Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides

We present a series of near-field experiments characterizing cutoff for the three lowest order leaky surface plasmon modes supported by Au stripes on glass substrates. These studies demonstrate that the propagation of light along surface plasmon waveguides is mediated by a discrete number of guided polariton modes as well as a continuum of radiation modes. To distinguish the contribution of the guided modes from that of the radiation continuum, a parametric study of propagation length as a function of varying stripe width is performed. Discontinuities consistent with the loss of a guided mode are observed near cutoff widths predicted by numerical simulations, and a severe decrease in propagation length is observed below cutoff for the fundamental surface plasmon mode. Contrary to previous interpretations, experimental and numerical investigations confirm that the finite propagation lengths observed along the narrowest stripes are in good agreement with an intuitive model for the radiation continuum. Furthermore, multimode interference studies provide direct evidence for multiple guided modes and support previous findings with regard to modal cutoff.

Figure 1

Simple ray optics schematics for the modes of a metal stripe waveguide. Total internal reflection of a surface polariton wave, (a), may lead under proper interference conditions to a guided surface polariton mode, (b). Surface polariton waves may also be transmitted, (c), which necessarily leads to a radiation mode (d). Note that the radiation mode must appear to have a source outside of the waveguide to be an eigenmode of the system, as depicted by the dashed lines.

Figure 2

(Color online) Schematic of photon scanning tunneling microscope (PSTM). A partially illuminated high numerical aperture objective is used to excite surface plasmon-polaritons along the Au-Air interface via attenuated total reflection. Light is scattered from these surface waves by an aperture cantilever probe and detected by a photomultiplier tube. Note that the sample and illumination objective are rigidly mounted to a $x,y,z$ piezostage which is scanned below the fixed cantilever.

Figure 3

(Color online) Experimental near-field images of surface plasmon propagation along varying width metal stripe waveguides ranging from $0.5\mu \mathrm{m}\text{to}3.5\mu \mathrm{m}$.

Figure 4

(Color online) Surface plasmon propagation length as a function of stripe width at $780\mathrm{nm}$ for Au stripes on glass substrates. Circular markers denote experimental data with error bars determined by 95% tolerance intervals. The solid, dashed, and dotted curves show the calculated decay behavior for the three lowest order leaky surface plasmon modes supported by these stripes, and the associated vertical lines denote the predicted cutoff widths for these mode. Note that numerical solutions were obtained using the full-vectorial finite-difference method described in Ref. 14 for $48\mathrm{nm}$ thick Au stripes $({\epsilon }_{\mathrm{Au}}=-24.13+1.725i)$ (Ref. 29) on a glass substrate $({\epsilon }_{\text{glass}}=2.25)$.

Figure 5

(Color online) Characterization of the radiation modes using the free-space approximation: (a) the radiation modes excited at the input of a metal stripe waveguide may be modeled to first order by (b) the free-space modes excited at the end of tapered launch-pad. Even without a stripe, the experimental near-field image at the end of taper (c) appears to show light propagation along the $y$ axis, and (d) a cross section along the dashed line can be well fit to an exponential decay. The fit propagation length $\left(3.25\mu \mathrm{m}\right)$ is in good agreement with the propagation length predicted by numerical simulations of scattered light above an extended edge discontinuity $\left(2.6\mu \mathrm{m}\right)$ as shown in the inset.

Figure 6

(Color online) Simulated field profiles for the leaky surface plasmon modes supported by 2, 4, and $6\mu \mathrm{m}$ Au stripe waveguides using the full-vectorial finite-difference method described in Ref. 14 (${\epsilon }_{\mathrm{Au}}=-24.13+1.725i$ for $\lambda =780\mathrm{nm}$) (Ref. 29). Insets depict the lateral mode profiles predicted by equivalent dielectric slab waveguides as outlined in Ref. 17. The core index of the dielectric slabs was determined by the effective index of the leaky SPP mode supported along an infinitely wide $48\mathrm{nm}$ thin Au film on a glass substrate ($n_{\mathrm{eff}}=k_{\mathrm{spp}}∕k_0=1.022+0.003i$, calculated using the reflection pole method) (Ref. 37).

Figure 7

(Color online) Experimental demonstration of multimode interference between the two guided modes supported by a $4\mu \mathrm{m}$ wide Au stripe as excited by a $2\mu \mathrm{m}$ wide input stripe. The dashed white lines indicate the outline of the Au structures. Frames (a) and (b) show near-field images acquired for symmetric and asymmetric alignment of the input stripe, respectively. Frames (c) and (d) show cross sections of the data shown in (a) and (b), respectively. Initial cross sections show the intensity above the input stripe (acquired at $y=-1\mu \mathrm{m}$), and subsequent cross sections are taken at $2.5\mu \mathrm{m}$ intervals (beginning with $y=-2.5\mu \mathrm{m}$) and offset by $-0.25$ increments.

Figure 8

(Color online) Demonstration of multimode interference between the two guided modes supported by a $6\mu \mathrm{m}$ wide Au stripe: (a) experimental near-field image; (b) simulated near-field intensity for an equivalent dielectric waveguide system calculated for the approximate modes shown in the insets of Figs. 6a, 6d, 6f. The dashed white lines indicate the outline of the Au structures. Frames (c) and (d) show cross sections of the data shown in (a) and (b), respectively. Initial cross sections show the intensity above the input stripe (acquired at $y=-1\mu \mathrm{m}$), and subsequent cross-sections are taken at $2.5\mu \mathrm{m}$ intervals (beginning with $y=-2.5\mu \mathrm{m}$) and offset by $-0.25$ increments.

Figure 9

(Color online) Experimental multimode interference study to investigate the cutoff width for the second order leaky surface plasmon mode. The dashed white lines indicate the outline of the Au structures. Frames (a), (b), and (c) show near-field images acquired stripe widths of $3.5\mu \mathrm{m}$, $3\mu \mathrm{m}$, and $2.5\mu \mathrm{m}$, respectively. Frames (d), (e), and (f) show cross sections of the data shown in (a), (b), and (c), respectively. Initial cross sections show the intensity above the input stripe (acquired at $y=-1\mu \mathrm{m}$), and subsequent cross-sections are taken at $2.5\mu \mathrm{m}$ intervals (beginning with $y=-2.5\mu \mathrm{m}$) and offset by $-0.25$ increments.

Figure 10

(Color online) Experimental multimode interference study to investigate the cutoff width for the third order leaky surface plasmon mode. The dashed white lines indicate the outline of the Au structures. Frames (a), (b), and (c) show near-field images acquired stripe widths of $5.5\mu \mathrm{m}$, $5\mu \mathrm{m}$, and $4.75\mu \mathrm{m}$, respectively. Frames (d), (e), and (f) show cross sections of the data shown in (a), (b), and (c), respectively. Initial cross-sections show the intensity above the input stripe (acquired at $y=-1\mu \mathrm{m}$), and subsequent cross-sections are taken at $2.5\mu \mathrm{m}$ intervals (beginning with $y=-2.5\mu \mathrm{m}$) and offset by $-0.25$ increments.