High-order spectral singularity

Exceptional point and spectral singularity are two types of that unique to non-Hermitian systems. Here, we report the high-order as a pole scattering matrix for system, is unification exceptional singularity. At singularity, coefficients have divergence system stimulates lasing. The wave emission intensity polynomially enhanced, order growth in polynomial linearly scales with Furthermore, coherent input controls alters Our findings provide profound insights into fundamentals applications singularities.