The group-velocity of the propagation-invariant optical wave-packet generated by the conical superposition can be controlled by introducing well-designed arbitrarily-axisymmetric pulse-front deformation, which permits realizing superluminal, subluminal, accelerating, decelerating, and even nearly-programmable group-velocities. To better understand the tunability of the group-velocity, the generation methods of this propagation-invariant optical wave-packet and the mechanisms of the tunable group-velocity in both the physical and Fourier spaces are investigated. We also have studied the relationship with the recently-reported space–time wave-packet, and this group-velocity-tunable propagation-invariant optical wave-packet should be a subset of the space–time wave-packet.

The space-time (ST) wave packet, a type of light source with many anomalous behaviors, has already found application in weak-field optics, however its generation method limits its energy and therefore its application in strong-field optics. Here we show that the type-I collinear optical parametric amplification (OPA) is a natural amplifier for a ST wave packet, because in it, the ST spectrum (i.e., angle-dependent phase-matching spectrum) of the signal and idler has the same analytical expression as that of a ST wave packet under the narrowband approximation. The high gain in a thin-crystal OPA allows for large energy amplification while ensuring unchanged ST correlation. Meanwhile, a double ST wave packet containing two collinear-propagating ones of the amplified signal and the generated idler via the nondegenerate OPA is reported, which with short- and long-wavelengths (relative to the degenerate-wavelength) have superluminal and subluminal velocities, respectively. This study realizes energy amplification, wavelength conversion, and velocity switching of a ST wave packet and will expand its application in many fields.