Quantitative Experimental Determination of Scattering and Absorption Cross-Section Spectra of Individual Optical Metallic Nanoantennas

Antennas convert propagating radiation to localized electromagnetic energy and to heat. To unambiguously separate between these two aspects, one needs to quantitatively determine the antenna scattering and absorption cross-section spectra. By using a spatial modulation technique combined with a common-path interferometer and lithographically fabricated individual gold nanoantennas, we experimentally determine the scattering and absorption cross-section spectra of different optical antennas simultaneously and quantitatively for the first time.

Figure 1

Setup for the quantitative measurement of scattering and absorption cross-section spectra of individual metallic nanoantennas. A spatial modulation technique is combined with a common-path interferometer using three Wollaston prisms (WP). For each wavelength, the sum signal ($P_{\mathrm{sum}}$) of the two detectors ($D$) delivers the sum of scattering and absorption (i.e., the extinction) cross section. Together with the difference signal ($P_{\mathrm{diff}}$) it gives the scattering cross section.

Figure 2

Example of a dimensionless scattering-amplitude spectrum $X(\lambda )$ versus vacuum wavelength $\lambda$ [for the case of the straight dipole antenna shown in Fig. 3 (top)]. Real and imaginary parts of $X(\lambda )$ are shown. Each data point results from a scan in the $xy$ plane (see top). The modulation frequency is $f=1.2\mathrm{kHz}$ and the modulation amplitude is $a=2.0\mu \mathrm{m}$. The focus radius changes with wavelength and is typically about $w_0=1.55\mu \mathrm{m}$.

Figure 3

First group of examples. Transition from a straight dipole antenna (top) to a split-ring resonator (bottom). In the left column, the dots show the measured scattering $C_{\mathrm{sca}}$, absorption $C_{\mathrm{abs}}$, and extinction cross-section spectra $C_{\mathrm{ext}}$ (see legend). The solid curves result from Lorentzian fits. The insets show electron micrographs of the 35 nm thin gold nanoantennas. For all cases, the incident linear polarization is horizontal (see double arrow). The results of corresponding numerical calculations are depicted in the right column on the same scale and in the same format to allow for direct comparison with experiment.

Figure 4

Second group of examples. Straight antenna with a 35 nm thin Au layer (top) and with an approximately 10 nm thick Cr layer underneath a 25 nm thin Au layer (bottom) to intentionally increase the antenna damping. The color code of the different curves is as in Fig. 3.