Abstract
In this paper we find the spectral bandwidth is more important than the duration of pulse for analyzing the evolution of ultrashort laser pulses. A general novel (3+1) dimensional propagation equation first-order in the propagation coordinate is derived, which is independent of the envelope and carrier frequency. This equation provide an accurate description of the evolution of the ultrashort pulsed beam through the dispersive nonlinear medium, with the numerical value of the bandwidth being bigger than the carrier frequency and considering the true frequency. A family of exact solutions of the novel linear (3+1) dimensional equation in the dispersive medium has been derived, which represents the pulse with ultrawide bandwidth evolving due to gain (losses), dispersion, and diffraction. The use of the novel dispersive and loss coefficients is analyzed.
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