  We present a general theory for the coherence of Fano lasers based on a bound
state in the continuum. We find that such lasers enable orders of magnitude
reduction of the quantum-limited linewidth, and by introducing mirror symmetry
breaking, the linewidth can be further reduced. In contrast to ordinary
macroscopic lasers, though, the linewidth may re-broaden due to optical
nonlinearities enhanced by the strong light localization. This leads to the
identification of optimal material systems. We also show that the coherence of
this new type of microscopic laser can be understood intuitively using a
simple, effective potential model. Based on this model, we examine the laser
stability and deduce the dependence of the laser linewidth on the general Fano
lineshape. Our model facilitates the incorporation of other degrees of design
freedom and can be applied to a general class of lasers with strongly
dispersive mirrors.
