Suppressing electromagnetic local density of states via slow light in lossy quasi-one-dimensional gratings

We propose a spectral-averaging procedure that enables the computation of bandwidth-integrated local density of states (LDOS) from a single scattering calculation, and exploit it to investigate the minimum extinction achievable from dipolar sources over nonzero bandwidths in structured media. Structure-agnostic extinction bounds are derived, providing analytical insights into scaling laws and fundamental design tradeoffs with implications to bandwidth and material selection. We find that perfect LDOS suppression over a nonzero bandwidth $\mathrm{\Delta }\omega$ is impossible. Inspired by limits which predict nontrivial $\sqrt{\mathrm{\Delta }\omega }$ scaling in systems with material dissipation, we show that the pseudogap edge states of quasi-one-dimensional bullseye gratings can—by simultaneously minimizing material absorption and radiation—yield arbitrarily close to perfect LDOS suppression in the limit of vanishing bandwidth.