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Timestamp: 2019-04-22 17:03:00+00:00

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We propose an all-silicon-based nano-antenna that functions as not only a wavelength demultiplexer but also a polarization one. The nano-antenna is composed of two silicon cuboids with the same length and height but with different widths. The asymmetric structure of the nano-antenna with respect to the electric field of the incident light induced an electric dipole component in the propagation direction of the incident light. The interference between this electric dipole and the magnetic dipole induced by the magnetic field parallel to the long side of the cuboids is exploited to manipulate the radiation direction of the nano-antenna. The radiation direction of the nano-antenna at a certain wavelength depends strongly on the phase difference between the electric and magnetic dipoles interacting coherently, offering us the opportunity to realize wavelength demultiplexing. By varying the polarization of the incident light, the interference of the magnetic dipole induced by the asymmetry of the nano-antenna and the electric dipole induced by the electric field parallel to the long side of the cuboids can also be used to realize polarization demultiplexing in a certain wavelength range. More interestingly, the interference between the dipole and quadrupole modes of the nano-antenna can be utilized to shape the radiation directivity of the nano-antenna. We demonstrate numerically that radiation with adjustable direction and high directivity can be realized in such a nano-antenna which is compatible with the current fabrication technology of silicon chips.
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Fig. 1 Schematic showing the structure of the proposed nano-antenna which functions as a wavelength (a) and a polarization (b) demultiplexer.
Fig. 2 (a) Evolution of the 2D scattering pattern resulting from two identical dipoles perpendicular to each other with increasing phase difference. (b) Evolution of the 2D scattering pattern resulting from two dipoles oscillating in phase with increasing ratio of their amplitudes.
Fig. 3 Multipole expansion of the total scattering of a single Si cuboid with w1 = 120 nm (a) and w2 = 200 nm (b). The electric field distributions at the ED and EQ resonances and the magnetic field distributions at the MD and MQ resonances are presented as insets.
Fig. 4 Multipole expansion of the total scattering spectrum of the nano-antenna in a spherical (a) and a cartesian (b) coordinate. The electric field distributions at the ED resonances (644 and 748 nm) and the magnetic field distributions at the MQ resonances (640 and 752 nm) are shown in the insets of (a). In (b), we present the electric and magnetic modes with relative large amplitudes (EDx, EDz, MDy, EQxz, MQyz) which determine the radiation direction and directivity of the nano-antenna.
Fig. 5 Schematic showing the 3D (first row) and 2D (second row) radiation patterns of MDy, EDz, and EDx induced in the nano-antenna. Also shown are the schematic radiation pattern resulting from the interference between MDy and EDz and that resulting from the interference between MDy and EDx (third row). The schematic radiation pattern of the nano-antenna, which is determined by the interference of these three modes, is presented in the fourth row.
Fig. 6 (a) Phase difference between MDy and EDz as a function of wavelength. (b) Deflection angle of the radiation as a function of wavelength. (c) Vector diagrams for MDy, EDz, and EDx.
Fig. 7 (a) Schematic showing the 3D and 2D radiation patterns of EDx and MQyz and the radiation pattern resulting from the interference of these two modes. (b) Schematic showing the 3D and 2D radiation patterns of MDy and EQxz and the radiation pattern resulting from the interference of these two modes.
Fig. 8 (a) Wavelength dependences of HPBWy and D. (b)-(g) Vector diagrams plotted for EDx, MDy, MQyz and EQxz at different wavelengths.
Fig. 9 (a) Wavelength dependence of the maximum radiation angle simulated for the nano-antenna. The 3D radiation patterns calculated at wavelengths of 405, 600, 680 nm are shown in (b), (d), (f) while the corresponding 2D radiation patterns are shown in (c), (e), (g).
Fig. 10 (a) Wavelength dependence of the maximum radiation angle of the nano-antenna calculated for the incident light whose polarizations are along the x and y directions. (b) and (d) show the 3D radiation patterns calculated at wavelengths of 680 and 860 nm for the x- and y-polarized light. The corresponding 2D radiation patterns are shown in (c) and (e).
Fig. 11 Transmission spectra calculated for the nano-antenna array whose periods in the x and y directions are designed to be 800 and 450 nm, respectively. Ttot is the total transmission while T-1, T0, and T+1 represent the transmissions of the orders of −1, 0, and + 1, respectively.
Fig. 12 2D electric field distribution of the nano-antenna on the xz plane calculated at wavelengths of (a) 583 nm and (b) 730 nm.
Fig. 13 Multipole expansion of the total scattering spectrum calculated for a Ge (a) and a Si (b) nanosphere with a diameter of 75 nm. The wavelength dependence of the phase difference between the Ed and MD induced in the Ge and Si NSs are shown in (c) and (d), respectively.
Fig. 14 Electric field distributions calculated for the small (a) and large (b) Si cuboids of the nano-antenna at 541 and 565 nm, respectively.
Fig. 15 (a) Radiation patterns calculated for the nano-antenna placed on a quartz substrate with a refractive index of 1.45 at (a) 615 nm and (b) 680 nm. The deflection angles achieved at these two wavelengths are + 18.8° and −30.6°.
(3) EQ αβ = 1 -i2ω = ∫ [ r α j β + r β j α − 2 3 (r⋅j) δ αβ ] d 3 r.
(4) MQ αβ = 1 3c ∫ [ ( r×j ) α r β + ( r×j ) β r α ] d 3 r.
(5) J(r)=−iω ε 0 [ ε r (r)− ε r,d ]E(r).
(8) D= P (θ,φ) max P (θ,φ) av .
(9) P (θ,φ) av = 1 4π ∫ φ=0 φ=2π ∫ θ=0 θ=π P(θ,φ)sinθdθdφ (W sr −1 ).

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