Beating of Coupled Ultraviolet Light Modes in Zinc Oxide Nanoresonators

Periodic spatial intensity modulations of near-band-gap luminescence light at 3.36 eV photon energy are reported in nanometer-sized resonators of single zinc oxide nanorods. These modulations are observed when the luminescence light, due to excitonic recombination, is excited by a focused low-energy electron beam scanned along the rods. The acceleration energy of only 2 keV allows for a spatial resolution of a few ten nanometers. Numerical calculations based on the theory of dielectric cylindrical waveguides are performed identifying the intensity modulations as beating patterns of coupled ${\mathrm{TE}}_{01}$ and ${\mathrm{TM}}_{01}$ modes in the nanoresonator.

Figure 1

SEM images (a),(c), corresponding color-coded CL intensity distributions (b),(d), and intensity profiles along the rods (e) for the two central nanoresonators with apparent lengths of $L_1=4\mu \mathrm{m}$ and $L_2=6.3\mu \mathrm{m}$ and hexagonal edge lengths (“radii”) of $R_1=(55\pm 5)\mathrm{nm}$ and $R_2=(62\pm 5)\mathrm{nm}$. Suppression of the second maximum from left for rod 2 at the bottom is discussed in the text. The inset in (e) shows the ZnO near-gap luminescence consisting of free and donor-bound exciton recombination. Vertical dashed lines indicate the spectral detection range $\Delta \lambda =3.3\mathrm{nm}$ of the CL images.

Figure 2

Mode diagrams $u_2$ versus $u_1$ for the ${\mathrm{HE}}_{11}$, ${\mathrm{TE}}_{01}$, ${\mathrm{TM}}_{01}$, and ${\mathrm{HE}}_{21}$ modes with intersecting circles of radius $V$ (see text) for $R=55\mathrm{nm}$, $\epsilon ={2.85}^2$ (green dash-dotted lines), $\epsilon =9$ (red dashed lines), and $\epsilon =10$ (black solid lines).

Figure 3

Dependence of $2\Delta \beta ={\beta }_{\mathrm{TE}}-{\beta }_{\mathrm{TM}}$ on the rod radius $R$ for four values of the dielectric constant $\epsilon$. $\Delta \beta =0$ corresponds to the zero of the Bessel function $J_0(u_1)$ at $u_1=2.405$ defining the lower existence limit with degeneracy of the ${\mathrm{TE}}_{01}$ and ${\mathrm{TM}}_{01}$ modes. Horizontal lines are at $2\Delta \beta =k_z=33397{\mathrm{cm}}^{-1}$ (bottom horizontal line) and $38829{\mathrm{cm}}^{-1}$ (top horizontal line), respectively, for the two rods of Fig. 1, with “true” optical lengths of $L_1=4\mu \mathrm{m}\sqrt{2}$ and $L_2=5.5\mu \mathrm{m}\sqrt{2}$.