Local density of electromagnetic states in finite 1D topological gratings

We analyze the local density of electromagnetic states (LDOS) in finite 1D topological gratings to unveil the unique nature of topological edge modes. At the frequency corresponding to the topological edge mode, the LDOS intensity decays exponentially from the topological phase transition interface toward both sides. Our results show that the topological edge state’s LDOS peak exceeds that of a defect mode by over 1.5× and that of a band edge mode by nearly 100×, with a correspondingly narrower FWHM, benefiting from intrinsic topological protection and strong spatial confinement. We investigate how structural symmetry breaking and polarization effects modify the LDOS distribution. In addition, the coupling between topological edge modes of different orders and dipoles with various orientations is analyzed through LDOS calculations. By adjusting the local perturbation strength of the nearest and next-nearest neighboring unit cells at the topological interface, the LDOS intensity at the resonance frequencies of different‑order topological edge modes can be modulated, thereby enabling selection of the dominant cavity mode. Consequently, LDOS calculations offer valuable insights for optimizing light–matter interaction and reducing laser thresholds. This work provides practical guidelines for designing topological lasers with improved efficiency and narrow spectral linewidth.