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About 9,669 papers for “eigenmodes”
K. Itoh, S.‐I. Itoh, P. H. Diamond et al. · Plasma and Fusion Research · 2006
The eigenmode of a geodesic acoustic mode in the presence of a temperature gradient is discussed. Eigenmodes are obtained and the characteristic wavelength scales as ρi2/3LT1/3 (ρi: ion gyroradius, LT: temperature gradient scale length). The direction of propagation is discussed.
Cited by 56Open access
Springer series in optical sciences/SPringer series in optical sciences · 2005
Cited by 2
Konstantin Y. Bliokh · Physical review. A/Physical review, A · 2018
Plane waves and cylindrical or spherical vortex modes are important sets of solutions of quantum and classical wave equations. These are eigenmodes of the energy-momentum and angular-momentum operators, i.e., generators of spacetime translations and spatial rotations, respectively. Here we describe another set of wave modes: eigenmodes of the ``boost momentum'' operator, i.e., a generator of Lorentz boosts (spatiotemporal rotations). Akin to the angular momentum, only one (say, $z)$ component of the boost momentum can have a well-defined quantum number. The boost eigenmodes exhibit invariance with respect to the Lorentz transformations along the $z$ axis, leading to scale-invariant wave forms and steplike singularities moving with the speed of light. We describe basic properties of the Lorentz-boost eigenmodes and argue that these can serve as a convenient basis for problems involving causal propagation of signals.
Cited by 12Open access
А. М. Игнатов · Bulletin of the Lebedev Physics Institute · 2014
It is shown that the spectra of a planar fixed-length cavity executing periodic oscillations are described by fractal curves of the devil’s staircase type. In the case of the cavity length comparable to the oscillation period, eigenmodes represent a sequence of short pulses.
Cited by 0
Lecture notes in physics · 2008
Cited by 0
Günzler, Antonio, Schumacher, Cédric, Steiner, Ullrich et al. · Figshare · 2022
Metamaterial homogenization theories usually start with crude approximations that are valid in certain limits in zero order, such as small frequencies, wave vectors and material fill fractions. In some cases they remain surprisingly robust exceeding their initial assumptions, such as the well-established Maxwell-Garnett theory for elliptical inclusions that can produce reliable results for fill fractions far above its theoretical limitations. We here present a rigorous solution of Maxwell’s equations in binary periodic materials employing a combined Greens-Galerkin procedure to obtain a low-dimensional eigenproblem for the evanescent Floquet eigenmodes of the material. In its general form, our method provides an accurate solution of the multi-valued complex Floquet bandstructure, which currently cannot be obtained with established solvers. It is thus shown to be valid in regimes where homogenization theories naturally break down. For small frequencies and wave numbers in lowest order, our method simplifies to the Maxwell-Garnett result for 2D cylinder and 3D sphere packings. It therefore provides the missing explanation why Maxwell-Garnett works well up to extremely high fill fractions of approximately 50% depending on the constituent materials, provided the inclusions are arranged on an isotropic lattice.
Cited by 0Open access
Michaël Mazilu, Joerg Baumgartl, Sebastian Kosmeier et al. · arXiv (Cornell University) · 2010
We report a mathematically rigorous technique which facilitates the optimization of various optical properties of electromagnetic fields. The technique exploits the linearity of electromagnetic fields along with the quadratic nature of their interaction with matter. In this manner we may decompose the respective fields into optical quadratic measure eigenmodes (QME). Key applications include the optimization of the size of a focused spot, the transmission through photonic devices, and the structured illumination of photonic and plasmonic structures. We verify the validity of the QME approach through a particular experimental realization where the size of a focused optical field is minimized using a superposition of Bessel beams.
Cited by 0Open access
Tamara Gratcheva · 2024
Spectra of systems with balanced gain and loss, described by Hamiltonians with parity and time-reversal (PT) symmetry is a rich area of research. This work studies by means of numerical techniques, how eigenvalues and eigenfunctions of a Schrodinger operator change as a gain-loss parameter changes. Two cases on a disk with zero boundary conditions are considered. In the first case, within the enclosing disk, we place a parity (P) symmetric configuration of three smaller disks containing gain and loss media, which does not have PT-symmetry. In the second case, we study a PT-symmetric configuration of two smaller disks with gain and loss media. We find a rich variety of exceptional points, re-entrant PT-symmetric phases, and a non-monotonic dependence of the PT-symmetry breaking threshold on the system parameters. Previous explorations of spectra of PT-symmetric systems have mainly been limited to finite discrete models or problems in one dimension. By leveraging systems on a two-dimensional continuum, we show how the complexity and variability of the spectral behavior increases. Finally, by considering small analytically computable examples, we study the concept of exceptional points and their relation to the PT-symmetry breaking threshold.
Cited by 0Open access
Betti, R., Freidberg, J.P. · DSpace@MIT (Massachusetts Institute of Technology) · 1991
Cited by 0Open access
Hans-Walter Glock, K. Rothemund, Ursula van Rienen · Lecture notes in computational science and engineering · 2003
Cited by 1
Günzler, Antonio, Schumacher, Cédric, Steiner, Ullrich et al. · Figshare · 2022
Metamaterial homogenization theories usually start with crude approximations that are valid in certain limits in zero order, such as small frequencies, wave vectors and material fill fractions. In some cases they remain surprisingly robust exceeding their initial assumptions, such as the well-established Maxwell-Garnett theory for elliptical inclusions that can produce reliable results for fill fractions far above its theoretical limitations. We here present a rigorous solution of Maxwell’s equations in binary periodic materials employing a combined Greens-Galerkin procedure to obtain a low-dimensional eigenproblem for the evanescent Floquet eigenmodes of the material. In its general form, our method provides an accurate solution of the multi-valued complex Floquet bandstructure, which currently cannot be obtained with established solvers. It is thus shown to be valid in regimes where homogenization theories naturally break down. For small frequencies and wave numbers in lowest order, our method simplifies to the Maxwell-Garnett result for 2D cylinder and 3D sphere packings. It therefore provides the missing explanation why Maxwell-Garnett works well up to extremely high fill fractions of approximately 50% depending on the constituent materials, provided the inclusions are arranged on an isotropic lattice.
Cited by 0Open access
Günzler, Antonio, Schumacher, Cédric, Steiner, Ullrich et al. · Figshare · 2022
Metamaterial homogenization theories usually start with crude approximations that are valid in certain limits in zero order, such as small frequencies, wave vectors and material fill fractions. In some cases they remain surprisingly robust exceeding their initial assumptions, such as the well-established Maxwell-Garnett theory for elliptical inclusions that can produce reliable results for fill fractions far above its theoretical limitations. We here present a rigorous solution of Maxwell’s equations in binary periodic materials employing a combined Greens-Galerkin procedure to obtain a low-dimensional eigenproblem for the evanescent Floquet eigenmodes of the material. In its general form, our method provides an accurate solution of the multi-valued complex Floquet bandstructure, which currently cannot be obtained with established solvers. It is thus shown to be valid in regimes where homogenization theories naturally break down. For small frequencies and wave numbers in lowest order, our method simplifies to the Maxwell-Garnett result for 2D cylinder and 3D sphere packings. It therefore provides the missing explanation why Maxwell-Garnett works well up to extremely high fill fractions of approximately 50% depending on the constituent materials, provided the inclusions are arranged on an isotropic lattice.
Cited by 0Open access
Günzler, Antonio, Schumacher, Cédric, Steiner, Ullrich et al. · Figshare · 2022
Metamaterial homogenization theories usually start with crude approximations that are valid in certain limits in zero order, such as small frequencies, wave vectors and material fill fractions. In some cases they remain surprisingly robust exceeding their initial assumptions, such as the well-established Maxwell-Garnett theory for elliptical inclusions that can produce reliable results for fill fractions far above its theoretical limitations. We here present a rigorous solution of Maxwell’s equations in binary periodic materials employing a combined Greens-Galerkin procedure to obtain a low-dimensional eigenproblem for the evanescent Floquet eigenmodes of the material. In its general form, our method provides an accurate solution of the multi-valued complex Floquet bandstructure, which currently cannot be obtained with established solvers. It is thus shown to be valid in regimes where homogenization theories naturally break down. For small frequencies and wave numbers in lowest order, our method simplifies to the Maxwell-Garnett result for 2D cylinder and 3D sphere packings. It therefore provides the missing explanation why Maxwell-Garnett works well up to extremely high fill fractions of approximately 50% depending on the constituent materials, provided the inclusions are arranged on an isotropic lattice.
Cited by 0Open access
M. Lachièze-Rey · Classical and Quantum Gravity · 2004
Cosmological models wherein spatial sections are the Poincaré dodecahedral space D have been recently invoked to explain the missing power in the low-order angular modes of the cosmic microwave background observed anisotropies. Further exploration of this possibility requires knowledge of the eigenmodes of the Laplacian of D. Only the first modes have been calculated numerically. Here we give an explicit form for these modes up to arbitrary order, in terms of the eigenvectors of a small rank matrix, which are very easy to calculate numerically. As an illustration we give numerical estimates of the first modes, up to the eigenvalue −k(k + 2) for k = 62. These results are obtained by application of a more general method (presented in a previous work) which allows one to express the properties of any eigenfunction of the Laplacian of the 3-sphere under an arbitrary rotation of SO(4).
Cited by 12
Yasushi TODO · Journal of Plasma and Fusion Research · 1999
This article describes recent progress in nonlinear simulation studies of Alfven eigenmodes, especially of the toroidicity-induced Alfven eigenmode (TAE). Early simulations showed clearly that wave-particle trapping saturates the growth of TAE, but experimental results such as recurrent bursts and steady saturation remain unexplained. Recent simulations, which take account of particle source and collisions, can solve the mystery of these qualitatively different behaviors.
Cited by 0Open access
A. E. Siegman · 2007
It is commonly assumed that the modes of optical waveguides and resonators form a complete set of normal modes in the same fashion as in many other physical systems. The equations that govern the propagating or resonant modes in many common optical systems are, however, nonhermitian in character, and as a result the eigenmodes of these systems are not orthogonal to each other and do not comprise a set of "normal modes" in the usual sense of that term. Many of our fundamental concepts related to optical systems and laser physics depend upon the assumed orthogonality of the modes of these systems, and are significantly changed if these modes are not orthogonal. This paper describes and gives physical interpretations for the unusual mathematical and physical properties of nonnormal optical systems, using as examples loss-guided or gain-guided optical waveguides and the resonant modes of unstable optical resonators.
Cited by 0
T.M. Roberts · IEEE Transactions on Magnetics · 1990
An exact computational algorithm that solves steady-state Maxwell equations for fields produced by electric currents in the presence of slabs with biaxial anisotropy is developed. Eigenmodes are computed explicitly and are used to study unattenuated propagation and transverse modes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Cited by 19
M. H-m. Syn, R. W. Prager · 1995
The Finite Element Method (FEM) solution of the wave equation which governs the behaviour of elastic structures leads to a generalised eigenproblem. The eigenvectors of this eigenproblem are known as eigenmodes or mode shapes, which we present as an ideal set of shape features for use in model-based 3D ultrasound imaging. We derive from first principles a framework for the modelling of volumetric linear elastic structures, using the Principal of Virtual Work. This allows us to construct mass and stiffness matrices which describe the shape and physical properties of a shape model. We go on to examine the properties of the FEM eigenmodes of an elastic shape model, and the suitability of such a model in describing shape changes in biological structures. We show that there is an intimate connection between this model, and a growth model based on diffusion processes. Contents 1 Introduction 2 1.1 Growth models : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.1.1 Di...
Cited by 0
BOFFI D, GASTALDI, Lucia · Institutional Research Information System (Università degli Studi di Brescia) · 2001
Cited by 0
Martin Costabel, Monique Dauge · arXiv (Cornell University) · 2018
This paper is devoted to Maxwell modes in three-dimensional bounded electromagnetic cavities that have the form of a product of lower dimensional domains in some system of coordinates. The boundary conditions are those of the perfectly conducting or perfectly insulating body. The main case of interest is products in Cartesian variables. Cylindrical and spherical variables are also addressed. We exhibit common structures of polarization type for eigenmodes. In the Cartesian case, the cavity eigenvalues can be obtained as sums of Dirich-let or Neumann eigenvalues of positive Laplace operators and the corresponding eigenvectors have a tensor product form. We compare these descriptions with the spherical wave function Ansatz for a ball and show why the cavity eigenvalue of the ball are also Dirichlet or Neumann eigenvalues of some scalar operators. As application of our general formulas, we find explicit eigenpairs in a cuboid, in a circular cylinder, and in a cylinder with a coaxial circular hole. This latter example exhibit interesting '' TEM '' eigenmodes that have a one-dimensional vibrating string structure, and contribute to the least energy modes if the cylinder is long enough.
Cited by 3Open access