Suppressing electromagnetic local density of states via slow light in lossy quasi-1d gratings

We propose a spectral-averaging procedure that enables 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 finite 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 finite 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 pseudogap edge states of quasi-1d bullseye gratings can – by simultaneously minimizing material absorption and radiation – yield arbitrarily close to perfect LDOS suppression in the limit of vanishing bandwidth.