Developed in recent decades, the optical phased array (OPA) technology represents a significant breakthrough in photonics, providing a versatile and dynamic method of manipulating light.1^–9 Similar to the phased arrays utilized in radar, an OPA is an array of closely spaced optical emitters, such as lasers or grating couplers. This technology enables precise control over the phase and amplitude of light waves, achieving the steering, shaping, and focusing of light beams without mechanical movement.10^–13 OPAs find applications in various domains, including communications, light detection and ranging (lidar) systems, medical imaging, and holographic displays.14^–25 Aiming for enhanced surveillance, imaging, and communication capabilities, multibeam OPA schemes have been proposed. Current implementations typically rely on two main approaches: (1) Dammann gratings,26^–28 which divide the input beam into multiple diffraction levels, producing multiple beams, and (2) sparse emitter arrays,11^,29^–37 where techniques such as thermal tuning or liquid crystals adjust the phase of individual subarrays, enabling each to emit in a different direction. Compared with the single-beam OPA scheme, multibeam OPA schemes can effectively expand the field of view (FOV), improve the scanning speed, and increase the number of simultaneously handled targets.28 To reduce the interference among various echoes in multibeam systems, a practical approach is coding the light with orthogonal waveforms, which facilitates the identification of different beams in lidar systems.38^,39 In addition, wavelength and time division multiplexing technologies can help discern the directions of the light beams.40 However, these approaches require complex digital signal processing (DSP) algorithms to mitigate cross talk among echoes.

Introducing orbital angular momentum (OAM) beams into lidar transmitters can simplify or even eliminate the need for complex DSP in systems, thereby reducing the complexity of electronic chips.41 OAM beams, characterized by rotating wavefronts of $\exp (il\theta )$ ($\theta$ is the azimuthal angle and $l$ is the topological charge) and spatial orthogonality among infinite channels,42^–44 introduce a novel dimension of beam control into the OPAs of lidar systems.45^–53 When an obstacle is illuminated by an OAM beam, a spatially varied echo carries more detailed information about the obstacle, providing higher-resolution imaging beyond the Rayleigh limit54^,55 and efficient detection of rotational Doppler shifts.56 Moreover, as an OAM light beam travels through the atmosphere, its phase and intensity distribution can be affected by atmospheric turbulence. Upon reflection, the echo experiences the same phase and intensity distortions in reverse order, effectively canceling out the atmosphere disturbances imposed on the propagation path of the beam.57 Thus, as the transmitter in a lidar system, using OAM beams in the OPA can provide a robust and accurate method of enhancing the imaging resolution and maintaining signal integrity despite atmospheric interferences.58^–60 The existing schemes generate multiple indistinguishable Gaussian beams or single OAM beams43^–47^,61^–64 for ranging or communication purposes. To date, no OPA scheme exists that can simultaneously diffract OAM beams that carry different topological charges for the purpose of beam identification.

To address this issue, we propose an on-chip multi-OAM-beam OPA scheme. The OPA consists of a pair of phase shifter arrays and a forked Dammann grating array, which effectively couple the in-plane guided mode to the out-of-plane OAM beams carrying different topological charges. We fabricated the proposed multibeam OAM OPA chip on a 220-nm-thick commercial silicon-on-insulator (SOI) platform. By injecting light beams from both the left and right sides of the $1\times 3$ Dammann grating, six ($3+3$) diffracted beams can cover a 140-deg FOV in azimuth within a wavelength range of 120 nm. These beams can also be precisely deflected using thermal phase shifters within $\pm 20\mathrm{deg}$ in elevation. The experimental results show that the proposed scheme enables an ultralarge FOV of $140\mathrm{deg}\times 40\mathrm{deg}$, significantly surpassing traditional two-dimensional (2D) beam-steering approaches. Our design serves as a practical integrated OPA for OAM multibeam generation and steering. Compared with other multibeam OPA schemes, this approach enables the identification of multiple beams by simply addressing multiple topological charges. By strategically selecting the diffraction orders and angles, we also achieved the largest FOV documented in this field, to the best of our knowledge.

Figure 1(a) shows the designed multiple-OAM OPA chip, which enables 2D multibeam forming and steering. This functionality is achieved by tuning the wavelength of light to steer beams in the $\theta$ dimension and by heating phase shifters to rotate beams in the $\phi$ dimension. The key feature of the design is the forked $1\times 3$ Dammann grating array, which is superimposed on a binary holographic fork grating. The forked $1\times 3$ Dammann grating array consists of two structures: a $1\times 3$ Dammann grating array and a waveguide–grating directional coupler (WG-DC) array. This configuration is essential for uniformly diffracting in-plane guided-mode light into three distinct OAM beams in free space. In Fig. 1(b), the distribution of the fork Dammann grating array is given by $$\begin{gathered} \varphi (r,\phi )=l\phi +kr\cos \phi , \\ \text{Hologram}(\varphi )=\{\begin{array}{ll}1& \mathrm{mod}(\varphi ,2\pi )\mathrm{\Lambda }\in L_1,L_3,L_5\\ 0& \text{others}\end{array}, \end{gathered}$$(1)where $l$ represents the topological charge of the holograph [$l$ is an integer number, and $l=+1$ in Fig. 1(a)], and $k$ is the propagation constant of the silicon waveguide mode. $L_1$ to $L_6$ are the optimized structural parameters of the $1\times 3$ Dammann gratings, as shown in Fig. 2(a).

For the $m$’th-order diffraction, the phase difference among the light diffracted by neighboring cells in a grating is multiplied times $m$. Therefore, each $m$’th-order vortex diffracted by the forked Dammann grating array carries a topological charge of $ml$. As depicted in Fig. 1(a), the forked Dammann grating array design enables the uniform diffraction of bidirectional input lights into six diffraction orders ($m=\pm 3$, $\pm 4$, and $\pm 5$). Consequently, six OAM beams, carrying different topological charges ($ml=\pm 3$, $\pm 4$, and $\pm 5$), effectively sweep six sub-FOVs.

We employed a $1\times 3$ Dammann grating and binary-phase Fourier hologram to generate an array of point sources, thereby simultaneously generating multiple beams. Because on-chip surface-emitting Dammann gratings have not been extensively discussed in the literature, we ran a parameter sweep to obtain the far-field intensities for various grating periods. The etching parameters are determined through subsequent optimization, as detailed in the Supplementary Material. Figure 2(a) shows a three-dimensional (3D) schematic of the optimized $1\times 3$ Dammann grating. We chose a grating width $W=0.5\mu \mathrm{m}$ and period $\mathrm{\Lambda }=2.6\mu \mathrm{m}$, which radiates diffraction orders $+3$ through $+5$ into free space. The red regions in Fig. 2(b) indicate blind zones, which remain despite the large bandwidth of 160 nm. To address the blind zones, two beams are input from both sides, causing the grating to diffract three OAM pairs of opposite orders, as illustrated in Fig. 2(c). In addition, the low efficiencies of the three diffractions at 1510 nm are attributed to the exact fulfillment of the high-order Bragg condition.

We propose a WG-DC structure [Fig. 2(e)] comprising a $1\times 3$ Dammann grating and a strip waveguide to extend the antenna aperture beyond $100\mu \mathrm{m}$ and to improve the mode purity of the OAM beams. Due to the exponential attenuation of power, the practical length of a 70-nm-etched grating is constrained to less than $35\mu \mathrm{m}$. In our design, we place a symmetrically bent waveguide adjacent to a straight grating to establish a DC structure. By precisely manipulating the gap between the grating and waveguide, the power distribution in the grating conforms to a Gaussian distribution. This approach enables the flexible enlargement of the grating aperture and concurrently boosts the mode purities of OAM (Laguerre–Gaussian mode) beams. Because the waveguide is symmetric along the $x$ axis, the spacing between the grating and the waveguide is a real, even function whose Fourier series is also a real, even function. The spacing between the grating and the waveguide is then apodized as a set of cosine series, $\sum a_n\cos (nx)$, as shown in Fig. 2(d). Neglecting the bend loss, the coefficients $a_n$ are optimized using the particle swarm optimization (PSO) algorithm in MATLAB to achieve a Gaussian distribution in the power intensity (detailed in Supplementary Material S2).

The power in the strip waveguide and Dammann grating can be expressed as$$\begin{gathered} \frac{\text{d}{P}_w}{\text{d}z}=-j{\kappa }_{wg}{P}_g{e}^{j2\delta z}, \\ \frac{\text{d}{P}_g}{\text{d}z}=-j{\kappa }_{gw}{P}_w{e}^{-j2\delta z-\alpha z}, \end{gathered}$$(2)where $P_w$ and $P_g$ are the complex amplitudes of the waveguide and grating, respectively; ${\kappa }_{wg}$ and ${\kappa }_{gw}$ are conjugated mode-coupling coefficients, which describe the interaction between the waveguide and the grating; and $\delta$ is the propagation constant of the guided mode, which equals that in the Dammann grating owing to the phase-matching condition. The loss factor $\alpha$ can be obtained from the 3D finite-difference time-domain (FDTD) simulation of the Dammann grating (see Supplementary Material S3 for the fitting of the loss factor of a grating and further discussion).

We define the figure of merit (FoM) to evaluate the similarity between the power distribution in the grating and the Gaussian distribution $$\mathrm{FoM}=1-\mathrm{XCorr}[P_B,N(\mu ,{\sigma }^2)],$$(3)where $N(\mu ,{\sigma }^2)$ represents the Gaussian distribution characterized by the parameters $\mu =L_{\text{grating}}/2$ and ${\sigma }^2=L_{\text{grating}}^2/16$, and XCorr represents the normalized cross-correlation of $P_B$ and $N(\mu ,{\sigma }^2)$ with a unity peak. We repeated the PSO algorithm 10 times, each with 200 iterations. All iterations converged to identical structural parameters, as shown in Fig. 2(d). The power distributions of the WG-DC at 1510, 1570, and 1630 nm are shown in Fig. 2(f).

To validate and improve the performance of the proposed OAM OPA, we simulated a quasi-square OPA with dimensions of $104.0\mu \mathrm{m}\times 106.4\mu \mathrm{m}$. The simulated far-field intensities, amplitudes, and phase profiles, illustrated in Fig. 3(a), demonstrate the efficient conversion of guided modes into OAM modes with topological charges of $+3$, $+4$, and $+5$, respectively. As the wavelength increases from 1480 to 1640 nm, vortices that carry $+3$, $+4$, and $+5$ topological charges sweep angles from $-40$ to $-13.5\mathrm{deg}$, $-7$ to $+20\mathrm{deg}$, and $+30$ to $+77\mathrm{deg}$, respectively, indicating that an FOV of 154 deg can be achieved by injecting light from two sides of the OPA. Furthermore, the divergence angles of the ${\mathrm{OAM}}_{\pm 3}$, ${\mathrm{OAM}}_{\pm 4}$, and ${\mathrm{OAM}}_{\pm 5}$ beams are $\sim 3$, 4, and 5 deg, respectively.

We fabricated an OAM OPA chip on a commercial 220-nm-thick SOI platform. Figure 3(d) shows the zoomed-in and microscopic images of the fabricated silicon OAM OPA chip. A fork structure can be observed at the center of the grating array. The fabricated chip was packaged using edge coupling and wire bonding and connected to a 64-channel voltage source via three 40-pin FPC connectors on the printed circuit board (PCB). The host computer controlled the 64-channel voltage source using a general-purpose interface bus (GPIB) connector. The detailed device fabrication and packing processes are described in Sec. 6.

Figure 3(e) shows a schematic of the experimental setup used to characterize the fabricated OAM OPA chip. A tunable laser source (Keysight 81960A) illuminated the fabricated device from 1505 to 1630 nm. The laser output was split into two branches using a 50:50 coupler. In the top branch, we used a polarization controller (PC) and variable optical attenuator (VOA) to control the polarization state and power of the light. After edge coupling, the guided ${\mathrm{TE}}_0$ mode was split into 64 copies using a six-stage $1\times 2$ MMI tree, and 56 copies were sent to the waveguide array. These ${\mathrm{TE}}_0$ lights in the waveguide array were coupled to the $1\times 3$ Dammann grating array (superposed holographic fork gratings) and emitted into free space as single-polarization OAM modes (${\mathrm{OAM}}_{+3}-{\mathrm{OAM}}_{+5}$). The other branch served as a reference Gaussian beam, whose power and polarization were adjusted using a PC and a VOA. The generated OAM modes and reference Gaussian beams with the same polarization, proper relative powers, and spot sizes were combined using a beam splitter (BS) to obtain the interferogram. We used an infrared charge-coupled device (IR-CCD, Luster) to monitor the intensity profiles of the generated OAM modes and corresponding interferograms.

The phase mismatch of the input lights caused random intensity profiles of the OAM beams. We used a genetic algorithm (GA) to align the input phases of the OPA according to $R^2$, which is the coefficient of determination for fitting the intensity profiles to the ideal OAM intensity in MATLAB. Here, we take the generation of ${\mathrm{OAM}}_{+4}$ at 1565 nm as an example. As shown in the inset of Fig. 3(e), the measured intensity profile exhibits a donut shape owing to the phase singularity after 100 iterations of GA optimization (see Supplementary Material S3). We recorded the intensity profiles of the ${\mathrm{OAM}}_{+3}-{\mathrm{OAM}}_{+5}$ beams, as depicted in Fig. 3(b). These profiles closely match the corresponding far-field patterns shown in Fig. 3(a), demonstrating the effectiveness of the GA in aligning the phase profiles. The topological charges of the generated OAM beams can be confirmed by counting the number of twists and twist directions of the interferograms. To verify the polarization state of light, we removed the reference light and inserted a polarizer before the IR-CCD [not shown in Fig. 3(e)]. Figure 3(c) presents the intensity profiles with the polarizer axis rotated to 0 (horizontal), 45, and 90 deg (vertical), where the power of the generated $y$-polarized ${\mathrm{OAM}}_{+4}$ is gradually enhanced. A discussion of the GA used to control the voltages of the thermal phase shifters to reconstruct the OAM light is provided in the Supplementary Material.

We measured the emission angles of the OAM beams to obtain the FOV along the $\theta$ axis of the fabricated device. Figure 4(b) presents the intensities measured at different wavelengths. The intensities of the far fields initially increase and then decrease with increasing wavelength, in contrast to the behavior of the simulated far-field shown in Fig. 4(a). This variation is due to the center wavelength of the $1\times 2$ MMI, which is $\sim 1570\mathrm{nm}$. Figure 4(c) illustrates emission angles of $-39.47$ to $-13.68\mathrm{deg}$, $-6.60$ to $+20.52\mathrm{deg}$, and $+30.03$ to $+76.65\mathrm{deg}$ for ${\mathrm{OAM}}_{+3}$, ${\mathrm{OAM}}_{+4}$, and ${\mathrm{OAM}}_{+5}$ beams, respectively, for a 1480- to 1640-nm input with left input. Specifically, within the wavelength range of 1505 to 1625 nm, the diffracted beams of the OAM OPA with bidirectional inputs covered an FOV of approximately $-75$ to $+75\mathrm{deg}$, as shown in the bottom images in Figs. 4(a) and 4(b). The FOV coverage and wavelength range in Fig. 4(c) agree well with the simulation results for the $1\times 3$ Dammann grating.

In the $\phi$ direction, the maximum deflection angle of the 0’th-order far field, quantified as $\mathrm{\Delta }\phi =\pm [90\mathrm{deg}-{\cos }^{-1}({\lambda }_{\min }/2{\mathrm{\Lambda }}_y)]$, was approximately $\pm 23.33\mathrm{deg}$ (${\mathrm{\Lambda }}_y$ represents the period of the OPA in the $y$ direction). If the phase differences among the neighboring waveguides are close to 180 deg, the far field will experience attenuation and distortion significantly; therefore, we limited the deflection angle of the chip to values from $-20$ to $+20\mathrm{deg}$. We adjusted the tilt angle of the OPA chip by $-20$, $-10$, 0, $+10$, and $+20\mathrm{deg}$ with respect to the $\phi$ axis and repeated the fitting and optimization processes for 13 wavelengths in the range of 1505 to 1625 nm. The far-field profiles for the ${\mathrm{OAM}}_{\pm 3}-{\mathrm{OAM}}_{\pm 5}$ beams with the left and right input, illustrated in Fig. 4(d), indicate the beam deflection of multiple OAM beams. Using a tunable laser and thermal phase shifters to steer the light beams, the angular resolution is determined by the divergence angle of the OAM beam. The theoretical resolution is $31\times 9$; however, for convenience and time efficiency, we used a $13\times 5$ resolution in our experiments. Details of the far-field patterns are provided in the Supplementary Material.

The experimental demonstration of a wide FOV, multibeam OPA marks a significant advancement in multibeam emission technology. This system uses different topological charges for precise beam steering. The direction of OAM beams with positive and negative topological charges can be controlled by adjusting the left and right thermal phase shifter arrays, respectively. Another key feature of our approach is the use of waveguide–grating directional couplers, which substantially increase the antenna aperture of the silicon grating compared with those of the conventional structures. Theoretically, three OPA chips can provide a complete 360-deg FOV, significantly reducing the number of optical components.

Our multibeam strategy accelerates angular scanning and maintains a wide FOV, enabling the use of fewer OPA chips in high-speed applications. Moreover, the proposed design is scalable; optimization of the grating size and reduction in the far-field spot diameter enhance adaptability. Including a nonredundant OPA using a Costas array can further expand the footprint of the aperture.9 This scalability, along with the simplicity of the proposed WG-DC structure, makes the wide FOV, multi-OAM OPA a versatile and promising solution for high-precision optical beam steering in broadcast systems,65^–69 secure quantum communications,55^,70^–74 applications in environments with complex atmospheric turbulence,45^,75 and detection of flying vehicle propellers.76^,77

Detailed descriptions of the optical simulation and optimization, characterization of the far field, and phase modulation of the thermal phase shifter are presented in the Supplementary Material.

The numerical results presented in Figs. 2–4 were obtained through 3D FDTD simulations using the commercial software ANSYS Lumerical. In the simulation setup, the $3\text{-}\mu \mathrm{m}$-thick substrate layer and the $2\text{-}\mu \mathrm{m}$-thick cladding layer were ${\mathrm{SiO}}_2$ with a refractive index of 1.44, and the material of the sandwiched waveguide was silicon with a refractive index of 3.47. The simulation region implemented a perfectly matched layer as the boundary condition, and a mesh accuracy of 2 was specified. Fifty-six mode sources were set to the fundamental transverse electric (${\mathrm{TE}}_0$) mode, and a frequency domain power monitor was positioned $1\mu \mathrm{m}$ above the interface between the cladding and air to capture the outgoing field.

Based on the structure design, theory, and simulation results, the devices were fabricated on an SOI platform with a 220-nm-thick silicon top layer and a $3\text{-}\mu \mathrm{m}$-thick ${\mathrm{SiO}}_2$ buried oxide layer. The waveguides and the Dammann grating array were patterned via electron beam lithography (Vistec EBPG-5200⁺). Full and partial etching was performed using an inductively coupled plasma (ICP, SPTS) etching process. After that, a $2\text{-}\mu \mathrm{m}$-thick ${\mathrm{SiO}}_2$ cladding layer was uniformly deposited on top of the devices using plasma-enhanced chemical vapor deposition (Oxford). A 400-nm-thick Ti layer functioned as a thermal phase shifter, and a 300-nm-thick gold layer was deposited using an e-beam evaporator (Denton Electron Beam Evaporator). Each phase shifter had a resistance of $\sim 5\mathrm{k}\mathrm{\Omega }$. A total of 112 gold wires were bonded from the gold pads on the silicon chip to a PCB using F&S BONDTEC 53XXBDA.

To characterize the optical performance of the fabricated device, we used a continuous-wave tunable semiconductor laser source (Santec TSL-770) to generate light ranging from 1480 to 1640 nm. A 50:50 coupler was utilized to split the light into two beams, which were sent to two PCs. One of the beams was coupled to the fabricated chip, and the other was collimated using a collimator. The diffracted light and collimated beam were subsequently combined using a BS and captured using an IR-CCD equipped with a four-lens system.

Zhen Wang received his PhD from the Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China, in 2024. He is currently a postdoctoral fellow at the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China. His current research interests include silicon photonics, optical phased arrays, and mode multiplexing technologies.

Yikai Su received his PhD in electrical engineering from Northwestern University, Evanston, Illinois, United States, in 2001. He served at Crawford Hill Laboratory of Bell Laboratories and joined Shanghai Jiao Tong University, Shanghai, China, as a full professor in 2004. His research areas cover silicon photonic devices, optical transmission, and signal processing. He has published over 600 publications and has given >70 invited talks at conferences including OFC, CLEO, and IPS. He is a senior member of IEEE and a fellow of Optica.

Biographies of the other authors are not available.