1. Introduction

Optical beam scanners (OBSs), capable of dynamically steering light beams, constitute a key building block for numerous technologies like sensing [1–2], imaging [3–4], image projections [5], displays [6], light detection and ranging (LiDAR) [7–8] and autonomous driving [9]. Traditionally, optical beam scanning can be achieved by mechanically rotating reflective mirrors or using liquid-crystal spatial light modulators. However, their low response speed and bulky structure have posed severe limitations on their practical applications.

For agile and compact OBSs, it has emerged over the past decade that solid-state OBSs, which allow for a dense integration of thousands of optical antennas into an area of fingernail sizes [10] and a beam scanning speed over GHz [11], could be a practical solution. Tremendous efforts have been made in the developments of solid-state OBSs, and different light-beam-steering mechanisms have been explored, including those based on micro-electro-mechanical systems (MEMSs) [12], those using on-chip phase modulators to align the phases of on-chip antennas [10,13–17] and those scanning the beam by controlling the input light wavelength [18–24]. Among them, MEMS-actuated OBSs provide simultaneously a relatively shorter response time of microsecond level and a large aperture of over 1mm² [12] for ultra-small beam divergence. However, the MEMS-based OBSs suffer from limited field-of-views (FOVs) [12], because the multi-wavelength sizes of each grating element give rise to grating lobes in the far-field zone. Meanwhile, the MEMS-based OBSs are driven by external out-of-plane far-field illuminations, which means the device cannot be fully integrated. As a result, the inherent flexibility of the on-chip OBS is reduced. Comparatively, phased OBSs deal with in-plane propagating light, which means the antennas, the phase modulators and even the optical sources could be integrated on the same wafer [25]. Moreover, because no mechanical actuations are involved in phase modulations, phased OBSs are totally inertial-free with potentially ultra-high scan rate above GHz using electro-optic modulators [11,26]. Unfortunately, a main drawback of OBSs is the difficulty in constructing large-aperture beam scanners. As the scale of the antenna array and the number of control units increase, the coherent controls over hundreds and even thousands of on-chip antennas become challenging [13]. Meanwhile, the crosstalk between on-chip waveguides prevents the spacing between adjacent on-chip antennas from being reduced to sub-wavelength scale [15–16,27]. With an inter-element spacing of over one wavelength, there are more than one emission angle that could fulfill the constructive interference condition of light and then grating lobes appear, significantly reducing the FOV and efficiency of the device.

Alternatively, optical beam scanning can also be achieved passively using on-chip antennas with wavelength-dependent beams, e.g. waveguide grating antennas, in conjunction with wavelength-tunable laser sources [18–24]. Compared to MEMS-based and phased OBSs, the wavelength-controlled OBSs can also be fast and show easier implementations and lower cost, because they do not require additional electronic control units and are free from complex power distribution networks. Meanwhile, in the wavelength-controlled manner, large-aperture small-beam-divergence scanners can be achieved by engineering the antenna structures to control the light emission rates along the antenna apertures [18–19], which are not as challenging as scaling up the phased on-chip antenna array. As shown in [18], an ultra-small beam divergence with a full-width-half-maximum below 0.1° can be achieved using silicon nitride as overlays. More importantly, the spacing between the grating elements or the nanoantenna elements in the wavelength-controlled beam scanners can be made significantly smaller than the wavelength even below ideal half-wavelength, which means the light beam steering is inherently grating-lobe-free and thus it provides higher device efficiency than those with grating lobes. The simple implementations, grating-lobe-free beam steering and the reach to narrow beam-divergence make wavelength-controlled OBSs very suitable for applications that are cost-conscious and require ultra-fine spatial resolutions like LIDAR systems on unmanned vehicles. As an example, the OBSs formed by a linear array of wavelength-agile gratings, controlling the beam direction by wavelength in one dimension while using the phased approach to steer the beam along the other dimension, have provided a practical solution for large-aperture two-dimensional scanning demanded by LIDAR [11,14,17,27–29], after intensive research efforts devoted. Two-dimensional-scanning beam scanner controlled purely by wavelength has also been demonstrated [24]. Except for silicon, wavelength-controlled OBSs are widely adopted in LIDAR researches involving various integrated photonic platforms including silicon nitride [30], plasmonic [22–23] and III-V materials [11].

For practical applications of OBSs, a large FOV is always pursued. Unfortunately, without special engineering, typical FOV of the wavelength-controlled OBS, e.g., the waveguide grating antenna, is only roughly 10° with a wavelength variation of 100 nm (0.1°/nm) [14,20,28–29]. Although further increasing the wavelength range could widen the scanning range, the wavelength tuning range of over 100 nm is not commonly available and could be challenging for on-chip laser sources. As a result, most of the existing 2-D solid-state OBSs feature a significantly smaller scanning range in their wavelength-controlled dimension compared to that in the phased dimension [14,17,27,29]. To solve this problem, lattice-shifted photonic crystal waveguides have been proposed to make the emission angle sensitivity against wavelength increase from 0.1°/nm of the standard waveguide grating antenna to 1.0°/nm with a steering range of 23° demonstrated [20]. However, the photonic bandgap can only be formed within a relatively narrow wavelength range (30 nm in [20]), preventing further expansion of the scanning range.

Nanoantennas, with their unique abilities to concentrate light into deep-subwavelength scale and tailor the emission pattern of light, have received great attention in the past decade. For chip-based applications, silicon photonic devices with different radiation characteristics have been demonstrated by taking full advantages of the flexible design freedoms provided by nanoantennas. These nanoantenna-based devices have enabled a lot of fascinating applications including reconfigurable on-chip interconnects [31], ultra-compact lab-on-a-chip microflow cytometers [32], wireless on-chip communications and networks [33–36]. However, the majority of these researches, focuses on the manipulation of in-plane light emission. The potential of using nanoantenna array as the on-chip OBS has largely remained unexplored.

In this paper, we report a nanoantenna-based wavelength-controlled OBS, achieving a FOV over 40°, significantly higher than the previously reported grating-based designs. The proposed device is based on the silicon-on-insulator (SOI) platform and the principles described here can also be applied to other integrated photonic platforms. The proposed device leverages the design flexibilities provided by the aperture-coupled nanopatch antennas and the integrated photonic mode multiplexing technique to engineer the waveguide-antenna couplings of multiple shared-aperture nanoantenna groups simultaneously, thereby enabling the independent controls over the light emissions from these nanoantenna groups. We show that with proper designs of the antenna structures, a large FOV can be obtained by combining the scanning ranges of all the constituent nanoantenna groups. Compared to the previous designs aiming to expand the FOV of the on-chip OBS [15,16], the proposed device is significantly different from the following two aspects. Firstly, light emission of the proposed device is vertical to the chip surface while the designs in [15,16] deal with in-plane light emission. The capability of achieving wide-angle vertical light beam steering is crucial for photonic integrated circuit applications in terms of bridging the gap between out-of-plane free space light and in-plane guided waves [37]. Secondly, beam scanning in the proposed device is achieved by the wavelength-controlled manner which does not require active control units and thus has the advantages of easy implementation and low cost. Regarding to wavelength-controlled OBSs, the already reported designs achieve 23° and 28° FOVs within 30 [20] and 200 nm [11] wavelength tuning range, respectively. In comparison, the proposed device achieves a 41.2° FOV within 100 nm wavelength tuning range.

2. Device overview and working principles

Figure 1(a) depicts a schematic overview of the proposed device. It consists of the optical multiplexing section, the antenna section and the transition section between them. The launched light from different input ports will excite different modes in the bus waveguide after the optical multiplexing section which is composed of a polarization beam splitter (PBS) and an asymmetrical directional coupler (ADC), as shown in Fig. 1(b). There are three nanoantenna groups arranged on top of the silicon nanostrip waveguide. There is only one nanoantenna group to interact with one mode launched in the bus waveguide to convert the guided waves into free space waves efficiently. Each of the nanoantenna group is designed to cover a specific angular range in free space and a large FOV can be obtained by combining the scanning ranges of all the three nanoantenna groups. Meanwhile, the covered angular range of each nanoantenna group must be continuous for blind-spot-free beam scanning and without overlapped angles for efficient scanning range expansion.

 

Fig. 1. Schematic and structure of the proposed device. (a) Schematic overview of the proposed device consisting of the optical multiplexer section, the transition section and the antenna section. The inset shows part of the aperture of the antenna section. (b) Top-view of the optical multiplexing section. (c) 3-D view of the antenna section of the proposed device. (d) Side-view of the antenna section of the proposed device.

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The above described functionalities necessitate the design flexibilities on the independent controls of the interactions between each launched mode in the bus waveguide and different nanoantenna groups. Conventional antennas used in the wavelength-controlled OBSs, e.g., waveguide grating antennas, however, fall short of this freedom. Here, the aperture-coupled nanopatch antenna based on the structure in [38] is adopted and engineered to control the interactions between the waveguide and different nanoantenna groups. Figures 1(c) and 1(d) show the 3-dimensional view and the cross-section view of the antenna structure. It is formed by stacking two additional metallic layers on top of the standard SOI nanostrip waveguide with low-index dielectrics, e.g., SU-8 photoresists, as the spacers. The first metallic layer is formed by etching a nanoslot array in the silver thin film, while the second layer is composed of a nanopatch array. The silicon nanostrip, the SU-8 cladding and the silver thin film form a hybrid plasmonic waveguide. The nanopatches couple with the waveguide through the nanoslots. Considering the practical fabrication process of the structure, the nanoslots are also filled with SU-8 in the simulations.

Depending on how the interactions between the waveguide modes and antennas are controlled, the working principles are described in the following two parts, i.e., the polarization-division multiplexed nanopatch arrays (PDMNA) and the spatial-division multiplexed nanopatch arrays (SDMNA). Finally, the combination of the two kinds of arrays is explored to achieve the wide-angle beam scanning. Here, the PDMNA is referring to two multiplexed nanopatch groups composed of two different antenna elements whose couplings with the waveguide are sensitive to the polarization of the launched mode, e.g., TE and TM modes. The SDMNA is referring to two multiplexed nanopatch groups with identical antenna elements but giving different response to waveguide modes with different orders and the same polarization, e.g., TE₀ and TE₂ modes.

The rest of the paper is organized as follows. In section 2.1, the design of the antenna elements is presented. Sections 2.2 and 2.3 respectively introduce PDMNA and SDMNA, explaining how two nanopatch groups can be multiplexed with low crosstalk. Then, based on the principles described in Section 2, the design of the proposed device in Fig. 1 is presented in Section 3, including the design of the antenna section, the optical multiplexing section and the transition section. Finally, the fabrication tolerance is discussed in Section 4.

2.1 Antenna element

Figures 2(a) and 2(b) show the models of the x- and y-polarized elements. The nanopatch in the x-polarized element has its longitudinal dimension (size along the y-direction) remarkably smaller than its lateral one (size along the x-direction), making its x- polarized fundamental mode resonate at around 1550 nm and the y-polarized one resonate at a much shorter wavelength. The x-polarized nanopatch couples with the silicon nanostrip waveguide via the y-oriented nanoslot (W_sa << L_sa) etched on the silver thin film. In contrast, the y-polarized element is excited by the x-oriented nanoslot (L_sb << W_sb). The parameters of the x- and the y-polarized elements are W_pa = 320, L_pa = 150, L_sa = 350, W_sa = 80 and W_pb = 150, L_pb = 320, L_sb = 80, W_sb = 250, respectively, all in nm. The other parameters are W = 1200, H = 240, T₁ = 80, H₁ = 200 and T₂ = H₂ = 100, all in nm. The x-polarized element is designed to interact with the TE₀ mode efficiently. The simulated coupling coefficients of the x-polarized element with the TE₀ and TM₀ mode are −28.67 and −46.83 dB at the wavelength of 1620 nm, respectively, with a difference of 18.16 dB. The coupling coefficient here is determined by doing the Poynting vector integral on the nanoslot upper surface, which denotes the power that goes up into the cavity formed by the nanopatch and the silver film. The simulations are performed using High-Frequency Structure Simulator (HFSS) from ANSYS which is based on finite element method [39]. The antenna radiation characteristics are obtained by near-to-far-field projections on a closed box surrounding the antenna. In the simulations, one pair of the excitation ports are added on both sides of the waveguide to excite and terminate the waveguide. The refractive indices of the silicon nanostrip, the silica substrate and the SU-8 cladding are 3.48, 1.444 and 1.575, respectively. The Drude model is employed to fit the permittivity of silver with ε_inf= 5, ω_p= 13.4×10¹⁵ rad/s and Γ = 1.12×10¹⁴ 1/s. The polarization-dependent couplings with the waveguide are achieved by engineering the nanoslot dimensions. Because the nanopatch is fed by etching the nanoslot on the silver thin film, which performs perturbations to the waveguide fields by cutting the currents flowing on the silver thin film, the way how the currents are disturbed results in different antenna-waveguide couplings. Figures 2(c) and 2(d) show the electric field distributions on the xoz plane and the induced surface currents on the bottom surface of the silver thin film for both the TE₀ and the TM₀ waveguide modes. It is seen that the induced currents of the TE₀ mode are mostly flowing along the x-direction, i.e., perpendicular to the wave propagation direction. In contrast, the currents of the TM₀ mode are dominated by their y-components which are in parallel to the wave propagation direction. For the x-polarized element, when the TE₀ mode is launched, the induced surface currents along the x-direction are cut off by the nanoslot. As a result, displacement currents polarized along the x-direction will be induced within the nanoslot to fulfill the current continuity formula. On the other hand, when the TM₀ mode is launched, the y-direction surface currents of the TM₀ mode experience a much weaker disturbance by the same y-oriented nanoslot, considering its small lateral dimension W_sa (80 nm). Following the similar principle, the y-polarized element couples with the TM₀ mode 35.9 dB stronger than with the TE₀ mode and the corresponding coupling coefficients between the TE₀ and the TM₀ mode are −55.12 and −19.22 dB, respectively. The coupling coefficients of the two types of elements versus the TE₀ and TM₀ modes are summarized in Table 1. It can be seen when the TE₀ and TM₀ modes are launched, the dominating element, i.e., the element exhibiting stronger interaction with the waveguide, is the x- and y-polarized one, respectively, with coupling coefficient differences of 26.45 and 27.61 dBc. In the following discussions, the parameters of the antenna elements are the same as those in Fig. 2. The dependences of the element coupling coefficient upon wavelength are investigated and shown in Fig. 2(e). The coupling coefficients of the two types of elements do not experience significant variation within a 100 nm wavelength range. More importantly, the polarization-sensitive couplings are well maintained within the 100 nm wavelength range.

 

Fig. 2. Antenna elements. (a) and (b). Models of the x- and y-polarized elements. To clearly show the nanoslot, the SU-8 spacer is set to be transparent. The parameters are W_pa = 320, L_pa = 150, L_sa = 350, W_sa = 80, W_pb = 150, L_pb = 320, L_sb = 80, W_sb = 250, W = 1200, H = 240, T₁ = 80, H₁ = 200 and T₂ = H₂ = 100, all in nm. (c) and (d). Electric field distributions on the xoz plane and the induced current distributions on the bottom surface of the silver film of the hybrid plasmonic waveguide under TE₀ (c) or TM₀ (d) mode excitations at the wavelength of 1620 nm. The parameters of the waveguide are the same as those in (a) and (b). (e) Element coupling coefficient versus wavelength.

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Table 1. Summary of the coupling coefficients of the x- and y-polarized antenna elements^a

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2.2 PDMNA

Figure 3(a) shows the structure of the PDMNA, which is used to illustrate the principles of the polarization-division shared-aperture technique. It consists of two nanopatch groups, respectively composed of the x- and y-polarized elements. In the designed PDMNA, both two nanopatch groups have 10 elements with an identical element spacing of 650 nm (D_y1p = D_y2p= 650 nm) and are arranged along the y-axis with D_x1p = D_x2p = 0, i.e., the central line of the waveguide on the xoy plane, as depicted in the top panel of Fig. 3(b). Since the element coupling coefficient is stable within the 100 nm range [Fig. 2(e)], the 1550 nm telecommunication wavelength is selected as the operating wavelength to illustrate the principles. As the dominant component of the cavity mode supported by the nanopatches [40–41], E_z below the nanopatches is monitored when the TE₀ or TM₀ mode is launched. As shown in the middle panel of Fig. 3(b), when the TE₀ mode is launched, the fundamental mode of Group P1, i.e., the x-polarized group, is efficiently excited with remarkable E_z distributed on the nanopatch short edges. On the contrary, the E_z intensities beneath Group P2, i.e., the y-polarized group, is negligible. In the case of TM₀-mode excitation, remarkable E_z distributed on the short edges of the y-polarized group is observed while E_z distributed beneath the x-polarized group becomes much weaker. The E_z distributions below the y-polarized group coincide with that of the nanopatch fundamental cavity mode polarized along the y-direction. The field distributions in Fig. 3(b) indicate that the element design make each waveguide mode interacts efficiently with only one nanopatch group (the x-polarized group for the TE₀ mode and the y-polarized group for the TM₀ mode). The far-field emission patterns of the PDMNA in Fig. 3(b) are plotted in Fig. 3(c). In Fig. 3(c), D_θ and D_φ denote the directivity of an antenna for the θ and φ field components and are expressed as: ${D_\theta } = 4\pi \frac{{{U_\theta }(\theta ,\varphi )}}{{{P_{rad}}}}$ and ${D_\varphi } = 4\pi \frac{{{U_\varphi }(\theta ,\varphi )}}{{{P_{rad}}}}$, where U_θ(θ, φ), U_φ(θ, φ) and P_rad represent the radiated power density contained in θ and φ field components and the total radiated power [42]. G_θ and G_φ denote the gain of an antenna for the θ and φ field components and are expressed as: ${G_\theta } = 4\pi \frac{{{U_\theta }(\theta ,\varphi )}}{{{P_{accepted}}}}$ and ${G_\varphi } = 4\pi \frac{{{U_\varphi }(\theta ,\varphi )}}{{{P_{accepted}}}}$, respectively, where P_accepted represents the accepted power of the antenna [42]. It is seen that the main beams are steered to 26° and −8° when the TE₀ and TM₀ mode are launched, respectively. Meanwhile, the cross-polarization levels are both below −50 dB and the sidelobe levels (SLLs) are both below −10 dB. The corresponding radiation efficiencies under TE₀ and TM₀ excitations are 63.58% and 57.78%, respectively.

 

Fig. 3. (a) Illustration of the PDMNA layer by layer. (b) Top panel: the model of the designed PDMNA. Other parameters are the same as those in Fig. 2. Middle and bottom panels: E_z intensity distributions on a cut-plane 10 nm below the nanopatches at 1550 nm when the TE₀ (the middle panel) or TM₀ mode (the bottom panel) is launched into the designed PDMNA, showing the polarization-division excitations of the two nanopatch groups. To clearly show the difference between the excitation states of two groups, the E_z intensity is normalized in dB scale. (c) The emission patterns of the designed PDMNA on the yoz plane when the TE₀ or TM₀ mode is launched into the waveguide at 1550 nm.

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2.3 SDMNA

The modal properties of the modes with different orders are exploited to construct the SDMNA. The electric field distributions of the TE₀, TE₁ and TE₂ modes and their corresponding induced currents in the silver thin film are depicted in Fig. 4(a). Depending on the mode order, the positions of the zeros and poles are different for three modes. As explained in Section 2.1, if y-oriented nanoslots are etched at the zeros of J_x, the interactions between the antenna and the waveguide is suppressed. The same holds true for x-oriented nanoslots etched at the zeros of J_y. Figure 4(b) plots the simulated coupling coefficients between the x-polarized element and the TE₀, TE₁ and TE₂ modes versus the element lateral positions. The J_x intensity along Reference line 1 on the inset of Fig. 4(b) of the TE₀, TE₁ and TE₂ modes are plotted in Fig. 4(c). As seen from Fig. 4(b), sharp dips of the coupling coefficient are observed at D_x = 0 and 200 nm for TE₁ and TE₂ modes, respectively, which are consistent with the positions of the minimum J_x in Fig. 4(c). The coupling coefficients of the TE₀ mode, in comparison, gradually decrease with the increasing D_x due to the evanescent decay of the field intensity. The spatial dependence of the antenna-waveguide coupling implies two possible feeding mode combinations for the SDMNA, i.e., TE₀ and TE₁ modes or TE₀ and TE₂ modes. Taking the latter one as the example, Fig. 4(c) shows the element arrangement for the SDMNA fed by the TE₀ and TE₂ modes. One pair of the x-polarized elements are placed at D_x1s = ±200 nm (Group S1), i.e., the minimum J_x of the TE₂ mode, and thus will couple with only TE₀ mode efficiently. Besides, there is another pair of the x-polarized elements placed at D_x2s = ±700 nm (Group S2), flanking Group S1. When the TE₀ mode is launched, due to the evanescent decay of the TE₀ mode modal field along the lateral direction, Group S1 will receive stronger coupled fields than Group S2. The simulations indicate that the difference is 19.71 dB, as marked out by the blue circles in Fig. 4(b). On the other hand, when the TE₂ mode is launched, only Group S2 can couple with the waveguide efficiently, because the lateral positions of Group S1 coincide with the minimum J_x of the TE₂ mode. As marked out by the red circles in Fig. 4(b), the elements of Group S2 couple with the TE₂ mode by 14.52 dB stronger than those of Group S1. It is also found that the elements of Group S2 show stronger couplings with the TE₂ mode than with the TE₀ mode, due to the two poles of J_x of the TE₂ mode at 500 nm away from the center.

 

Fig. 4. (a) Upper panel: J_x and J_y distributions of the TE₀, TE₁, TE₂, TM₀, and TM₁ modes in the silver thin film. The black solid lines denote the geometrical profile of the silver thin film and the silicon waveguide. For each mode, the intensities are normalized by the maximum value of the current component with higher intensity so that the relative relations of the two components can be revealed. Bottom panel: E_x distributions of the TE₀, TE₁ and TE₂ modes and E_z distributions of the TM₀ and TM₁ modes at the wavelength of 1620 nm. All on the xoz cross section. (b) Coupling coefficients of the x-polarized element between the TE₀, TE₁ and TE₂ modes versus the element lateral position at 1620 nm. (c) Upper panel: normalized J_x intensity along Reference line 1 in (b) of the TE₀, TE₁ and TE₂ modes at 1620 nm. Bottom panel: schematic showing the corresponding antenna element positions for the designed SDMNA. Other parameters are the same as those in Fig. 2.

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Based on the above described method, a SDMNA is designed to illustrate the principles of the spatial-division shared-aperture technique. The structure of the designed SDMNA are shown in Figs. 5(a) and 5(b). The parameters are D_x1s = ±200, D_y1s = 650, D_x2s = ±700 and D_y2s = 771, all in nm. Each nanopatch group has 10 elements along the y-direction. The E_z intensity distributions below the nanopatches when the TE₀ or TE₂ modes are launched at 1550 nm are shown in the bottom panel of Fig. 5(b). It is seen that they are concentrated below Groups S1 and S2 when the TE₀ and TE₂ modes are launched, respectively. The corresponding far-field emission patterns are plotted in Fig. 5(c). The main beam directions are 28° and 15° under TE₀ and TE₂ excitations, respectively. Moreover, the SLLs for both cases are below −9 dB. The SLL could be further optimized by engineering the nanoslot dimensions to control the amplitude distribution along the antenna aperture.

 

Fig. 5. (a) Illustration of the SDMNA layer by layer. (b) Top panel: model of the designed SDMNA. Other parameters are the same as those in Fig. 2. Bottom panel: E_z intensity distributions on the cut-plane 10 nm below the nanopatches at 1550 nm when the TE₀ (the bottom-left panel) or TE₂ mode (the bottom-right one) is launched into the SDMNA, showing the mode-division excitation behaviors. The E_z intensity is normalized in dB scale to clearly show the difference between the excitation states of two groups. (c) Emission patterns of the designed SDMNA on the yoz plane at 1550 nm when the TE₀ or TE₂ mode is launched. G and D represent antenna gain and directivity, respectively. (d) n_eff” of the TE₀ and TE₂ modes. (e) Element coupling coefficients of the SDMNA versus wavelength.

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The radiation efficiencies under TE₀ and TE₂ excitations are 69% and 35%, respectively. The antenna radiation efficiency η can be expressed as: η = P_rad/(P_rad+ L_a+ L_wg), where L_a and L_wg denote the dissipated loss in the antenna and waveguide, respectively. The lower radiation efficiency under TE₂ excitation is caused by two reasons: the higher L_wg and the lower P_rad. Figure 5(d) depicts the imaginary part of the effective mode indies n_eff = n_eff’ - jn_eff” of the TE₂ and TE₀ modes. The waveguide attenuation constant α is expressed as α = n_eff”k₀. n_eff can be obtained by the eigenmode analysis of the waveguide structure. As seen from Fig. 5(d), n_eff” of the TE₂ mode is at least 1.73 times higher than that of the TE₀ mode, giving rise to higher L_wg and the reduced radiation efficiency. Figure 5(e) depicts the antenna element coupling coefficients of the two groups. The element coupling coefficient of the dominant group under TE₂ excitation (Group S2) is at least 4.36 dB lower than that under TE₀ excitation (Group S1). Because P_rad is proportional to the antenna-waveguide coupling coefficient, the lower element coupling coefficients under TE₂ excitation also give rise to the reduced radiation efficiency.

Note that, in principle, TE₀ and TE₁ modes can also be exploited to construct the SDMNA. In that case, Group S1 is replaced with a x-polarized group at the center of the waveguide, i.e., the position of the minimum J_x of the TE₁ mode. Group S2 can be retained to couple with the TE₁ mode. However, it is observed in Fig. 4(a) that the phases of J_x of the TE₁ mode are opposite with respect to the symmetrical plane of the waveguide. It means the emitted light of the elements of Group S2 will unfortunately cancel each other in the yoz plane, i.e., the scanning plane. Therefore, TE₀ and TE₁ modes are not an ideal combination to construct the SDMNA.

3. Design and results

3.1 Antenna section: wide-angle beam scanning enabled by combination of PDMNA and SDMNA

The combination of the PDMNA and the SDMNA provides more design freedoms to expand the device FOV, but proper engineering of the element types (x- or y-polarized) and positions of the nanopatch groups is required to insure their compatibility. Figure 6(a) depicts the structure of a shared-aperture nanopatch array consisting of three multiplexed nanopatch groups. Based upon the design principles of the SDMNA, one can multiplex two nanopatch groups fed by TE₀ and TE₂ modes by controlling the lateral positions of the two nanopatch groups. The PDMNA in Fig. 3, in contrast, does not require staggering two nanopatch groups laterally, facilitating its integration. The design goal is to insure that, for each of the launched mode, there is only one nanopatch group interacting efficiently with the launched mode. Hence, as depicted in Case I in Fig. 6(b), an intuitive way to multiplex three nanopatch groups is directly adding a TM₀-mode-fed y-polarized group into the SDMNA in Fig. 5(b), at the same lateral positions of Group S1. Table 2 lists the coupling coefficients of the elements of the three nanopatch groups in Case I, i.e., the x-polarized group at D_x1 = ±200 nm (Group 1), the y-polarized one at D_x2 = ±200 nm (Group 2) and the x-polarized one at D_x3 = ±700 nm (Group 3), calculated at 1620 nm. It is seen that when the TM₀ mode is launched, the elements of Group 2 indeed exhibit a coupling over 10 dB stronger than the elements of the other two nanopatch groups. The same holds true for Group 1 when the TE₀ mode is launched. Nonetheless, the TE₂ mode, which is expected to couple with Group 3, shows unwanted high coupling coefficients (−22.72 dB, the bold number in Table 2) with the elements of Group 2. This unwanted coupling results from the disturbance of J_y of the TE₂ mode [Fig. 4(a)]. Although the phases of J_y of the TE₂ mode are opposite with respect to the symmetrical plane of the waveguide, the unwanted coupling still reduces the device efficiency.

 

Fig. 6. (a) Illustration of the structure of the shared-aperture nanopatch array with three multiplexed nanopatch groups. (b) Schematics of two cases investigated. (c) Upper panel: J_x and J_y intensity distributions along Reference line 1 in the inset of Fig. 4(b) for the TE₀, TM₀ and TM₁ modes, calculated at 1620 nm. Lower panel: schematic showing the antenna element positions in Case II. Other parameters are the same as those in Fig. 2.

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Table 2. Summary of the element coupling coefficients of the three nanopatch groups in Case I in Fig. 6(b)

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To solve this issue, an alternative method is proposed. The design is shown in Figs. 6(b) and 6(c), referred to as Case II. The three nanopatch groups are fed by TE₀, TM₀ and TM₁ modes. Table 3 lists the element coupling coefficients of the nanopatch groups in Case II between the TE₀, TM₀ and TM₁ modes at 1620 nm. In Case II, Groups 1 and 2 are composed of the x-polarized elements at D_x1 = ±350 nm and the y-polarized elements at D_x2 = 0 nm, respectively. Groups 1 and 2 are multiplexed in the polarization-division manner. As seen in Table 3, the coupling coefficient of the TE₀ mode between Group 1 is 23.81 dB higher than that between Group 2. The coupling coefficient of the TM₀ mode between Group 2 is 16.59 dB higher than that between Group 1. Figure 6(c) depicts the J_x and J_y intensity distributions of the TE₀, TM₀ and TM₁ modes along Reference line 1 in the inset of Fig. 4(b). For each mode, the intensities are normalized by the maximum value of the current component with higher intensity so that the relative relations of the two components can be revealed. Groups 1 and 2 are placed at the minimum points of J_x [the green curve with dots in Fig. 6(c)] and J_y [the orange curve in Fig. 6©] of the TM₁ mode, respectively. As a result, the coupling coefficients between Groups 1 and 2 and the TM₁ mode are both below −45 dB (the 3^rd row of Table 3). Note that similar strategy can also be applied to the TE₂ mode, whose J_x and J_y distributions both feature at least one minimum [Fig. 4(a)]. Nonetheless, the minimum J_x of the TE₂ mode are distributed at 200 nm away from the center [Fig. 4(c)]. Considering the sizes of the nanopatch element, it would be challenging to accommodate two nanopatch groups within the 200 nm space. Group 3 is composed of the x-polarized elements at D_x3 = ±700 nm. It is excited by cutting J_x of the TM₁ mode [the green curve with dots in Fig. 6(c)]. The coupling coefficient between the TM₁ mode and the element of Group 3 is −29.87 dB. Because the couplings between the TM₁ mode and Groups 1 and 2 are suppressed by taking advantages of the current distributions, the coupling of the TM₁ mode between Group 3 is 16.19 and 20.98 dB stronger than between Groups 1 and 2, respectively. In addition, in spatial-division manner, the coupling coefficients of the TE₀ and TM₀ modes between Group 3 are 17.72 and 16.91 dB lower than between Groups 1 and 2, respectively. The coupling coefficients of the dominant groups, i.e., the group exhibiting the strongest interaction with the waveguide, are shown in bold in Table 3. It is seen that under TE₀, TM₀ and TM₁ mode excitations, the dominant groups are Groups 1, 2 and 3, respectively, with coupling coefficients at least 17.72, 16.59 and 16.19 dB higher than those of other two groups, respectively.

Table 3. Summary of the coupling coefficients of the antenna elements of the proposed OBS [Case II in Fig. 6(b)] fed by TE₀, TM₀ and TM₁ modes

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The beam direction θ_i of the i^th nanopatch group can be calculated according to: ${k_0}{D_{yi}}\sin ({\theta _i}) = {\rho _i}$, where D_yi and ρ_i are element spacing of the i^th group and the element feeding phase step of the i^th group, respectively. ρ_i is determined by:${\rho _i} = 2\pi (\frac{{n_{eff}^i{D_{yi}}}}{{{\lambda _0}}} - 1)$, where nⁱ_eff and λ₀ represent the waveguide mode index and the free space wavelength, respectively. For continuous and blind-spot-free beam scanning, the beam scanning ranges of the three nanopatch groups must satisfy: θ_U1≤ θ_L2 and θ_U2≤ θ_L3. Here, θ_U1 and θ_U2 represent the beam directions of Groups 1 and 2 at the upper edge wavelength of the available wavelength tuning range, respectively, while θ_L2 and θ_L3 represent the beam directions of Groups 2 and 3 at the lower edge wavelength of the available wavelength tuning range, respectively. When θ_U1 = θ_L2 and θ_U2 = θ_L3, there are no overlapped angles and the total beam scanning range is the sum of their respective ones. In this design, the wavelength tuning range is set to be 100 nm (1520-1620 nm), which is within the range available with commercial C-L band laser sources, as adopted in literatures relating to wavelength-controlled OBSs [27–28]. Moreover, the 100 nm bandwidth is a reasonable one achievable for optical multiplexers.

Based on the above described principles and the three nanopatch groups in Case II, a wavelength-controlled OBS is designed. The mode indices of the TE₀, TM₀ and TM₁ modes are 2.8632, 2.2722, 2.0762 at 1520 nm, respectively and 2.8078, 2.1729 and 1.9566 at 1620 nm, respectively. Groups 1, 2 and 3 in Case II are designed to cover angular range from 11.2° to 24.3°, from −2.1° to 11.5° and from −16.9° to −1.8°, respectively. The corresponding element spacings of Groups 1, 2 and 3 are D_y1 = 620 nm, D_y2 = 733 nm and D_y3 = 721 nm, respectively. In this case, θ_U1, θ_L2, θ_U2 and θ_L3 are 11.2°, 11.5°, −2.1° and −1.8°, respectively. Figure 7(a) shows the model of the proposed OBS, in which each nanopatch group has 16 elements along the y-direction. From left to right, Fig. 7(b) gives the E_z intensity distributions below the nanopatches at 1550 nm when the TE₀, TM₀ and TM₁ modes are launched into the waveguide, respectively. Consistent with the above analysis, when TE₀, TM₀ and TM₁ modes are launched, the E_z fields are concentrated below Groups 1, 2 and 3, respectively. The simulated emission patterns of the proposed OBS at different wavelengths are shown in Fig. 7(c). It is observed that as the wavelength increases from 1520 to 1620 nm, the main beam is steered from 24.5° to 11.3°, from 11.3° to −2.2° and from −1.8° to −16.7° when the TE₀, TM₀ and TM₁ modes are launched into the waveguide, respectively. The simulated beam scanning ranges show reasonable agreements with the calculated ones. Meanwhile, for all the patterns, the SLLs are below −10 dB. Note that the three nanopatch groups in the proposed OBS are with different element spacings along y-direction. It means if the couplings of the undesired nanopatch groups are not suppressed, the emissions contributed by other groups will be pointed to a direction different from the desired one and parasitic beams appear. Hence, the low SLLs observed in Fig. 7(c) further demonstrate the effectiveness of the proposed design. By combining the beam scanning ranges of the three nanopatch groups, a total scanning range of 41.2° is obtained, almost tripling that of the waveguide grating antenna within the same 100 nm wavelength tuning range. To evaluate the radiation performance under different feeding modes, the ratios of the radiated power, the antenna loss and the waveguide loss to the total power loss are calculated and shown in Fig. 7(d). The radiation efficiencies under TE₀, TM₀ and TM₁ mode excitations are 64%, 65% and 22% at 1550 nm, respectively. The relatively low radiation efficiency under TM₁ mode excitation is mainly caused by the dissipated loss in the waveguide, as seen from the bottom panel of Fig. 7(d). One possible way to improve the radiation efficiency is to control the antenna-waveguide coupling to increase P_rad by engineering the nanoslot dimensions.

 

Fig. 7. Results of the proposed wavelength-controlled OBS. (a) Model of the proposed OBS. (b) E_z intensity distributions on the cut-plane 10 nm below the nanopatches when the TE₀, TM₀ or TM₁ mode is launched into the waveguide at 1550 nm. (c) Emission patterns of the proposed OBS on the yoz plane at different wavelengths showing the wavelength-controlled optical beam scanning and the expansion of the device FOV. The patterns under TM₀ excitation are plotted by the solid curves with dots while those under TE₀ and TM₁ excitations are plotted by the solid and dashed curves without dots, respectively. The numbers in the legend denote the wavelengths of the input light in nm. (d) Ratios of the radiated power, dissipated loss in waveguide and dissipated loss in antenna to the total power loss under TE₀, TM₀ and TM₁ excitations.

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A procedure of the proposed OBS design is suggested as follows.

Step 1) determine the initial dimensions of the nanopatch to make it resonate within the required bandwidth. The typical resonate length of the nanopatch is roughly λ/5 [22,43];

Step 2) optimize the nanoslot dimensions to achieve the polarization-sensitive antenna-waveguide coupling for both the x- and y-polarized elements;

Step 3) determine the feeding mode combination and the corresponding D_x1, D_x2 and D_x3. The suggested method utilizes the combination of two zeroth-order modes, i.e., the TE_0­ and TM₀ modes, and one high-order mode, i.e., the TM₁ mode;

Step 4) verify the design by listing the coupling coefficients of all the groups. The criteria is that for each of the launched mode, there is only one nanopatch group interacting efficiently with the launched mode. Special attention needs to be paid on the phase distribution of the current. An anti-symmetrical phase distribution will give rise to canceled light emission at the yoz plane, for example, J_x of the TE₁ mode [Fig. 4(a)];

Step 5) determine D_y1, D_y2 and D_y3 based on the targeted beam scanning ranges for each group.

3.2 Optical multiplexer

The optical multiplexer is designed to excite the desired TE₀, TM₀ and TM₁ modes in the bus waveguide within the 1520 to 1620 nm wavelength range required by the antenna section. Specifically, the PBS is used to excite the TE₀ and TM₀ modes in the bus waveguide while the ADC is used to excite the TM₁ mode in the bus waveguide. The silicon thickness in the optical multiplexer section is the same with that of the antenna section (240 nm) and the whole structure is cladded by the SU-8 photoresist with the same thickness to the antenna section (440 nm). Here, the PBS and the ADC are designed based upon the waveguide coupler systems introduced in [44–45], which feature a simple structure, a high flexibility and a broadband property [45] and thus are suitable for our design. Taking the ADC as an example, to efficiently excite the TM₁ mode in the 1200 nm wide bus waveguide of the antenna section, the width of the narrow input waveguide is designed according to the phase matching conditions [45], which is 501.8 nm in our case. When the coupling length between the input waveguide and the bus waveguide is optimized, a high coupling efficiency can be obtained. The left-sided inset of Fig. 8 shows the structure and the field distributions of the designed ADC when the TM₀ mode is launched at the I₃ port at 1580 nm. It is seen that with a coupling length of 17 µm, the TM₀ mode in the input waveguide is efficiently coupled to the desired TM₁ mode in the bus waveguide with a coupling efficiency of −0.14 dB. The simulated coupling efficiencies versus wavelength is plotted in Fig. 8. Within the desired 1520 to 1620 nm wavelength range, an insertion loss below 0.99 dB is obtained. The right-sided inset of Fig. 8 shows the simulated field distributions of the PBS formed by cascading two ADCs. It can be seen when the TM₀ mode is launched at the I₂ port, the TM₀ mode in the bus waveguide is efficiently excited with the aid of the middle wide waveguide. In contrast, when the TE₀ mode is launched at the I₁ port, light propagates directly through the straight waveguide with low crosstalk between the adjacent waveguide. Figure 8 gives the wavelength dependence of the transmission/coupling efficiencies of the designed PBS. Within the desired 1520 to 1620 nm wavelength range, the transmission efficiency between the TE₀ mode launched at the I₁ port and the TE₀ mode in the bus waveguide is above −0.03 dB, and the coupling efficiency between the TM₀ mode launched at the I₂ port and the TM₀ mode in the bus waveguide is better than −1.82 dB with a maximum of −0.19 dB.

 

Fig. 8. Efficiencies of the optical multiplexer. The purple/blue/green solid curve shows the simulated transmission/coupling/coupling efficiency between the TE₀/TM₀/TM₀ mode launched from the I₁/I₂/I₃ port in Fig. 1(a) and the TE₀/TM₀/TM₁ mode in the bus waveguide, respectively. The left-sided inset shows the structure of the ADC and the H_x distributions on the cut plane 120 nm above the silica substrate at 1580 nm. The right-sided inset shows the structure of the PBS and the E_x/H_x distributions on the cut plane 120 nm above the silica substrate when the TE₀/TM₀ mode is launched from I₁/I₂ port at 1580 nm, respectively. The parameters are as follows: W₁ = W₃ = W₅ = 0.5018, G₁ = G₂ = G₃ = 0.3, W₂ = W₄ = 1.2, L_c1 = 17, L_c2 = L_c3 = 18 and L₁ = L₂ = 5, all in µm.

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3.3 Transition section

The coupling efficiency of the transition between the bus waveguide and the hybrid plasmonic waveguide (HPW) in the antenna section is studied, as shown in the inset of Fig. 9(a). Figures 9(a) and 9(b) investigate the dependences of the coupling efficiencies and the reflections of the transition upon H₁, respectively. For all the three modes, the coupling efficiencies increase with H₁ while the reflections decrease with H₁. This is not counter-intuitive because the perturbations introduced by the silver thin film increase with the decrease of H₁. In the design of the antenna section in Fig. 7, H₁ is chosen as 200 nm in order to reach the compromise between the strength of the antenna-waveguide interaction and the waveguide loss. The coupling efficiencies and reflections of the transition within the required 1520-1620 nm wavelength range when H₁= 200 nm are shown in Figs. 9(c) and 9(d). Within the 100 nm wavelength range, the coupling efficiencies for all the three modes are above −1 dB and the reflections are all below −25 dB.

 

Fig. 9. Efficiencies of the transition section. (a) Coupling efficiency versus H₁ at 1550 nm. (b) Reflection versus H₁ at 1550 nm. (c) Coupling efficiency versus wavelength with H₁ = 200 nm. (d) Reflection versus wavelength with H₁ = 200 nm. The parameters of the waveguide are the same as those in Fig. 2.

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3.4 Device overall efficiency

The loss of the system is mainly caused by the hybrid plasmonic waveguide. Figure 10(a) shows how the waveguide loss varies with H₁. Remarkable plasmonic loss is observed for H₁ below 50 nm. The plasmonic loss will result in reduced efficiencies of the antenna and the transition sections, whose structures are involved with metal. Figure 10(b) shows how the radiation efficiency of the antenna section in Fig. 7 varies with H₁. When H₁ is below 50 nm, the high waveguide losses give rises to low radiation efficiencies for all the three modes. The efficiencies of the transition section are depicted in Fig. 9(a). A transition loss over 1.72 dB is observed for the TM₀ and TM₁ modes when H₁ = 100 nm.

 

Fig. 10. (a) Waveguide loss versus H₁. (b) Antenna section radiation efficiency versus H₁. (c) Device overall efficiency versus H_1. The legends denote the input ports and the corresponding excited modes in the bus waveguide. (d) Element coupling coefficients of the dominant group under different excitation modes. The parameters are the same as those in Fig. 7. Each group has 8 elements along the y-direction. The wavelength is 1550 nm.

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Figure 10(c) depicts the device overall efficiency versus H₁ when light is launched from I₁, I₂ and I₃ ports of the device. The corresponding excited modes in the bus waveguide are TE₀, TM₀ and TM₁ modes, respectively. The device overall efficiency is the product of the efficiencies of the three sections, i.e., the optical multiplexer, the antenna and the transition sections. The transmission/coupling efficiencies for launching the TE₀, TM_­0 and TM₁ modes in the bus waveguide are 0.99, 0.90 and 0.92 at 1550 nm, respectively. By comparing Figs. 10(b) and 10(c), it is found that the high transition loss results in a drop of the device overall efficiency at H₁ = 100 nm, especially for the TM­₀ mode. Figure 10(d) shows how the element coupling coefficient varies with H₁. The element coupling coefficients monotonically decrease as H₁ increases. When H₁ exceeds 300 nm, the element coupling coefficient under TE_­0 excitation is below −40 dB, making the antenna-waveguide interaction inefficient. Therefore, H₁ is chosen as 200 nm in our design to provide an efficient antenna-waveguide coupling and minimize the impact of metal loss. For small H₁, the high waveguide/transition loss will give rise to a reduced device overall efficiency while for large H₁, the antenna-waveguide coupling becomes inefficient.

4. Fabrication tolerance

Figure 11(a) depicts a schematic showing part of the antenna aperture when misalignments between the nanoslot and nanopatch layers occur in the OBS in Fig. 7. In Fig. 11(a), M_x and M_y denote the misalignments along the x- and y-directions, respectively. The element number along the y­-direction is 8 for all the three groups for ease of simulation. Figures 11(b) and 11(c) show the emission patterns for different feeding modes when up to 100 nm misalignment occur along the y- and x-direction, respectively. Figures 11(d) and 11(e) show how the peak directivity and radiation efficiency vary with M_y and M_x­, respectively. It is observed that both the emission patterns and the radiation efficiencies do not exhibit significant variations within the 100 nm misalignment for all the three modes. The maximum directivity drops are 0.62 and 0.90 dB for the x- and y-direction misalignments, respectively.

 

Fig. 11. (a) Schematic showing the misalignment. The dashed boxes indicate the nanopatch positions without misalignment. (b) and (c) Emission patterns at the yoz plane at 1550 nm when y- (b) and x-direction (c) misalignments occur, respectively. The numbers in the legend denote the value of M_y in (b) and M_x in (c) in nm, respectively. (d) and (e) Peak directivity and radiation efficiency versus M_y (d) and M_x (e).

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Figure 12(a) shows the emission patterns of the OBS in Fig. 7 when ± 100 nm errors are applied to the nominal sizes of the nanopatches. Figures 12(b)–12(d) investigate the dependences of the peak directivity and radiation efficiency upon the nanopatch fabrication error for TE_­0, TM₀ and TM₁ excitations, respectively. For sake of brevity, only the emission patterns under TE­₀ excitation are shown. The main beam directions are robust against fabrication errors while drops of the peak directivities are observed. This is mainly caused by the mutual coupling between different nanopatch groups. To distinguish the effects of the mutual coupling, the directivities when only the dominant group is presented are simulated. Taking TE₀ excitation as an example, the blue curve in Fig. 12(b) represents the directivity of the nanopatch array having the same parameters as those in Fig. 7 but with Groups 2 and 3 removed. As shown by comparing the directivity curves in two cases, the deviation between the two curves becomes more evident with the increase of the nanopatch sizes, because of the reduced distance between the adjacent nanopatches.

 

Fig. 12. (a) Emission patterns at the yoz plane at 1550 nm with different fabrication errors of the nanopatches. The numbers in the legend denote the error value in nm. (b) (c) and (d) Peak directivity and radiation efficiency versus nanopatch size error for TE₀ (b), TM₀ (c) and TM₁ (d) excitations. (e) Peak directivity and radiation efficiency versus nanoslot size error.

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Figure 12(e) investigates the dependences of the peak directivity and radiation efficiency upon the nanoslot fabrication error. Because the nominal size of the nanoslot is below 100 nm, the lower limit of the fabrication error is set to be −50 nm. The maximum directivity drop is 2.47 dB, observed under TE₀ excitation. It is also observed that the radiation efficiencies are increasing with the increase of the nanoslot sizes for all the three modes. This is because the increased nanoslot sizes result in enhanced element coupling coefficient and P_rad increases correspondingly, as discussed in Section 2.3.

In general, the structure is robust against the misalignment error while the mutual coupling effect results in a reduced tolerance against the nanopatch fabrication errors, as shown by comparing the directivity curves of the shared-aperture array and the single group array in Figs. 12(b)–12(d). This could be improved by slightly reducing the nominal sizes of the nanopatch layer because the structure is more robust against negative errors, as observed in Figs. 12(b) and 12(c). In addition, the structure could be fabricated using modern electron beam lithography technique which provides the capability of high-precision fabrication for multi-layer metal structure, as demonstrated in [46]. Furthermore, it is observed that the main beam directions are very robust against the fabrication errors, which is crucial for the expansion of the FOV.

5. Conclusion

In this paper, the polarization-division and spatial-division multiplexed nanopatch arrays are studied to expand the FOV of the wavelength-controlled OBS. The design principles of both the polarization-division and spatial-division nanopatch arrays are investigated in detail. The PDMNA is discussed in the first place. It is found that by engineering the antenna dimensions, the couplings of the antenna element between the waveguide can be made sensitive to the polarizations of the launched waveguide modes. Based on the antenna elements with the polarization-dependence coupling to the waveguide, a PDMNA consists of two nanopatch groups is designed. The simulated field distributions clearly show the polarization-division excitations of the two multiplexed nanopatch groups. Secondly, the design principles of the SDMNA are investigated. It is demonstrated that the first- and third-order TE modes can be exploited to feed two laterally staggered x-polarized nanopatch groups. Finally, with the simultaneous implementations of the polarization-division and spatial-division nanopatch arrays, a wavelength-controlled OBS composed of three shared-aperture nanopatch groups and achieving a scanning range over 40°, is successfully demonstrated. In addition, the SLLs of all the nanopatch groups are below −10 dB. Furthermore, the presented design methodology allows independent control over the interactions between multiple nanoantenna groups and the waveguide. Thus it could be useful for various optical devices with different functions, e.g., dual-polarization OBSs with low polarization-dependent gain loss, polarization splitters with controllable beam projection directions and free-space optical (de)multiplexers.