Epsilon-near-zero media coupled with localized surface plasmon modes

Epsilon-near-zero (ENZ) media are an emerging platform, embracing the great potential for novel nanophotonic phenomena. One method to obtain an ENZ medium is to operate at the cutoff wavelength of the fundamental mode of a plasmonic waveguide. Control over this mode is limited to the waveguide's material and size properties. Here, we demonstrate that a plasmonic nanostructure (nanorod) can be strongly coupled to the plasmonic waveguide, providing two new hybrid resonance modes exhibiting characteristics of both guided ENZ modes and localized surface plasmon modes. Strong coupling gives rise to a Rabi splitting of 300 meV, which is demonstrated by finite-difference time domain simulations where we calculate the decay rate enhancement of a dipole emitter located in the coupled system. The hybrid modes are retrieved using the analytic coupled harmonic oscillator model. This suggested method via hybridization of modes can be used to generate and manipulate ENZ media where the unique ENZ property of wavelength extension enables effectively shrinking spatially long distances down to optically short distances.

Figure 1

(a) Dispersion curves of the fundamental mode for different core sizes $w_x$, with $w_y=300$ nm and $d=200$ nm for an infinite rectangular hollow silver waveguide, obtained in finite-element simulations. The inset shows the schematics. (b) Electric and magnetic field profiles at the $xy$ plane, at the cutoff wavelength (870 nm) of the waveguide with $w_x=360$ nm. (c) The $y$ component of the electric field along the waveguide axis at the $yz$ plane at the ENZ wavelength (870 nm) and at a shorter random wavelength (600 nm) with a nonzero index. White lines indicate the core borders.

Figure 2

Decay rate enhancement of a $y$-oriented dipole emitter located at the core of the waveguide with different core sizes $w_x$ for $w_y=300$ nm and $d=200$ nm kept fixed. The inset shows the schematics of the waveguide.

Figure 3

Decay rate enhancement spectra for the coupled waveguide-nanorod system. Each spectrum is shifted vertically to provide better visualization. (a) Each color stands for a different waveguide size. $w_x$ ranges between 300 and 420 nm, while $w_y=300$ nm and the length of the gold nanorod $L=140$ nm are kept fixed. (b) Each color stands for a different nanorod length. $L$ ranges between 80 and 200 nm for a fixed ENZ waveguide with $w_x=360$ nm and $w_y=300$ nm.

Figure 4

(a) Decay rate enhancement spectra for the coupled waveguide-nanorod system as a function of wavelength and nanorod size for $w_x=360$ nm and $w_y=300$ nm. White circles and white squares show the uncoupled localized surface plasmon resonances and uncoupled fundamental waveguide mode, respectively. (b) Spectra for the uncoupled and coupled modes for $L=140$ nm, $w_x=360$ nm, and $w_y=300$ nm.

Figure 5

(a) Complete hybridization scheme, showing the resonance wavelengths of the coupled hybrid modes (red) and uncoupled ENZ waveguide and localized surface plasmon (LSP) modes (blue and black, respectively), calculated in FDTD simulations (symbols) and the coupled harmonic oscillator model (solid lines), with respect to the nanorod length $L$ for $w_x=360$ nm and $w_y=300$ nm. (b) The $y$ component of the electric field at the lower and upper hybrid mode resonances, 940 and 780 nm (left and middle, respectively), for the coupling configuration and the waveguide alone at 780 nm (right) for comparison. White lines indicate the core borders.