Diffraction of waves by screens (apertures in screens) with time-varying dimensions. Time-varying Kirchhoff's integral representation for moving boundaries

TL;DR

This paper develops a generalized Kirchhoff's integral representation to analyze electromagnetic wave diffraction by screens with dimensions that change over time, providing a method to adapt stationary formulas to dynamic scenarios.

Contribution

It introduces a time-varying Kirchhoff's integral representation for moving boundaries, extending stationary diffraction formulas to cases with slowly changing screen dimensions.

Findings

Derived generalized vector Kirchhoff's representation for time-varying screens.

Showed that stationary diffraction formulas can be adapted by substituting time-dependent parameters.

Provided expressions for scattered waves and power with accuracy up to v/c<<1.

Abstract

The diffraction of electromagnetic waves by screens (apertures in screens) with time-varying dimensions is studied. The generalized vector Kirchhoff's representation for this case is obtained. It is also shown that with accuracy up to the terms of the order of v/c<<1, the expressions for the scattered wave and instantaneous power can be derived from the appropriate expressions for a stationary case by substituting the time-dependent parameters of the screen dimensions (e.g. time-dependent radius) for constant parameters of screen dimensions (e.g., the screen radius) appearing in the formulas describing the stationary case.