Capacity theory of parallel cavity-soliton reservoir computing in an injected laser with a saturable absorber

Localized cavity solitons in a broad-area injected semiconductor laser with a saturable absorber follow a period-doubling route to a spatially confined form of optical chaos, a regime recently characterized by Eslami et al. We discuss whether an array of such solitons, addressed in parallel on a single holding beam, can serve as a high-throughput physical reservoir, and we develop the theory that governs its computational capacity. We prove three results, a contraction condition that guarantees the echo-state and fading-memory properties of the driven soliton reservoir, a rank bound showing that the total information-processing capacity cannot exceed the number of linearly independent readout observables, and an additivity theorem expressing the capacity of a multi-soliton array through the dimensions of the readout subspaces, so that parallel capacity falls below the additive value by exactly the dimension of their overlap, with a corollary of linear scaling for independent solitons. Computation on the laser rate equations confirms each prediction, and a Fourier neural operator surrogate is provided for the spatially resolved study. Two applications follow a reconfigurable multi-task processor in which added solitons render an unsolvable nonlinear task solvable, and a feedback-enabled channel equalizer that is competitive with classical equalizers and improves with parallel capacity as the theory predicts.