Simple unidirectional few-cycle electromagnetic pulses

The paper is aimed at constructing exact solutions of Maxwell’s equations for homogeneous media, convenient for modeling ultrashort pulses of various shapes. An analytical description of a family of simple closed-form few-cycle electromagnetic pulses that are free of backward propagating components and have finite energy is presented. The mathematical framework rests on using, as a component of Hertz’s potential, a certain axisymmetric exact solution of the linear wave equation, which is studied here in detail. Depending on the choice of free parameters in this solution and on polarization of the potential, the resulting electromagnetic pulses can be pancake-like, ball-like, needle-like, and doughnut-like. Expressions for spectra of the electric field components of the pulses are obtained. Based on the derived formulas, typical examples of pulses with different types of localization and their spectra are calculated and plotted.