  We use the scattering matrix formalism to analyze photon blockade in
coherently-driven CQED systems with a weak drive. By approximating the weak
coherent drive by an input single- and two-photon Fock state, we reduce the
computational complexity of the transmission and the two-photon correlation
function from exponential to polynomial in the number of emitters. This enables
us to easily analyze cavity-based systems containing $\sim$50 quantum emitters
with modest computational resources. Using this approach we study the coherence
statistics of polaritonic photon blockade while increasing the number of
emitters for resonant and detuned multi-emitter CQED systems --- we find that
increasing the number of emitters worsens photon blockade in resonant systems,
and improves it in detuned systems. We also analyze the impact of inhomogeneous
broadening in the emitter frequencies on both polaritonic and subradiant photon
blockade through this system.
