We study theoretically the lasing properties and the cavity lifetime of super and sub-luminal lasers. We find that obtaining the necessary conditions for superluminal lasing requires care and that a laser operating under these conditions can under some conditions tend towards bi-frequency lasing. In contrast, conditions for a subluminal laser are less stringent, and in most situations its steady-state properties are well predicted by the self-consistent single-frequency laser equations. We also study the relaxation time of power perturbation in super and sub-luminal lasers using a finite-difference-time-domain tool and present the impact of the lasing power, the group velocity and the dispersion properties of the cavity on the relaxation dynamic of such perturbations. For the subluminal laser, we find that the time constant changes by a factor that is close to the group index. In contrast, for the superluminal laser, we find that the time constant does not change by the factor given by the group index, and remains close to or above the value for an empty cavity. These finding may be interpreted to imply that the quantum noise limited linewidth of the subluminal laser decreases with increasing group index, while the same for the superluminal laser does not increase with decreasing group index. The implications of these findings on the sensitivity of sensors based on these lasers are discussed in details.
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