182,619 research outputs found
Coupled-mode theory for photonic band-gap inhibition of spatial instabilities
We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean-field models for singly and doubly degenerate optical parametric oscillators. Analytical expressions for the new (higher) modulational thresholds and the size of the "band gap" as a function of the system and photonic crystal parameters are obtained via a coupled-mode theory. Then, by means of a nonlinear analysis, we derive amplitude equations for the unstable modes and find the stationary solutions above threshold. The form of the unstable mode is different in the lower and upper parts of the band gap. In each part there is bistability between two spatially shifted patterns. In large systems stable wall defects between the two solutions are formed and we provide analytical expressions for their shape. The analytical results are favorably compared with results obtained from the full system equations. Inhibition of pattern formation can be used to spatially control signal generation in the transverse plane
Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons
Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a comprehensive investigation across diverse simulated and experimental systems, encompassing star and complex networks of Rössler systems, coupled hysteresis-based electronic oscillators, microcircuits of leaky integrate-and-fire model neurons, and finally recordings from in-vitro cultures of spontaneously-growing neuronal networks. We systematically consider a range of dynamical measures, including the correlation dimension, nonlinear prediction error, permutation entropy, and other information-theoretical indices. The empirical evidence gathered reveals that under situations of weak synchronization, wherein rather than a collective behavior one observes significantly differentiated dynamics, denser connectivity tends to locally promote the emergence of stronger signatures of nonlinear dynamics. In deterministic systems, transition to chaos and generation of higher-dimensional signals were observed; however, when the coupling is stronger, this relationship may be lost or even inverted. In systems with a strong stochastic component, the generation of more temporally-organized activity could be induced. These observations have many potential implications across diverse fields of basic and applied science, for example, in the design of distributed sensing systems based on wireless coupled oscillators, in network identification and control, as well as in the interpretation of neuroscientific and other dynamical data
Nonlinear Spectroscopy and All-Optical Switching of Femtosecond Soliton Molecules
The emergence of confined structures and pattern formation are exceptional
manifestations of concurring nonlinear interactions found in a variety of
physical, chemical and biological systems[1]. Optical solitons are a hallmark
of extreme spatial or temporal confinement enabled by a variety of
nonlinearities. Such particle-like structures can assemble in complex stable
arrangements, forming "soliton molecules"[2,3]. Recent works revealed
oscillatory internal motions of these bound states, akin to molecular
vibrations[4-8]. These observations beg the question as to how far the
"molecular" analogy reaches, whether further concepts from molecular
spectroscopy apply in this scenario, and if such intra-molecular dynamics can
be externally driven or manipulated. Here, we probe and control such ultrashort
bound-states in an optical oscillator, utilizing real-time spectroscopy and
time-dependent external perturbations. We introduce two-dimensional
spectroscopy of the linear and nonlinear bound-state response and resolve
anharmonicities in the soliton interaction leading to overtone and sub-harmonic
generation. Employing a non-perturbative interaction, we demonstrate
all-optical switching between distinct states with different binding
separation, opening up novel schemes of ultrafast spectroscopy, optical logic
operations and all-optical memory.Comment: 3 figure
Parametric generation of second sound in superfluid helium: linear stability and nonlinear dynamics
We report the experimental studies of a parametric excitation of a second
sound (SS) by a first sound (FS) in a superfluid helium in a resonance cavity.
The results on several topics in this system are presented: (i) The linear
properties of the instability, namely, the threshold, its temperature and
geometrical dependencies, and the spectra of SS just above the onset were
measured. They were found to be in a good quantitative agreement with the
theory. (ii) It was shown that the mechanism of SS amplitude saturation is due
to the nonlinear attenuation of SS via three wave interactions between the SS
waves. Strong low frequency amplitude fluctuations of SS above the threshold
were observed. The spectra of these fluctuations had a universal shape with
exponentially decaying tails. Furthermore, the spectral width grew continuously
with the FS amplitude. The role of three and four wave interactions are
discussed with respect to the nonlinear SS behavior. The first evidence of
Gaussian statistics of the wave amplitudes for the parametrically generated
wave ensemble was obtained. (iii) The experiments on simultaneous pumping of
the FS and independent SS waves revealed new effects. Below the instability
threshold, the SS phase conjugation as a result of three-wave interactions
between the FS and SS waves was observed. Above the threshold two new effects
were found: a giant amplification of the SS wave intensity and strong resonance
oscillations of the SS wave amplitude as a function of the FS amplitude.
Qualitative explanations of these effects are suggested.Comment: 73 pages, 23 figures. to appear in Phys. Rev. B, July 1 st (2001
Purcell Enhancement of Parametric Luminescence: Bright and Broadband Nonlinear Light Emission in Metamaterials
Single-photon and correlated two-photon sources are important elements for
optical information systems. Nonlinear downconversion light sources are robust
and stable emitters of single photons and entangled photon pairs. However, the
rate of downconverted light emission, dictated by the properties of
low-symmetry nonlinear crystals, is typically very small, leading to
significant constrains in device design and integration. In this paper, we show
that the principles for spontaneous emission control (i.e. Purcell effect) of
isolated emitters in nanoscale structures, such as metamaterials, can be
generalized to describe the enhancement of nonlinear light generation processes
such as parametric down conversion. We develop a novel theoretical framework
for quantum nonlinear emission in a general anisotropic, dispersive and lossy
media. We further find that spontaneous parametric downconversion in media with
hyperbolic dispersion is broadband and phase-mismatch-free. We predict a
1000-fold enhancement of the downconverted emission rate with up to 105 photon
pairs per second in experimentally realistic nanostructures. Our theoretical
formalism and approach to Purcell enhancement of nonlinear optical processes,
provides a framework for description of quantum nonlinear optical phenomena in
complex nanophotonic structures.Comment: 29 pages, 10 figure
Optically controlled orbital angular momentum generation in a polaritonic quantum fluid
Applications of the orbital angular momentum (OAM) of light range from the
next generation of optical communication systems to optical imaging and optical
manipulation of particles. Here we propose a micron-sized semiconductor source
which emits light with pre-defined OAM components. This source is based on a
polaritonic quantum fluid. We show how in this system modulational
instabilities can be controlled and harnessed for the spontaneous formation of
OAM components not present in the pump laser source. Once created, the OAM
states exhibit exotic flow patterns in the quantum fluid, characterized by
generation-annihilation pairs. These can only occur in open systems, not in
equilibrium condensates, in contrast to well-established vortex-antivortex
pairs
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