1. Introduction

In the past few years, photonic integrated circuits (PICs) have emerged as a new industrial platform that has been considered a promising platform for high-density integrated optics. It can integrate optical components on a single chip and has great potential to overcome the challenges of future integrated computing systems, optical interconnects, and optical networks. Optical nanoantennas, as one of the optical components, play an important role in PICs. Because of their unique resonance and scattering properties, optical nanoantennas are ideal for connecting free-space and on-chip light. Researchers have proposed nanoantennas of different materials and structures to achieve various functions. For example, waveguide-hybridized Yagi–Uda antennas can realize directional in-coupling of free-space waves and out-coupling of guided waves [1], and a gold nanodisk and a nanoslit integrated waveguide could routine linearly polarized beam in opposite directions at two different wavelengths [2]. In recent years, the application of optical antennas-dressed waveguide is an emerging direction of PICs [3]. Arrays of dielectric or plasmonic nanoantennas can be used to control guided waves via strong optical scattering at subwavelength intervals, enabling a variety of devices such as waveguide mode converters [4], polarization rotators, high efficiency mode-selective directional couplers [5,6], and programable mode converters based on phase-change nanoantennas [7]. So far, nanoantennas have been widely used in optical interconnects [8,9], photonic detection [10–12], biological sensors [13,14], nano imaging [15–17], nonlinear optics [18–21] and holography [22]. More features and functions of nanoantennas are being developed to meet various applications of the PICs platform.

Antennas with photonic crystal-derived structures are compact optical antennas. It usually consists of a degenerated photonic crystal (a single row of pillars or holes) for the light transmission part, and a size-changed unit cell for the light scattering part [23]. The degenerated photonic crystal inherits the excellent light-guiding characteristics, and can realize the flexibly bent light path [24]. The size-changed unit cell is designed as a scatterer, which can replace the original ones at any position of the structure and realize light scattering. With careful selection of parameters, the antenna can achieve 46% vertical scattering within the scattering area of one wavelength [23]. In this paper, we explore the ability to selectively switch on and off states under different input phases and wavelengths and propose a novel optical nanoantenna composed of subwavelength silicon pillars of two different sizes. The smaller columns are arranged in chains, in which light could be highly localized and propagate without divergence. The larger pillars are able to scatter the propagating light into free space. By choosing appropriate structural parameters, the antenna can be modulated on and off under different input optical modes and exhibit opposite on-off characteristics at different wavelengths. When integrated with a Mach–Zehnder interferometer or a programmable mode converter, the nanoantenna has the potential to build a more multifunctional 3D optical link for photonic integrated circuits, such as an adjustable 3D optical switch, or even as the basic block for 3D analogue optical gate.

2. Results

Figure 1(a) shows the structure of the proposed optical nanoantenna. The antenna is composed of two parallel, closely spaced chains of silicon nanopillars. The length of the pillar chain is L = 18 µm, and the period of the pillars is p = 400 nm. The pillar chain is composed of common pillars and defect pillars, most of which are common pillars with radius r₀= 110 nm. The first and third pillars at the end of each chain are replaced with defective pillars with a radius of r_d = 190 nm. The center spacing of the two chains is S = 350 nm (the defect pillars are partially overlapped). The height of all pillars is h = 810 nm. The index of refraction of the pillars is n = 3.46, and they are placed on a silicon dioxide substrate with index of refraction n_sub= 1.5.

 

Fig. 1. (a) The normalized scattering spectra when the phase differences of the incident dipole source are Δφ=0 and Δφ=π. The inset picture shows schematic structure of the optical nanoantenna. (b) Left: incident field profile ant xOy plane. Right: the normalized scattered field disruibution for point A in the scattering spectrum. It is the superposition of Ex and Ey with comparable intensities. The Ex field consists of 2 spots symmetrical about the xOz plane, and Ey is a spot on the xOz plane. The 3 spots form an scattered field in the shape of the letter “C”. (c) Left: incident field profile ant xOy plane. Right: the normalized scattered field disruibution for point B in the scattering spectrum. The intensity mainly comes from the Ex field, which can be considered as the superposition of the scattered fields of the two chains in the xOz plane.

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3D finite-difference time-domain (FDTD) method is used to simulate the scattering of the antenna. We set up an Ez-polarized dipole source 10 nm before each column chain, respectively. The height of the sources is at the center of the pillars. The two dipole sources are identical except for the phase difference of Δφ. Light from the dipole sources can be coupled into the pillar chain to propagate and be scattered into free space at the defect pillar. Here we used the dipole source because it contains all the wave vectors, which is more convenient to analyze transmission and scattering attributes of light at the same time. A monitor was placed 3.5µm right above the defect pillar to record the upward scattering field and calculate the scattering efficiency. We calculated the scattering efficiency for Δφ=0 and Δφ=π at the operating wavelength of 1460-1650 nm, as shown in Figure 1(a). It can be seen that when Δφ=0, there is resonant scattering at wavelengths greater than 1560 nm, but not at wavelengths less than 1560 nm. On the contrary, when Δφ=π, only wavelengths less than 1560 nm have significant scattering. The scattered fields for A and B are shown in Figure 1(b)(c). When λ=1640 nm and Δφ=0, the scattered field presents a spot with a size of 3µm × 5µm and scattering efficiency of 30%. When λ=1500 nm, Δφ=π, the scattered field presents a letter “C” shape and scattering efficiency of 10%.

We first analyze the propagation characteristics of the device. Figure 2 shows the electric field distribution of the xOy plane at wavelengths of 1500 nm and 1640 nm. Obviously, the light propagation in the column chain directly affects the scattering efficiency. When λ=1500 nm, Δφ=π, or λ=1640 nm, Δφ=0, light can propagate in the column chain and scatter into free space. When λ=1640 nm, Δφ=π, or λ=1500 nm, Δφ=0, light can hardly propagate in the column chain, so the scattering efficiency is low. This is due to the superposition of the modes in the double-row chains. For a better understanding, we place a dipole source at an asymmetric position of the structure to excite the mode of the double-row chains and calculate the electric field E(x,y). In fact, we can just remove one of the dipole sources. Thus, when two light sources with a phase difference of Δφ exist, the total electric field can be calculated by the following equation:

 

Fig. 2. Electric field distributions for xOy plane at wavelengths 1500 nm and 1640 nm. E_x, E_y and E_z are excited by single dipole source. E_total is the magnitude of electric field excited by two dipole sources with different phase differences. The scale bars in the figure are 1 µm. The normalized colorbars are plotted in the right.

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Then equation (1) can be written as:

The intensity of the Ez component is dominant, so light can propagate inside the column when Δφ=π, but it is difficult to propagate when Δφ=0. The case for 1640 nm is based on the same principle. However, the symmetry of the electric field components are just opposite to that at 1500 nm. Thus, the propagation state of light is also reversed.

When designing nanoantennas, some key parameters r₀, r_d, H, p and S need to be carefully designed to meet the requirements of light propagation, scattering and fabrication conditions. We first calculate the band structure of the photonic crystal for the transmission part. Generally, the band structure can be calculated by FDTD method or plane wave expansion method. The FDTD method is to excite all possible modes of the system by using multiple randomly placed broadband dipoles. An advantage of this method is that it can be used to calculate structures in 3D or planar geometries, which is very useful for most photonic crystal devices compatible with CMOS technology. We calculated the band structure under different parameters, and finally chose H = 810 nm, r₀= 110 nm and p = 400 nm, so that light can be transmitted for the wavelengths between 1500 nm and 1640 nm, because the 1^st band Bloch mode is supported, as shown in Figure 3(a). Then, we scan the spacing S and calculate the energy band structure for the double-row chains. S = 0.35µm is chosen that the 1550 nm wavelength falls in the bandgap, while the 1640 nm wavelength is still in the 1st band. So, when Δφ=0, 1640 nm wavelength can propagate in double-row chains, while 1550 nm cannot. The situation for Δφ=π cannot be seen directly in the band structure, but we can deduce from Figure 2 that when Δφ=π, the propagation of the two wavelengths is opposite to that of Δφ=0. The length of the pillar chain is set to L = 18 µm, which is enough to greatly attenuate the transmitted energy for λ=1640 nm, Δφ=π and λ=1500 nm, Δφ=0.

 

Fig. 3. (a) The band structures of a single periodic nano pillar chain and double-row chains. (b) The scattering intensities spectrum for defect pillars in the nano pillar chains.

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The scattering characteristics of the device are mainly due to defect pillars. Defective pillars are larger in size and cause mode mismatches. Part of the electric field can no longer be bound in the pillar chain and leaks in the z direction, forming an out-of-plane scattering field. Figure 3(b) simulates the scattering intensities generated by defect pillars of different sizes. The scattering intensity reaches the maximum value of 18% at r = 190 nm. We also set up 2 defect pillars in each chain to form a 2 × 2 array, so that the shape of the scattered field can be better constrained in the x and y directions. The normal pillar chain behind the defective pillar is eliminated, which can increase the scattering efficiency while reducing the size of the device. This is because light propagating to the end of the pillar chain will reflect, and the reflected light will pass through the defective pillar again and cause another scattering, which is constructed in free space. The defective pillars partially merged because they were too close. But the size is deep subwavelength, so it has little effect on the overall effect, which is also proved by the simulation results.

The chain spacing S is determined by the scattering spectrum, because changing Δφ to switch the scattered field can only occur when the spacing between the two chains is within a certain range. Figure 4(a)(b) shows the scattering efficiency distributions for Δφ=0 and Δφ=π under different chain spacing S. It can be seen that when S > 0.9µm, the range of their scattering regions is almost the same, except for some small shifts in the peak positions. This is because the mode coupling is weak when the distance between the two chains is large enough. They can be regarded as independent single chains, and their scattering wavelength range basically corresponds to that of a single chain. And when S < 0.9µm, the two chains have strong mode coupling because of the close distance. This results in a change in the propagation mode and scattering spectrum. When Δφ=0, the scattering region is red-shifted, and when Δφ=π, the scattering region is blue-shifted. Figure 4(c) shows the distribution of the ratio of T(Δφ=0) to T(Δφ=π). It can be seen that when S = 0.35µm, the two scattering regions are just separated, resulting in the opposite distribution of the scattering spectrum in wavelength and phase.

 

Fig. 4. Scattering efficiency distributions for (a) Δφ=0 and (b) Δφ=π under different chain spacings. (c) Distribution of the ratio of T(Δφ=0) to T(Δφ=π) in logscale. The green dotted rectangle indicates that the two scattering regions are just separated.

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In the simulation, we use a dipole source for the input light. In practical designs, we can achieve similar effects with symmetric or anti-symmetric incident fields. A typical example is the mode input with a multimode waveguide. Figure 5 shows a silicon multimode waveguide with a height of 810 nm and a width of 650 nm. We calculated the TM modes of this waveguide and found that TM0 is symmetric, corresponding to the situation where the dipole source phase difference Δφ=0, and TM1 is antisymmetric, corresponding to the situation where the phase difference Δφ=π. By selecting the corresponding modes, we used the mode sources instead of dipole sources for simulation, as shown in Figure 5(c). We calculated the coupling efficiency of light incident from the multimode waveguide into the pillar chains. The coupling coefficient is 41.9% at λ=1500 nm, Δφ=π, and 59.2% at λ=1640 nm, Δφ=0. According to the total scattering efficiencies of 10.3% and 22.2%, we calculated the local scattering efficiencies at the defect pillars to be 24.6% and 37.5%, respectively. Obviously, the result is consistent with that of dipole source input. We can further optimize the coupling efficiency to increase the total scattering efficiency. In fact, the nanoantennas are well suited for integration with antennas-dressed waveguides in terms of design and fabrication. Recently, it has been reported that antannas-dressed waveguides can achieve TE0 to TM0 and TM1 mode conversion [4], and phase-change materials can be used to achieve programmable waveguide mode conversion [7]. We believe that with careful design, the nanoantenna and programmable waveguide mode converter can be integrated together to realize a 3D coupler switch.

 

Fig. 5. 650 nm × 810 nm multimode waveguide (black rectangle) and the corresponding (a) TM0 mode and (b) TM1 mode. (c) The normalized scattering spectra under TM0 and TM1 mode incidence. The inset picture shows schematic structure.

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The proposed nanoantennas can be fabricated on SOI (silicon-on-insulator), where the thickness of the top silicon layer and buried oxide layer are 810 nm and 3 µm, respectively. First the top silicon layer is thermally oxidized to form a 60 nm thick SiO₂ layer as a hard mask. The pattern is then transferred to the hard mask by electron beam lithography and reactive ion etching. Finally, a well-designed ICP-DRIE (Inductively Coupled Plasma Deep Reactive Ion Etching) process was used to complete the etching of the nanoantennas. According to our previous experience, this process can achieve a maximum aspect ratio (height to diameter) of 5:1. Therefore, it can be used to fabricate pillars with a radius of 110 nm and 190 nm.

3. Conclusion

In conclusion, we have numerically demonstrated an optical nanoantenna composed of silicon nanopillars. The antenna can exhibit different on and off scattering states in two dimensions of wavelength and incident phase difference. It can achieve 10%∼30% scattering efficiency in subwavelength size, and has the potential to form a 3D coupler switch with a programmable mode converter. We suggest that it will provide more solutions for couplers and 3D optical routine design for IC chips.