  We demonstrate for the first time the occurrence of a sixth order exceptional
point of degeneracy (EPD) in a realistic multimode optical photonic structure
by using a modified periodic coupled resonators optical waveguide (CROW), at
the optical wavelength ${\lambda_e} = 1550 nm$. The 6th order EPD is obtained
in a CROW without the need of loss or gain and such an EPD corresponds to a
very special band edge of the periodic photonic structure where six eigenmode
coalesce, so we refer to it as the 6th order degenerate band edge (6DBE).
Moreover, we report a new scaling law of the quality factor Q of an optical
cavity made of such a periodic 6DBE-CROW with cavity length as $Q{\propto}N^7$
with $N$ being the number of unit cells in the periodic finite-length CROW.
Furthermore, we elaborate on the application of the 6DBE to ultra-low-threshold
lasers. We present a novel scaling law of the lasing threshold that scales as
$N^{-7}$when operating near the 6DBE. Also, we show the superiority of the
threshold scaling of the 6DBE-CROW to the scaling of another CROW with the same
size operating near a 4th order EPD that is often referred to as the degenerate
band edge (DBE). The lasing threshold scaling of the DBE-CROW laser is shown
here for the first time. We also discuss the high sensitivity of the proposed
6DBE-CROW to perturbations, that may find applications in sensors, modulators,
optical switches, nonlinear devices, and Q-switching cavities.
