  We characterise stationary fronts and dark solitons for counterpropagating
waves in micro-ring and fibre resonators with two input fields, normal
dispersion and nonlocal coupling. These features are different from those in
systems with local coupling in that their existence and stability are due to a
careful balance of the areas of offset from homogeneous solutions. When
scanning one of the two cavity detunings, stable solutions formed plateaus
separated by two fronts are present in one of the counter-propagating fields
with the power of the other field being homogeneous. Two front plateau
solutions have a one-to-one correspondence to solutions of a Lugiato-Lefever
equation at the unique Maxwell point. By defining effective detunings and for
fixed values of the input powers where the fronts are found, we determine
expressions for both the Maxwell point and the distance of the stable fronts as
functions of detunings and input powers of both fields in good agreement with
numerical simulations. For certain values of the detunings we find multi-stable
states of plateaus with fronts, oscillating homogeneous states and
non-oscillating homogeneous states of the counter-propagating fields.
Robustness and parameter ranges of these unusual dynamical states coexisting
with stable non-homogeneous front solutions are provided.
