Morphological Tuning of the Plasmon Dispersion Relation in Dielectric-Loaded Nanofiber Waveguides

Understanding the impact of lateral mode confinement in plasmonic waveguides is of fundamental interest regarding potential applications in plasmonic devices. The knowledge of the frequency-wave vector dispersion relation provides the full information on electromagnetic field propagation in a waveguide. This Letter reports on the measurement of the real part of the surface plasmon polariton dispersion relation in the near infrared spectral regime for individual nanoscale plasmonic waveguides, which were formed by deposition of para-hexaphenylene ($p\mathrm{\text{−}}6\mathrm{P}$) based nanofibers on top of a gold film. A detailed structural characterization of the nanofibers provides accurate information on the dimensions of the investigated waveguides and enables us to quantify the effect of mode confinement by comparison with experimental results from continuous $p\mathrm{\text{−}}6\mathrm{P}$ films and calculations based on the effective index method.

Figure 1

Characterization of a $p\mathrm{\text{−}}6\mathrm{P}$ nanofiber by complementary microscopy techniques: (a) atomic force micrograph of a single $p\mathrm{\text{−}}6\mathrm{P}$ nanofiber (fiber 1) on top of a 100 nm thick gold film (composed of six AFM scans); (b) the same nanofiber mapped by SEM; (c),(d) fiber 1 as imaged by threshold PEEM ($h\nu =4.9\mathrm{eV}$) and 2P-PEEM ($h\nu =1.55\mathrm{eV}$, laser incident from the left); (e) cross-sectional shapes of three different nanofibers from AFM measurements: fiber 1 (dotted dashed line), fiber 2 (dashed line), fiber 3 (solid line). The dashed line in (a) indicates the position of the displayed cross section of fiber 1.

Figure 2

Fiber 1 imaged in 2P-PEEM mode at varying excitation wavelengths ${\lambda }_{\mathrm{Laser}}$: (a) 872 nm, (b) 827 nm, (c) 777 nm, and (d) 728 nm. The gray lines indicate the position of the observed beating pattern maxima. (e) Intensity profile along the nanofiber for ${\lambda }_{\mathrm{Laser}}=728\mathrm{nm}$ (solid line) including a fit to the beating pattern maxima (dashed line).

Figure 3

Experimental SPP dispersion curves of fiber 1 (asterisk), 2 (circled dot) and 3 (squared dot). (a) Comparison to different effective index calculations (dashed and solid lines, see text for further information); the dash-dotted line is the dispersion line of light $\omega =ck$. The short dashed line is an experimental SPP dispersion curve of a gold-vacuum interface. (b) Calculated imaginary part of the SPP dispersion relation [dashed and solid lines corresponding to (a)].

Figure 4

The electric field distributions $|E_z|$ of the fundamental SPP modes.