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Register a new userComputing leaky modes of optical fibers using a FEAST algorithm for polynomial eigenproblems
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An efficient contour integral technique to approximate a cluster of nonlinear eigenvalues of a polynomial eigenproblem, circumventing certain large
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We propose a new algorithm for numerical path tracking in polynomial homotopy continuation. The algorithm is `robust in the sense that it is designed to prevent path jumping and in many cases, it can be used in (only) double precision arithmetic. It is based on an adaptive stepsize predictor that uses Pade techniques to detect local difficulties for function approximation and danger for path jumping. We show the potential of the new path tracking algorithm through several numerical examples and compare with existing implementations.
Multimode fibers (MMFs) support abundant spatial modes and involve rich spatiotemporal dynamics, yielding many promising applications. Here, we investigate the influences of the number and initial energy of high-order modes (HOMs) on the energy flow from the intermediate modes (IMs) to the fundamental mode (FM) and HOMs. It is quite surprising that random distribution of high-order modes evolves to a stationary one, indicating the asymptotic behavior of orbits in the same attraction domain. By employing the Lyapunov exponent, we prove that the threshold of the HOMs-attractor is consistent with the transition point of the energy flow which indiactes the HOMs-attracotr acts as a valve in the modal energy flow. Our results provide a new perspective to explore the nonlinear phenomena in MMFs, such as Kerr self-cleaning, and may pave the way to some potential applications, such as secure communications in MMFs.
We present a new fast algorithm for computing the Boys function using nonlinear approximation of the integrand via exponentials. The resulting algorithms evaluate the Boys function with real and complex valued arguments and are competitive with previously developed algorithms for the same purpose.
While conventional optical trapping techniques can trap objects with submicron dimensions, the underlying limits imposed by the diffraction of light generally restrict their use to larger or higher refractive index particles. As the index and diameter decrease, the trapping difficulty rapidly increases; hence, the power requirements for stable trapping become so large as to quickly denature the trapped objects in such diffraction-limited systems. Here, we present an evanescent field based device capable of confining low index nanoscale particles using modest optical powers as low as 1.2 mW, with additional applications in the field of cold atom trapping. Our experiment uses a nanostructured optical micro-nanofiber to trap 200 nm, low index contrast, fluorescent particles within the structured region, thereby overcoming diffraction limitations. We analyze the trapping potential of this device both experimentally and theoretically, and show how strong optical traps are achieved with low input powers.
In this paper, we study how to quickly compute the <-minimal monomial interpolating basis for a multivariate polynomial interpolation problem. We address the notion of reverse reduced basis of linearly independent polynomials and design an algorithm for it. Based on the notion, for any monomial ordering we present a new method to read off the <-minimal monomial interpolating basis from monomials appearing in the polynomials representing the interpolation conditions.
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