Caustic Data Modulation (CDM)

This work proposes a novel framework—Caustic Data Modulation (CDM)—that encodes information not in amplitude, phase or frequency, but within the geometric and temporal structure of caustic light fields. Caustics are high-intensity intensity patterns formed by the convergence of light rays through refractive or diffractive media, whose topology (folds, cusps, singularities) can be controlled and classified. In the CDM paradigm, each caustic topology is treated as a discrete symbol; by shaping input phase fields and propagation media, information is embedded in the formation of caustic patterns. We develop the theoretical foundations (optical propagation, symbol manifold, morphological distance metric), define encoding and decoding frameworks, model transmission through turbulent channels using a topological stability metric, and propose variants including spatial, temporal, spectral and polarization-multiplexed caustic encoding. We quantify capacity in terms of symbol rate, caustic alphabet size and decoding efficiency, introduce a dynamic caustic resolvability concept for adaptive error control, and discuss computing architectures where caustic transformations perform logic-like operations. CDM opens a new frontier in optical communication and computation: geometry becomes the language of information.