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In this work, we propose a numerical solver combining the spectral element - boundary integral (SEBI) method with the periodic layered medium dyadic Green's function. The periodic layered medium dyadic Green's function is formulated under matrix representation. The surface integral equations (SIEs) are then implemented as the radiation boundary condition to truncate the top and bottom computation domain. After describing the interior computation domain with the vector wave equations, and treating the lateral boundaries with Bloch periodic boundary conditions, the whole computation domains are discretized with mixed-order Gauss- Lobatto-Legendre basis functions in the SEBI method. This method avoids the discretization of the top and bottom layered media, so it can be much more efficient than conventional methods. Numerical results validate the proposed solver with fast convergence throughout the whole computation domain and good performance for typical multiscale nano-optical applications.

Graphene's relatively poor absorption is an essential obstacle for designing graphene-based photonic devices with satisfying photo-responsivity. To enhance the tunable light absorption of graphene, appropriate excitation of localized surface plasmon resonance is considered as a promising approach. In this work, the strategy of incorporating periodic cuboid gold nanoparticle (NP) cluster arrays and cylindrical gold NP arrays with Bragg reflectors into graphene-based photodetectors are theoretically studied by the boundary-integral spectral element method (BI-SEM). With the BI-SEM, the models can be numerically analyzed with excellent accuracy and efficiency. Numerical simulation shows that the proposed structures can effectively engineer the light absorption in graphene by tuning plasmon resonance. In the spectra of 300 nm to 1000 nm, a maximum light absorption of 67.54% is observed for the graphene layer with optimal parameters of the photodetector model.

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