23,863 research outputs found
The Strange Eigenmode in Lagrangian Coordinates
For a distribution advected by a simple chaotic map with diffusion, the
"strange eigenmode" is investigated from the Lagrangian (material) viewpoint
and compared to its Eulerian (spatial) counterpart. The eigenmode embodies the
balance between diffusion and exponential stretching by a chaotic flow. It is
not strictly an eigenmode in Lagrangian coordinates, because its spectrum is
rescaled exponentially rapidly.Comment: 15 pages, 6 figures. RevTeX4 format with psfra
Optical eigenmode imaging
We present an indirect imaging method that measures both amplitude and phase
information from a transmissive target. Our method is based on an optical
eigenmode decomposition of the light intensity and the first-order cross
correlation between a target field and these eigenmodes. We demonstrate that
such optical eigenmode imaging does not need any a priori knowledge of the
imaging system and corresponds to a compressive full-field sampling leading to
high image extraction efficiencies. Finally, we discuss the implications with
respect to second-order correlation imaging
Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters
Spatial modes have received substantial attention over the last decades and are used in optical communication applications. In fiber-optic communications, the employed linearly polarized modes and phase vortex modes carrying orbital angular momentum can be synthesized by fiber vector eigenmodes. To improve the transmission capacity and miniaturize the communication system, straightforward fiber vector eigenmode multiplexing and generation of fiber-eigenmode-like polarization vortices (vector vortex modes) using photonic integrated devices are of substantial interest. Here, we propose and demonstrate direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters. By exploiting vector vortex modes (radially and azimuthally polarized beams) generated from silicon microring resonators etched with angular gratings, we report data-carrying fiber vector eigenmode multiplexing transmission through a 2-km large-core fiber, showing low-level mode crosstalk and favorable link performance. These demonstrations may open up added capacity scaling opportunities by directly accessing multiple vector eigenmodes in the fiber and provide compact solutions to replace bulky diffractive optical elements for generating various optical vector beams
The Decay of Passive Scalars Under the Action of Single Scale Smooth Velocity Fields in Bounded 2D Domains : From non self similar pdf's to self similar eigenmodes
We examine the decay of passive scalars with small, but non zero, diffusivity
in bounded 2D domains. The velocity fields responsible for advection are smooth
(i.e., they have bounded gradients) and of a single large scale. Moreover, the
scale of the velocity field is taken to be similar to the size of the entire
domain. The importance of the initial scale of variation of the scalar field
with respect to that of the velocity field is strongly emphasized. If these
scales are comparable and the velocity field is time periodic, we see the
formation of a periodic scalar eigenmode. The eigenmode is numerically realized
by means of a deterministic 2D map on a lattice. Analytical justification for
the eigenmode is available from theorems in the dynamo literature. Weakening
the notion of an eigenmode to mean statistical stationarity, we provide
numerical evidence that the eigenmode solution also holds for aperiodic flows
(represented by random maps). Turning to the evolution of an initially small
scale scalar field, we demonstrate the transition from an evolving (i.e., {\it
non} self similar) pdf to a stationary (self similar) pdf as the scale of
variation of the scalar field progresses from being small to being comparable
to that of the velocity field (and of the domain). Furthermore, the {\it non}
self similar regime itself consists of two stages. Both the stages are examined
and the coupling between diffusion and the distribution of the Finite Time
Lyapunov Exponents is shown to be responsible for the pdf evolution.Comment: 21 pages (2 col. format), 11 figures. Accepted, to appear in PR
Dynamic Calibration of Higher Eigenmode Parameters of a Cantilever in Atomic Force Microscopy Using Tip-Surface Interactions
We present a theoretical framework for the dynamic calibration of the higher
eigenmode parameters (stiffness and optical lever responsivity) of a
cantilever. The method is based on the tip-surface force reconstruction
technique and does not require any prior knowledge of the eigenmode shape or
the particular form of the tip-surface interaction. The calibration method
proposed requires a single-point force measurement using a multimodal drive and
its accuracy is independent of the unknown physical amplitude of a higher
eigenmode.Comment: 4 pages, 4 figure
Generalized Berry Conjecture and mode correlations in chaotic plates
We consider a modification of the Berry Conjecture for eigenmode statistics
in wave-bearing systems. The eigenmode correlator is conjectured to be
proportional to the imaginary part of the Green's function. The generalization
is applicable not only to scalar waves in the interior of homogeneous isotropic
systems where the correlator is a Bessel function, but to arbitrary points of
heterogeneous systems as well. In view of recent experimental measurements,
expressions for the intensity correlator in chaotic plates are derived.Comment: 5 pages, 1 figur
Stability domains for time-delay feedback control with latency
We generalize a known analytical method for determining the stability of
periodic orbits controlled by time-delay feedback methods when latencies
associated with the generation and injection of the feedback signal cannot be
ignored. We discuss the case of extended time-delay autosynchronization (ETDAS)
and show that nontrivial qualitative features of the domain of control observed
in experiments can be explained by taking into account the effects of both the
unstable eigenmode and a single stable eigenmode in the Floquet theory.Comment: 9 pages, 6 figures; Submitted to Physical Review
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