Transmission of plasmonic waveguide modulated by side-coupled resonators: Theoretical analysis and numerical simulation

Plasmonic waveguide, e.g., metal-dielectric-metal (MDM) waveguide, utilizes surface plasmon polariton (SPP) to confine the light propagation in deep sub-wavelength. As the light wave is evanescent in the direction perpendicular to the interface, it couples to side placed resonators, yielding intriguing modulation phenomena, such as Fano resonance and electromagnetically induced transparency (EIT). The EIT-like phenomenon can be understood by the coherent interference between different transition paths formed in the coupled resonances and waveguide propagation modes. Furthermore, we find that for the three coupled resonator case, double EIT occurs. The mechanics and evolution can be analytically described by the coupled mode theory, and numerically verified by the finite element method. When the resonator is cascaded periodically, i.e., the unit cell consisting side coupled resonator, the system can be illustrated by the transfer matrix method. Accompanying the coupled mode theory, the forward and backward waves at each port of a unit cell are connected. Then the dispersion relation and transmission spectrum of a finite scale can be obtained, according to the Bloch theorem. Interestingly, the interaction between Bragg gap and polariton gap happens which can also lead to EIT-like phenomena. It is to see when the Bragg resonance (related to the period length) is spectrally near the polariton resonance (related to the local resonant frequency), a flat band would appear in the original gap, giving rise to a sharp transmission. The method and observations remain effective for other resonator-waveguide coupling system and the parity-time symmetry in the periodic coupled resonator optical waveguides system is involved and discussed.