Propagation-invariant space-time caustics of light

Caustics are responsible for a wide range of natural phenomena, from rainbows and mirages to sparkling seas. Here, we present caustics in space-time wavepackets, class pulsed beams featuring strong coupling between spatial temporal frequencies. Space-time wavepackets have attracted much attention with their propagation-invariant intensity profiles that travel at tunable superluminal subluminal group velocities. These profiles, however, been largely restricted an X-shape or similar pattern. We show combine the propagation invariance flexible design caustics, allowing customizable patterns wavepackets. Our method directly provides phase distribution needed realize user-designed caustic can feature broad intriguing optical including backward traveling formed purely forward propagating waves, nondiffracting evolve time. findings should open doors even wider structured light spatiotemporal coupling.