Retrieving the Size of Deep-Subwavelength Objects via Tunable Optical Spin-Orbit Coupling

We propose a scheme to retrieve the size parameters of a nanoparticle on a glass substrate at a scale much smaller than the wavelength. This is achieved by illuminating the particle using two plane waves to create rich and nontrivial local polarization distributions, and observing the far-field scattering pattern into the substrate. By using this illumination to control the induced complex dipole moment, the exponential decay of power radiated into the supercritical region, as well as directional scattering due to spin-orbit coupling can be exploited to retrieve the particle’s shape, size, and position directly from the far-field scattering with high sensitivity and without the need for a complicated and time-consuming optimization algorithm. Our method brings about a far-field superresolution nanometrology scheme based on the interaction of vectorial light with nanoparticles.

Figure 1

(a) Far-field radiation pattern into the glass substrate when a horizontal dipole $p_x$ is placed at different distances $z_0$ from the interface. The radiation pattern in UAR is the same for all $z_0$. (b) Power ratio between the SAR and the UAR as the horizontal dipole is moved away from the interface. (c) Far-field radiation pattern into the glass substrate for a spin dipole. (d) Power ratio between the RSAR and the LSAR for different $\gamma$ for a general spin dipole located at $z_0=0.005{\lambda }_0$.

Figure 2

(a) Geometry of the considered 2D system. A nanowire is placed on top of a glass substrate. Two $p$-polarized plane waves are incident at the Brewster angle on the nanowire, forming an interference pattern. The nanowire is moved along the $x$ axis. The polarization state along $x$ changes from linear to circular of different handedness as schematically shown by the blue arrows and circles. (b) Power ratio in the RSAF and LSAF region as the nanowire is moving along $x$. The insets show different shapes of the cross sections with aspect ratio $a:b=1:1(\mathrm{blue})$, $2:1(\mathrm{red})$, and $3:1(\mathrm{yellow})$ when $b=10\mathrm{nm}$. (c) Far-field scattering (red dashed curve) pattern of a nanowire placed at $x=0$ into the substrate simulated by COMSOL. The scattering pattern can be well described by an equivalent horizontal dipole placed at the center of the nanowire (blue curve). (d) Same as Fig. 2 except the nanowire is placed at $x=x_0$ and can be approximated by a spin dipole with ${\gamma }_{\mathrm{opt}}$.

Figure 3

(a) Retrieval of the height $b$ of silicon nanowires of a circular cross section from the power ratio in the UAR and SAR. (b) Retrieval of the aspect ratio from the power ratio of the RSAR and LSAR. The height $b$ is fixed as 10 nm.

Figure 4

(a) Geometry of the considered 3D system. A nanorod is placed on a glass substrate. Two successive illuminations in the $YZ$ (yellow) plane and $XZ$ (green) plane are used to illuminate the nanorod. The calculated optimum displacements $x_0$ and $y_0$ are shown in the top-right inset for a nanorod of dimensions $a=30$, $b=20$, and $c=10\mathrm{nm}$. Bottom right is the retrieved parameters. (b) Retrieval of the radius of a nanosphere. (c) Retrieval of the aspect ratio $a/c$ of different nanorods with fixed height $c=10\mathrm{nm}$.