  We study theoretically the mechanisms of square-wave (SW) formation in
vertical external-cavity Kerr-Gires-Tournois interferometers in presence of
anti-resonant injection. We provide simple analytical approximations for their
plateau intensities and for the conditions of their emergence. We demonstrate
that SWs may appear via a homoclinic snaking scenario, leading to the formation
of complex-shaped multistable SW solutions. The resulting SWs can host
localized structures and robust bound-states.
