Multimode metal-insulator-metal waveguides: Analysis and experimental characterization

The analysis and experimental characterization of the propagation constants and attenuation coefficients of surface plasmon (SP) modes in planar multimode metal-insulator-metal (MIM) waveguides are presented. The experimental characterization is based on determining the width of the reflection angular spectrum in the attenuated total reflection (ATR) configuration. Due to its transverse character, the ATR configuration provides a more straightforward and simpler way to determine the propagation constants and attenuation coefficients of plasmonic modes in MIM structures, compared to using tapered end-couplers with multiple waveguide samples or near-field scanning optical microscopy (NSOM). In this paper, the propagation constants and attenuation coefficients of multimode MIM structures are investigated, and MIM waveguide structures with 730 and 1460 nm ${\mathrm{SiO}}_2$ cores and Au claddings are fabricated and experimentally characterized. The measurement results indicate that the absorption of Au is responsible for the high attenuation in MIM plasmonic modes, while scattering loss is another source of attenuation for higher-order modes (smaller zigzag angles). To the best of the authors’ knowledge, the present work represents the first time the attenuation coefficient and propagation constant of each mode in a multimode MIM waveguide have been individually measured.

Figure 1

Configuration and coordinate system of a metal-insulator-metal (MIM) structure. The structure is invariant in the $y$ direction.

Figure 2

(a) Effective mode indices $N\equiv \beta /k_0$ and (b) propagation lengths $L\equiv 1/\left(2\right|\alpha \left|\right)$ for the TM${}_{0-3}$ modes as functions of the dielectric core thickness $d_i$ in MIM (Au-SiO${}_2$-Au) waveguides at $\lambda =1550$ nm. The curves for the MIM TM${}_{0-3}$ modes and the single Au/SiO${}_2$ interface are labeled TM${}_{0-3}$ and SP, respectively. The effective mode index for the latter is $1.5020$. The light line in (a) represents light propagation in bulk SiO${}_2$, with an effective mode $\mathrm{index}=1.4877$.

Figure 3

(a) Effective mode indices $N$ and (b) propagation lengths $L$ for the TE${}_{0-2}$ modes as functions of $d_i$ in MIM (Au-SiO${}_2$-Au) waveguides at $\lambda =1550$ nm. The curves for the MIM TE${}_{0-2}$ modes and the single Au/SiO${}_2$ interface are labeled TE${}_{0-2}$ and SP, respectively.

Figure 4

(a) Schematic diagram of the ATR configuration applied to a symmetric MIM structure. The transmission matrix corresponding to each numbered layer is labeled. (b) A single metal/dielectric interface (Otto configuration, Ref. 17). (c) A symmetric MIM structure.

Figure 5

Schematic diagram of the ATR configuration applied to the MIM structures.

Figure 6

(a) TM reflectance angular spectra for the structure in Fig. 5 with $d_i=730\mathrm{nm}$ measured at various air gap thicknesses $d_g$, which correspond to pressures of the coupling head, $P_c=30,35,40,45,\mathrm{and}50\mathrm{psi}$. (b) The normalized propagation constants $N_{{\mathrm{TM}}_0}^{\prime }\equiv {\beta }_{{\mathrm{TM}}_0}^{\prime }/k_0$ corresponding to the “resonance minima” and (c) the normalized attenuation coefficients ${\alpha }_{{\mathrm{TM}}_0}^{\prime }/k_0=\mathrm{HWHMs}$ of the TM${}_0$ resonances at various values of $P_c$. (d) The normalized propagation constants $N_{{\mathrm{TM}}_1}^{\prime }$ and (e) the normalized attenuation coefficients ${\alpha }_{{\mathrm{TM}}_1}^{\prime }/k_0$ of the TM${}_1$ resonances at various values of $P_c$.

Figure 7

(a) TE reflectance angular spectra for the structure in Fig. 5 with $d_i=730\mathrm{nm}$ measured at various $P_c$ values. (b) $N_{{\mathrm{TE}}_0}^{\prime }$ and (c) ${\alpha }_{{\mathrm{TE}}_0}^{\prime }/k_0$ of the TE${}_0$ mode.

Figure 8

(a) TM reflectance angular spectra for the structure in Fig. 5 with $d_i=1460\mathrm{nm}$ measured at various $P_c$. (b) $N_{{\mathrm{TM}}_0}^{\prime }$ and (c) ${\alpha }_{{\mathrm{TM}}_0}^{\prime }/k_0$ of the TM${}_0$ resonances. (d) $N_{{\mathrm{TM}}_1}^{\prime }$ and (e) ${\alpha }_{{\mathrm{TM}}_1}^{\prime }/k_0$ of the TM${}_1$ resonances. (f) $N_{{\mathrm{TM}}_2}^{\prime }$ and (e) ${\alpha }_{{\mathrm{TM}}_2}^{\prime }/k_0$ of the TM${}_2$ resonances.

Figure 9

(a) TE reflectance angular spectra for the structure in Fig. 5 with $d_i=1460\mathrm{nm}$ measured at various $P_c$ values. (b) $N_{{\mathrm{TE}}_0}^{\prime }$ and (c) ${\alpha }_{{\mathrm{TE}}_0}^{\prime }/k_0$ of the TE${}_0$ resonances. (d) $N_{{\mathrm{TE}}_1}^{\prime }$ and (e) ${\alpha }_{{\mathrm{TE}}_1}^{\prime }/k_0$ of the TE${}_1$ resonances.

Figure 10

Estimated scattering attenuations for the TM and TE modes based on the $\Delta \alpha /k_0$ column in Table . The general trend is shown by the dashed curve.