Abstract
Based on the radiation field emitted by a pair of oscillating electric dipoles under the complex-source-point model, an analytical formula is proposed for describing a series of time-domain Gaussian pulses propagating in free space. According to the formula, we analyze the spatiotemporal propagation of the real part of the electric field, the square of electric field envelope and the energy density. The intrinsic chirps of the pulses are calculated. The ultrashort Gaussian pulse in time-domain will become flat Gaussian, and eventually turn into a time-domain dark hollow Gaussian (TDHG) pulse as the order term of the analytic expression increases. The TDHG pulses can keep dark hollow even for a long propagating distance. Furthermore, we discuss the energy density of the TDHG pulses in the off-axis situation and find out the characteristics of the spatiotemporal coupling.
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