Efficient electromagnetic modeling method for large-scale arrays of optical nanoresonators on a metallic substrate based on the coupling theory of quasinormal mode

In a recent work [ Opt. Express 32 ( 5 ), 7171 ( 2024 ) 10.1364/OE.515087 ], an efficient method based on the coupling theory of quasinormal mode (QNM) was proposed for the electromagnetic modeling of large-scale arrays of optical nanoresonators. In this method, the problem of QNM far-field divergence in the QNM-coupling theory is solved by introducing regularized QNM (RQNM). However, this method requires that each scatterer of resonator in the array is located in a homogeneous background medium, so that the RQNM far field over a large spatial range can be computed efficiently through the plane-wave expansion calculated by the stationary-phase principle (PESP). In this paper, we extend the method to the case where each resonator in the array is located on a metallic substrate. We propose to use radially propagating surface plasmon (RSP) to achieve an efficient calculation of the RQNM far field over a large spatial range near the metallic substrate surface for every single resonator. Thus, based on the QNM-coupling theory, an efficient computation of the electromagnetic response of a large-scale array of optical nanoresonators on a metallic substrate can be achieved. The numerical example of a large-scale periodic array of nanoantennas on a gold substrate with a dielectric spacer shows that compared to traditional full-wave numerical methods, this method can reduce the computation time by 1∼2 orders of magnitude while maintaining a moderate computational accuracy, and enable the calculation of the electromagnetic response of arrays with an overall size exceeding 50 × 50 wavelengths. Benefiting from the high computational efficiency and physical intuitiveness of this method, we elucidate the impact of array size, period, and field coupling range (far beyond the tight-binding approximation) on the optical response. This method provides an efficient and intuitive tool for the analysis and design of devices based on optical nanoresonator arrays on a metallic substrate.