Antibonding plasmon mode coupling of an individual hole in a thin metallic film

The polarization dependence of the optical properties of individual subwavelength holes in a thin metallic film is studied using terahertz time-domain spectroscopy. We show that for parallel polarization of the incident light, the coupling is predominantly to short-range bonding film plasmons while for perpendicular polarization the incident light couples more efficiently to long-range antibonding film plasmons. These results represent a direct observation of antisymmetric hybridized plasmons and clarify the nature of plasmonic excitations in metallic structures with subwavelength-scale geometrical features. They show that polarization can be used as a means for selective excitation of film plasmon modes.

Figure 1

Plasmon-dispersion relations calculated using Eq. (1) for films of thicknesses 0.01 (solid), 0.05 (dashed), and $10\mu \mathrm{m}$ (dotted). The black curves are the short-range symmetric bonding film plasmon mode and the gray curves are the long-range antisymmetric antibonding film plasmon mode. The plasmon energies are normalized to the surface-plasmon frequency, ${\omega }_S\left({\omega }_S={\omega }_B/\sqrt{2}\right)$. The light gray straight line represents the dispersion relation of a light in a vacuum and the small box denotes the THz region.

Figure 2

(Color online) Upper row: electric-charge configuration for the bonding (left) and antibonding (right) film plasmon modes. Middle row: optimal coupling mechanism for parallel polarized light (blue arrow) and the induced dipole moment (red arrows) from a bonding film plasmon of half wavelength equal to the hole diameter. Lower row: optimal coupling mechanism for perpendicularly polarized light (blue arrow) and the induced dipole moment (red arrows) from an antibonding film plasmon of wavelength equal to the hole diameter.

Figure 3

(Color online) THz transmission amplitude spectra through a $700\mu \mathrm{m}$ diameter hole fabricated by laser machining. A stainless-steel film used to make the hole has a thickness of about $10\mu \text{m}$ which is much smaller than the wavelength of the incident THz radiation but much larger than the skin depth in the THz range. Angle-dependent THz transmission measurements are carried out by tilting the sample stage, varying the incidence angle $\theta$ of light from $0°$ to $50°$ with a step of $10°$. These spectra are normalized to the one measured at normal incidence and also normalized by the effective area of the hole as seen by the incident THz beam, in order to highlight angle-dependent features. The dotted lines, located at the frequencies of 0.26 and 0.52 THz, represent the spectral positions of the bonding and antibonding film plasmon modes, respectively.

Figure 4

(Color online) (a) Normalized THz transmission amplitude spectra, measured at the incidence angle of $10°$, for different sizes of holes. There is no clear feature seen in the spectra. (b) Normalized THz transmission amplitude spectra measured at the incidence angle of $50°$. The resonant peaks and dips due to the bonding and antibonding film plasmon coupling both show a strong redshift with increasing hole diameter. (c) Comparison between theoretical predictions and experimental measurement. The red (blue) line denotes the theoretically predicted hole plasmon resonance frequencies associated with the bonding (antibonding) film plasmon modes as a function of hole diameter. Red square (blue diamond) data points are obtained by the dip (peak) positions observed in the THz spectra, for different hole sizes.