Determination of Electric-Field, Magnetic-Field, and Electric-Current Distributions of Infrared Optical Antennas: A Near-Field Optical Vector Network Analyzer

In addition to the electric field $\mathit{E}(\mathit{r})$, the associated magnetic field $\mathit{H}(\mathit{r})$ and current density $\mathit{J}(\mathit{r})$ characterize any electromagnetic device, providing insight into antenna coupling and mutual impedance. We demonstrate the optical analogue of the radio frequency vector network analyzer implemented in interferometric homodyne scattering-type scanning near-field optical microscopy for obtaining $\mathit{E}(\mathit{r})$, $\mathit{H}(\mathit{r})$, and $\mathit{J}(\mathit{r})$. The approach is generally applicable and demonstrated for the case of a linear coupled-dipole antenna in the midinfrared spectral region. The determination of the underlying 3D vector electric near-field distribution $\mathit{E}(\mathit{r})$ with nanometer spatial resolution and full phase and amplitude information is enabled by the design of probe tips with selectivity with respect to $E_{\parallel }$ and $E_{\perp }$ fabricated by focused ion-beam milling and nano-chemical-vapor-deposition methods.

Figure 1

Schematic of coupled-dipole antenna geometry (a) with current density $\mathit{J}(y)$ through cross sectional surface $\mathit{S}$ and associated magnetic field $H_x(y,z)$ on contour $\mathit{C}$ related to the measured curl of the electric field $\mathit{E}(y,z)$ in the antenna $y-z$ mirror plane. Inset: SEM image, scale bar 500 nm. (b) Schematic of amplitude-, phase-, and polarization-resolved interferometric homodyne 3D $\mathit{E}(\mathit{r})$ vector near-field $s$-SNOM imaging. (c) Pt point dipole probe antenna fabricated on a Si AFM tip by FIB and nano-CVD. SEM images of the tip before (left) and after (right) Pt deposition with Si (red) and Pt (yellow) regions highlighted.

Figure 2

Measured (a),(c) and theoretical (b),(d) near-field vector distribution of linear Au IR optical dimer antenna: (a) $\mathit{E}(y,z)$ in the $y-z$ plane and (b) corresponding theory. Field magnitude is given by vector length and color map. A line scan (white line) for $|\mathit{E}(y,z)|$ at $z=90\mathrm{nm}$ is shown. Inset: Close-up views of the near-field vector distribution near $y=0$. Line scans (c),(d) show topography and measured $E$-field components $E_y$ and $E_z$ at $z=90\mathrm{nm}$ above the antenna surface. The 80 nm gap is not fully resolved in topography due to the probe tip size.

Figure 3

Magnetic field $H_x$ ($y$, $z$) above coupled-dipole antennas (position indicated by gray dashed lines) derived from the the electric near-field distribution $\mathit{E}(\mathit{r})$, experiment (a) and theory (b). Horizontal variation of $H_x(y)$ (c) and vertical distance dependence of $H_x(z)$ (d) [black dashed lines in (a) and (b)]. Because of the antenna symmetry, $H_x(y,z)$ in the $y-z$ mirror plane represents the full magnetic antenna response.

Figure 4

Current distribution $I(y)$ along antenna dimer reconstructed from $E_y$ (a, total and b, masked to remove scattering due to metal roughness) and $H_x$ (c) with normalized amplitude $|I|$ and phase $\varphi$ [radians]. A shift in current maximum (dashed line) of 100–200 nm with respect to geometric center (dotted lines) results from capacitive gap coupling. For comparison, (d) and solid line in (c) show $I(y)$ from theory.