Search results for "Linear"
showing 10 items of 7165 documents
Two-dimensional Helmholtz equation with zero Dirichlet boundary condition on a circle: Analytic results for boundary deformation, the transition disk…
2019
A deformation of a disk D of radius r is described as follows: Let two disks D1 and D2 have the same radius r, and let the distance between the two disk centers be 2a, 0 ≤ a ≤ r. The deformation transforms D into the intersection D1 ∩ D2. This deformation is parametrized by e = a/r. For e = 0, there is no deformation, and the deformation starts when e, starting from 0, increases, transforming the disk into a lens. Analytic results are obtained for the eigenvalues of Helmholtz equation with zero Dirichlet boundary condition to the lowest order in e for this deformation. These analytic results are obtained via a Hamiltonian method for solving the Helmholtz equation with zero Dirichlet boundar…
Two frequency oscillation of a photorefractive oscillator as a perturbation of the mirrorless oscillation
2010
We consider the properties of the non-degenerate two frequency regime of oscillation of the semi-linear photorefractive oscillator and analyze its relation with the mirrorless oscillation. We consider the oscillator with or without a frequency shifted feedback by a vibrating mirror. This study shows that these two apparently different phenomena are closely related. We conclude from the obtained results that the two frequency oscillation can be considered as a perturbation of the mirrorless oscillation.
Lacunary Bifurcation of Multiple Solutions of Nonlinear Eigenvalue Problems
1991
In order to describe the type of nonlinear eigenvalue problems we are going to discuss, consider a densely defined closed linear operator T in a real Hilbert space H and let H1 be the Hilbert space which consists of the domain of T together with the graph norm. Also, let H 1 * be the dual space of H1 and denote the dual operator corresponding to T: H1 → H by T’:H → H 1 * . Since H1 is dense in H, we may view H as a subspace of H1, and then the scalar product (·,·) on H and the dual pairing on H1 × H 1 * coincide on H1 × H.
Orientation dependence of high-order harmonic generation in molecules
2003
We present two- and three-dimensional model calculations of high-order harmonic generation in ${\mathrm{H}}_{2}^{+}.$ The harmonic spectra exhibit clear signatures of intramolecular interference. An interference minimum appears at a harmonic order that depends on the molecular orientation. Harmonic generation in three-center molecules is studied on the basis of two-dimensional calculations for a ${\mathrm{H}}_{3}^{2+}$ model system. From analytical considerations, the orientation dependence of the harmonic intensities in three-center molecules exhibits a double minimum due to intramolecular interference. In the numerical results, the double minimum is broadened into a single wide minimum. T…
Investigating surface magnetism by means of photoexcitation electron emission microscopy
2002
The imaging of surfaces by means of photoexcitation electron emission microscopy (PEEM) has recently received considerable interest. This is mainly due to the extended use and availability of brilliant synchrotron radiation in the soft x-ray regime which generally facilitates studies with surface specificity and chemical selectivity. The most popular application of the x-ray PEEM (XPEEM) technique concerns studies of magnetic systems and phenomena. By exploiting the high degree of circular or linear polarization of the synchrotron light, the magnetic microstructure in both ferromagnets and antiferromagnets can be visualized. In this contribution we demonstrate the unique potential and the v…
Modeling of photonic crystal fibers from the scalar wave equation with a purely transverse linearly polarized vector potential
2011
In this work, we propose a new technique for modeling light propagation in photonic crystal fibers where the electric field is evaluated from a purely transverse linearly polarized vector potential. The vector potential in a nonuniform dielectric obeys a wave equation coupled to the scalar potential, but it can be reduced to a scalar wave equation when the coupling term is ignored to the lowest order approximation. We show that this method gives reliable results for photonic crystal fibers when the scalar analysis is improved by a perturbational correction.
On-Sky Tests of a High-Power Pulsed Laser for Sodium Laser Guide Star Adaptive Optics
2016
We present results of on-sky tests performed in the summer of 2013 to characterize the performance of a prototype high-power pulsed laser for adaptive optics. The laser operates at a pulse repetition rate (PRR) of 600–800[Formula: see text]Hz, with a 6% duty cycle. Its coupling efficiency was found to be, in the best test case (using 18[Formula: see text]W of transmitted power), [Formula: see text] photons s[Formula: see text] sr[Formula: see text] atom[Formula: see text] W[Formula: see text] m2 when circular polarization was employed and [Formula: see text] photons s[Formula: see text] sr[Formula: see text] atom[Formula: see text] W[Formula: see text] m2 with linear polarization. No impro…
Efficient on-axis SLM engineering of optical vector modes
2020
Abstract This work presents a method for the efficient experimental generation of arbitrary polarized vector beam modes. The optical system employs two liquid-crystal on silicon (LCOS) spatial light modulators (SLM) in a common path architecture, avoiding the use of beam-splitters. Each SLM displays a different phase-only mask, each one encoding a different pattern onto two orthogonal linear polarization components of the input beam. These phase-only masks are designed using a recently proposed random technique to encode complex amplitude values. This encoding technique reconstructs the complex function on-axis, thus avoiding incorporating carrier phases. By addressing such properly designe…
Dielectric Collimators for Beam Delivery Systems*
2012
Abstract Wakefield generation by the collimation system is known to be a critical linear collider design issue. Optimization of the collimators represents a tradeoff between beam quality (halo reduction) and luminosity reduction. The primary objective is to reduce both short range (resonant) and long range (resistive) deflecting wakefields from collimators that reduce the luminosity of the machine. We consider the CLIC BDS (beam delivery system) and examine the potential for using dielectric rather than highly conducting materials for collimation. We present some examples of the flexibility gained by having control over the permittivity and conductivity of the collimator. We discuss simulation …
Relaxation, postponement, and features of the attractor in a driven varactor oscillator
1990
The driven varactor oscillator is investigated by numerical integration of its ODEs using the standard model of circuit theory. Attention is given to some properties of the basic relaxation mechanism. For time dependent amplitudes of the sinusoidal driving voltage the post-ponement of the bifurcations is characterized by transient Lyapunov numbers. The postponement of the first bifurcation shows the same dependence on the sweep velocity as in the case of the nonautonomous quadratic map. The shapes of the attractors are displayed in extended phase space. Generalized Renyi-dimensionsD 0 andD 1 have been determined in the chaotic region. A corresponding twodimensional Pioncare map indicates se…