Slow light on a printed circuit board

Slow-light effects induced by stimulated Raman scattering in polymer waveguides on a printed circuit board are shown to enable a widely tunable delay of broadband optical signals, suggesting an advantageous platform for optical information processing and ultrafast optical waveform transformation.     

Compact interrogator for fiber optic Bragg sensors based on an acousto-optic filter formed by photonic crystal rows of air holes

Fiber optic sensors are typically used with expensive tunable lasers or optical spectrum analyzers for wavelength interrogation. We propose to replace the tunable laser by a broadband optical source incorporated with a novel thin linewidth acousto-optic tunable filter. It utilizes optical beam expanders constituted by photonic crystal rows of air holes in LiNbO(3) waveguide. A new design is numerically studied for a short structure (with 32 photonic crystal rows) by a two-dimensional finite-difference time-domain method. Extrapolation of these results to larger structure sizes (about 1 cm) demonstrates the possibility to develop compact interrogators with 0.4 pm wavelength resolution and 40 nm tunable range around 1550 nm.     

Ionization penalty in nonlinear Raman neuroimaging

Light-assisted ionization accompanying coherent anti-Stokes Raman scattering (CARS) of ultrashort laser pulses in brain tissue is shown to manifest itself in a detectable blueshift of the anti-Stokes signal. This blueshift can serve as an indicator of ionization processes in CARS-based neuroimaging.     

Magnetostatic Green's functions for the description of spin waves in finite rectangular magnetic dots and stripes

We present derivation of the magnetostatic Green's functions used in calculations of spin-wave spectra of finite-size non-ellipsoidal (rectangular) magnetic elements. The elements (dots) are assumed to be single domain particles having uniform static magnetization. We consider the case of flat dots, when the in-plane dot size is much larger than the dot height (film thickness), and assume the uniform distribution of the variable magnetization along the dot height. The limiting cases of magnetic waveguides with rectangular cross-section and thin magnetic stripes are also considered. The developed method of tensorial Green's functions is used to solve the Maxwell equations in the magnetostatic limit, and to represent the Landau–Lifshitz equation of motion for the magnetization of a magnetic element in a closed integro-differential form.     

Essential points of conformal vector fields

An essential point of a conformal vector field ξ$\xi$ on a conformal manifold (M,c)$(M,c)$ is a point around which the local flow of ξ$\xi$ preserves no metric in the conformal class c$c$. It is well-known that a conformal vector field vanishes at each essential point. In this note we show that essential points are isolated. This is a generalization to higher dimensions of the fact that the zeros of a holomorphic function are isolated. As an application, we show that every connected component of the zero set of a conformal vector field is totally umbilical.     

On Sharp Aperture-Weighted Estimates for Square Functions

Let \(S_{\alpha ,\psi }(f)\) be the square function defined by means of the cone in \({\mathbb R}^{n+1}_{+}\) of aperture \(\alpha \) , and a standard kernel \(\psi \) . Let \([w]_{A_p}\) denote the \(A_p\) characteristic of the weight \(w\) . We show that for any \(1<p<\infty \) and \(\alpha \ge 1\) , $$\begin{aligned} \Vert S_{\alpha ,\psi }\Vert _{L^p(w)}\lesssim \alpha ^n[w]_{A_p}^{\max \left( \frac{1}{2},\frac{1}{p-1}\right) }. \end{aligned}$$ For each fixed \(\alpha \) the dependence on \([w]_{A_p}\) is sharp. Also, on all class \(A_p\) the result is sharp in \(\alpha \) . Previously this estimate was proved in the case \(\alpha =1\) using the intrinsic square function. However, that approach does not allow to get the above estimate with sharp dependence on \(\alpha \) . Hence we give a different proof suitable for all \(\alpha \ge 1\) and avoiding the notion of the intrinsic square function.     

T-functions revisited: new criteria for bijectivity/transitivity

The paper presents new criteria for bijectivity/transitivity of T-functions and a fast knapsack-like algorithm of evaluation of a T-function. Our approach is based on non-Archimedean ergodic theory: Both the criteria and algorithm use van der Put series to represent 1-Lipschitz p-adic functions and to study measure-preservation/ergodicity of these.     

Positivity and tameness in rank 2 cluster algebras

We study the relationship between the positivity property in a rank 2 cluster algebra, and the property of such an algebra to be tame. More precisely, we show that a rank 2 cluster algebra has a basis of indecomposable positive elements if and only if it is of finite or affine type. This statement disagrees with a conjecture by Fock and Goncharov.     

A random coordinate descent algorithm for optimization problems with composite objective function and linear coupled constraints

In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz continuous gradient, then we prove that our method obtains an ?-optimal solution in $\mathcal{O}(n^{2}/\epsilon)$ iterations, where n is the number of blocks. For the class of problems with cheap coordinate derivatives we show that the new method is faster than methods based on full-gradient information. Analysis for the rate of convergence in probability is also provided. For strongly convex functions our method converges linearly. Extensive numerical tests confirm that on very large problems, our method is much more numerically efficient than methods based on full gradient information.     

Erratum to: Organic–inorganic hybrid melting gels

Melting gels are a class of organically modified silica gels that are rigid at room temperature, flow at temperature T1 and consolidate at temperature T2 (T2 > T1), when crosslinking is complete. The process of (a) softening, (b) becoming rigid and (c) re-softening can be repeated many times. Mixtures of mono-substituted alkoxysilanes and di-substituted alkoxysilanes have been studied in a systematic way to identify suitable melting gel compositions. The mixtures and the resulting melting gels have been characterized for their softening temperatures and consolidation temperatures. With an interest in using these materials for sealing microelectronics, their physical properties have been measured.