  The concept of lasers based on the frozen mode regime in active periodic
optical waveguides with a 3rd-order exceptional point of degeneracy (EPD) is
advanced. The frozen mode regime in a lossless and gainless waveguide is
associated with a stationary inflection point (SIP) in the Bloch dispersion
relation, where three Bloch eigenmodes coalesce forming the frozen mode. As a
practical example, we consider an asymmetric serpentine optical waveguide
(ASOW). An ASOW operating near the SIP frequency displays a large group delay
of a non-resonant nature that scales as the cube of the waveguide length,
leading to a strong gain enhancement when active material is included.
Therefore, a laser operating in the close vicinity of an SIP has a gain
threshold that scales as a negative cube of the waveguide length. We determine
that this scaling law is maintained in the presence of small distributed
losses, such as radiation associated with waveguide bends and roughness. In
addition, we show that although gain causes a distortion in the modes
coalescing at the SIP, the properties of the frozen mode are relatively
resistant to such small perturbations and we still observe a large degree of
exceptional degeneracy for gain values that bring the system above threshold.
Finally, our study also reveals that lasing near an SIP is favored over lasing
near a photonic band edge located in close proximity to the SIP. In particular,
we observe that an SIP-induced lasing in an ASOW displays lower gain threshold
compared to lasing near the photonic regular band edge (RBE), even though the
SIP resonance has a lower quality factor than the RBE resonance.
