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Arrays of metal–dielectric–metal (MDM) multilayer nanostructure can support various kinds of plasmonic modes including in-plane (IP) localized/delocalized surface plasmons or lattice resonances, photonic waves, as well as out-of-plane (OP) plasmon modes. Hybridization between different modes offers rich physics such as lasing, sub- and super-radiant modes, and efficient light absorption. While interplays between different sets of in-plane modes have been intensively investigated, the interaction between in-plane and out-of-plane modes is rarely explored. Here, we propose a MDM nanostructure with 2D nanocylinder array and study in detail the strong coupling between the in-plane photonic modes at the dielectric layer and the out-of-plane plasmon modes excited at the cylinder sidewalls. We demonstrate the strong coupling between the localized second-order IP mode and the first-order OP mode with a Rabi splitting up to 250 meV in the near-infrared region. A new IP mode arising from the radiative field can induce another kind of strong coupling with OP modes as the cylinder radius is larger than 98 nm. The underlying physics within this plasmon–photon system is quantitatively revealed by the coupled oscillator model and calculated E-field distribution. The proposed MDM system provides a good platform for investigating multimode coupling and nano-optics devices.

The Goos–Hanchen shift at the surface of a uniaxially anisotropic left-handed material film is investigated, for the situation of that there is an arbitrary angle between the optical axis and the interface of the material. The analytical expressions of the Goos–Hanchen shifts are derived, for both cases of that the total reflection occurs and does not occur at the first interface. The sign of the Goos–Hanchen shifts in the two situations is analysed. The results show that the Goos–Hanchen shift of the reflected wave is the same as that of the transmitted one for the case that the total reflection does not occur at the first interface; the Goos–Hanchen shift of the transmitted wave oscillates as the thickness of the film is increased, and its overall tendency is increased; the Goos–Hanchen shift of the transmitted wave realizes its absolute maximum when the transmitted wave resonances, the absolute maximum is almost several 10 times of the wavelength of the incident wave; the Goos–Hanchen shift of the transmitted wave is significantly influenced by the incident angle and the angle between the optical axis and the interface.