The broadband pulse diffraction on a half-plane screen and caustic

TL;DR

This paper investigates how ultrashort broadband pulses diffract around a half-plane screen and near caustics, analyzing their evolution in space and time for applications in communication and localization.

Contribution

It formulates basic equations for broadband pulse diffraction in spectral and time domains and provides integral representations for arbitrary initial pulse forms near caustics.

Findings

Derived integral representation for pulse fields near caustics.

Compared diffraction effects for different pulse shapes.

Analyzed the evolution of broadband pulses in diffraction scenarios.

Abstract

The diffraction of ultrashort pulse changes its spatial and temporal structure that is crucial for multi-channel communication and location via such pulses. The features of the evolution of broadband pulses discussed for two general problems: diffraction at the edge of a flat absorbing screen and the field near a simple caustic. The basic equations are formulated for spatial distribution of the pulse field after the screen in the spectral and time domain. Calculations of pulse diffraction for different wave shapes and comparison of results are presented. We obtain an integral representation for pulse field with arbitrary initial form near a caustic and analyze the results for different waveforms.