1.

Introduction

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 limit^54,55 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 beams^{43–47,61–64} 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.

2.

Results

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

Fig. 1

Working principle of emitting OAM beams with different topological charges using an on-chip OPA. (a) Schematic of the proposed OAM OPA chip, detailing the essential components and interconnection structures. (b) Method of generating the proposed multiple-OAM OPA. The etching pattern of the forked grating is achieved using a spiral phase distribution ($l=1$) and a $1\times 3$ Dammann grating array. The layout of the multiple-OAM OPA is the intersection of the forked grating and the waveguide array.

Fig. 2

(a) Schematic of the designed $1\times 3$ Dammann grating. The grating pitch ($\mathrm{\Lambda }$) is $2.6\mu \mathrm{m}$, and the lengths of the various segments within the grating are $L_1=0.838\mu \mathrm{m}$, $L_2=0.160\mu \mathrm{m}$, $L_3=0.666\mu \mathrm{m}$, $L_4=0.349\mu \mathrm{m}$, $L_5=0.282\mu \mathrm{m}$, and $L_6=0.305\mu \mathrm{m}$. (b) Emitted diffraction orders $+3$, $+4$, and $+5$ of far-field patterns with the left input as a function of wavelength. The red regions indicate the blind zone. (c) Far-field patterns with left and right inputs as a function of wavelength. The dashed box indicates that six diffractions (orders $\pm 3$ through $\pm 5$) with bidirectional inputs cover a 180-deg FOV in the wavelength range of 1510 to 1630 nm. (d) Spacing between the waveguide and grating as a function of distance before and after PSO. (e) Schematic of the WG-DC structure. (f) Optical power distributions within the proposed WG-DC structure at 1510, 1570, and 1630 nm. The power distributions at these wavelengths resemble Gaussian distributions.

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.

3.

Simulation and Experimental Demonstration

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.

Fig. 3

Simulated and measured far-field intensities for vertical emission ($\phi =0\mathrm{deg}$). (a) Simulated far-field patterns, amplitudes, and phase profiles of three orders ($+3$, $+4$, and $+5$) at 1565 nm with left input. (b) Measured far-field intensities and interference patterns of the emitted OAM lights. (c) Measured far-field intensity profiles of the $y$-polarized ${\mathrm{OAM}}_{+4}$ at 1565 nm following a rotation of the polarizer (0, 45, and 90 deg). The arrows indicate the angles of the polarizer. (d) Zoomed-in and microscopic images of the packaged device, consisting of the $3.5\mathrm{mm}\times 4.5\mathrm{mm}$ multiple OAM OPA chip wire bonded to a silicon interposer, along with left and right optical fiber inputs. (e) Experimental setup used to characterize the far-field profiles of the multibeam OPA (laser: Keysight 81960A). PC, polarization controller; VOA, variable optical attenuator; HWP, half-wave plate; P1 and P2, polarizers; BS, beam splitter; $\text{L}1$, $\text{L}2$, and $\text{L}3$, lenses; IR-CCD, infrared charge-coupled device. Inset: FoM versus iteration and far-field profiles before and after phase alignment.

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.

4.

Sweeping in $\theta$ and $\phi$ Directions

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.

Fig. 4

Simulated and measured far-field intensities of emitted multiple vortices with different wavelength inputs. (a) and (b) Simulated and measured far-field emission patterns in a wavelength range from 1480 to 1640 nm with left input (up) and left and right inputs (down), respectively. (c) Angle sweeping of emitted diffraction orders $\pm 3$, $\pm 4$, and $\pm 5$ with bidirectional inputs. (d) Measured far fields of multiple vortices at different emission angles with respect to the $\phi$ axis.

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.

5.

Discussion

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

6.

Appendix: Methods

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.