Demonstration of Accelerating Talbot Effect

Self-imaging is a hallmark of quadratic wave evolution, underlying phenomena ranging from the optical Talbot effect to quantum revivals of matter waves. Despite numerous generalizations, a persistent assumption has been that exact recurrences occur at uniformly spaced positions along the physical evolution coordinate. Here we show that this apparent rigidity is not fundamental. By formulating quadratic propagation within its natural symplectic framework, we identify a unique canonical evolution parameter—the metaplectic time—in which all self-imaging phenomena are strictly periodic. The physical propagation coordinate is revealed to be an embedding of this canonical clock, whose geometry can be freely engineered.

Within this framework, we derive a general self-imaging law stating that recurrence planes occur at positions given by the inverse mapping of a uniform lattice in metaplectic time. Uniform Talbot spacing arises only for affine embeddings; nonlinear embeddings produce accelerating, decelerating, or otherwise structured recurrence patterns while preserving exact reconstruction in canonical time. Using a single programmable spatial light modulator, we experimentally sculpt this embedding by imposing controlled transverse phase profiles on periodic fields. We observe Talbot carpets with recurrence spacings that follow polynomial, fractional-power, exponential, and sinusoidal trajectories along the propagation axis, all in quantitative agreement with theory.

These results establish metaplectic time as the fundamental invariant governing self-imaging across quadratic wave systems and uncover a previously inaccessible degree of freedom: programmable axial dynamics without loss of coherence. Beyond classical optics, the framework applies directly to matter-wave Talbot effects and quantum revivals, suggesting new routes for engineering wave-packet dynamics, analog quantum simulations, and structured spatiotemporal control in atomic, molecular, and optical physics.