Cavity Eigenfrequencies Research Articles

Cavity Mode Wave Frequency Variation Associated With Inward Motion of the Magnetopause During Interplanetary Shock Compression

AbstractA cavity mode wave, referring to a trapped or radially standing fast mode wave between different magnetospheric boundaries, has been developed in theory and reported in observation studies. In this study, we present an interplanetary shock (IPS)‐induced cavity mode wave event observed outside the plasmasphere on 31 August 2017 with multispacecraft measurements. The phase delay of 90° between the azimuthal electric field and compressional magnetic field indicates that the fast‐mode wave triggered by the IPS is a standing wave, presumably radially trapped in the cavity between the magnetopause and plasmapause. Taking advantage of the location of Van Allen Probe B spacecraft right outside the plasmapause and the Arctic and Antarctic Research Institute ground‐based high‐latitude array mapped in the noon sector, it is suggested that the observed compressional wave associates to cavity mode with its inner boundary at the plasmapause and its outer boundary at the magnetopause. The peak frequency of the wavelet spectrum of the compressional magnetic field increases from 10.5 to 12.5 mHz, which is consistent with the theoretically calculated cavity eigenfrequencies before and after the IPS. We also provide the first evidence that the peak frequency of the cavity mode increases due to the inward motion of the magnetopause during IPS compression.

Enhancing the force sensitivity of a squeezed light optomechanical interferometer.

Application of frequency-dependent squeezed vacuum improves the force sensitivity of an optomechanical interferometer beyond the standard quantum limit by a factor of e-r, where r is the squeezing parameter. In this work, we show that the application of squeezed light along with quantum back-action nullifying meter in an optomechanical cavity with mechanical mirror in middle configuration can enhance the sensitivity beyond the standard quantum limit by a factor of e-reff, where reff = r + ln(4Δ/ζ)/2, for 0 < ζ/Δ < 1, with ζ as the optomechanical cavity decay rate and Δ as the detuning between cavity eigenfrequency and driving field. The technique described in this work is restricted to frequencies much smaller than the resonance frequency of the mechanical mirror. We further studied the sensitivity as a function of temperature, mechanical mirror reflectivity, and input laser power.

Reshaping the Jaynes-Cummings ladder with Majorana bound states

We study the optical properties of a hybrid device composed by a quantum dot (QD) resonantly coupled to a photonic mode of an optical microcavity and a Majorana nanowire: a topological superconducting segment hosting Majorana bound states (MBSs) at the opposite ends. In the regime of strong light-matter coupling, it is demonstrated that the leakage of the Majorana mode into the QD opens new optical transitions between polaritonic states formed due to hybridisation of material excitation with cavity photons, which leads to the reshaping of the Jaynes-Cummings ladder and can lead to the formation of a robust single-peak at cavity eigenfrequency in the emission spectrum. Moreover, weak satellite peaks in the low and high frequency regions are revealed for the distinct cases of highly isolated MBSs, overlapped MBSs and MBSs not well localized at the nanowire ends.

Practical lineshape of a laser operating near an exceptional point

We present a practical laser linewidth broadening phenomenon in the viewpoint of high sensitivity of an exceptional point (EP). A stochastic simulation model is implemented to describe the fluctuations in the cavity resonance frequencies. The linewidth originated from external noises are maximized at the EP. The linewidth enhancement factor behaves similarly to the Petermann factor although the Petermann effect is not considered. In the long coherence time limit, the power spectral density of the laser exhibits a splitting in the vicinity of the EP although the cavity eigenfrequencies coalesce at the EP.

Determination of Biconical Cavity Eigenfrequencies Using Method of Partial Intersecting Regions and Approximation by Rational Fractions

The paper considers the problem of determining the eigenfrequencies of biconical cavity making it possible to simplify the eigenfrequency-based design of devices. We used the solving of the excitation problem for biconical cavity using the method of partial intersecting regions in combination with the collocation method. Based on the concept of the search of quasisolution for determining eigenfrequencies, it was proposed to apply the fractionally rational approximation of cavity response obtained as a result of solving the problem of resonator excitation. The efficiency of finding eigenfrequencies of biconical cavity was substantiated by using the fractionally rational approximation based on the chain fraction interpolation of cavity response calculated only at collocation points. Using the above approach, we have obtained the relationship of eigenfrequencies of azimuth-symmetric oscillations of biconical cavity as a function of the aperture angle, and the typing of lower azimuth-symmetric transverse electric modes of biconical cavity has been performed.

Simple technique for biconical cavity eigenfrequency determination

A number of features of biconical cavities make them attractive for various applications. Expressions for the calculation of the eigenfrequencies of a biconical cavity with large cone angles can be derived using the overlapping domain decomposition method in combination with the collocation method; however, the expressions reported in the literature involve only a single pair of collocation points, thus giving no way to estimate the eigenfrequency determination accuracy. The aim of this paper is to calculate the biconical cavity eigenfrequencies for an arbitrary number of collocation point pairs. An equation in the biconical cavity eigenfrequencies for an azimuthally symmetric transverse electric field at an arbitrary number of collocation point pairs is derived. The equation reduces to two equations, whose solution requires far less computational effort in comparison with the original equation. The solution of one of the two equations are based on modes symmetric about the cavity symmetry plane, and the solutions of the other are based on antisymmetric modes. The calculated eigenfrequencies converge rapidly with increasing number of collocation point pairs, while the use of only one collocation point pair may introduce noticeable error. The proposed technique may be used in the development of components and units on the basis of biconical cavities.

Optimisation of the prism coupling of optical whispering-gallery-mode microcavities

The methods for increasing the coupling efficiency of a prism with spheroidal microcavities, aimed at exciting whispering-gallery modes, have been analytically investigated. Optimal angles of incidence and incident beam parameters are obtained for a spheroidal cavity. The cavity eigenfrequency shift caused by the presence of a prism and the introduced loss by it is calculated.

Measurement of the transfer function for a spoke cavity of C-ADS Injector I**Supported by Proton Linac accelerator I of China Accelerator Driven Sub-critical System (Y12C32W129)

The spoke cavities mounted in the China Accelerator Driven sub-critical System (C-ADS) have high quality factor (Q) and very small bandwidth, making them very sensitive to mechanical perturbations, whether external or self-induced. The transfer function is used to characterize the response of the cavity eigenfrequency to the perturbations. This paper describes a method to measure the transfer function of a spoke cavity. The measured Lorentz transfer function shows there are 206 Hz and 311 Hz mechanical eigenmodes excited by Lorentz force in the cavity of C-ADS, and the measured piezo fast tuner transfer function shows there are 12 mechanical eigenmodes from 0 to 500 Hz. According to these results, some effective measures have been taken to weaken the influence of helium pressure fluctuation, avoid mechanical resonances and improve the reliability of the RF system.

Geometry-invariant resonant cavities.

Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modelling to everyday life devices. The eigenfrequencies of conventional cavities are a function of their geometry, and, thus, the size and shape of a resonant cavity is selected to operate at a specific frequency. Here we demonstrate theoretically the existence of geometry-invariant resonant cavities, that is, resonators whose eigenfrequencies are invariant with respect to geometrical deformations of their external boundaries. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, such as epsilon-near-zero media, which enable decoupling of the temporal and spatial field variations in the lossless limit. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices.

Sound signature of propeller tip vortex cavitation

The design of an efficient propeller is limited by the harmful effects of cavitation. The insufficient understanding of the role of vortex cavitation in noise and vibration reduces the maximum efficiency by a necessary safety margin. The aim in the present study is to directly relate propeller cavitation sound to tip vortex cavity dynamics. This is achieved by a dedicated experiment in a cavitation tunnel on a specially designed two-bladed propeller using a high-speed video camera and a hydrophone. The sound signature of a tip vortex cavity is not evidently present in the sound spectrum above the tunnel background. The addition of a simulated wake inflow results in a high amplitude broadband sound. With a decrease in the free-stream pressure the centre frequency of this sound decreases as a result of a larger vortex cavity diameter. In the near future each blade passage in the high-speed video will be analyzed in detail. The frequency content of the cavity dynamics can then be directly related to the measured sound. An analytic model for vortex cavity dynamics resulting in a cavity eigenfrequency using a vortex velocity model can finally be evaluated as a design instrument for estimation of broadband sound from propeller cavitation.

Quantized optical mode in a phase-switching feedback loop

We investigate the steady state of quantized monochromatic cavity mode excited by coherent pumping and placed in a feedback loop that changes the mode phase by π upon each detection of the photon that left the cavity. Such type of feedback is used for fighting decoherence of Schrobinger cat states. Results of numerical calculations of the Glauber P-function for different detunings of mode frequency from pumping frequency are presented. Qualitative explanation for certain peculiarities of the behavior of the P-function is provided. We also suggest a simplified model that gives accurate description of the behavior of the system in the case where external coherent pumping is far detuned from the cavity eigenfrequency.

On the possibility of using the phase characteristic of a ring interferometer in microoptical gyroscopes

The prototype schemes of a microoptical gyroscope (MOG) developed to date on the basis of passive ring cavities imply the use of the amplitude characteristic only, since they operate using the dip in the transmission coefficient. We have analysed the possibility of creating a MOG, in which the phase characteristic is used as well. The phase characteristic of a ring interferometer has distinctive features in the vicinity of the cavity eigenfrequencies, which may be used to determine the angular velocity. A method for the angular velocity determination using both the phase and the amplitude characteristics of the interferometer is considered.

Disorder-induced transparency in a one-dimensional waveguide side coupled with optical cavities

Disorder influence on photon transmission behavior is theoretically studied in a one-dimensional waveguide side coupled with a series of optical cavities. For this sake, we propose a concept of disorder-induced transparency appearing on the low-transmission spectral background. Two kinds of disorders, namely, disorders of optical cavity eigenfrequencies and relative phases in the waveguide side coupled with optical cavities are considered to show the disorder-induced transparency. They both can induce the optical transmission peaks on the low-transmission backgrounds. The statistical mean value of the transmission also increases with increasing the disorders of the cavity eigenfrequencies and relative phases.

Structural-acoustic coupling characteristics of honeycomb sandwich plate based on parameter sensitivity analysis

The structural-acoustic coupling model for isotropic thin elastic plate was extended to honeycomb sandwich plate (HSP) by applying Green function method. Then an equivalent circuit model of the weakly-strongly coupled system was proposed. Based on that, the estimation formulae of the coupled eigenfrequency were derived. The accuracy of the theoretical predictions was checked against experimental data, with good agreement achieved. Finally, the effects of HSP design parameters on the system coupling degree, the acoustic cavity eigenfrequency, and sound pressure response were analyzed. The results show that mechanical and acoustical characteristics of HSP can be improved by increasing the thickness of face sheet and reducing the mass density of material.

A system for matching the spectrum of injected single-frequency radiation with the cavity eigenfrequencies of a pulsed laser

A method for automatically setting the cavity eigenfrequencies of a pulsed laser to the emission frequency of a continuous single-frequency master oscillator has been developed and investigated. The operating principle of the given system is explained, and the results of a study of how it affects the characteristics of the radiation of a pulsed laser are presented. The system described here can be used to stabilize the process of single-frequency lasing of a pulsed laser with the injection of an external signal and to reduce the jitter of the light pulses by a factor of 2 and the scatter of their amplitude by a factor of more than 3.

Observation of backaction and self-induced trapping in a planar hollow photonic crystal cavity.

The optomechanical coupling between a resonant optical field and a nanoparticle through trapping forces is demonstrated. Resonant optical trapping, when achieved in a hollow photonic crystal cavity is accompanied by cavity backaction effects that result from two mechanisms. First, the effect of the particle on the resonant field is measured as a shift in the cavity eigenfrequency. Second, the effect of the resonant field on the particle is shown as a wavelength-dependent trapping strength. The existence of two distinct trapping regimes, intrinsically particle specific, is also revealed. Long optical trapping (>10 min) of 500 nm dielectric particles is achieved with very low intracavity powers (<120 μW).

Influence of the field-detector coupling strength on the dynamical Casimir effect

We consider the problem of photon creation from a vacuum inside an ideal cavity with vibrating walls in the resonance case, taking into account the interaction between the resonant field mode and a detector modeled by a quantum harmonic oscillator. The frequency of wall vibrations is taken to be twice the cavity normal frequency, modified due to the coupling with the detector. The dynamical equations are solved with the aid of the multiple scales method. Analytical expressions are obtained for the photon mean numbers and their variances for the field and detector modes, which are supposed to be initially in the vacuum quantum states. We analyze different regimes of excitation, depending on the ratio of the modulation depth of the time-dependent cavity eigenfrequency to the coupling strength between the cavity mode and detector. We show that statistical properties of the detector quantum state (variances of the photon numbers, photon distribution function, and the degree of quadrature squeezing) can be quite different from that of the field mode. Besides, the mean number of quanta in the detector mode increases with some time delay, compared with the field mode.

Approximate calculation of eigenfrequencies of biconical microwave cavities

Simplified expressions are obtained for the calculation of the eigenfrequencies of a biconical cavity with large apex angles with the use of two symmetrical points at the boundaries of overlapping partial regions in the form of a spherical sector. Using these expressions, the dependence of the cavity eigenfrequencies on the apex angles of the conical elements is studied, and the results are compared with those obtained by the classical finite-element method. The applicability range of the simplified expressions is identified, and recommendations on their use are given.

Theoretical and experimental analysis of the electromechanical behavior of a compact spherical loudspeaker array for directivity control

Sound directivity control is made possible by a compact array of independent loudspeakers operating at the same frequency range. The drivers are usually distributed over a sphere-like frame according to a Platonic solid geometry to obtain a highly symmetrical configuration. The radiation pattern of spherical loudspeaker arrays has been predicted from the surface velocity pattern by approximating the drivers membranes as rigid vibrating spherical caps, although a rigorous assessment of this model has not been provided so far. Many aspects concerning compact array electromechanics remain unclear, such as the effects on the acoustical performance of the drivers interaction inside the array cavity, or the fact that voltages rather than velocities are controlled in practice. This work presents a detailed investigation of the electromechanical behavior of spherical loudspeaker arrays. Simulation results are shown to agree with laser vibrometer measurements and experimental sound power data obtained for a 12-driver spherical array prototype at low frequencies, whereas the non-rigid body motion and the first cavity eigenfrequency yield a discrepancy between theoretical and experimental results at high frequencies. Finally, although the internal acoustic coupling affects the drivers vibration in the low-frequency range, it does not play an important role on the radiated sound power.

Resonator spectrometer for precise broadband investigations of atmospheric absorption in discrete lines and water vapor related continuum in millimeter wave range

The instrument and methods for measuring spectral parameters of discrete atmospheric lines and water-related continuum absorption in the millimeter wave range are described. The instrument is based on measurements of the Fabry-Pérot resonance response width using fast phase continuous scanning of the frequency-synthesized radiation. The instrument allows measurement of gas absorptions at the cavity eigenfrequencies ranging from 45 to 370 GHz with the highest to date absorption variation sensitivity of 4x10(-9) cm(-1). The use of a module of two rigidly bounded maximum identical resonators differing in length by exactly a factor of two allows accurate separation of the studied gas absorption and spectrometer baseline, in particular, the absorption by water adsorbed on the resonator elements. The module is placed in a chamber with temperature controlled between -30 and +60 degrees C, which permits investigation of temperature dependence of absorption. It is shown that systematic measurement error of discrete atmospheric line parameters does not exceed the statistical one and the achieved accuracy satisfies modern demands for the atmospheric remote sensing data retrieval. Potential systematic error arising from the neglect of the effect of water adsorption on mirror surfaces is discussed. Examples of studies of water and oxygen spectral line parameters as well as continuum absorption in wet nitrogen are given.