Energy analysis of a transient wave process excited by a rectangular pulse

Abstract

Background. With the rapid advancement of ultrawideband technologies, pulsed antennas are becoming increasingly essential tools in applications involving radio communication, location, and remote sensing. Unlike harmonic sources, whose dynamics are well-described in the frequency domain, real pulsed emitters operate with finite-duration excitations, which significantly alter both the nature of the electromagnetic field and the process of energy transfer. One of the physically realistic excitation scenarios is the rectangular pulse, which models a situation where the source is active for a limited time interval and then turned off. This type of pulse more accurately reflects the actual operating conditions of pulsed systems than idealized step-like excitation. Investigating the energy characteristics in the time domain not only deepens the understanding of radiation mechanisms but also contributes to the improved design of efficient antennas and sources. Such insights directly impact the enhancement of range, noise immunity, and accuracy in communication and observation systems, as well as the reduction of energy losses and near-field exposure. Analyzing the transformation of pulsed energy at different stages of excitation, from the formation of wavefronts to their propagation, is key to developing high-fidelity models of the electromagnetic field.

Objectives. To derive analytical and numerical dependencies that describe the energy characteristics of the electromagnetic field excited by a rectangular pulse. Specifically, the aim is to obtain expressions for the energy flux through the transverse plane at an arbitrary distance from the aperture, as well as to determine the total wave energy at different stages of its spatiotemporal evolution. Where analytical solutions are unattainable, apply numerical methods. Provide a physical interpretation of the obtained results, and assess the influence of pulse duration on wave behavior.

Materials and methods. The problem is formulated as a transient three-dimensional propagation scenario of an -wave excited by a rectangular pulse from a circular aperture into the free half-space. General field solutions are constructed using the evolutionary approach. These solutions are expressed through the evolutionary coefficients, which are obtained as solutions of the inhomogeneous Klein-Gordon equation using the Riemann function method. To determine the energy flux, the longitudinal component of the Poynting vector is used. Numerical computations are carried out via the Gauss-Kronrod method.

Results. Exact analytical expressions for the energy flux and total energy at the aperture under rectangular excitation have been obtained. Generalized formulas have been derived for arbitrary planes, taking into account the temporal and spatial evolution of the field. A comparison with the far-field approximation shows that it may overestimate energy values in the near zone. A three-dimensional visualization of the spatiotemporal dynamics has been constructed, clearly demonstrating the formation and interaction of wavefronts. The process of energy accumulation in the near field has been analyzed, along with the manifestation of the “electromagnetic missile” effect, where the excitation exists in the form of a compact energy pulse.

Conclusions. This study presents, for the first time, analytical and numerical models for rectangular excitation of an -wave from an aperture radiator in the time domain. It is shown that, in the case of finite-duration pulses, the field exhibits more complex temporal dynamics than under step-like excitation. It is established that the energy flux near the aperture arises from the interaction of static and wave components, which render far-field approximations inaccurate at low values of the longitudinal coordinate. The slow decay of energy with distance indicates that a significant portion is concentrated in a compact front that retains its structure during propagation. The analysis refines the applicability conditions of approximate models and provides a foundation for further research aimed at optimizing pulsed antennas and radiation systems.