1,222 research outputs found
The nonlinear directional coupler. An analytic solution
Linear and nonlinear directional couplers are currently used in fiber optics
communications. They may also play a role in multiphoton approaches to quantum
information processing if accurate control is obtained over the phases and
polarizations of the signals at the output of the coupler. With this
motivation, the constants of motion of the coupler equation are used to obtain
an explicit analytical solution for the nonlinear coupler.Comment: 6 pages Late
New nonlinear dielectric materials: Linear electrorheological fluids under the influence of electrostriction
The usual approach to the development of new nonlinear dielectric materials
focuses on the search for materials in which the components possess an
inherently large nonlinear dielectric response. In contrast, based on
thermodynamics, we have presented a first-principles approach to obtain the
electrostriction-induced effective third-order nonlinear susceptibility for the
electrorheological (ER) fluids in which the components have inherent linear,
rather than nonlinear, responses. In detail, this kind of nonlinear
susceptibility is in general of about the same order of magnitude as the
compressibility of the linear ER fluid at constant pressure. Moreover, our
approach has been demonstrated in excellent agreement with a different
statistical method. Thus, such linear ER fluids can serve as a new nonlinear
dielectric material.Comment: 11 page
Online Deliberation and the Public Sphere:Developing a Coding Manual to Assess Deliberation in Twitter Political Networks
Phase Controlled All-Optical Switching In Rocking Filter Fibers
We demonstrate experimentally that all-optical switching of a strong beam can be controlled by the phase of a weak beam in a rocking rotator fiber
Smoothed Analysis of Tensor Decompositions
Low rank tensor decompositions are a powerful tool for learning generative
models, and uniqueness results give them a significant advantage over matrix
decomposition methods. However, tensors pose significant algorithmic challenges
and tensors analogs of much of the matrix algebra toolkit are unlikely to exist
because of hardness results. Efficient decomposition in the overcomplete case
(where rank exceeds dimension) is particularly challenging. We introduce a
smoothed analysis model for studying these questions and develop an efficient
algorithm for tensor decomposition in the highly overcomplete case (rank
polynomial in the dimension). In this setting, we show that our algorithm is
robust to inverse polynomial error -- a crucial property for applications in
learning since we are only allowed a polynomial number of samples. While
algorithms are known for exact tensor decomposition in some overcomplete
settings, our main contribution is in analyzing their stability in the
framework of smoothed analysis.
Our main technical contribution is to show that tensor products of perturbed
vectors are linearly independent in a robust sense (i.e. the associated matrix
has singular values that are at least an inverse polynomial). This key result
paves the way for applying tensor methods to learning problems in the smoothed
setting. In particular, we use it to obtain results for learning multi-view
models and mixtures of axis-aligned Gaussians where there are many more
"components" than dimensions. The assumption here is that the model is not
adversarially chosen, formalized by a perturbation of model parameters. We
believe this an appealing way to analyze realistic instances of learning
problems, since this framework allows us to overcome many of the usual
limitations of using tensor methods.Comment: 32 pages (including appendix
All-Optical Integrated Mach-Zehnder Switching Due To Cascaded Nonlinearities
We demonstrate all-optical switching using the cascaded second order nonlinearity in a fully integrated, asymmetric Mach Zehnder interferometer implemented in lithium niobate channel waveguides. We obtained an 8:1 switching ratio
Comparison of resolving power and separation time in thermal field-flow fractionation, hydrodynamic chromatography, and size-exclusion chromatography.
All-optical switching in lithium niobate directional couplers with cascaded nonlinearity
We report on intensity-dependent switching in lithium niobate directional couplers. Large nonlinear phase shifts that are due to cascading detune the coupling between the coupler branches, which makes all-optical switching possible. Depending on the input intensity, the output could be switched between the cross and the bar coupler branches with a switching ratio of 1:5 and a throughput of 80%
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