Spatiotemporal control of laser intensity through cross-phase modulation

Spatiotemporal pulse shaping provides control over the trajectory and range of an intensity peak. While this control can enhance laser-based applications, the optical configurations required for shaping the pulse can constrain the transverse or temporal profile, duration, or orbital angular momentum (OAM). Here we present a novel technique for spatiotemporal control that mitigates these constraints by using a "stencil" pulse to spatiotemporally structure a second, primary pulse through cross-phase modulation (XPM) in a Kerr lens. The temporally shaped stencil pulse induces a time-dependent focusing phase within the primary pulse. This technique, the "flying focus X," allows the primary pulse to have any profile or OAM, expanding the flexibility of spatiotemporal pulse shaping for laser-based applications. As an example, simulations show that the flying focus X can deliver an arbitrary-velocity, variable-duration intensity peak with OAM over distances much longer than a Rayleigh range.