Harnessing cavity-soliton chaos for reservoir computing in an injected laser with saturable absorber

A cavity soliton in a broad-area semiconductor laser with a saturable absorber loses stability as the injection is detuned out of the locking band, and the state it settles on is chaotic while remaining a single localised structure. We give this observation a rigorous foundation and an applied consequence. Working in the natural function space of the coupled field-carrier model, we prove global well-posedness, construct a bounded absorbing set, show by parabolic smoothing that the field is bounded pointwise on it, and establish a compact global attractor whose fractal dimension is finite and admits an explicit bound proportional to the transverse area and inversely proportional to the field-diffusion coefficient. The estimate is closed by splitting the trace of the linearised generator over field and carrier directions, so that directions carried by the carriers, which contribute no transverse gradient, are charged instead to the strictly negative carrier relaxation rates. The theory therefore certifies that the observed chaos is finite-dimensional. Direct simulation of the same model then realises the attractor: adiabatic continuation in the injection detuning follows the destabilisation of a single localised state into a chaotic one, four diagnostics that fail for different reasons on a regular state agree that the terminal regime is chaotic, and a delay reconstruction gives a correlation dimension of 2.85 for a trajectory of an infinite-dimensional system, far below the bound. The predicted growth of the dimension with transverse area is followed, for an extended chaotic state, by a separate measurement of the mode count, while the predicted dependence on the gain bandwidth is not resolved. Driving the device with a masked holding beam turns it into a physical reservoir: the echo-state property is checked by a measured conditional Lyapunov exponent over a grid of operating points instead of being inferred from dissipativity, the NARMA-10 error is lowest on the ordered side of the onset of chaos while the linear memory capacity is flat across the operating window, and four transverse solitons in one aperture are addressed and read as four channels, each recovering the most recent sample of its own input stream on average an order of magnitude better than its neighbours’. The work connects the analysis of a localised optical state to its use as computational hardware.