Classical analogues of the quantum-mechanical Moshinsky effect: “Stretching” and “freezing” of gradient interference effects for rectangular-shaped laser pulses in dispersion-decreasing optical fibers

We study classical optical analogues of the transient quantum mechanical Moshinsky effect, also known as “diffraction in time”, which can be observed in the linear propagation dynamics of rectangular-shaped super-Gaussian laser pulses and beams. We find critical field gradients at the pulse fronts and beam edges, at which the Fresnel-type diffraction patterns completely fill the flat top of the super-Gaussian field profile, and their interference leads to the linear dispersive/diffractive “self-focusing” effect. We show that the dependencies of both the “self-focusing length” and the corresponding effective “gain” on the steepness of the field gradients demonstrate a tendency towards saturation. We highlight that the accuracy of quasioptical computational modeling based on the Schrödinger-type equations must always be controlled by the principal conservation laws in both ordinary space/time and the Fourier spectral domains. In particular, we demonstrate that significant Fresnel-type diffraction patterns arising in the linear dynamics of super- Gaussian pulses and beams are accompanied by their completely stationary Fourier spectral distributions calculated with an accuracy up to 8 orders of magnitude. Since the considered optical analogues of the quantum-mechanical Moshinsky effect manifest themselves only at the rather small distances compared to the dispersion and diffraction lengths, we concentrate on possible experimental realizations of these features in nonautonomous systems, a typical example of which is represented by the optical fiber with group velocity dispersion decreasing along the fiber length. We reveal that dispersion-decreasing optical fibers provide a unique opportunity to slow down (“stretch”) the formation of the Moshinsky-type dispersion patterns at the flat tops of super-Gaussian pulses and even “freeze” the linear gradient interference “self-focusing” of the central parts of rectangular-shaped laser pulses.