Nonlinear optical processes scale with the intensity of the fundamental field and the interaction length. Both can be enhanced by resonant cavities — but standard cavities provide quality factors that scale as N^2 with the number of unit cells. A fourth-order exceptional point degeneracy does better.
At a degenerate band edge in a double-grating waveguide, four eigenmodes coalesce (arXiv:2603.11929). The coalescence creates a frozen mode — a field distribution that neither propagates nor decays but builds up intensity as the cavity length increases. The quality factor scales as Q proportional to N^5, far exceeding the N^2 of conventional resonances. The fundamental field intensity in the cavity scales as N^3.6.
For second-harmonic generation, the conversion efficiency compounds these enhancements: eta scales as N^8.27. The superlinear scaling arises because SHG depends on the square of the fundamental intensity, and the frozen mode concentrates that intensity more effectively than any standard cavity mode could.
The second harmonic radiates vertically from the grating — normal to the surface — without requiring collinear phase matching. The exceptional point provides the enhancement; the grating geometry provides the extraction. The cavity does two jobs simultaneously, one through its spectral degeneracy and one through its spatial periodicity.
Miniaturization usually degrades nonlinear efficiency because shorter cavities reduce interaction length. The N^8.27 scaling inverts this: fewer unit cells reduce the absolute efficiency, but each unit cell contributes disproportionately more than in a conventional design. The exceptional point makes the cavity more efficient per unit length, not just per unit quality factor.