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In this paper, we investigate numerically the trapped modes with near zerogroup velocities supported in the ring array composed of dielectric nanorods,based on a two-dimensional model. Two sorts of trapped modes in the ring arrayhave been identified: the BCR trapped modes which correspond to the bound modesbelow the light line at the edge of the first Brillouin zone in thecorresponding planar structure (namely the infinite linear chain); thequasi-BIC trapped modes corresponding to the bound states in the continuumsupported in the infinite linear chain. According to the whispering gallerycondition, the BCR trapped modes can be supported in the ring array only whenthe number of dielectric elements N is even, while the quasi-BIC ones alwaysexist no matter whether N is odd or even. For both two kind of trapped modes,the lowest one of each kind possesses the highest Q factor, which are ~105 forBCR kind and ~1011 for quasi-BIC kind with N=16 respectively, and the radiationloss increases dramatically as the structural resonance increases. Finally, thebehavior of the Q factor with N is explained numerically for the lowest one ofeach kind of trapped modes. The Q factor scales as Q~exp(0.662N) for thequasi-BIC trapped mode and Q~exp(0.325N) for the BCR one. Intriguingly, the Qfactor of the quasi-BIC trapped mode can be as large as ~105 even at N=8.Compared to the finite linear chain, the structure of ring array exhibitsoverwhelming advantage in Q factor with the same N because there is noarray-edge radiation loss in the ring array. We note that the principles cancertainly be extended to particles of other shapes (such as nanospheres,nanodisks, and many other experimentally feasible geometries).

Trapped modes with extremely high quality factor in the subwavelength ring resonator composed of dielectric nanorods