Characteristics of Longitudinal SPR Modes with Varying Gap

Size

3.3.1 Nanodisk Dimer

In longitudinal polarization, the dipole mode would be much red shift when the nanodisk dimers come in close, as described in the last section. Figure 3.9 shows a simulated plot of the longitudinal dipole mode shift versus the gap size variation. The shift can be fit very nearly to an exponential decay function.

Figure 3.9: Simulated plot of longitudinal dipole mode wavelength shift as a function of gap size, which fits to an exponential-decay function. The inset is the illustration of the electromagnetic interaction between the nanodisks dimers in the longitudinal polarization.

The observed gap size dependent behavior of the longitude mode shift suggests a qualitative interpretation by a simple dipole-dipole interaction model which is well

32

explained by W. Rochberger et al. [20]. The electric field of the incident light would induce surface charges which feel repulsive force in the nanodisk at resonance. When another nanodisk is nearby, upon polarization additional force act on both nanodisks as sketch in the inset of Fig.3.9. If the driving field is parallel to the dimer-axis (longitudinal polarization), this effect results in a weakening of the repulsive forces for the surface charges. The positive charge of the left nanodisk in Fig.3.9 faces the corresponding negative charge of the right nanodisk. Due to the attractive forces between these two charge distributions of the different nanodisks, the repulsive forces within each nanodisk are weakened, leading to a correspondingly red shift of resonance wavelength.

In addition, the intensity of the electric field is more concentrated and enhanced with decreasing gap size as shown in Fig.3.10 and is nearly exponential decay with increasing gap size as shown in Fig.3.11. The field intensity in the gap of 10 nm is even 70 times stronger than that in the gap of 350 nm. The enhancement effect indicates that dimer system is critical for near-infrared sensitivity.

33

Figure 3.10: Simulated electric field distributions of the longitudinal dipole mode with different gap sizes are shown in (a) top view at mid-height of the dimer and (b) side view along the dash line of inset. The position where y = 0 in (b) is the center of the gap shown as white area.

Figure 3.11: Simulated electric field intensities of the longitudinal dipole mode in the gap center with different gap sizes.

Figure 3.12 shows a plot of the longitudinal mode shift versus the gap size variation for fabricated gold nanodisk dimers. The shift can also be fit very nearly to an exponential decay function, which is as the same as predicted in simulation.

34

Figure 3.12: Experimental results of the longitudinal dipole mode wavelength shift as a function of the gap size, which fits to an exponential-decay function.

3.3.2 Nanoring Dimer

Figure 3.13 shows a simulated plot of the longitudinal bonding mode shift versus the gap size variation. The shift can be fit very nearly to an exponential decay function, similar to the behavior of the longitudinal dipole mode for the nanodisk dimers where the charge distributions are almost the same, so it may be also attributed to the weakening repulsive force in the dimers modeled by the dipole-dipole interaction.

35

Figure 3.13: Simulated plot of the wavelength shift as a function of the gap size for the longitudinal bonding mode, which fits to an exponential-decay function.

Magda O. El-Shenawee also suggested this characteristic as a simple equivalent LC circuit oscillation [28]. In longitudinal polarization, the incident electric field in the gap is normal to the nanorings’ wall surface consistent with the charge signs in Fig.3.5(b). As the gap size decreases, the equivalent capacitance value increases. As a result, the resonance frequency proportional to 1/C decreases. This concept is consistent with the results observed in Fig. 3.4(a). In transverse polarization, the incident electric field in the gap is parallel to the nanorings’ wall surfaces.

Accordingly, there is no effective capacitance caused by the gap, leading to insignificant effect of the gap size on the resonant wavelength observed in Fig. 3.4(b).

36

Fig. 3.14: Simulated electric field distributions of the longitudinal bonding mode with different gap sizes are shown in (a) top view at mid-height of the dimer and (b) side view along the dash line of inset. The position where y = 0 in (b) is the center of the gap shown as white area.

In addition, the intensity of the electric field is more concentrated and enhanced as gap size decreases for longitudinal bonding mode as shown in Fig. 3.14 and nearly exponential decay with increasing gap size as shown in Fig.3.16. The field intensity in the gap of 10 nm is about 57 times stronger than that in the gap of 350 nm and also stronger than that in the nanodisk dimers of the same gap size. This enhancement effect is similar to that for the nanodisk dimer because the bonding charge distribution of nanoring dimer is similar to the dipole mode of nanodisk dimer.

However, longitudinal anti-bonding mode doesn’t shift significantly with different gap sizes, as shown in Fig. 3.4(a). It attributed to the electric field intensity in the gap independent to gap size as shown in Fig. 3.15 & 3.16, maybe due to the anti-bonding charge distribution.

37

Figure 3.15: Simulated electric field distributions of the longitudinal anti-bonding mode with different gap sizes are shown in (a) top view at mid-height of the dimer and (b) side view along the dash line of inset. The position where y = 0 in (b) is the center of the gap shown as white area.

38

Figure 3.16: Simulated electric field intensities of the longitudinal bonding and anti-bonding modes in the gap center with different gap sizes.

Figure 3.17 shows a plot of the longitudinal bonding mode shift versus the gap size variation for fabricated gold nanoring dimers. The shift can also be fit very nearly to an exponential decay function, which is as the same as predicted in simulation.

Figure 3.17: Experimental results of the longitudinal bonding mode wavelength shift as a function of the gap size, which fits to an exponential-decay function.

39

3.4 Summary

In this chapter, we identified and characterized the properties of SPR modes with gap size variation in nanodisk and nanoring dimers by simulations then realized by experiments. For nanodisk dimers, there is a dipole mode in each polarization and appearing a high-order mode in longitudinal polarization when the nanodisk dimers come in close. On the other hand, for nanorings dimers, there are anti-bonding mode and bonding mode in each polarization and also appearing a high-order mode in longitudinal polarization when the nanoring dimers come in close, which can be characterized by hybridization model. We further find that the wavelengths of longitudinal dipole mode in nanodisk dimers and longitudinal bonding mode in nanoring dimers are red-shift as an exponential function with decreasing gap size.

Moreover, the electric field intensities are more enhanced with decreasing gap size and also decay as an exponential function with increasing gap size. And the electric field intensity in the gap for nanoring dimer is stronger than nanodisk dimer, which indicates better sensing ability in nanoring dimer system.

40