Magnetic field integral equation analysis of interaction between a surface plasmon polariton and a circular dielectric cavity embedded in the metal

Abstract

A rigorous integral equation (IE) analysis of the interaction between a surface plasmon polariton (SPP) and a circular dielectric cavity embedded in a metal half-space is presented. The device is addressed as the plasmonic counterpart of the established integrated optics filter comprising a whispering gallery (WG) resonator coupled to a waveguide. The mathematical formulation is that of a transverse magnetic scattering problem. Using a magnetic-type Green's function of the two-layer medium with boundary conditions that cancel the line integral contributions along the interface, an IE for the magnetic field inside the cavity is obtained. The IE is treated through an entire-domain method of moments (MoM) with cylindrical-harmonic basis functions. The entries of the MoM matrix are determined analytically by utilizing the inverse Fourier transform of Green's function and the Jacobi-Anger formula for interchanging between plane and cylindrical waves. Complex analysis techniques are applied to determine the transmitted, reflected, and radiated field quantities in series forms. The numerical results show that the scattered SPPs' spectra exhibit pronounced wavelength selectivity that is related to the excitation of WG-like cavity modes. It seems feasible to exploit the device as a bandstop or reflective filter or even as an efficient radiating element. In addition, the dependence of transmission on the cavity refractive index endows this structure with a sensing functionality.