Approximate Analytical Solutions for the Time-Domain Shielding of Plane Electromagnetic Waves Through an Infinite Conducting Plate

The “conducting-plate–plane-wave” configuration is a canonical problem in electromagnetic shielding. An exact analytical solution is available in the frequency domain, whereas in the time domain two seemingly distinct analytical impulse-response formulas have been reported. This article revisits time-domain analytical solutions of the transmitted field. First, we prove that the two approximate solutions are mathematically equivalent; for one of them we provide a physically transparent derivation based on multiple round-trip reflections. Next, we derive the suitability range over which these solutions remain valid, and we determine how short a realistic pulse can emulate a Dirac delta pulse. On the other hand, for sufficiently long pulses we show that the transmitted field reduces to the incident waveform multiplied by a simple scale factor. In addition, we introduce a simple substitution rule that extends the normal-incidence solution to oblique incidence for both TE and TM polarizations. These analytical results were validated by numerical inverse Fourier transformation of the exact frequency-domain transfer function expressed in normalized form to reveal the dominant parameters and the truncation criterion.