the scattering potentials are next approximated by the small potential approximation, so that the solutions of fields in the spectral domain can be readily computed. Numerical results are illustrated for the surface fields on the rough surface and the fields in the image plane. For periodic roughness, small periods, on the order of 0.1λ, and small heights, on the order of 0.01λ, are used. For the case of random roughness, we choose the correlation length to be much smaller than a wavelength, on the order of 0.1λ, and height on the order of 0.01λ. The results of the fields on the rough surface in the spectral domain show that subwavelength roughness creates fields with wave vector components that are many times larger than the free-space wavenumber (∼10k0 or larger). In the spatial domain, the imaging is enhanced by the deep subwavelength roughness. Results of the small roughness approximation are in good agreement with that of exact potential and that of the method of moments.

Optical Phonon Modes and Electron-optical Phonon Interaction in Core-shell Semiconductor Quantum Wires

Within the framework of the macroscopic dielectric continuum model the longitudinal optical (LO) phonon modes are derived for a cylindrical semiconductor quantum wire made of semiconductor 1 (well material) embedded in another finite semiconductor 2 (barrier material). The phonon states of modes are given by solving the generalized Born-Huang equation. It is shown that there may exist four types of longitudinal optical phonon modes according to the concrete materials forming the wire. The dispersion equations for phonon frequencies with wave-vector components parallel to the wire are obtained. After having quantized the phonon field we derive the Fröhlich Hamiltonian describing the electron--LO-phonon interaction. The influence of the thickness of the barrier layer as well as the thin metallic shell on the phonon frequencies and their interaction with electrons is studied.

A Dispersive Nonlocal Model for In-Plane Wave Propagation in Laminated Composites With Periodic Structures

In this paper, the problem of in-plane wave propagation with oblique incidence of the wave in an isotropic bilaminated composite under perfect contact between the layers and periodic distribution between them is studied. Based on an asymptotic dispersive method for the description of the dynamic processes, the dispersion equations were derived analytically from the average model. Numerical examples show that the dispersion curves obtained from the present model agree with the exact solutions for a range of wavelengths. Detailed numerical simulations are provided to illustrate graphically the phase and group velocities. Such illustrations allow the identification and comparison of the effects of the unit cell size, wave number and incident angle. It was observed that, as the incident angle increases, the dimensionless quasi-longitudinal phase velocity increases, and the dimensionless quasi-shear phase velocity decreases. In addition, the phase and group velocities decrease as the size of the unit cell increases. The frequency band structure, as a function of the wave-vector components is calculated.

Experimental solution for scattered imaging of the interference of plasmonic and photonic mode waves launched by metal nano-slits.

Using an L-shaped metal nanoslit to generate waves of the pure photonic and plasmonic modes simultaneously, we perform an experimental solution for the scattered imaging of the interference of the two waves. From the fringe data of interference, the amplitudes and the wavevector components of the two waves are obtained. The initial phases of the two waves are obtained from the phase map reconstructed with the interference of the scattered image and the reference wave in the interferometer. The difference in the wavevector components gives rise to an additional phase delay. We introduce the scattering theory under Kirchhoff's approximation to metal slit regime and explain the wavevector difference reasonably. The solution of the quantities is a comprehensive reflection of excitation, scattering and interference of the two waves. By decomposing the polarized incident field with respect to the slit element, the scattered image produced by slit of arbitrary shape can be solved with the nanoscale Huygens-Fresnel principle. This is demonstrated by the experimental intensity pattern and phase map produced by a ring-slit and its consistency with the calculated results.

Surface plasmon polaritons at the interface between dielectric and anisotropic nanocomposite

Specific features of surface-wave propagation along the interface between an isotropic dielectric and an anisotropic nanocomposite containing ellipsoidal metal inclusions whose axes of rotation are perpendicular to the interface between the media have been studied. Frequency dependences of the propagation constant and wave-vector transverse components, of the penetration depths and propagation lengths in each of the media, and of the longitudinal and transverse energy fluxes have been obtained. The effect of the shape of the inclusions on the wave and energy characteristics of the surface waves is shown.

Scattering of Plasma Anisotropic Spherical Particle Incident by a High-order Bessel Beam

The analytical theory for the electromagnetic (EM) scattering of plasma anisotropic sphere illuminated by a high-order Bessel beam (HOBB) is investigated in this paper. The HOBB is presented using vector wave theory in which electric and magnetic field vectors satisfy Maxwell's equations. The fields inside the plasma sphere are expressed using eigenfunctions in spectral domain. Combing with the tangential continuous boundary condition at the surface of the sphere, the scattering coefficients are derived. The influence of plasma dielectric material, the spherical size and wave vector components of the beam on the radar cross section (RCS) are numerically analyzed which shows that the scattered field still has a peak at forward and backward direction, whereas for the higher order HOBB, the minimum appear at the forward and backward direction.