Related papers: Computing the laser beam path in optical cavities:…
We discuss one possible method for suppression of the nonlinear effect of a parametric oscillatory instability in a Fabry-Perot cavity of the next generation of gravitational wave detectors by determination of optimal radii of curvature of…
The use of second order information on the forward operator often comes at a very moderate additional computational price in the context of parameter identification probems for differential equation models. On the other hand the use of…
We propose a new globally convergent stochastic second order method. Our starting point is the development of a new Sketched Newton-Raphson (SNR) method for solving large scale nonlinear equations of the form $F(x)=0$ with $F:\mathbb{R}^p…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
Nonlinear optics underpins quantum photonics by enabling the generation and control of quantum states of light. We present new applications of optical resonators as mode selectors in nonlinear processes. First, we show that cavity-enhanced…
Our problem is to accurately solve linear systems on a general purpose graphics processing unit with double double and quad double arithmetic. The linear systems originate from the application of Newton's method on polynomial systems.…
The Fermat principle is used to define trajectories in nonhomogenous optical media. The Poincare model of the Lobachevskii geometry is derived. The index of refraction is determined for the light confined in the circular trajectory in the…
The Zernike radial polynomials are a system of orthogonal polynomials over the unit interval with weight x. They are used as basis functions in optics to expand fields over the cross section of circular pupils. To calculate the roots of…
Non-smooth regularization is widely used in image reconstruction to eliminate the noise while preserving subtle image structures. In this work, we investigate the use of proximal Newton (PN) method to solve an optimization problem with a…
Higher order Laguerre-Gauss (LG) beams have been proposed for use in future gravitational wave detectors, such as upgrades to the Advanced LIGO detectors and the Einstein Telescope, for their potential to reduce the effects of the thermal…
Applications of cavity optomechanics span from gravitational wave detection to the study of quantum motion states in mesoscopic mechanical systems. The engineering of resonators supporting strongly interacting mechanical and optical modes…
In this paper we present the design, simulation, and proof of principle results of an optimization based adaptive feed-forward algorithm for beam-loading compensation in a high impedance room temperature cavity. We begin with an overview of…
We apply two families of novel fractional $\theta$-methods, the FBT-$\theta$ and FBN-$\theta$ methods developed by the authors in previous work, to the fractional Cable model, in which the time direction is approximated by the fractional…
This paper presents the first optimal-rate $p$-th order methods with $p\geq 1$ for finding first and second-order stationary points of non-convex smooth objective functions over Riemannian manifolds. In contrast to the geodesically convex…
This work is on constrained large-scale non-convex optimization where the constraint set implies a manifold structure. Solving such problems is important in a multitude of fundamental machine learning tasks. Recent advances on Riemannian…
Detection dead zones and heading errors induced by light shifts are two important problems in optically pumped scalar magnetometry. We introduce an atomic orientation based single-beam magnetometry scheme to simultaneously solve these…
Significant progress has been made in ultrasonic guided wave (UGW) technology for pipe signal processing and defect imaging recently. However, developing a defect localization and imaging algorithm that requires fewer parameters, offers a…
We study optical cavity locking for laser stabilization through spatial modulation of the phase front of a light beam. A theoretical description of the underlying principle is developed for this method and special attention is paid to…
Retraction-free approaches offer attractive low-cost alternatives to Riemannian methods on the Stiefel manifold, but they are often first-order, which may limit the efficiency under high-accuracy requirements. To this end, we propose a…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…