Explicit TE/TM scheme for particle beam simulations

In this paper we propose an explicit two-level conservative scheme based on a TE/TM like splitting of the field components in time. Its dispersion properties are adjusted to accelerator problems. It is simpler and faster than the implicit version [I. Zagorodnov, T. Weiland, TE/TM scheme for computation of electromagnetic fields in accelerators, J. Comput. Phys. 207 (2005) 69]. It does not have dispersion in the longitudinal direction and the dispersion properties in the transverse plane are improved. The explicit character of the new scheme allows a uniformly stable conformal method without iterations and the scheme can be parallelized easily. It assures energy and charge conservation. A version of this explicit scheme for rotationally symmetric structures is free from the progressive time step reducing for higher order azimuthal modes as it takes place for Yee’s explicit method used in the most popular electrodynamics codes.     

Azimuthal behaviour of flow-excited diametral modes of internal shallow cavities

The aerodynamic excitation of ducted cavity diametral modes gives rise to complex flow-sound interaction mechanisms, in which the axisymmetric free shear layer interacts with the asymmetric acoustic modes. This results in various azimuthal patterns and behaviours depending on different flow and geometrical parameters. The azimuthal behaviour of this self-excitation mechanism is investigated experimentally. Axisymmetric shallow cavities in a duct have been tested over the range of cavity length to depth ratio from 1 to 6 and at Mach numbers up to 0.4. A set of pressure transducers flush mounted to the cavity floor is used to determine the acoustic mode amplitude and orientation. The excited acoustic modes are classified into spinning, partially spinning, and stationary diametral modes. An analytical representation based on the duct acoustics theory is used to analyse the measurements and provides a physical explanation of the observed behaviour of the diametral modes. Splitter plates are installed inside the cavity to form a geometrical preference. The acoustic response of this geometrically altered case show that pressure oscillations at different azimuthal angles along the cavity circumference can be uncorrelated, or even oscillate at different frequencies, while the diametral modes are still strongly excited. Two hot-wire probes are also used in a separate set of measurements to investigate the azimuthal behaviour of the shear layer oscillation. The results show that the shear layer oscillation has the same azimuthal distribution as that of the excited acoustic modes, indicating that the shear layer oscillation at different azimuthal angles can be not only uncorrelated but also occur at different frequencies.     

Intra-cavity generation of superpositions of Laguerre–Gaussian beams

In this paper we demonstrate experimentally the intra-cavity generation of a coherent superposition of Laguerre–Gaussian modes of zero radial order but opposite azimuthal order. The superposition is created with a simple intra-cavity stop that creates equal losses for the two azimuthal modes, and we show that by adjustment of the stop we can produce modes up to azimuthal order 8. The fact that we have a coherent superposition rather than an incoherent superposition is verified by intensity measurements, propagation measurements and a decomposition of the field by an inner product executed on a phase-only spatial light modulator. Such fields have relevance in quantum information and optical trapping.     

Vector erf-Gaussian beams: fractional optical vortices and asymmetric TE and TM modes

We have considered the paraxial vector erf-Gaussian beams with field distribution in the form of the error function that are shaped by the cone of plane waves with a fractional step of the azimuthal phase distribution modulated by the Gaussian envelope. We have revealed that the initial distributions of the transverse electric and transverse magnetic fields have a far from standard form but at the far diffraction field the field distributions recover nearly the symmetric form.     

Micromagnetic dissipation, dispersion, and mode conversion in thin permalloy platelets

Micron-sized ferromagnetic Permalloy disks exhibiting an in-plane ferromagnetic vortex structure are excited by a fast rise time perpendicular magnetic field pulse and their modal structure is analyzed. We find azimuthal and axial modes. By a Fourier filtering technique we can separate and analyze the time dependence of individual modes. Analysis of the experimental data demonstrates that the azimuthal modes damp more quickly than the axial modes. We interpret these results as mode conversion from low-frequency azimuthal modes to the fundamental mode which is higher in frequency, i.e., mode-mode coupling in a system with a single Landau-Lifshitz-Gilbert phenomenological damping constant alpha.     

Characteristics of self-excited spinning azimuthal modes in an annular combustor with turbulent premixed bluff-body flames

In this paper we investigate self-excited azimuthal modes in an annular combustor with turbulent premixed bluff-body stabilised flames. Previous studies have shown that both swirl and equivalence ratio influence modal dynamics, i.e. the time-varying nature of the modes. However, self-excited azimuthal modes have not yet been investigated in turbulent flames without bulk swirl, which do not generate any preferential flow in either azimuthal direction, and may therefore lead to different behaviour. Joint probability density functions of the instability amplitudes at various flowrates and equivalence ratios showed a strong bi-modal response favouring both ACW and CW spinning states not previously observed. Operating conditions leading to a bi-modal response provide a unique opportunity to investigate whether the structure of the global fluctuating heat release rate of self-excited spinning modes in both directions exhibit similar dynamics and structure. This was investigated using high-speed OH* chemiluminescence images of the annular combustor and a new rotational averaging method was applied which decomposes the spinning components of the global fluctuating heat release rate. The new rotational averaging, which differs from standard phase-averaging, produces spatial averages in a frame of reference moving with the spinning wave. The results show that the structure of the fluctuating heat release rate for spinning modes is highly asymmetric as characterised by large, crescent shaped regions of high OH* intensity, located on the far side of each flame, relative to the direction of the azimuthally propagating pressure wave. In comparison with interacting swirling flames, these results indicate that the previously observed radial asymmetry of OH* fluctuations may be introduced through advection by local swirl.     

Dynamics of Magnetic Skyrmions in Nanodots

Bloch and Neel magnetic skyrmions have been studied in systems of confined geometry (nanodots, a linear array of nanodots). The spectra of low- and high-frequency excitation modes of a skyrmion state have been calculated. It has been shown that skyrmion spectrum asymmetry, namely, the characteristic difference between the frequencies of the azimuthal modes of the azimuthal skyrmion modes rotating clockwise and counterclockwise, is associated with asymmetry in the magnetization profiles of high-frequency spin waves propagating on the background of a skyrmion state in a nanodot. The low-frequency spectrum contains the only gyrotropic mode localized near the center of a nanodot. The gyrotropic frequency depends on the material parameters of a nanodot and the size of a skyrmion. The eigenfrequency of the gyrotropic mode of an isolated skyrmion in a nanodot in ultrathin films (L ~ 1 nm) does not depend on the internal structure of a skyrmion and is the same for Bloch and Neel skyrmions. The interaction of skyrmions, in particular, in a linear chain of nanodots with the ground skyrmion state, leads to distinctions in low-frequency spectra. The structure of a skyrmion (of Bloch or Neel type) is exhibited as a shift of dispersion curves and a difference between the frequencies of ferromagnetic resonance in a system of interacting skyrmions.     

Transverse electric (TE) and transverse magnetic (TM) X-ray guided modes in a two-layer crystalline heterostructure: A comparison

Polarization effects upon Bragg-case hard X-ray dynamical diffraction in a two-layer crystalline heterostructure waveguide have been investigated with the help of numerical modeling. A difference is shown to exist in both intensities and excitation conditions between TE (transverse electric) and TM (transverse magnetic) X-ray guided modes that are inherent to the waveguide. A comparison of σ- and π-polarized X-ray reflectivity curves from such a waveguide is performed. Possibilities for the experimental excitation of the TE and TM X-ray guided modes are discussed.     

Quasioptical dielectric resonators in millimeter-wave band experiments

New results of theoretical and experimental investigations of non-uniform dielectric resonators with the higher order azimuthal waves (whispering gallery modes) have been presented. Their application for study of various materials (dielectric, high-T_c superconductor) and for generation obtaining of millimeter wave oscillations has been considered.     

Vibration Spectrums of Polar Interface Optical Phonons in GaAs/AlAs Cylindrical Quantum Dots

The dispersions of the top interface optical phonons and the side interface optical phonons in cylindrical quantum dots are solved by using the dielectric continuum model. Our calculation mainly focuses on the frequency dependence of the IO phonon modes on the wave-vector and quantum number in the cylindrical quantum dot system. Results reveal that the frequency of top interface optical phonon sensitively depends on the discrete wave-vector in z direction and the azimuthal quantum number, while that of the side interface optical phonon mode depends on the radial and azimuthal quantum numbers. These features are obviously different from those in quantum well, quantum well wire, and spherical quantum dot systems. The limited frequencies of interface optical modes for the large wave-vector or quantum number approach two certain constant values, and the math and physical reasons for this feature have been explained reasonably.     

椭圆纳米盘中磁涡旋结构的方位角自旋波模式

本文针对坡莫合金椭圆形盘中的磁涡旋结构, 采用微磁学模拟与傅里叶分析相结合的技术研究了磁涡旋自旋波的本征激发模式. 通过沿样品短轴方向施加一面内方向的脉冲磁场, 观察到一系列方位角自旋波模式. 观察到的自旋波模式具有两重对称性, 可以通过C₂群理论来进行类型的划分. 此外, 自旋波模式的频率随着方位角指标的变化而线性增加. 模拟结果显示样品的平均交换能量密度明显的高于平均静磁能量密度; 局域交换能量密度主要集中在涡核初始位置, 而局域静磁能量密度主要分布在长轴附近. 交换作用对受限于铁磁薄膜椭圆盘中的单个涡旋态的能量要起主导作用, 从而导致方位角自旋波模式频率随着方位角指标的增加而增加.     

Are Coaxial Super Power Gyrotrons Feasible?

Limits on the power generated by coaxial gyrotrons are investigated. It is shown that among all the operating modes suggested recently for coaxial super power gyrotrons only modes with azimuthal index m lower than about 44 pass the spatial stochasticity test. Modes with higher azimuthal indices cannot be used as operating modes because gyrotron oscillations become chaotic in the azimuthal direction and efficiency is very low. It is argued that there exists a natural upper limit on power generated by gyrotrons which is about 4 MW.     

Stimulated Raman backward scattering of a laser beam in a magnetized plasma

Stimulated Raman scattering of a laser beam is investigated in the plasma with strong self generated magnetic field. The magnetized plasma supports various localized radial and azimuthal modes of lower hybrid frequencies. The density fluctuations due to lower hybrid modes couple with the oscillating velocity due to the pump, and drive the scattered wave. Equations describing the Raman process are derived and effects of various modes are studied on the growth rate analytically. Self generated magnetic field has a strong localization effect on the Raman process and growth rate is maximum for radial eigen mode number q = 0 and azimuthal eigen mode number l = 3. The frequency shift has signatures of self generated magnetic field and could serve as a diagnostic.     

The separation of TM and TE wave in multi-layer metamaterial structure

A mixed-structure form of one-dimensional metamaterial structure composed of single negative permittivity material and anisotropic metamaterial has been investigated in this paper. Such a multi-layer metamaterial structure constitutes special resonant structures, which can be used to control wave propagation and realize the complete separation of TM and TE wave by choosing specific parameters. Theoretical analysis and numerical calculations have been performed to confirm the above results. Specifically, augments in incident angles of TM and TE waves make complete transmission frequencies right shift, and the thicknesses of this resonant structure determine propagation modes and propagation frequencies.     

Full-field quantum correlations of spatially entangled photons

Spatially entangled twin photons allow the study of high-dimensional entanglement, and the Laguerre-Gauss modes are the most commonly used basis to discretize the single-photon mode spaces. In this basis, to date only the azimuthal degree of freedom has been investigated experimentally due to its fundamental and experimental simplicity. We show that the full spatial entanglement is indeed accessible experimentally; i.e., we have found practicable radial detection modes with negligible cross correlations. This allows us to demonstrate hybrid azimuthal-radial quantum correlations in a Hilbert space with more than 100 dimensions per photon.     

Using large eddy simulation to explore sound-source mechanisms in jets

This paper presents an analysis of data generated by means of large eddy simulation for a single-stream, isothermal Mach 0.9 jet. The acoustic field is decomposed into Fourier modes in the azimuthal direction, and filtered by means of a continuous wavelet transform in the temporal direction. This allows the identification of temporally localised, high-amplitude events in the radiated sound field for each of the azimuthal modes. Once these events have been localised, the flow field is analysed so as to determine their cause. Results show high-amplitude, intermittent sound radiation for azimuthal modes 0 and 1. The mode-0 radiation, which dominates low-angle emission, is found to result from the temporal modulation of a basic axisymmetric wave-packet structure within the flow. Similar intermittent activity, observed, again within the flow, for azimuthal mode 1 suggests a link between the modes 0 and 1 dynamics. Both the amplitude and spatial extent of the axisymmetric wave-packet are modulated, and the strongest axisymmetric propagative disturbances are found to radiate from the downstream end of the wave-packet at moments when the wave envelope becomes truncated. The observed behaviour is modelled using a line-source wave-packet ansatz which includes parameters that account for the said modulation. Inclusion of these parameters, which allow the wave-packet to “jitter” in a manner similar to that observed, leads to good quantitative agreement (accurate to within 1.5 dB), at low emission angles, with the acoustic field of the LES. This result is in contrast with results obtained using a time-averaged wave-packet (one which does not jitter), for which a 12 dB error is observed. This result shows that the said modulations are the salient source feature for the low-angle sound emission of the jet considered. Analysis of a longer time series shows the occurrence of several similar high-amplitude bursts in the axisymmetric mode of the acoustic pressure, and a calculation of the radiated sound for this longer time-series, again using the wave-packet ansatz, once again leads to good agreement with the LES (now accurate to within 1 dB).     

Interactions of spin waves with a magnetic vortex

We have investigated azimuthal spin-wave modes in magnetic vortex structures using time-resolved Kerr microscopy. Spatially resolved phase and amplitude spectra of ferromagnetic disks with diameters from 5 microm down to 500 nm reveal that the lowest order azimuthal spin-wave mode splits into a doublet as the disk size decreases. We demonstrate that the splitting is due to the coupling between spin waves and the gyrotropic motion of the vortex core.     

Atmospheric turbulence and orbital angular momentum of single photons for optical communication

The effects of propagation through random aberrations on coherence for single-photon communication systems based on orbital angular momentum states are quantified. A rotational coherence function is derived which leads to scattering equations for azimuthal modes of different orbital angular momentum states. The effect on a single-photon communication system is quantified using the channel capacity. The work shows that the decoherence effect of atmospheric turbulence on such systems is important even for weak turbulence.     

Electrocapillary instability of a conducting liquid cylinder

The electrocapillary instability of a conducting liquid cylinder is analyzed. Exact solutions to the linearized Navier-Stokes equations are examined. Growth rates are found for several unstable modes, including both axisymmetric and nonaxisymmetric ones. Special attention is given to the electric field effects on the temporal growth and length scales of unstable modes. It is shown that, whereas capillary instability is axisymmetric in the absence of electric field, nonaxisymmetric surface modes also become unstable in a nonzero electric field, growing with time. With increasing electric field strength, azimuthal modes are “switched on” (begin to grow with time) sequentially and the highest temporal growth rate monotonically increases.     

Controlled observation of nondegenerate cavity modes in a microdroplet on a superhydrophobic surface

We demonstrate controlled lifting of the azimuthal degeneracy of the whispering gallery modes (WGMs) of single glycerol-water microdroplets standing on a superhydrophobic surface by using a uniform electric field. A good agreement is observed between the measured spectral positions of the nondegenerate WGMs and predictions made for a prolate spheroid. Our results reveal fewer azimuthal modes than expected from an ideal spherical microdroplet due to the truncation by the surface. We use this difference to estimate the contact angles of the microdroplets.