Pure Radial Modes Research Articles

Radial spectrum spread of Laguerre-Gaussian beam transmission in weak compressible turbulence

Turbulence effects can seriously affect the propagation of structured light, especially for orbital angular momentum (OAM) modes, causing spread and crosstalk. We derive an analytical solution to the mode spectrum of a Laguerre-Gaussian beam (LGB) propagating in weak compressible turbulence. The influence of the radial number and turbulence strength in the mode spectrum on the probability of LGB propagation is mainly considered. The results show that the weak compressible turbulence interferes strongly with the LGB, and this effect is mainly reflected in the sharp drop of the signal mode energy at short transmission distance. We find that the pure radial mode has a higher signal mode energy than the pure OAM mode, which means that the pure radial mode is more resilient to compressible turbulence than the pure OAM mode. In addition, the increase of radial number can improve the performance of the OAM dimension, but on the other hand, it reduces the probability of the radial dimension. Finally, we discussed the propagation properties of higher-order modes. Our research clarifies the interaction of OAM mode and radial mode in turbulence, and provides a theoretical basis for applications based on radial modes in the field of free-space communication.

Laguerre-Gaussian beam and plasma interaction under relativistic and ponderomotive nonlinearities

Self-focusing of the laser plays a decisive role in achieving higher intensity. This article investigates the beam width evolution of the Laguerre-Gaussian laser beam in an underdense, cold, and collisionless plasma in the presence of weakly relativistic and ponderomotive nonlinearities. We consider pure radial mode of the LG beam (LG10) as it plays a key role in phenomenon like higher harmonic generation and can dominate diffraction effect in the self-focusing. Wentzel–Kramers–Brillouin (WKB) approach under paraxial approximation is used to reduce the nonlinear wave equation to a differential equation for the beam width parameter to study the self-focusing and defocusing phenomena. The optimum values of the initial intensity and beam waist of the laser beam are then calculated and plotted, for which the diffraction divergence is cancelled out by the self-focusing.

Arbitrary polarization conversion for pure vortex generation with a single metasurface

AbstractThe purity of an optical vortex beam depends on the spread of its energy among different azimuthal and radial modes, also known as $\ell $- and p-modes. The smaller the spread, the higher the vortex purity and more efficient its creation and detection. There are several methods to generate vortex beams with well-defined orbital angular momentum, but only few exist allowing selection of a pure radial mode. These typically consist of many optical elements with rather complex arrangements, including active cavity resonators. Here, we show that it is possible to generate pure vortex beams using a single metasurface plate—called p-plate as it controls radial modes—in combination with a polarizer. We generalize an existing theory of independent phase and amplitude control with birefringent nanopillars considering arbitrary input polarization states. The high purity, sizeable creation efficiency, and impassable compactness make the presented approach a powerful complex amplitude modulation tool for pure vortex generation, even in the case of large topological charges.

In-duct identification of fluid-borne source with high spatial resolution

Source identification of acoustic characteristics of in-duct fluid machinery is required for coping with the fluid-borne noise. By knowing the acoustic pressure and particle velocity field at the source plane in detail, the sound generation mechanism of a fluid machine can be understood. The identified spatial distribution of the strength of major radiators would be useful for the low noise design. Conventional methods for measuring the source in a wide duct have not been very helpful in investigating the source properties in detail because their spatial resolution is improper for the design purpose. In this work, an inverse method to estimate the source parameters with a high spatial resolution is studied. The theoretical formulation including the evanescent modes and near-field measurement data is given for a wide duct. After validating the proposed method to a duct excited by an acoustic driver, an experiment on a duct system driven by an air blower is conducted in the presence of flow. A convergence test for the evanescent modes is performed to find the necessary number of modes to regenerate the measured pressure field precisely. By using the converged modal amplitudes, very-close near-field pressure to the source is regenerated and compared with the measured pressure, and the maximum error was −16.3dB. The source parameters are restored from the converged modal amplitudes. Then, the distribution of source parameters on the driver and the blower is clearly revealed with a high spatial resolution for kR<1.84 in which range only plane waves can propagate to far field in a duct. Measurement using a flush mounted sensor array is discussed, and the removal of pure radial modes in the modeling is suggested.

Identification of the Sectional Distribution of Sound Source in a Wide Duct

덕트 내 음원 면에서의 음압과 입자 속도분포를 상세히 알 수 있다면, 주된 소음원들의 위치와 강도를 분석하여 전파특성을 잘 이해할 수 있고, 이에 따라 저소음화 설계에 유용한 정보로 활용가능하다. 이를 위한 기존의 방법들은 대개 단면상 위치와 무관한 일정 변수로 나타내는 제한점이 있다. 본 논문에서는 음원의 단면 분포를 높은 공간분해능으로 관찰할 수 있는 방법에 대해 연구하였다. 모드 합성법을 기반으로 감쇠파의 영향과 근접장 측정을 포함하는 행렬식을 유도하였으며, 컴프레션 드라이버에 의해 일부 단면이 가진된 유동이 없는 덕트 시스템에서 검증하였다. 감쇠파모드 개수의 증가에 따라 음압 스펙트럼을 더욱 정확하게 근사화 할 수 있었으며, 26개의 감쇠파 모드를 포함한 수렴 결과로부터 관심 헬름홀쯔 수 영역에서 -25 dB 이하의 오차로 예측할 수 있었다. 수렴된 모드 진폭들을 이용하여 kR = 1에서 음원 면에서의 음원변수 분포를 관찰한 결과, 실제 음원이 설치된 국소 위치에서 높은 음압과 입자 속도 값을 분명히 나타내는 것을 보였다. 또한, 감쇠 모드의 역추산시에 정규화기법을 도입하여, 과결정된 반경방향 모드에 의해 발생된 무의미한 피크들을 효과적으로 제거할 수 있었다. If one identifies the detailed distribution of pressure and axial velocity at a source plane, the position and strength of major noise sources can be known, and the propagation characteristics in axial direction can be well understood to be used for the low noise design. Conventional techniques are usually limited in considering the constant source characteristics specified on the whole source surface; then, the source activity cannot be known in detail. In this work, a method to estimate the pressure and velocity field distribution on the source surface with high spatial resolution is studied. The matrix formulation including the evanescent modes is given, and the nearfield measurement method is proposed. Validation experiment is conducted on a wide duct system, at which a part of the source plane is excited by an acoustic driver in the absence of airflow. Increasing the number of evanescent modes, the prediction of pressure spectrum becomes further precise, and it has less than -25 dB error with 26 converged evanescent modes within the Helmholtz number range of interest. By using the converged modal amplitudes, the source parameter distribution is restored, and the position of the driver is clearly identified at kR = 1. By applying the regularization technique to the restored result, the unphysical minor peaks at the source plane can be effectively suppressed with the filtering of the over-estimated pure radial modes.

Modal dependence of dissipation in silicon nitride drum resonators

We have fabricated large (≤400 μm diameter) high tensile stress SiN membrane mechanical resonators and measured the resonant frequency and quality factors (Q) of different modes of oscillation using optical interferometric detection. We observe that the dissipation (Q−1) is limited by clamping loss for pure radial modes, but higher order azimuthal modes are limited by a mechanism which appears to be intrinsic to the material. The observed dissipation is strongly dependent on size of the membrane and mode type. Appropriate choice of size and operating mode allows the selection of optimum resonator designs for applications in mass sensing and optomechanical experiments.

Structure of the breathing mode of the nucleon from high-energyp−pscattering

Spectra of $p\text{\ensuremath{-}}p$ and $\ensuremath{\pi}\text{\ensuremath{-}}p$ scattering at beam momenta between 6 and 30 GeV/c have been reanalyzed. These show strong excitation of ${N}^{*}$ resonances, the strongest one corresponding to the ``scalar'' ${P}_{11}$ excitation (breathing mode) at ${m}_{0}=1400\ifmmode\pm\else\textpm\fi{}10\phantom{\rule{0.3em}{0ex}}\text{MeV}$ with $\ensuremath{\Gamma}=200\ifmmode\pm\else\textpm\fi{}20\phantom{\rule{0.3em}{0ex}}\text{MeV}$. The result of a strong scalar excitation is supported by a large longitudinal amplitude ${S}_{1/2}$ extracted from $e\text{\ensuremath{-}}p$ scattering. From exclusive data on $p+p\ensuremath{\rightarrow}\mathit{pp}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, a large $2\ensuremath{\pi}\text{\ensuremath{-}}N$ decay branch for the ${P}_{11}$ resonance of ${B}_{2\ensuremath{\pi}}=75\ifmmode\pm\else\textpm\fi{}20$% has been extracted.The differential cross sections were described in a double-folding approach, assuming multigluon exchange as the dominant part of the effective interaction between the constituents of projectile and target. First, the parameters of the interaction were fitted to elastic scattering; then, with this interaction, the inelastic cross sections were described in the distorted wave Born approximation (DWBA). A good description of the data requires a surface peaked transition density, quite different from that of a pure radial mode. In contrast, the electron scattering amplitude ${S}_{1/2}$ is quite well described by a breathing mode transition density with radial node. This large difference between charge and matter transition densities suggests that in $p\text{\ensuremath{-}}p$ scattering the coupling to the multigluon field is much more important than the coupling to the valence quarks. A multigluon (or sea-quark) transition density is derived, which also shows breathing, indicating a rather complex multiquark structure of N and ${N}^{*}$ including additional multigluon (or ${q}^{2n}{\overline{q}}^{2n}$) creation out of the ground state vacuum.

A Vibrational Mode Analysis of Free Finite-Length Thick Cylinders Using the Finite Element Method

Based on their three-dimensional mode shapes, the vibrational modes of free finite length thick cylinders can be classified into 6 categories, consisting of pure radial, radial motion with radial shearing, extensional, circumferential, axial bending, and global modes. This classification, together with the numbers of both the circumferential and the longitudinal nodes, is sufficient to identify each mode of a finite length thick cylinder. The mode classification was verified experimentally by measurements on a thick cylinder. According to the displacement distribution ratio in the radial, tangential and longitudinal directions, the effect of varying cylinder length on the vibrational modes is such that all the modes can be broadly categorized as either pure radial modes, or non pure radial modes. The natural frequencies and mode shapes of the former are dependent upon only the radial dimensions of the models, while the natural frequencies and mode shapes of the latter are dependent upon both the axial length and radial thickness.

A New Pulsation Spectrum and Asteroseismology of delta Scuti.

We present the results of a five-year Str{umlt o}mgren y photometric campaign on {delta} Scuti. Our data set consists of 6515 discrete differential magnitudes, and spans the period of 1983 June to 1988 September. We found the primary pulsation mode at 59.731129{plus_minus}0.000002 {mu}Hz, in close agreement with the frequency determination of Fitch (1976, IAU Colloquium, 29, 167), but we find our best-fit observed frequencies for other pulsation modes differ by 0.5{endash}2 cycles per year from Fitch{close_quote}s results. In the case of the second strongest pulsation mode, we found a frequency of 61.936104{plus_minus}0.000009 {mu}Hz{emdash}one cycle per year off of the commonly quoted frequency. All of the other modes not classified as harmonics or beating modes were identified in our data, as well as a new pulsation frequency at 96.21443{plus_minus}0.00005 {mu}Hz discovered in both Str{umlt o}mgren y and b observations. We measured the phase differences between our Str{umlt o}mgren y data and a short string of Str{umlt o}mgren b data taken during the 1987 multisite campaign, and find phase differences ranging from 0 to 0.33 radians, suggesting that there are modes of different spherical harmonic order present in {delta} Scuti. Finally, we evolved a set of M=1.8{endash}2.4 M{sub {circle_dot}} models with solarmore » abundances (X=0.7,Z=0.02) and two (M=2.2 and M=2.4 M{sub {circle_dot}}) models with solar abundances scaled to (X=0.66,Z=0.06), using recent opacity and reaction rate data, and applied linear, nonadiabatic pulsation analysis to models in the shell hydrogen burning phase. The Z=0.02 model which best fit the observed spectral type of F2III, the {ital Hipparcos} absolute magnitude of M{sub V}=1.0, and the radius estimate of Cugier and Monier of R=4.1 R{sub {circle_dot}}, and which has a pure radial mode at 59.731 {mu}Hz has a mass of 2.1 M{sub {circle_dot}}, with T{sub eff}=6894 K, R=4.14 R{sub {circle_dot}}, and M{sub V}=1.0. (Abstract Truncated)« less

EFFECTS OF LAMINATIONS ON THE VIBRATIONAL BEHAVIOUR OF ELECTRICAL MACHINE STATORS

An electrical machine stator is a laminated thick cylinder. For simplicity, a homogeneous thick cylinder has often been used as a model of a stator for the purposes of vibrational analysis. Experiments show that the vibrational behaviour of a stator is quite different from that of an homogeneous thick cylinder. Among all of the vibrational modes, predicted by using the homogeneous cylinder model, only a few of them are the modes of a realistic stator, and most of the predicted modes are ones which cannot be traced experimentally. In this paper, based on the analytical results for the vibrations of solid annular plates, and the experimental results for the vibrations of laminated annular plates under a range of clamping pressures, it is found that the vibrational behaviour of a laminated thick cylinder is dominated by that of an individual cylinder lamination. Laminations have significant effects on the vibrations of a cylinder and the effects are mode type dependent. As either the number of laminations or the clamping pressure increases, all of the transverse vibrational modes of a laminated cylinder are eliminated, leaving only the in-plane vibrational modes—that is, the pure radial modes—as the only ones which persist. A laminated stator exhibits mainly pure radial vibrational characteristics, which are quite different from those of an homogeneous thick cylinder.

VIBRATIONAL MODES OF THICK CYLINDERS OF FINITE LENGTH

The natural frequencies and mode shapes of finite length thick cylinders are of considerable engineering importance. A comprehensive classification of the modes of such thick cylinders, based on three-dimentional mode shapes, is presented in this paper. In addition to the 5 groups consisting of pure radial, radial motion with radial shearing, extensional, axial bending, and global modes, as previously adopted for thin cylinders, a futher sixth circumferential category is proposed. This classification, together with the numbers of both the circumferential and the longitudinal nodes, is sufficient to identify each mode of a finite length thick cylinder. The classification for the modes of thick cylinders is applied to four groups of cylinder whose radial thickness to median radius ratio varies from 0·1 to 0·4. Each group contains a set of 8 cylinders with similar inside and outside diameters, but with different axial lengths; these were used to verify the validity of the classifications, and to study the effects of varying axial length and varying radial thickness on each of the different types of modes. Analytical finite element analysis was applied to all four groups, and experimental anlysis was applied to those cylinders whose radial thickness to the medium radius ratio was 0·4. The results support the method of classification, although very short cylinders behave essentially as annular circular plates. The effects of varying axial length and radial thickness on the vibrational modes are such that all modes can be broadly categorized as either pure radial modes, or non-pure radial modes. The natural frequencies of the former are dependent upon only the radial dimensions of the models, while the natural frequencies of the latter are dependent upon both axial length and radial thickness.

Pulsation periods in the? Scuti star HR 1170

All knownV data from the literature for the δ Scuti star HR 1170 have been reanalysed by using single-frequency Fourier and multiple-frequency least squares analysis. The calculated periods areP1=0.d09942 andP2=0.d08392. The second frequency has not been found before and gives better residuals and almost constant amplitudes for the individual data sets. The period ratio andQ values indicate that this star is not pulsating in pure radial modes.

Acoustic resonance frequencies of deformed spherical resonators. II

The effects of imperfect spherical shape on the modes of a spherical acoustic resonator are considered. The resonator boundary is described by a series of spherical harmonics r=a+εa∑ clkYlk, where ε is a small parameter. It is convenient to summarize the results by considering deformations which do not change the resonator volume. Earlier work showed, for pure radial modes subject to axisymmetric shape perturbations, that the fractional shift of the resonance frequency is proportional to ε2. This work extends this result to arbitrary shape perturbations. Nonradial modes, for which the acoustic pressure is proportional to jn (kns r) Ynm (θ, φ) with n≥1 are (2n+1)-fold degenerate for a perfect spherical resonator. Deformation of the resonator normally shifts the resonance frequencies by an amount which is linear in ε. However, the average shift of a degenerate set of modes with indices {ns} is of order ε2. Axisymmetric shape perturbations normally reduce the degeneracy of the nonradial modes to (n+1)-fold, and arbitrary deformations normally lift the degeneracy completely. The modes with indices {ns} are sensitive only to the terms clk with even values of l in the range l≤zn. A formalism for quantitative estimates is developed. Numerical results are obtained for some n=1 and n=2 cases.

Perturbation Theory Generalized to Arbitrary (p,l) Modes in a Fabry-Perot Resonator (Letters)

The first-order perturbation calculation that was carried out to include the effects of the usually neglected delta/sup 2/psi / delta z/sup 2/ term in the wave equation for pure radial modes (l = 0) is generalized to the case of arbitrary p,l modes. The result, although requiring more algebra, is similar to that of the l= 0 case; the correction term is a monotonically increasing function of both p and l, and reduces to the original expression as l --> 0.

Radial vibration of a thick-shell hollow piezoceramic sphere

A thick-shell hollow piezoceramic sphere electroded completely on both inside and outside surfaces and radially polarized can be used as a source and receiver of underwater sound. Restricting the analysis to moderately thick shells the electromechanical equations of displacement are solved to generate the frequency equation for the pure radial modes. The frequency equation is specialized to reflect the behavior of a barium-titanate shell and numerical values are tabulated for the first three frequencies for a broad range of shell thicknesses.

Classical Viscosity in Tubes and Cavities of Large Dimensions

A method for the calculation of viscous losses in acoustic wave guides and cavities is described, similar to that used by Carson, Mead, and Schelkunoff for electromagnetic waves. The loss in a plane wave in a round tube is discussed and the results agree with those previously obtained by others. The attenuation for two higher modes in hard wall guides is computed, as well as the decay constants for a cylindrical cavity for longitudinal and pure radial modes.