We propose a novel class of lasers based on a fourth order exceptional point
of degeneracy (EPD) referred to as the degenerate band edge (DBE). EPDs have
been found in Parity-Time-symmetric photonic structures that require loss
and/or gain, here we show that the DBE is a different kind of EPD since it
occurs in periodic structures that are lossless and gainless. Because of this
property, a small level of gain is sufficient to induce single-frequency lasing
based on a synchronous operation of four degenerate Floquet-Bloch eigenwaves.
This lasing scheme constitutes a new paradigm in the light-matter interaction
mechanism that leads also to the unprecedented scaling law of the laser
threshold with the inverse of the fifth power of the laser-cavity length. The
DBE laser has the lowest lasing threshold in comparison to a regular band edge
laser and to a conventional laser in cavities with the same loaded quality (Q)
factor and length. In particular, even without mirror reflectors the DBE laser
exhibits a lasing threshold which is an order of magnitude lower than that of a
uniform cavity laser of the same length and with very high mirror reflectivity.
Importantly, this novel DBE lasing regime enforces mode selectivity and
coherent single-frequency operation even for pumping rates well-beyond the
lasing threshold, in contrast to the multifrequency nature of conventional
uniform cavity lasers.