  We study theoretically the optical response of a monolayer comprizing
regularly spaced quantum emitters with a doublet in the ground state (the
so-called $\Lambda$-emitters). The emitters' self-action through the retarded
dipole-dipole interaction provides a positive feedback, interplay of which with
the intrinsic nonlinearity of an isolated emitter, leads to an exotic optical
dynamics of the system and prominent effects, such as multistability,
self-oscillations, and quasi-chaotic behavior. %The bifurcation diagram
approach is used to classify different scenarios of the system's behavior. In a
certain spectral domain, the monolayer operates as a bistable mirror. The
optical response of the monolayer manifests high sensitivity to the doublet
splitting and relaxation within the doublet, suggesting the latter to be the
key parameters to tailor the monolayer optical response. These properties make
such a system very promising for nanophotonic applications. We discuss the
relevance of the predicted nonlinear effects for nano-sized all-optical
devices.
