Correlation between helical surface waves and guided modes of an infinite immersed elastic cylinder

Scattering of obliquely incident plane acoustic waves from immersed infinite solid elastic cylinders is a complex phenomenon that involves generation of various types of surface waves on the body of the cylinder. Mitri [F.G. Mitri, Acoustic backscattering enhancement resulting from the interaction of an obliquely incident plane wave with an infinite cylinder, Ultrasonics 50 (2010) 675-682] recently showed that for a solid aluminum cylinder, there exist acoustic backscattering enhancements at a normalized frequency of ka?0.1. The incidence angle α_c at which these enhancements are observed lies between the first (longitudinal) and second (shear) coupling angles of the cylinder. He also confirmed the observations previously reported by the authors that there exist backscattering enhancements of the dipole mode at large angles of incidence where no wave penetration into the cylinder is expected. In this paper, physical explanations are provided for the aforementioned observations by establishing a correlation between helical surface waves generated by oblique insonification of an immersed infinite solid elastic cylinder and the longitudinal and flexural guided modes that can propagate along the cylinder. In particular, it is shown that the backscattering enhancement observed at ka?0.1 is due to the excitation of the first longitudinal guided mode travelling at the bar velocity along the cylinder. It is also demonstrated that the dipole resonance mode observed at incidence angles larger than the Rayleigh coupling angle is associated with the first flexural guided mode of the cylinder. The correlation established between the scattering and propagation problems can be used in both numerical and experimental studies of interaction of mechanical waves with cylinders.     

Spherical silicon optical resonators: Possible applications to biosensing

We observed whispering gallery modes in the 90^° elastic light scattering and 0^° transmission spectra of a 500 μm silicon microsphere in the near-infrared telecommunication wavelengths. The whispering gallery modes have quality factors on the order of 10⁵. An autocorrelation function analysis of the 90^° elastic light scattering and 0^° transmission spectra is performed. The differential autocorrelation of the 90^° elastic light scattering and 0^° transmission spectra reveal a spectral mode spacing 0.23 nm of the whispering gallery modes, which can be used for spectral calibration as well as the calibration of the microsphere size. The spectral shift of the whispering gallery modes can be measured for biosensing applications. An estimation analysis is performed for the adsorption of 30 DNA base pairs on the microsphere results in a wavelength shift of 0.57 nm, which is approximately 40 times the linewidth of the whispering gallery modes. This high sensitivity heralds silicon microspheres as possible candidates for biosensing applications.     

Pure elastic resonance scattering of an obliquely incident plane acoustic wave by a submerged infinite cylinder

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Millimeter-wave whispering gallery modes in an ellipsoidal dielectric resonator with a small ellipticity

It is found that, when the shape of a dielectric sphere (hemisphere) operating under the whispering gallery mode conditions is perturbed by a surface curvature gradient (ellipticity), the unloaded Q factor of the sphere degrades and its resonance frequencies change. It is shown theoretically and experimentally that an elliptic irregularity removes frequency degeneracy of whispering gallery modes at millimeter waves.     

Whispering-gallery-mode resonances: a new way to accelerate charged particles

Looking for future high energy accelerators we point at a very strong interaction between relativistic electrons and powerful electromagnetic fields existing in the vicinity of a dielectric cylinder in conditions of resonantly excited whispering gallery modes (WGM). A particular example of the WGM resonance, corresponding to angular index n=22, shows that the accelerating fields are almost 100 times stronger than these in the incident wave. That yields an acceleration rate of about 5 GeV/m with the incident microwave radiation beam of the wavelength lambda=1 cm and a moderately high intensity of P=1 MW/cm2.     

Multiple scattering of an obliquely incident plane acoustic wave from a grating of immersed cylindrical shells

The study of the interaction of acoustic waves with cylindrical structures has numerous applications including the ultrasonic nondestructive testing of materials. In this paper, using a new mathematical model presented for the scattering of obliquely incident plane acoustic waves from a grating of immersed cylindrical shells, a detailed study of the resonant interaction of A-wave resonances originating from the shells is conducted. The nature of A-wave resonances and the effect of center-to-center distance of the shells on these resonances are examined. It is observed that this resonant interaction not only results in the splitting of A-wave resonances, but also causes an increase in resonance amplitudes. This interaction phenomenon is not seen in Rayleigh, whispering gallery and guided wave resonances. It is also shown that increasing the angle of wave incidence to the grating weakens the A-wave resonant interactions. The numerical results obtained from the mathematical model are compared to experimental results available in the literature for gratings composed of two and three aluminum shells. The numerical results are in very good agreement with their experimental counterparts.     

柱形微腔回音壁激光光谱模式的精确标定

由柱形微腔中回音壁模式满足的本征值方程,得到确定回音壁模式位置和间距的近似解析公式。以此近似解析公式,首次对直径在215～328 μm间的5个柱形微腔回音壁激光光谱做了模式标定。在用近似解析公式对柱形微腔激光光谱的数值作拟合的计算中,除了回音壁模的径向模式数(l)和角动量模式数(n)外无需其他拟合参数,解析公式的拟合值和实验激光光谱波长值间的偏差小于0.05 nm,拟合结果精确可靠。柱形微腔回音壁激光光谱模式的精确标定在模式的场分布计算以及频移型微腔生物传感器的研究应用中具有重要作用,文章介绍的方法亦可应用于柱形微腔直径和折射率的精密测量。     

Whispering-Gallery-Mode Gyrotron Operation with a Quasi-Optical Antenna

High-frequency gyrotron operation in the TE611 whispering gallery mode is reported. Powers as high as 112 kW and an efficiency as high as 25.4 percent have been obtained. In addition to the TE611 mode, ten other fundamental modes with frequencies between 133.9 and 216.4 GHz were observed. A quasi-optical antenna for whispering gallery modes has been tested for the TE611 mode. The combination of this antenna and a reflector produces a well-collimated linearly polarized RF beam suitable for electron cyclotron resonance heating (ECRH) or plasma diagnostics. The experimental conversion efficiency was determined to be 89 percent, and the cross polarization was down by 25 dB. A new quasi-optical transmission line employing this antenna has also been tested with the gyrotron. The absence of mode competition for the TE611 mode, as well as the efficient conversion of the output radiation into a linearly polarized Gaussian-like beam, substantiates the arguments for operation in surface modes in high-power gyrotrons. The implications of quasi-optical antennas for megawatt gyrotron window design are discussed.     

Acoustic backscattering enhancements resulting from the interaction of an obliquely incident plane wave with an infinite cylinder

Background and objective

The analysis of the acoustic backscattering enhancements from tilted cylinders is of particular importance in determining some of the (visco)elastic properties of the cylinder, and/or its surrounding fluid in ultrasonic non-destructive evaluation (NDE) and imaging (NDI) applications. Previous related investigations on an aluminum cylinder limited to incidence angles varying from 0° to 40°, revealed the existence of an anomalous “pseudo-Rayleigh” mode (above the critical Rayleigh angle) identified as the rigid-body translational dipole (n = 1) mode. The objective here is to provide a complete investigation on the backscattering enhancements for incidence angles larger than 40° for various elastic and viscoelastic cylinder materials.

Method

Using the partial-wave series solution for the linear scattering by an infinite circular cylinder, the acoustic backscattering from isotropic elastic and viscoelastic (polymer-type) cylinders excited by an obliquely incident plane acoustic wave is investigated. Total and resonance backscattering form functions are calculated for several elastic and viscoelastic cylinder materials immersed in water versus the angle of incidence 0° ? α < 90°. The “pure” resonance peaks are isolated by subtracting a rigid background from the total form function, so the associated resonance modes are properly identified.

Results and conclusion

The plots of the partial-wave series reveal acoustic backscattering enhancements (not shown in previous investigations) generally occurring at ka? 0.1 at a critical angle α_c bounded by the longitudinal and shear waves coupling angles θ_L=sin^-1(c/c_L) and θ_S=sin^-1(c/c_S) such that θ_L<α_c<θ_S (where c_L and c_S are the phase velocities of the longitudinal and shear waves inside the elastic cylinder, and c is the speed of sound in the surrounding medium). It is shown here that the backscattering enhancements with a critical angle θ_L<α_c<θ_S result from the excitation of the monopole (n = 0) resonance mode. Moreover, additional acoustic backscattering enhancements still occur in the range 1 ?ka? 6 even though the angle of tilt is greater than the Rayleigh wave coupling angle θ_R=sin^-1(c/c_R) (where c_R is the Rayleigh wave velocity in an elastic half-space). The resonance scattering theory shows that such additional enhancements are associated with the excitation of a dipole (n = 1) resonance mode which may result from the interference of meridional and/or helical waves propagating along the cylinder’s surface. It is therefore essential to consider tilt angles ranging from normal to end-on incidence for a complete analysis of the backscattering by elastic and viscoelastic cylinders.     

Enhanced nanoparticle detection with liquid droplet resonators

Whispering gallery mode particle sensing experiments are commonly performed with solid resonators, whereby the sensing volume is limited to the weak evanescent tail of the mode near the resonator surface. In this work we discuss in detail the sensitivity enhancements achievable in liquid droplet resonators wherein the stronger internal fields and convenient means of particle delivery can be exploited. Asymptotic formulae are derived for the relative resonance shift, line broadening and mode splitting of TE and TM modes in liquid droplet resonators. As a corollary the relative fraction of internal and external mode energy follows, which is shown to govern achievable sensitivity enhancements of solute concentration measurements in droplet sensors. Experimental measurements of nanoparticle concentration based on whispering gallery mode resonance broadening are also presented.     

Higher-order optical resonance node detection of integrated disk microresonator

We have demonstrated higher-order optical resonance node detection by using an integrated disk microresonator from through port of the coupling bus waveguide. In addition to the fundamental mode, the disk resonator has higher-order whispering gallery modes. The excited second-order higher-order mode has a node at the position where the electromagnetic energy of the fundamental mode is close to a maximum. This high resolution measurement of optical resonance mode profile has a variety of applications for optical sensing and detection. The self-referencing characteristics of the two optical resonance modes have potential to achieve optical detection independent of external perturbation, such as temperature change.     

Directly mapping whispering gallery modes in a microsphere through modal coupling and directional emission

We fabricate slightly deformed fused-silica microspheres in which whispering gallery modes possess remarkably directional escape emission from the microsphere boundary. With efficient flee-space excitation and collection, the lateral spatial distribution of whispering gallery modes with different azimuthal mode numbers, rn, is directly observed through modal coupling and directional emission. Excellent agreement with theory is obtained.     

Development of multi-wavelength microsphere fibre laser system for potential sensor applications

A multi-wavelength microsphere laser system, using a chirped fibre Bragg grating and a microsphere resonator as wavelength-selective elements and a high dopant erbium doped fibre as the gain material, has been successfully demonstrated. The multi-wavelength generation of the laser system arises from both the microsphere whispering gallery mode selection and from the additional Raman scattering inside the microsphere cavity when the erbium laser is operating at resonance with the whispering gallery modes. Through an appropriate design and fabrication of a microsphere and of a fibre taper, a selective multi-wavelength fibre laser has been realized when the pump power is above threshold required. The laser output lines created have shown much narrower linewidths than those from conventional fibre lasers and these characteristics are particularly suitable for the range of sensor applications envisaged in the work.     

Surface acoustic wave opto-mechanical oscillator and frequency comb generator

We report on realization of an efficient triply resonant coupling between two long lived optical modes and a high frequency surface acoustic wave (SAW) mode of the same monolithic crystalline whispering gallery mode resonator. The coupling results in an opto-mechanical oscillation and generation of a monochromatic SAW. A strong nonlinear interaction of this mechanical mode with other equidistant SAW modes leads to mechanical hyperparametric oscillation and generation of a SAW pulse train and associated frequency comb in the resonator. We visualized the comb by observing the modulation of the light escaping the resonator.     

Vectorial whispering gallery mode solvers based on straight waveguide modes

In this paper, whispering gallery mode solvers based on a set of corresponding straight waveguide modes are proposed. The solvers project whispering gallery modes onto a linear combination of straight waveguide modes through a cavity residual operator eigensolution formalism and direct straight waveguide expansion procedures. With these implementations, a perfectly matched layer can be imposed at the cavity computation window edges automatically and optical properties of plain and metal coated silica microtoroids can be analyzed from a novel viewpoint. Additionally, the techniques can be employed in cavity mode matching methods for the modelling of cavities that strongly scatter light.     

Acoustic field excited by a pulsed laser line source in a cylinder

The excitation and propagation of the acoustic waves in an elastic cylinder are studied by laser ultrasonics both theoretically and experimentally. The theoretical analysis of the two-dimensional acoustic field excited by a pulsed laser line source impacting on the generatrix of an elastic cylinder is presented. The dispersive properties for both cylindrical Rayleigh wave and the higher modes--whispering gallery (WG) modes are analyzed in detail. The numerical transient displacement waveforms for a detecting point located another terminal of the cylinder diameter opposite the source are calculated. The experimental excitation and detection of the acoustic waves in an aluminum cylinder are carried out on a laser ultrasonic system, which mainly consists of a Q-switched Nd:YAG laser and a laser interferometer. The wave components of bulk waves and surface waves (cylindrical Rayleigh waves and WG modes) are analyzed by comparing the numerical and experimental waveforms. The results are in good agreement.     

Design of MMICs employing whispering-gallery mode dielectric resonators at microwave and millimeter wave frequencies

A simple theoretical model for predicting the resonant frequencies of the modes of the whispering — gallery (WG) mode dielectric resonators MICs (Microwave Integrated Circuits) at microwave and millimetre wave frequencies is presented. The unsymmetric field distribution for WGE mode in the axial direction is taken into account. The theoretical results are found to be in good agreement with the practical results taken at microwaves C-X bands. In addition, the variation of resonant modes against dielectric resonator's dimensions and dielectric constant is modelled. The effect of the width of dielectric substrate on resonant modes is also illustrated.     

Internal field of an insonified elastic plate

The displacement field within an infinite, fluid-loaded elastic plate insonified by a plane wave at arbitrary incidence angle is examined. For a water-immersed steel plate which is 0·55 shear wavelengths thick extensive graphical data are presented showing the evolution of the displacement field with variation of incidence angle from very close to normal incidence to very close to grazing incidence. Particular attention is paid to the behaviour at angles at which Lamb modes are excited, and it is incidentally shown by the decomposition of the normal boundary motions into antisymmetrical and symmetrical constituents that at the coincidence angles these motions are neither totally antisymmetrical nor totally symmetrical. New expressions derived for the displacement components at the critical angles illustrate the transition between oscillatory and exponentially decaying waves within the plate. Some clarification is obtained of the physical behaviour at transmission nulls.     

Dynamic viscoelastic effects on sound wave scattering by an eccentric compound circular cylinder

The classical method of separation of variables in conjunction with the translational addition theorem for cylindrical wave functions are employed to obtain an exact solution for two-dimensional interaction of a harmonic plane acoustic wave with an infinitely long (visco)elastic circular cylinder which is eccentrically coated by another (visco)elastic material and is submerged in an ideal unbounded acoustic medium. The novel features of Havriliak-Negami model for dynamic viscoelastic material behaviour are used to take the rheological properties of the coating (and/or core) material into consideration. The analytical results are illustrated with numerical examples in which a steel rod eccentrically coated with (an eccentric steel shell filled with) dissipative materials of distinct viscoelastic properties is insonified by plane sound waves at selected angles of incidence. The effects of incident wave frequency, angle of incidence, core eccentricity and dynamic viscoelastic material properties on the backscattered form function spectra are examined. Limiting cases are considered and fair agreements with available solutions are obtained.