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A. Grigis

Publications and source records attributed to A. Grigis.

7 recordsLinked to original sources
arXiv2024

Exploring non-Euclidean photonics: Pseudosphere microlaser

Classical and wave properties of microlasers with the shape of a truncated pseudosphere are investigated through experiments and numerical simulations. These pseudosphere microlasers are surface-like organic microlasers with constant negative curvature, which were fabricated with high optical quality by direct laser writing. It is shown that they behave, in many ways, similar to two-dimensional flat disks, regardless of their different Gaussian curvature. We derive the monodromy matrices for geodesics on the pseudosphere and demonstrate that the periodic geodesics are marginally stable. Actually, due to the rotational symmetry, the pseudosphere is an integrable system.

physics.optics↗
arXiv2020

PySAP: Python Sparse Data Analysis Package for Multidisciplinary Image Processing

We present the open-source image processing software package PySAP (Python Sparse data Analysis Package) developed for the COmpressed Sensing for Magnetic resonance Imaging and Cosmology (COSMIC) project. This package provides a set of flexible tools that can be applied to a variety of compressed sensing and image reconstruction problems in various research domains. In particular, PySAP offers fast wavelet transforms and a range of integrated optimisation algorithms. In this paper we present the features available in PySAP and provide practical demonstrations on astrophysical and magnetic resonance imaging data.

astro-ph.IM↗
arXiv2019

Three-dimensional micro-billiard lasers: the square pyramid

Microlasers are of ample interest for advancing quantum chaos studies at the intersection of wave dynamics and geometric optics in resonators. However, the mode structures of three-dimensional microlasers without rotational symmetry remain largely unexplored due to fabrication limitations. Previous studies of such cavities revealed lasing modes localized on periodic orbits exclusively confined to a single plane. In this work, we report on the characterization of pyramidal, polymer-based microlasers and demonstrate that the lasing modes are localized on a genuine three-dimensional periodic orbit. The consequences on the laser features are further discussed, in particular stability and polarization issues.

physics.optics↗
arXiv2014

Localized lasing modes of triangular organic microlasers

We investigated experimentally the ray-wave correspondence in organic microlasers of various triangular shapes. Triangular billiards are of interest since they are the simplest cases of polygonal billiards and the existence and properties of periodic orbits in triangles are not yet fully understood. The microlasers with symmetric shapes that were investigated exhibited states localized on simple periodic orbits, and their lasing characteristics like spectra and far-field distributions could be well explained by the properties of the periodic orbits. Furthermore, asymmetric triangles that do not feature simple periodic orbits were studied. Their lasing properties were found to be more complicated and could not be explained by periodic orbits.

physics.optics↗
arXiv2004

Methods for determination and approximation of domains of attraction in the case of autonomous discrete dynamical systems

A method for determination and two methods for approximation of the domain of attraction $D_{a}(0)$ of an asymptotically stable steady state of an autonomous, $\mathbb{R}$-analytical, discrete system is presented. The method of determination is based on the construction of a Lyapunov function $V$, whose domain of analyticity is $D_{a}(0)$. The first method of approximation uses a sequence of Lyapunov functions $V_{p}$, which converges to the Lyapunov function $V$ on $D_{a}(0)$. Each $V_{p}$ defines an estimate $N_{p}$ of $D_{a}(0)$. For any $x\in D_{a}(0)$ there exists an estimate $N_{p^{x}}$ which contains $x$. The second method of approximation uses a ball $B(R)\subset D_{a}(0)$ which generates the sequence of estimates $M_{p}=f^{-p}(B(R))$. For any $x\in D_{a}(0)$ there exists an estimate $M_{p^{x}}$ which contains $x$. The cases $\|\partial_{0}f\|<1$ and $ρ(\partial_{0}f)<1$ are treated separately (even though the second case includes the first one) because significant differences occur.

math.DS↗