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Precise modeling of extended sources is a central challenge in modern optical engineering, laser physics, and computational lithography. Unlike ideal point sources or completely incoherent thermal radiation sources, real-world light sources…

Optics · Physics 2025-12-09 Rongqi Shang , Donglin Ma

We study the Wigner kernel and the Gabor matrix associated with the propagators of a broad class of linear evolution equations, including the complex heat, wave, and Hermite equations. Within the framework of time-frequency analysis, we…

Analysis of PDEs · Mathematics 2025-11-25 Elena Cordero , Gianluca Giacchi , Luigi Rodino

Warped time-frequency systems have recently been introduced as a class of structured continuous frames for functions on the real line. Herein, we generalize this framework to the setting of functions of arbitrary dimensionality. After…

Functional Analysis · Mathematics 2024-04-25 Nicki Holighaus , Felix Voigtlaender

We show that every rationally sampled dilation-and-modulation system is unitarily equivalent with a multi-window Gabor system. As a consequence, frame theoretical results from Gabor analysis can be directly transferred to…

Functional Analysis · Mathematics 2025-06-24 Jakob Lemvig

As time can be introduced as an additional degree of freedom, temporal metamaterials nowadays open up new avenues for wave control and manipulation. Among these advancements, temporal metamaterial-based antireflection coatings have recently…

Optics · Physics 2025-11-19 Haonan Hou , Kai Peng , Yangkai Wang , Jiarui Wang , Xudong Zhang , Ren Wang , Hao Hu , Jiang Xiong

A general principle says that the matrix of a Fourier integral operator with respect to wave packets is concentrated near the curve of propagation. We prove a precise version of this principle for Fourier integral operators with a smooth…

Functional Analysis · Mathematics 2014-07-17 Elena Cordero , Karlheinz Gröchenig , Fabio Nicola

We study the problem of constructing a graph Fourier transform (GFT) for directed graphs (digraphs), which decomposes graph signals into different modes of variation with respect to the underlying network. Accordingly, to capture low,…

Spectral Theory · Mathematics 2017-06-01 Rasoul Shafipour , Ali Khodabakhsh , Gonzalo Mateos , Evdokia Nikolova

We establish a broad notion of admissible tilings of frequency space which admit associated wave packet frames with elements which are smooth and compactly supported. The framework is designed to allow for tile geometries which are…

Classical Analysis and ODEs · Mathematics 2022-08-08 Philip T. Gressman

Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply…

Functional Analysis · Mathematics 2016-10-31 Firdous A. Shah

We study the coherence in time and space of electromagnetic fields propagated through complex media. Whether for localization, imaging or telecommunication, the development of dedicated numerical techniques is generally based on the…

Computational Physics · Physics 2022-04-21 Thomas Fromenteze , Matthieu Davy , Okan Yurduseven , Yann Marie-Joseph , Cyril Decroze

We present a novel approach to the analysis of a full model of scalar modulation instability (MI) by means of a simple geometrical description in the power vs. frequency plane. This formulation allows to relate the shape of the MI gain to…

Optics · Physics 2017-01-20 S. M. Hernandez , P. I. Fierens , J. Bonetti , A. D. Sánchez , D. F. Grosz

Spatio-temporally modulated impedance surfaces can be good candidates for generation of radiating waves with arbitrary eigenstates by breaking momentum and energy conservations. Here, we present a theoretical framework based on the…

Applied Physics · Physics 2021-12-16 Amrollah Amini , Homayoon Oraizi

We present an explicit multiscale algorithm for solving differential equations for problems with high-frequency modes that can be averaged over by separating and scaling the fast and slow dynamics within a single equation. We introduce a…

Plasma Physics · Physics 2026-05-29 Maxwell H. Rosen , Manaure Francisquez , Gregory W. Hammett

Given a non-quasianalytic subadditive weight function $\omega$ we consider the weighted Schwartz space $\mathcal{S}_\omega$ and the short-time Fourier transform on $\mathcal{S}_\omega$, $\mathcal{S}'_\omega$ and on the related modulation…

Functional Analysis · Mathematics 2017-06-27 Chiara Boiti , David Jornet , Alessandro Oliaro

A novel single-sideband (SSB) time-modulated technique with 2-bit phase shifters is proposed. The timemodulated module is implemented by adding periodic phase modulation to 2-bit phase shifters, which is simpler without performance loss…

Signal Processing · Electrical Eng. & Systems 2020-10-14 Yanchang Gao , Gang Ni , Kun Wang , Yiqing Liu , Chong He , Ronghong Jin , Xianling Liang

We investigate nonlinear, higher-order dispersive equations with measure (or even less regular) potentials and initial data with low regularity. Our approach is of distributional nature and relies on the phase space analysis (via Gabor wave…

Analysis of PDEs · Mathematics 2024-07-23 Sonia Mazzucchi , Fabio Nicola , S. Ivan Trapasso

An accurate and fast method is presented for scattering of electromagnetic waves from an array of time-modulated graphene ribbons. We derive a time-domain integral equation for induced surface currents under subwavelength approximation.…

Optics · Physics 2023-06-28 Mahdi Rahmanzadeh , Behzad Rejaei , Amin Khavasi

We review the geometrical framework required for understanding the moduli space of $(2,2)$ superconformal-field theories, highlighting various aspects of its phase structure. In particular, we indicate the types of phase diagrams that…

High Energy Physics - Theory · Physics 2008-02-03 Ti-ming Chiang , Brian R. Greene

The time-frequency content of a signal can be measured by the Gabor transform or windowed Fourier transform. This is a function defined on phase space that is computed by taking the Fourier transform of the product of the signal against a…

funct-an · Mathematics 2008-02-03 Jayakumar Ramanathan , Pankaj Topiwala

A systematic study of small, time-dependent, perturbations to geometric wave-equation domains is hardly existent. Acoustic enclosures are typical examples featuring locally reacting surfaces that respond to a pressure gradient or a pressure…

Mathematical Physics · Physics 2018-01-03 David T. Heider , J. Leo van Hemmen