Frequency Splitting Of Modes Research Articles

Study of the Solar Cycle Dependence of Low‐Degreep‐Modes with Michelson Doppler Imager and VIRGO

Studying variations of observational properties of low-degree solar acoustic p-modes (radial, dipole, and quadrupole) with the activity cycle is important for understanding potential effects of the cycle in the deep interior, obtaining more accurate inversions for the sound speed and rotation, and also for estimating prospective investigation of stellar activity by asteroseismology. We have analyzed changes of low-degree p-mode parameters during the current solar cycle (number 23) by using velocity and intensity oscillation data from two instruments on the Solar and Heliospheric Observatory (SOHO): the Michelson Doppler Imager (MDI) and Variability of Solar Irradiance and Gravity Oscillations (VIRGO). We show a clear dependence of mode frequency, line width, frequency splitting, and line asymmetry on the solar cycle. Moreover, we demonstrate that these properties change differently for modes of different frequency, angular degree, and order. The greatest changes are observed for sectorial modes of frequencies higher than 3 mHz, corresponding to the fact that the most significant variations of the solar structure occur in low-latitude regions close to the solar surface.

Vortex dipole in a trapped atomic Bose-Einstein condensate

We calculate the angular momentum and energy of a vortex dipole in a trapped atomic Bose-Einstein condensate. Fully analytic expressions are obtained. We apply the results to understand a novel phenomenon in the MIT group experiment, an excellent agreement is achieved, and further experimental investigation is proposed to confirm this vortex dipole mechanism. We then suggest an effective generation and detection of vortex dipole for experimental realization. Application of the sum rule to calculate collective mode frequency splitting is also discussed.

Temporal beating of nondegenerate azimuthal modes in nonspherical microdroplets: technique for determining the distortion amplitude

Oscillations that are superimposed on the smooth, exponential decay of light from microcavity modes are observed, and they are characteristic of the temporal beating of adjacent, degeneracy-split azimuthal modes in distorted spheres. The perturbation theory result for the frequency splitting of azimuthal modes in distorted spheres is used to determine the distortion amplitude from the temporal oscillations associated with mode beating. The beating period can be used to determine whether the spectrally measured resonance linewidth Deltaomega(l,n) is broadened by closely spaced, degeneracy-split azimuthal modes of slightly nonspherical droplets.

Circular anisotropy of a rotating Fabry-Perot cavity

A theoretical investigation was done concerning the resonant properties of a rotating Fabry-Perot cavity with dielectric media inside. The frequency splitting of orthogonal circularly-polarized modes had been predicted. Formula for the frequency splitting was obtained taking into account refractive index dispersion, dynamic-optical effect and the transversal structure of the electromagnetic field. We represent a simplified analysis, based on the geometrical optical theory, and we also present an accurate analysis on the basis of the general theory of relativity.

Birefringence cavity dual-frequency lasers and relative mode splitting

An intracavity HeNe birefringent dual-frequency laser is investigated for applications. The substrate of such a laser cavity mirror is made of quartz crystal instead of ordinary optical glass. The surface that functions as the laser cavity mirror is coated with a high-reflecting thin film layer, while the surface joined to the discharge tube is coated with an antireflecting thin film layer. Thus, the laser is an intracavity laser and the quartz crystal located inside the cavity causes the longitudinal mode to split into two modes (frequencies). To obtain the appropriate design parameters for various frequency differences, a series of quartz crystal cavity mirrors with different cut angles is experimentally investigated. The relationship of mode splitting and the cut angle are observed. To estimate the splitting by one mirror for different cavity lengths, the following concepts are presented: relative mode (frequency) splitting (ration of mode splitting versus longitudinal mode spacing) and relative optical path difference (ration of optical path difference versus half-wavelength).

Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets

High-resolution interferometric spectra of the stimulated Raman scattering (SRS) spectra from flowing ethanol droplets are presented. The linewidths of the SRS peaks are less than 0.005 cm(-1), and the equal frequency spacings of the SRS peaks are an order of magnitude smaller than the spacings for morphology-dependent resonances of a perfect sphere. The observed results from droplets that are deformed by inertial effects are consistent with T-matrix and perturbation predictions of frequency splitting into the various azimuthal modes of a (2n + 1)-degenerate morphology-dependent resonance with angular momentum n in a perfect sphere.

Effect of a global plume distribution on Earth normal modes

We show that a global distribution of small scale heterogeneities in the lower mantle induces both frequency splitting and amplitude scatter of low angular order modes. These effects can be used in order to map the global distribution of small scale structures in the mantle, such as plumes. Two independent datasets, consisting respectively of lower mantle modes interaction coefficients and of observed amplitudes of core modes, can then be used to constrain the low angular degrees of the spatial distribution and the mean size of heterogeneities, allowing us to constrain the mantle structure at different scales. If these heterogeneities are assumed to be plumes associated with hotspot activity, the mean size of plumes obtained using the two datasets is then in good agreement with that obtained from geodetical or numerical convection studies.

On frequency shift and splitting induced by a deformation of the cross-section of a pinch

The influence of noncircularity of the plasma cross-section on the MHD spectrum of pinches is studied by applying a standard expansion method to a simple model equation. Conditions for frequency shift and splitting of circular modes in terms of the angular dependence of the shape of the cross-section are derived. It is found that the splitting always is symmetric, implying that removal of the degeneracy to first order always decreases the stability margin. Higher-order splitting is, however, always superimposed on a simple second-order frequency shift which in principle can be stabilizing. It is also found that the expansion breaks down for specific axial wavenumbers. This breakdown is due to a jump in the degree of the degeneracy when the wavenumber passes a value at which modes coupled by the noncircularity have the same zero-order eigenfrequency. The conclusions are tested on a surface current Z-pitch. An additional conclusion emerging from this test is that a noncircularity causes a resonance coupling between m=1 and some higher mode, which pushes the Kruskal-Shafranov limit towards higher q values.

The effect of toroidal magnetic fields in the overshoot layer on the eigenfrequencies of stellar oscillations

The overshoot layer in stellar convection zones is slightly subadiabatic and can be considered as a stable region for storage of magnetic flux. Belvedere, Pidatella and Stix (1986) estimated the size of the overshoot layer and computed the magnetic field strength, beyond which toroidal flux tubes become unstable to buoyancy, for a number of main sequence spectral types ranging from F5 to K0. Here we estimate the relative frequency perturbation of high order acoustic modes due to the presence of a non-oblique axisymmetric magnetic field in the overshoot layer. We find that increases with the advancing spectral type, the predicted frequency splitting being large enough to be detected by observations, at least for the Sun.We conclude that magnetic field induced frequency splitting of high order acoustic modes may well be due to a toroidal field of relatively moderate strength just beneath the bottom of the convection zone.

Solar equatorial rotation rate inferred from inversion of frequency splitting of high-degree modes

The equatorial rotation rate has been inferred as a function of depth through the outer 16 Mm of the Sun from observations of high-degree five-minute oscillations. An optimal averaging inversion procedure due to Backus & Gilbert (1970) has been applied to frequency splittings measured from power spectra obtained using Doppler data spanning three and five consecutive days. The resulting rotation curves have proven to be much more stable than the curves obtained from data sets of single days. The results imply that the solar rotation rate increases with depth by 0.023 μHz reaching a maximum at about 2 Mm below the surface, then decreases by 0.037 μHz down to 16 Mm.

Dipolar Coupling and Molecular Vibration in Crystals. I. General Theory

Coupling of the transition dipoles associated with infrared-active vibrations produces one source of frequency shift and splitting of transverse and lingitudinal modes in solids. The intrinsic part of the dipole is distinguished from the induced part, the latter being related to the electronic polarizabilities of the molecular or atomic units in the structure. Although approximate treatments neglecting the induced part of the dipole have been given previously and, also, certain estimates of the effective field (related to the induced dipole) have appeared earlier in the literature, we here take both effects fully into account for a number of noncubic crystal structures.