Optical Beam Steering Based on the Symmetry of Resonant Modes of Nanoparticles

We report a phenomenon that an optical beam transmits in a negative direction when passing through a single array of high-refractive-index dielectric nanorods. The mechanism of the negative directional transmission is believed to be due to the symmetry of resonant modes in the dielectric nanoparticles. It is expected to find applications in designing compact optical components to achieve the on-chip beam steering in photonic circuits.

Figure 1

The $H$ field distribution at the resonance in the 0th (a) and 1st (b) AMCs, corresponding to $\lambda =2362$ and 1550 nm, respectively, for a single Si nanorod of radius $r_s=255\mathrm{nm}$. The black arrows display the direction of the $E$ field on the mesh points at regular intervals outside the rod. Distribution of $H$ field intensity when a Gaussian beam strikes a single-layer array in the $y$ direction composed of 15 Si nanorods at frequencies corresponding to the resonance in the 0th (c) and 1st (d) AMCs. The arrows in (c) display the direction of four different Bragg diffracted orders.

Figure 2

(a) The scattered $H$ field intensity of an isolated rod at the 1st AMC resonance. (b) The time-averaged Poynting vector inside a rod located in the array, showing a vortex of energy flow and implying a rotating dipole excited in the rod. (c) The longitudinal mode and transverse mode, with the excited dipole aligned along and normal to the linear array, respectively. (d) The scattered $H$ field intensity from one rod located in the array. (e) The scattered $H$ field intensity from a pair of adjacent rods in the array. The presence of many rods in (d) and (e) implies the interrod coupling is considered compared to the case in (a).

Figure 3

(a) $|\tan {\eta }_n|$ versus frequency for a single Si rod with radius $r_s=255\mathrm{nm}$. The peaks denote the 0th and 1st AMC resonances. (b) Reflectivity and transmissivity versus frequency for a linear array of rods, with $a_0=\lambda /\sqrt{2}$ and the incident angle ${\theta }_i=45°$. (c) Reflectivity and transmissivity versus ${\theta }_i$ for a linear array of rods with $a_0=\lambda /\sqrt{2}$ and $\lambda =1550\mathrm{nm}$, corresponding to the 1st AMC resonance.

Figure 4

(a) The transmissivity $T_{-1}$ of the $-1$st order transmitted wave for the arrays made up of singlets (black dashed line) and doublets [gray (red) dashed line]. The inset shows the unit cell of the singlet and doublet. Both lattice separations are $a_0=1096\mathrm{nm}$ for the singlet and doublet structures for which the beam steering can be realized near the wavelength $\lambda =1550\mathrm{nm}$. (b) Total scattering cross section (dashed lines) and collective resonance spectrum [10] (solid lines) for singlet (black) and doublet [gray (red)] structures.

Figure 5

Distribution of the $H$ field intensity when a linear array composed of (a) square rods of side length 462 nm and (b) $4\mu \mathrm{m}$-high circular rods with radius 255 nm is illuminated by a Gaussian beam, demonstrating beam steering using a single array of rods with noncircular cross section and three-dimensional particles. The incident wavelength is $\lambda =1550\mathrm{nm}$ for both cases.