Changes In Eigenmodes Research Articles

AI-assisted spectrometer based on multi-mode optical fiber speckle patterns

Speckle patterns at the output end of a multi-mode fiber (MMF) are generated by the interference of eigenmodes propagating along the fiber. A MMF can support thousands of eigenmodes, and the amplitude and phase of each eigenmode changes rapidly with the properties of input light, thus changing the speckle that emerges at the output. Therefore, a MMF can provide ultra-high sensitivity to the changes of the properties of the input light. However, environmental fluctuations of parameters such as temperature, humidity, and vibration limit the applicability of MMF sensors. In this paper, we theoretically and experimentally demonstrate an AI-assisted MMF spectrometer, and examine the limits of the method. The resolution of the spectrometer reached 0.1 picometer (pm, the resolution of the laser source) for linearly polarized monochromatic incidence. The integration of a deep learning algorithm effectively eliminated the perturbation from environmental fluctuations and made the spectrometer ultra-robust. At the end, we have also demonstrated that by using parallel network configuration, the bandwidth of the system can be easily increased without sacrificing the resolution of the system. The AI-assisted fiber spectrometer is compact, super-robust, and low-cost and provides ultrahigh resolution.

Effect of the Interfacial Dzyaloshinskii–Moriya Interaction on the Spin Waves Eigenmodes of Isolated Stripes and Dots Magnetized In-Plane: A Micromagnetic Study

The influence of the Dzyaloshinskii–Moriya interaction (DMI) on the eigenmodes of magnetic nanostructures is attracting interest for both fundamental reasons and prospects in applications. In this study, the characteristics of spin waves eigenmodes in either long stripes or elliptical dots magnetized in-plane, with lateral dimensions of the order of 100 nm, are analyzed by micromagnetic simulations in presence of a sizeable DMI. Using the GPU-accelerated software MuMax3, we show that the eigenmodes spectrum is appreciably modified by the DMI-induced non-reciprocity in spin-waves propagation: the frequencies of the eigenmodes are red-shifted and their spatial profiles appreciable altered due to the lack of stationary character in the direction orthogonal to the magnetization direction. As a consequence, one finds a modification of the expected cross-section of the different modes in either ferromagnetic resonance or Brillouin light scattering experiments, enabling one to detect modes that would remain invisible without DMI. In this respect, the modifications of the spectrum can be directly connected to a quantitative estimation of the DMI constant. Moreover, it is seen that for sufficiently large values of the DMI constant, the low-frequency odd eigenmode changes its profile and becomes soft, reflecting the transition of the ground state from uniform to chiral.

On the dynamic stability of shear deformable beams under a tensile load

Loss of stability of beams in a linear static context due to the action of tensile loads has been disclosed only recently in the scientific literature. However, tensile instability in the dynamic regime has been only marginally covered. Several aspects concerning the role of shear deformation on the tensile dynamic instability on continuous and discontinuous beams are still to be addressed.It may appear as a paradox, but also for the case of the universally studied Timoshenko beam model, despite its old origin, frequency-axial load diagrams in the range of negative values of the load (i.e. tensile load) has never been brought to light.In this paper, for the first time, the influence of a conservative tensile axial loads on the dynamic behaviour of the Timoshenko model, according to the Haringx theory, is assessed. It is shown that, under increasing tensile loads, regions of positive/negative fundamental frequency variations can be distinguished. In addition, the beam undergoes eigen-mode changes, from symmetric to anti-symmetric shapes, until tensile instability of divergence type is reached. As a further original contribution on the subject, taking advantage of a new closed form solution, it is shown that the same peculiarities are recovered for an axially loaded Euler–Bernoulli vibrating beam with multiple elastic sliders. This latter model can be considered as the discrete counterpart of the Timoshenko beam-column in which the internal sliders concentrate the shear deformation that in the Timoshenko model is continuously distributed. Original aspects regarding the evolution of the vibration frequencies and the relevant mode shapes with the tensile load value are highlighted.

Eigenmode changes in a misaligned triangular optical cavity

We derive relationships between various types of small misalignments in a triangularoptical cavity and associated geometrical eigenmode changes. We focus on the changes ofbeam spot positions on cavity mirrors, the beam waist position and its angle. A comparisonof analytical and numerical results shows excellent agreement. The results are applicable toany triangular cavity close to an isosceles triangle, with the lengths of two sides muchbigger than the third, consisting of a curved mirror and two flat mirrors (the curved mirroris the distant one) yielding a waist equally separated from the two flat mirrors. This cavityshape is most commonly used in laser interferometry. The analysis presented herecan easily be extended to more generic cavity shapes. The geometrical analysisnot only serves as a method of checking a simulation result, but also gives anintuitive and handy tool to visualize the eigenmode of a misaligned triangular cavity.

Analytic theory of curvature effects for wave problems with general boundary conditions

A formalism based on a combination of differential geometry and perturbation theory is used to obtain analytic expressions for confined eigenmode changes due to general curvature effects. In cases of circular-shaped and helix-shaped structures, where alternative analytic solutions can be found, the perturbative solution is shown to yield the same result. The present technique allows the generalization of earlier results to arbitrary boundary conditions. The power of the method is illustrated using examples based on Maxwell's and Schr\odinger's equations for applications in photonics and nanoelectronics.

Highly sensitive mass detection and identification using vibration localization in coupled microcantilever arrays

We study the use of vibration localization in large arrays of mechanically coupled, nearly identical microcantilevers for ultrasensitive mass detection and identification. We demonstrate that eigenmode changes in such an array can be two to three orders of magnitude greater than relative changes in resonance frequencies when an analyte mass is added. Moreover, the changes in eigenmodes are unique to the cantilever to which mass is added, thereby providing a characteristic “fingerprint” that identifies the particular cantilever where mass has been added. This opens the door to ultrasensitive detection and identification of multiple analytes with a single coupled array.

Eigenvalues associated with relaxed states of toroidal plasmas

In the theory of relaxed states of toroidal plasmas certain eigenvalues of the equation ∇×B=μB play a crucial role. These eigenvalues are associated with vanishing toroidal flux and determine the onset of current limitation in a toroidal discharge. In axisymmetric systems there are both periodic and axisymmetric eigenfunctions and it is important to know whether the eigenmode associated with the lowest eigenvalue is periodic or axisymmetric. This depends on the shape of the poloidal cross section and determines the nature of the current-limited discharge. The eigenvalues of periodic and axisymmetric modes have been computed in rectangular and elliptical cross sections and in reentrant Multipinch-like cross sections. The reentrant case required new numerical techniques, which are described. It is found that in rectangular and elliptic cross sections the lowest mode is always periodic. However, in the Multipinch a transition occurs in which the lowest eigenmode changes from periodic to axisymmetric as the ‘‘waist’’ in the cross section is made narrower. The critical width is determined. These calculations suggest that in the GA Multipinch experiment [Nucl. Fusion 26, 255 (1986)] the current saturated discharge should be axisymmetric—unlike all other existing pinch experiments where it is periodic.