Eigenmode Theory Research Articles

Collective dynamics in fully hydrated phospholipid bilayers studied by inelastic x-ray scattering.

The short wavelength density fluctuation of DLPC (dilaurylphosphatidylcholine) bilayers close to full hydration has been studied by the inelastic x-ray scattering technique below and above the main transition temperature. The analysis based on a generalized three effective eigenmode theory allows us to construct the dispersion relation of the high frequency sound mode for the first time. The marked softening of the excitation near k = 14 nm(-1), corresponding to the lipid chain-chain correlation peak in the structure factor, in the L(alpha) phase implies prevalent occurrences of short-wavelength in-plane motions of lipid chains that might be of importance for transportation of small molecules across membranes.

Analysis of inelastic x-ray scattering spectra of low-temperature water

We analyze a set of high-resolution inelastic x-ray scattering (IXS) spectra from H2O measured at T=259, 273, and 294 K using two different phenomenological models. Model I, called the "dynamic cage model," combines the short time in-cage dynamics described by a generalized Enskog kinetic theory with a long-time cage relaxation dynamics described by an alpha relaxation. This model is appropriate for supercooled water where the cage effect is dominant and the existence of an alpha relaxation is evident from molecular-dynamics (MD) simulation data of extended simple point charge (SPC/E) model water. Model II is essentially a generalized hydrodynamic theory called the "three effective eigenmode theory" by de Schepper et al. 11. This model is appropriate for normal liquid water where the cage effect is less prominent and there is no evidence of the alpha relaxation from the MD data. We use the model I to analyze IXS data at T=259 K (supercooled water). We successfully extract the Debye-Waller factor, the cage relaxation time from the long-time dynamics, and the dispersion relation of high-frequency sound from the short time dynamics. We then use the model II to analyze IXS data at all three temperatures, from which we are able to extract the relaxation rate of the central mode and the damping of the sound mode as well as the dispersion relation for the high-frequency sound. It turns out that the dispersion relations extracted from the two models at their respective temperatures agree with each other giving the high-frequency sound speed of 2900+/-300 m/s. This is to be compared with a slightly higher value reported previously, 3200+/-320 m/s, by analyzing similar IXS data with a phenomenological-damped harmonic oscillator model 22. This latter model has traditionally been used exclusively for the analysis of inelastic scattering spectra of water. The k-dependent sound damping and central mode relaxation rate extracted from our model analyses are compared with the known values in the hydrodynamic limit.

Theory, simulation, and observation of discrete eigenmodes associated with lower hybrid solitary structures

A three‐dimensional fluid description of nonlinear lower hybrid waves is investigated in the context of plasma density depletions. The objective is a basic understanding of lower hybrid solitary structures associated with transverse ion acceleration in the topside auroral ionosphere. The equations are linearized about a parabolic density depletion and solved. The solution consists of potential structures (eigenfunctions) which rotate in angle about the center of the density depletion. The eigenfrequencies are discrete for |ω| < ωLH. These eigenfunctions rotate in a left‐handed sense about the geomagnetic field and the solutions fall off exponentially outside the density depletion. The eigenfrequencies are continuous for |ω| > ωLH and κz ≠ 0 but become discrete for kz = 0 in agreement with previous two‐dimensional results [Seyler, 1994]. Simulations of the full nonlinear system are performed, and rotating eigenmodes are extracted from the spectrum. The results agree with the analytic results obtained from the linearized equations. The spectral properties of a lower hybrid solitary structure from the TOPAZ III sounding rocket are reexamined and found to be consistent with theoretical predictions for lower hybrid waves trapped within a density depletion as presented herein. A local wavelet frequency‐wavenumber spectrum is constructed from data taken by moving an interferometer through a simulation at a typical rocket velocity. The results compare favorably with the local frequency‐wavenumber spectrum of a lower hybrid solitary structure observed by the TOPAZ III sounding rocket.

Spun linear birefringence fibres and their sensing mechanism in current sensors with temperature compensation

A single-mode spun linear birefringence fibre is investigated as a periodic structure. By using coupled-mode theory, the modal fields and the propagation coefficients of the two eigenmodes in this fibre are given theoretically for the first time. A spun highly linear birefringence (SHB) fibre is capable of acting as a sensing coil of relatively high sensitivity and temperature stability in current sensors. The mechanism of compensation and the sensitivities of current with SHB fibres and temperature compensation are studied extensively with the above eigenmode theory. The relations of sensitivity and temperature stability to parameters of SHB fibres and light sources are derived. The averaging effect caused by the broadband spectrum of the light source, which effectively eliminate the temperature instability, is investigated quantitatively with the partial-coherent-light theory.

Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles

We extend the rigorous eigenmode theory of binary surface-relief gratings to accommodate three-dimensional-modulation profiles, to formulate a synthesis problem for doubly periodic resonance-domain diffractive elements, and to demonstrate some of the problem’s symmetry properties. Several solutions for multiple beam splitters with ~90% transmission-mode diffraction efficiency are obtained by nonlinear parametric optimization. The polarization sensitivity and the required fabrication accuracy are analyzed for some solutions.

Analysis of passive additive-pulse mode locking with eigenmode theory

The equation of motion for the coupled cavities of additive-pulse mode locking is solved by the eigenvalue method. The pulse evolution and self-starting condition for passive operation is analyzed. It is shown that the laser configuration is equivalent to an intracavity interferometer, and a phase modulation across the pulse is the essential element for mode locking. With the method developed, transient pulse evolution of an initial seed pulse can be calculated and thereby optimized. It is found that the pulse shortening rate is linear with respect to the number of round trips. The duration for the initial pulse to shorten to a steady state is proportional to its initial width and inversely proportional to the nonlinear coefficient. >

Nonuniform phase diffusion in a laser.

The simple intuitive picture of phase diffusion in a traveling wave is introduced to calculate the fundamental (Schawlow-Townes) limit to the laser linewidth. Contrary to the usual phase-diffusion model, our variety is not limited to the regime of low outcoupling; it predicts an enhancement of the linewidth for large outcoupling. It is demonstrated that the results of the traveling-wave phase-diffusion model are identical to those of the theory of nonorthogonal eigenmodes. Finally, the effects of saturation on the linewidth are estimated.

Matched gaussian apodization of pulsed acoustic phased arrays

Gaussian apodization weighting functions matched to the time delay distribution for focusing of phased arrays are introduced. The matching concept is based upon the theory of eigenmodes of freely propagating acoustic beams with a finite cross-section. The effect of this matched gaussian apodization on the beam cross-section is analysed for several acoustic phased array configurations generating acoustic wavefronts in a weakly attenuating and homogeneous medium. A strength of focusing parameter is introduced. The relation between apodization parameters and the strength of focusing is analyzed and illustrated. For strong focusing the parameters of the gaussian matched apodization become independent of the focal range. A simulator was developed which allows the study of acoustic pressure waves in the near-field and far-field generated by a linear phased array excited with short pulses. The simulator provides 2-D and 3-D representations of acoustic wave fronts generated by a pulsed phased array, illustrating the effects of apodization for pulsed acoustic beams in the time-space domain.

Matched gaussian apodization of pulsed acoustic phased arrays.

Gaussian apodization weighting functions matched to the time delay distribution for focusing of phased arrays are introduced. The matching concept is based upon the theory of eigenmodes of freely propagating acoustic beams with a finite cross-section. The effect of this matched gaussian apodization on the beam cross-section is analysed for several acoustic phased array configurations generating acoustic wavefronts in a weakly attenuating and homogeneous medium. A strength of focusing parameter is introduced. The relation between apodization parameters and the strength of focusing is analyzed and illustrated. For strong focusing the parameters of the gaussian matched apodization become independent of the focal range. A simulator was developed which allows the study of acoustic pressure waves in the near-field and far-field generated by a linear phased array excited with short pulses. The simulator provides 2-D and 3-D representations of acoustic wave fronts generated by a pulsed phased array, illustrating the effects of apodization for pulsed acoustic beams in the time-space domain.

Variational theory of drift and tearing eigenmodes in slab geometry

A variational formulation of the radial eigenmode equations describing kink-tearing modes, drift-tearing modes, and drift modes, in slab geometry, is derived. The formalism is shown to provide accurate dispersion relations for a wide range of problems, with fewer approxmimations and less analytical effort than conventional methods require. Furthermore, derivation from a unified framework illuminates the relationships between different instabilities. The variational method is particularly well suited to the approximate solution of physically realistic problems, heretofore considered tractable only by numerical methods.