Subwavelength atomic arrays are a leading platform for engineering light-matter interactions, enabling near-perfect single-photon mirrors and robust quantum memories based on long-lived dark spin waves. However, a comprehensive theory of their nonlinear, multi-excitation dynamics has remained a significant challenge. We present a unified quantum scattering theory that treats both photons and collective atomic spin waves as distinct propagating excitations interacting across different spatial dimensions. Our central result is a powerful analytical reduction: we demonstrate that the complete multichannel $S$-matrix and the associated scattering cross sections are exactly determined by the effective scattering dynamics solely within the atomic spin-wave subspace. This maps the complex physical problem of photon-atom interactions to a conceptually simpler one involving only atomic modes. We apply this formalism to the two-excitation case, deriving the complete analytical $S$-matrix and scattering cross sections for systems with two-level nonlinearities. Our work provides a versatile analytic tool for analyzing and engineering complex quantum nonlinear phenomena, including multi-excitation subradiance, in large-scale atomic systems.

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• Light-matter interaction
• Scattering theory
• Atomic systems
• Two-level models