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

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

Nrf2 and Nrf2-related proteins in development and developmental toxicity : insights from studies in zebrafish (Danio rerio)

© The Author(s), 2015. This is the author's version of the work and is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Free Radical Biology and Medicine 88B (2015): 275-289, doi:10.1016/j.freeradbiomed.2015.06.022.Oxidative stress is an important mechanism of chemical toxicity, contributing to developmental toxicity and teratogenesis as well as to cardiovascular and neurodegenerative diseases and diabetic embryopathy. Developing animals are especially sensitive to effects of chemicals that disrupt the balance of processes generating reactive species and oxidative stress, and those anti-oxidant defenses that protect against oxidative stress. The expression and inducibility of anti-oxidant defenses through activation of NFE2-related factor 2 (Nrf2) and related proteins is an essential process affecting the susceptibility to oxidants, but the complex interactions of Nrf2 in determining embryonic response to oxidants and oxidative stress are only beginning to be understood. The zebrafish (Danio rerio) is an established model in developmental biology and now also in developmental toxicology and redox signaling. Here we review the regulation of genes involved in protection against oxidative stress in developing vertebrates, with a focus on Nrf2 and related cap’n’collar (CNC)-basic-leucine zipper (bZIP) transcription factors. Vertebrate animals including zebrafish share Nfe2, Nrf1, Nrf2, and Nrf3 as well as a core set of genes that respond to oxidative stress, contributing to the value of zebrafish as a model system with which to investigate the mechanisms involved in regulation of redox signaling and the response to oxidative stress during embryolarval development. Moreover, studies in zebrafish have revealed nrf and keap1 gene duplications that provide an opportunity to dissect multiple functions of vertebrate NRF genes, including multiple sensing mechanisms involved in chemical-specific effects.This work was supported in part by National Institutes of Health grants R01ES016366 (MEH), R01ES015912 (JJS), and F32ES017585 (ART-L).2016-06-2

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%

Rotating optical soliton clusters

We introduce the concept of soliton clusters -- multi-soliton bound states in a homogeneous bulk optical medium, and reveal a key physical mechanism for their stabilization associated with a staircase-like phase distribution that induces a net angular momentum and leads to cluster rotation. The ringlike soliton clusters provide a nontrivial generalization of the concepts of two-soliton spiraling, optical vortex solitons, and necklace-type optical beams.Comment: 4 pages, 5 figure

Ultrafast optical nonlinearity in quasi-one-dimensional Mott-insulator Sr2CuO3{\rm Sr_2CuO_3}

We report strong instantaneous photoinduced absorption (PA) in the quasi-one-dimensional Mott insulator ${\rm Sr_2CuO_3}$ in the IR spectral region. The observed PA is to an even-parity two-photon state that occurs immediately above the absorption edge. Theoretical calculations based on a two-band extended Hubbard model explains the experimental features and indicates that the strong two-photon absorption is due to a very large dipole-coupling between nearly degenerate one- and two-photon states. Room temperature picosecond recovery of the optical transparency suggests the strong potential of ${\rm Sr_2CuO_3}$ for all-optical switching.Comment: 10 pages, 4 figure

Magnetization of polydisperse colloidal ferrofluids: Effect of magnetostriction

We exploit magnetostriction in polydisperse ferrofluids in order to generate nonlinear responses, and apply a thermodynamical method to derive the desired nonlinear magnetic susceptibility. For an ideal gas, this method has been demonstrated to be in excellent agreement with a statistical method. In the presence of a sinusoidal ac magnetic field, the magnetization of the polydisperse ferrofluid contains higher-order harmonics, which can be extracted analytically by using a perturbation approach. We find that the harmonics are sensitive to the particle distribution and the degree of field-induced anisotropy of the system. In addition, we find that the magnetization is higher in the polydisperse system than in the monodisperse one, as also found by a recent Monte Carlo simulation. Thus, it seems possible to detect the size distribution in a polydisperse ferrofluid by measuring the harmonics of the magnetization under the influence of magnetostriction.Comment: 23 pages, 4 figures. To be accepted for publication in Phys. Rev.