Related papers: Optimization methods for achieving high diffractio…
We study the diffraction produced by a slab of purely reflective PT-symmetric volume Bragg grating that combines modulations of refractive index and gain/loss of the same periodicity with a quarter-period shift between them. Such a complex…
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…
The recently proposed concept of metagrating enables wavefront manipulation of electromagnetic (EM) waves with unitary efficiency and relatively simple fabrication requirements. Herein, two-dimensional (2D) metagratings composed of a 2D…
Quadratic convergence throughout the active space is achieved for the gradient ascent pulse engineering (GRAPE) family of quantum optimal control algorithms. We demonstrate in this communication that the Hessian of the GRAPE fidelity…
The Zero Contrast Grating (ZCG) is a promising candidate for moded and dispersive mid-infrared (MIR) photonics for its broadband transmittance and reflectance greater than 99.9%. The optimal grating design including refractive index and…
Recently several methods were proposed for sparse optimization which make careful use of second-order information [10, 28, 16, 3] to improve local convergence rates. These methods construct a composite quadratic approximation using Hessian…
First-order optimization methods tend to inherently favor certain solutions over others when minimizing an underdetermined training objective that has multiple global optima. This phenomenon, known as implicit bias, plays a critical role in…
Gratings and holograms are patterned surfaces that tailor optical signals by diffraction. Despite their long history, variants with remarkable functionalities continue to be discovered. Further advances could exploit Fourier optics, which…
The diffraction contrast modalities accessible by X-ray grating interferometers are not imaged directly but have to be inferred from sine like signal variations occurring in a series of images acquired at varying relative positions of the…
Applications such as unbalanced and fully shuffled regression can be approached by optimizing regularized optimal transport (OT) distances, such as the entropic OT and Sinkhorn distances. A common approach for this optimization is to use a…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
Ensuring adequate wireless coverage in upcoming communication technologies such as 6G is expected to be challenging. This is because user demands of higher datarate require an increase in carrier frequencies, which in turn reduce the…
We present a new computation method for simulating reflection high-energy electron diffraction and the total-reflection high-energy positron diffraction experiments. The two experiments are used commonly for the structural analysis of…
A theoretical approach for uniformly extracting light propagating through a light guide plate is developed here. Typically, liquid crystal display modalities utilize a backlit lighting system illuminated from the edge with light emitting…
This work demonstrates the utility of gradients for the global optimization of certain differentiable functions with many suboptimal local minima. To this end, a principle for generating search directions from non-local quadratic…
This study proposes a Newton based multiple objective optimization algorithm for hyperparameter search. The first order differential (gradient) is calculated using finite difference method and a gradient matrix with vectorization is formed…
Newton's method is the most widespread high-order method, demanding the gradient and the Hessian of the objective function. However, one of the main disadvantages of Newtons method is its lack of global convergence and high iteration cost.…
We present an experimental demonstration of a subwavelength diffraction grating performing first-order differentiation of the transverse profile of an incident optical beam with respect to a spatial variable. The experimental results are in…
Transverse magnetic (TM) scattering of an electromagnetic wave from a periodic dielectric diffraction grating can mathematically be described by a volume integral equation. This volume integral equation, however, in general fails to feature…
This paper optimizes the step coefficients of first-order methods for smooth convex minimization in terms of the worst-case convergence bound (i.e., efficiency) of the decrease in the gradient norm. This work is based on the performance…