The waveguide mode dispersion of hexagonal-cylinder-shaped 1D ZnO nanostructures has been derived by assuming the shape to be a circular cylinder; this assumption does not clearly reflect the strong exciton–photon coupling effect in the nanostructure. We report a rational pathway to produce an exciton–polariton dispersion in the waveguide of hexagonal-cylinder-shaped ZnO nanorods using the coupled oscillator model (COM). The multiple peaks in the photoluminescence emissions from the nanorod ends were considered as lower polariton (LP) eigenmodes with energy and momentum spacings following the E-k_z relation. To calculate the dispersion curve that satisfies the LP eigenmodes, the effective mode dispersion, as a photon contribution of COM, was calculated using the finite-difference time-domain (FDTD) method. The calculation considered the actual experimental circumstances, namely, a hexagonal-cylinder-shaped nanocavity lying on a SiO₂/Si substrate. The FDTD results show that a relative loss of the mode profile may occur due to the dielectric surroundings, such as the SiO₂ substrate. Calculating the effective mode dispersion is a more realistic approach to study the polariton feature in a hexagonal-cylinder-shaped waveguide than the ideal cylindrical waveguide theory, which excludes the substrate effect. This study presents a realistic route for calculating the E-k_z dispersion in a ZnO nanocavity.

Keywords: Waveguide, ZnO nanorod, Exciton–,polariton, Polariton dispersion