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Slow-light has enriched many intriguing optics phenomena in which nonlinearities and gain/absorption among other features can be significantly enhanced. We link the concepts of slow light and exceptional points of degeneracy (EPDs) and discuss the relation with PT-symmetry. They emerge in coupled waveguides when multiple eigenmodes coalesce in both their eigenvalues (wavenumbers) and eigenvectors (polarizations), when varying a specific system parameter, like coupling, dimension, frequency, etc. The number of eigenmodes that coalesce at the EPD determines the order of the EPD. For example, in lossless structures, the regular band edge (RBE), the stationary inflection point (SIP), and degenerate band edge (DBE); are 2nd, 3rd, and 4th order EPDs, respectively. We explore the existence of various orders of EPDs in mainly two types of periodic coupled waveguides: the modified coupled resonators optical waveguide (CROW) and in coupled dielectric slabs with multiple gratings. The formulation is based on coupled mode theory and it can be generally applied to several other periodic structures. The existence of EPDs in optical structures provide unique properties like the giant scaling of the quality factor and high density of states and these two can also be made independent of each other. The unique properties of EPDs make it possible to induce single-frequency lasing just by introducing a small level of gain. Guiding periodic systems with EPD exhibit unprecedented scaling of the lasing threshold. Such scaling in a N-unit cells periodic structure follows new physical scaling laws as a function of the order of the EPD. We show an example of CROW based on Silicon-on-insulator (SOI) technology and report the lasing action in such configuration using the finite-different time domain (FDTD).
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