Lasing in para-Fermi class-B microring resonator arrays.

We demonstrate lasing in arrays of microring resonators with underlying para-Fermi symmetry. The properties of the algebra allow the analytic prediction of propagation constants and normal modes of an array of passive resonators that show the optical analogue of a zero-energy mode that is its own chiral pair. The rest of the normal modes in the linear model form chiral pairs that are evenly distributed around the pseudo zero-energy mode. We use this information to construct a class-B laser model where even and odd sites are driven with different strength in a pattern following para-Fermi algebra chirality to demonstrate lasing with enhancement or suppression of the zero-energy mode. Zero-energy mode lasing is stable to initial conditions for a large set of driving ratios. Lasing with zero-energy mode suppression is unstable and more susceptible to initial field configurations.