Photonic Flatband Resonances in Multiple Light Scattering

We introduce the concept of photonic flatband resonances and demonstrate it for an array of high-index dielectric particles. We employ the multiple Mie scattering theory and demonstrate that both short- and long-range interactions between the resonators are crucial for the emerging collective resonances and their associated photonic flatbands. By examining both near- and far-field characteristics, we uncover how the flatbands emerge due to a fine tuning of resonators’ radiation fields, and predict that hybridization of a flatband resonance with an electric hot spot can lead to giant values of the Purcell factor for the electric dipolar emitters.

Figure 1

Schematic of multipole Mie scattering for an electric dipole $S_{\mathrm{ED}}$ interacting with a chain of dielectric spheres. The flatband resonance and electric hot spot modes are inseparable from the collective resonances and their far-field patterns.

Figure 2

Collective Mie resonances and their crossing regime. (a) Electric near-field distributions of the three collective quadrupole resonances excited by a dipolar emitter in a 30-sphere chain with the interparticle gap size $G=0\mathrm{nm}$. (b) The tight-binding (TB) model, which considers short-range couplings only, fails to capture the collective resonances present in the red line of the exact multiple scattering theory (MST). (c) Crossing and disappearance of the three collective $L_{1;2;3}$ resonances from the fine-tuning of $G$.

Figure 3

(a) Magnitude and phase of the EQ coefficient ${\zeta }_{2;0}^{(8)}$ for the two cases of $G=1.8\mathrm{nm}$ and $G=3.225\mathrm{nm}$. Far-field patterns of the $L_1$ resonance for the two cases of $G=0\mathrm{nm}$ (b) and $G=3.225\mathrm{nm}$ (c) show the merging of the scattering channels.

Figure 4

Dependence of the supercavity $L_1$ resonance on the number of spheres. (a) The optimal gap and its associated wavelength of the mode converge to $G=4.5\mathrm{nm}$ and $\lambda =986\mathrm{nm}$, respectively. (b) Purcell factor in logarithmic scale. Two plots associating with the supercavity $L_1$ resonance (optimal $G$) and the normal $L_1$ resonance at $G=10\mathrm{nm}$ are presented for comparison.

Figure 5

Band structures for three different gap sizes indicate that the flatband occurs at $G=4.5\mathrm{nm}$.