Introduction

Spatial modes have attracted significant interest due to their applications in spatial division multiplexing (SDM)1, sensing, quantum information processing2, and on-chip machine learning3. The choice of mode set, such as orbital angular momentum (OAM), linearly polarized (LP) modes, and cylindrical vector modes (CV)1, is typically guided by specific system requirements. Programmable photonic devices offer inherent flexibility compared to custom-designed components, making them particularly advantageous for applications needing real-time adaptability, such as adaptive sensing, dynamic alignment to variable external optical conditions, and mode switching.

Spatial light manipulation traditionally uses free-space optics, such as Dove prism4, spiral phase plates5, holographic gratings6, q-plates7, multi-plane light conversion (MPLC) with gold mirrors8, etc. However, these devices are tailored for specific spatial modes and thus have fixed functionality. Spatial light modulators (SLMs) offer programmability for reconfigurable mode manipulation, capable of supporting multiple modes simultaneously9. Nevertheless, SLMs face challenges, including complex alignment, stabilization concerns, limited scalability, and large physical dimensions.

Photonic integrated circuits (PICs) offer a scalable technological platform for SDM due to their compact size and potential for extensive integration10,11,12,13, distinguishing them from bulkier free-space optical alternatives. Recent advances in programmable PIC technology have enabled dynamic (re)configuration of chip functionalities14,15,16, providing promising solutions for reconfigurable spatial light manipulation.

An optical mode converter using a multi-layer metasurface was demonstrated in ref. 17. By combining the concepts of MPLC and metasurface, the device can transform the spatial distributions of both intensity and polarization of the optical field in an arbitrary manner, enabling the generation of OAM, LP, and CV modes. Nevertheless, the device is not reconfigurable and therefore supports only fixed functionality. Zhou et al. demonstrated a programmable silicon photonic integrated mode generator18, achieving precise polarization control of LP and CV modes, though this device can not generate OAM modes and is constrained to mode order one. Additionally, the architecture presents scalability challenges since both the number of Mach-Zehnder interferometers (MZIs) and routing complexity grow exponentially with increasing mode counts. A reconfigurable structured light generator was proposed by Zhao et al.19, capable of generating first-order OAM, LP, and CV modes; however, it is limited to the simultaneous generation of only two OAM modes.

In ref. 20, the approach for OAM mode generation had many scalable features not found in ref. 19. With ref. 20, higher-order modes can be generated by adding antennas to the 2D antenna array emitter; the antenna design is independent of mode orders. The design in ref. 19 faces scaling challenges due to reliance on on-chip multi-mode components. Several critical components would have to be redesigned: the silica multi-mode bus waveguide and the couplers to convert fundamental TE and TM modes to higher-order modes. In addition, the silica multimode bus waveguide is less compact compared to the 2D antenna array, especially when scaling to higher-order modes.

In this paper, we examine a novel, reconfigurable spatial mode multiplexer based on a programmable silicon photonic chip that was introduced in ref. 21. The proposed device integrates a linear optical circuit with a polarization-multiplexed OAM mode generator, forming a universal architecture capable of flexible and scalable manipulation of spatial and polarization distributions of light. We experimentally demonstrated the simultaneous generation of ten OAM modes or eight LP modes. Although CV modes were not generated on the fabricated chip due to experimental imperfections, our analysis indicates that they can, in principle, be achieved with only modest modifications to the chip design. The device’s versatility also enables dynamic switching across multiple mode bases, facilitating the creation and optimization of hybrid SDM networks supporting various mode configurations. Furthermore, using only modular components independent of topological charges or mode orders, our proposed architecture provides a scalable solution for high-order SDM systems.

Results

Principle: a universal architecture

The schematic of the proposed device is shown in Fig. 1a and comprises two primary functional blocks. The first is a linear optical circuit (LOC) made of cascaded tunable MZIs, which, depending on the desired mode configuration, splits the input optical power equally into one, two, or four paths. On-chip phase shifters (PSs) then adjust the relative phases between these paths. The LOC outputs are routed to an orbital angular momentum generator circuit (OAM-GC), where the programmed LOC configuration defines the coherent superposition of OAM modes, enabling the generation of the desired spatial modes.

Fig. 1: Schematic and configurations of the mode generator.
Fig. 1: Schematic and configurations of the mode generator.
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a Schematic of the reconfigurable spatial mode generator, including a linear operational circuit (light green) and an OAM generator circuit (beige). By correctly biasing the linear operational circuit, one input can be split into four outputs with certain relative phases and routed to the inputs of the OAM generator circuit. A detailed illustration of the OAM generator circuit is in Fig. 4c. After that, four OAM modes can be generated from the emitter to combine and form an LP mode. Intensity pattern and polarization arrows of the simulated (b) OAM modes, c LP modes, and d CV modes. The polarization distribution of the modes is labeled by the arrows. LOC configurations to generate, e OAM modes, f LP mode, and g CV modes. The diagrams take the example of channel #1, and the signal path is colored in red. For e, by setting MZI #7 with phase difference φ7 = π and MZI #10 with φ10 = π, the input is routed to generate \(OA{M}_{-1}^{+}\). For f, by setting MZI #7 with φ7 = π/2 and MZI #10, #13 with φ10 = φ13 = π/2, the input is routed to generate \(L{P}_{11}^{odd,y}\) by combining \(OA{M}_{-1}^{+}\) and \(OA{M}_{+1}^{-}\). For g, by setting MZI #7 with φ7 = π/2 and MZI #10, #13 with φ10 = φ13 = π, the input is routed to generate \(E{H}_{01}^{odd}\) by combining \(OA{M}_{+1}^{+}\), \(OA{M}_{-1}^{+}\), \(OA{M}_{+1}^{-}\) and \(OA{M}_{-1}^{-}\). h Input channel mapping to generated modes.

The OAM-GC section of our design follows the principle we described in ref. 20, with a brief outline provided here. The device is not programmable and only generates OAM modes. It has multiple single-mode inputs, each mapped to a specific OAM mode distinguished by its topological charge, phase-front rotation direction, and polarization (left or right circular). Separate star couplers are used for each circular polarization. Each star coupler transforms the topological charge and imparts the appropriate phase-front rotation to its outputs. The outputs are then routed to a multi-mode interferometer (MMI) array to produce the required polarization. Finally, two-dimensional (2D) optical antennas generate the OAM modes by mapping the TE modes from the two branches into linearly polarized beams, applying a +90∘ phase shift to produce LCP emission and a -90∘ phase shift for RCP. The antennas are arranged in a circular pattern following the intensity profile of the target OAM mode.

The proposed reconfigurable architecture exploits the versatility of OAM modes to achieve spatial mode manipulation through the combined functionality of the LOC and OAM-GC. As an example, an LP mode can be generated by coherently combining four circularly polarized OAM modes of the same order l with a specific phase configuration22. The mathematical relationship between LP and OAM modes can be expressed as:

$$\begin{array}{rcl}L{P}_{l1,x}^{even} & = & OA{M}_{l}^{+}+OA{M}_{-l}^{+}+OA{M}_{l}^{-}+OA{M}_{-l}^{-}\\ L{P}_{l1,x}^{odd} & = & OA{M}_{l}^{+}-OA{M}_{-l}^{+}+OA{M}_{l}^{-}-OA{M}_{-l}^{-}\\ L{P}_{l1,y}^{even} & = & OA{M}_{l}^{+}+OA{M}_{-l}^{+}-OA{M}_{l}^{-}-OA{M}_{-l}^{-}\\ L{P}_{l1,y}^{odd} & = & OA{M}_{l}^{+}-OA{M}_{-l}^{+}-OA{M}_{l}^{-}+OA{M}_{-l}^{-}\,\text{,}\end{array}$$
(1)

where l denotes the transverse index for LP modes and the topological charge for OAM modes. The symbol “+” represents left-circular polarization (LCP), while “-” represents right-circular polarization (RCP). The radial index m equals one in this work; increasing m would require high-order Laguerre-Gaussian (LG) modes as the basis. The relationships (1) hold in free space and in fiber propagation. The 2D antennas implement a unitary transformation between the electric field at the antenna array; superposition creates the target mode while propagating out of the PIC plane (see illustration in the upper right corner of Fig. 1a). The LP modes generated could be coupled to a few-mode fiber (FMF)23.

We simulate OAM modes using the numerical model from20, with intensity profiles shown in Fig. 1b. Figure 1c presents the simulated resulting LP mode intensity patterns using (1). The simulated LP mode intensity profiles agree well with theoretical LP modes, confirming the capability of the proposed architecture to manipulate spatial light distributions. The unwanted side lobes observed in the profiles may arise from higher-order interference between beams emitted by neighboring 2D antennas24. Reducing antenna pitch can suppress these side lobes24, although achieving this requires a more compact 2D antenna design, which remains a challenge.

We can also generate CV modes using OAM modes as the basis22:

$$\begin{array}{rcl}E{H}_{(l-1)1}^{even} & = & OA{M}_{-l}^{+}+OA{M}_{l}^{-}\\ E{H}_{(l-1)1}^{odd} & = & OA{M}_{-l}^{+}-OA{M}_{l}^{-}\\ H{E}_{(l+1)1}^{even} & = & OA{M}_{l}^{+}+OA{M}_{-l}^{-}\\ H{E}_{(l+1)1}^{odd} & = & OA{M}_{-l}^{-}-OA{M}_{l}^{+}.\end{array}$$
(2)

When l = 1, \(E{H}_{01}^{even}\) and \(E{H}_{01}^{odd}\) are also commonly named as TM01 and TE01, respectively. Figure 1d shows the simulated CV mode intensity patterns, with arrows indicating the polarization states. These results demonstrate that the proposed architecture can also manipulate the polarization of light in vector modes.

The remarkable advantage of the proposed architecture lies in its excellent scalability. The highest achievable order lmax of the LP modes corresponds to the highest order supported by the OAM-GC. Therefore, the number of LP modes that can be generated simultaneously by this device is 4lmax (excluding LP01), considering \(L{P}_{l1,x\,\text{or}y}^{even\text{or}\,odd}\) where l = 1, 2, . . . , lmax. Likewise, when the LOC is biased to generate CV modes, the number of CV modes that can be generated simultaneously by this device is also 4lmax, considering \(E{H}_{(l-1)1}^{even\,\text{or}\,odd}\) and \(H{E}_{(l+1)1}^{even\,\text{or}\,odd}\) where l = 1, 2, . . . , lmax. For OAM modes, the number of OAM modes that can be generated simultaneously is 4lmax + 2, considering \(OA{M}_{+l\,\text{or}-l}^{+\text{or}\,-}\) where l = 0, 1, 2, . . . , lmax. Taken together, the total number of modes supported is 12lmax + 2, albeit not simultaneously.

In our previous work, we demonstrated an OAM multiplexer on a silicon on insulator (SOI) chip that supported the simultaneous generation of OAM modes with orders as high as lmax = 11 in circular polarization with independent input signals10. Therefore, in theory, the architecture proposed in this work could generate modes up to LP11,1. The device also supports hybrid generation of different mode sets as long as the mode order for different modes is not equal. For example, simultaneous generation of \(OA{M}_{{l}_{1}}\), \(E{H}_{({l}_{2}-1)1}\) and \(L{P}_{{l}_{3}1}\), with l1 ≠ l2 ≠ l3. A detailed comparison between our work and the literature is in Supplementary Information Section 1.

The number of required building blocks, such as MZIs, phase shifters (PSs), variable optical attenuators (VOAs), and antennas, scales linearly with the topological charge. For the LOC, the number of MZIs is given by NMZI = NLOC, P = 4lmax + 1, where NLOC, P is the number of PSs for the LOC. Additional on-chip PSs and VOAs can be used to compensate for fabrication errors in the OAM-GC. Firstly, (2lmax + 1) PSs and (2lmax + 1) VOAs are required at the inputs of each star coupler to tune the relative phase and intensity relation between the OAM modes for CV and LP modes generation. Moreover, (2lmax + 3) PSs and (2lmax + 3) VOAs are required at the outputs of each star coupler to ensure the spiral phase-front and the uniform intensity distribution for the antennas for the generation of OAM modes. Therefore, the total number of the PSs and VOAs for the OAM-GC is given by NOAM-GC, P = NOAM-GC, V = 8lmax + 8. The number of antennas can be calculated as NA = 2lmax + 3. In theory, (2lmax + 1) antennas can support the generation of LP modes up to order lmax20,25. In our chip design, we used a higher number of antennas to enhance the phase resolution and thus the quality of the resulting OAM beams26.

Experimental results

The fabricated chip is shown in Fig. 2a, with zooms of various sections of the chip. Experimental characterization begins with calibrating the OAM-GC. The first manipulation has the 2D antennas generating a mode. We adjust the VOAs coarsely so that a laser injected into one input of a star coupler results in uniform intensity in the near-field across the antenna array. The second manipulation adjusts the PSs when an OAM mode is injected into the 2D antennas - only one fiber output should have power. We generate a second-order OAM beam with a q-plate and inject it into the antennas, and monitor crosstalk at the OAM-GC inputs. An optimization routine is used to fine-tune the PSs following the star coupler to minimize crosstalk. The calibration and optimization procedure for the OAM modes is detailed in the Methods section. This process is repeated for both the LCP and RCP star couplers.

Fig. 2: Fabrication of the mode generator.
Fig. 2: Fabrication of the mode generator.
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Photo of (a) the fabricated chip, and scanning electron microscope images of (b) the antenna array, c one 2D antenna, and d one MZI and crossings in the LOC.

The measured crosstalk for reception of OAM2 with LCP and RCP is shown in Fig. 3c, d. The blue dot for the target mode simply indicates that crosstalk is not defined for this mode. The colored bars show poor crosstalk for the chip as fabricated. The on-chip thermo-optic phase shifters (TOPSs) and silicon p-i-n junction VOAs we employ for phase and intensity tuning significantly improve crosstalk performance for both polarizations, see white bars. For OAM2 in LCP, the worst-case and average crosstalk becomes −10.55 dB and −13.35 dB, respectively. For RCP, the corresponding values are −9.58 dB and −14.04 dB. Under the assumption of an ideal 50:50 MMI splitting ratio, the predicted worst-case crosstalk for OAM2 is approximately −20 dB20. The gap between simulation and experiment is primarily attributed to intensity non-uniformity and imperfect phase tuning. Further reduction in crosstalk could be achieved through additional tuning iterations with smaller adjustment steps for both intensity and phase. Redesigning the emitter to incorporate more antennas is another option, though it would require additional phase shifters and attenuators.

Fig. 3: Performance of the mode generator.
Fig. 3: Performance of the mode generator.
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a Interferograms for the generated OAM modes. Clear spiral interference patterns can be observed, indicating the successful generation of 10 OAM modes. b Measured far-field intensity profile of the generated LP modes. LP modes with desired polarization include white boxes to illustrate the main spots. The color bar for each mode is normalized to the maximum power, from 0 to 1. The polarization extinction ratio for each LP mode is shown in the yellow rectangle. \(L{P}_{11}^{even,x}\), \(L{P}_{11}^{even,y}\) and \(L{P}_{21}^{odd,x}\) modes show relatively low extinction ratios due to imperfect nonuniformity and phase errors. Through simulations, we predict that the average polarization extinction ratio can be larger than 20 dB, and the detailed analysis on the impact of experimental errors will be discussed in Supplementary Information Section 2. Measured crosstalk for (c) \(OA{M}_{2}^{+}\) and d \(OA{M}_{2}^{-}\); as fabricated (red bar) and after phase tuning (hollow bar). The dashed line shows the worst crosstalk by simulation, assuming perfect uniformity and phase-front across the antennas.

Following the crosstalk measurements, we sequentially injected the laser into each input of the OAM-GC to validate OAM mode generation. Each output beam was combined with a Gaussian reference beam and the interference measured; the resulting interferograms are shown in Fig. 3a. Distinct spiral fringes are observed for all generated OAM modes in both LCP and RCP; the number of spirals matches the target topological charge. The device is designed to support modes up to l = 3; however, one MZI (MZI #11) exhibited abnormal tuning behavior due to heater fabrication defects, preventing the generation of right-circularly polarized third-order OAM modes on this chip.

Once the OAM-GC was calibrated, we biased the LOC to the LP mode configuration by tuning the relative phase between the constituent OAM states. Since third-order RCP OAM modes could not be generated, the LP31 mode was not accessible with this device. We therefore targeted all degenerate LP11 and LP21 modes. The far-field intensity distributions for the LP configuration are shown in Fig. 3b. The number of main lobes agrees with simulation results, with measured orientation differences of approximately 90∘ between \(L{P}_{11}^{even}\) and \(L{P}_{11}^{odd}\), and 45∘ between \(L{P}_{21}^{even}\) and \(L{P}_{21}^{odd}\), consistent with simulated patterns.

To assess polarization properties, a polarizer was placed before the camera; the polarizer angle is indicated in the second column in Fig. 3b. We measure polarization extinction ratio defined as ERpol = Px/y/Py/x, where the numerator represents the optical power recorded at the desired polarization. Measurements in dB are included in the shaded boxes in the matrix in Fig. 3b. Variations in lobe intensity and extinction ratio were observed across different LP modes. The main source of crosstalk is attributed to the limited mode purity of the excited OAM states, while additional degradation arises from intensity non-uniformity and imperfect phase control between the constituent OAM modes.

Impact of modal purity

The proposed reconfigurable architecture is flexible and scalable, but the quality of the output modes is ultimately limited by the purity of the OAM modes used as a basis. The high level of complexity in design, fabrication, and operation of this architecture leads to challenges for modal purity. The impact of compromised spectral purity can be observed in LP modes that have intensity profiles exhibiting high crosstalk.

Consider launching a single mode i, and observing the power received both on that mode (Pi) and another mode j ≠ i (Pj). Supposing j to be the target channel, the crosstalk on channel j due to channel i is defined as XTi = Pi/Pj. This is plotted in Fig. 3c, d for \(OA{M}_{2}^{+}\) and \(OA{M}_{2}^{-}\), respectively. The worst-case crosstalk after phase tuning for these modes is -10 dB. We define the modal purity of an OAM mode indexed by i to be

$${\eta }_{i}=\frac{1}{1+{\sum }_{j\ne i}X{T}_{j}}.$$
(3)

This is the total crosstalk from all other modes in the basis. The modal purity for \(OA{M}_{2}^{+}\) and \(OA{M}_{2}^{-}\) is 64% and 66%, respectively. These values are lower than the average modal purity of approximately 76% reported in19.

The modal purity of the OAM modes can be enhanced by using a smaller step size for the phase and intensity tuning during the chip calibration process. Including more antennas also increases the resolution of the emitter. There is a trade-off between the modal purity improvement and device complexity26.

Reducing the antenna pitch can also suppress side lobes in the intensity profile of the OAM modes to enhance the modal purity, as mentioned in “Principle: a universal architecture”. In the fabricated chip, the pitch is approximately 12.6 μm and is limited by the footprint of the antenna, as shown in Fig. 2b, c. More compact antenna designs or placing the antennas closer to each other in a multi-layer platform (e.g., silicon nitride-on-silicon platform)27 are promising in reducing the antenna pitch.

The fabricated chip generates OAM modes with nonuniform intensity and imperfect phase relation. Our calibration procedure (see “Chip calibration“) adjusts phase and attenuation per path. While the tuning greatly improves uniformity, it is still far from ideal. Additional VOAs and PSs between the first and second stages of the MZIs would improve intensity uniformity and phase relation, with the added benefit of improving thermal isolation. More uniform OAM modes would translate to better quality LP modes. A numerical model to discuss these experimental error sources is provided in Supplementary Information Section 2.

Discussion

We have realized a programmable silicon photonic chip capable of reconfigurable spatial mode multiplexing, generating OAM and LP modes that add full control over polarization in addition to amplitude and phase. The architecture scales efficiently to higher orders, supporting up to l = 11 with an appropriate OAM-GC, and enables simultaneous generation of multiple modes, either within the same family or across different types.

As a proof of concept, we demonstrated second-order OAM and LP modes from a single device, achieving worst-case crosstalk of −9.58 dB for OAM2 and far-field LP patterns in close agreement with simulations. The platform's versatility extends to CV mode generation, with straightforward design modifications to further improve mode purity, reduce tuning complexity, and shrink the footprint through enhanced MZI accuracy, better thermal isolation, and optimized waveguide geometries. The device can also operate reciprocally, enabling reconfigurable spatial-mode demultiplexing and decomposition28.

Our approach offers a scalable and programmable interface for next-generation reconfigurable SDM systems, quantum information processing, on-chip machine learning, microscopy, and other applications requiring precise spatial mode control.

Methods

Chip design and fabrication

The LOC consists of a dual-stage MZI matrix with 14 input channels. The first stage contains seven MZIs with identical design parameters, each having balanced arms and thermo-optic phase shifters (TOPSs) to control the splitting ratio. Since forming an LP mode requires four OAM modes, the second stage includes six additional MZIs. The 0th-order OAM modes are not involved in LP mode formation and are therefore not routed to any MZI in the second stage. When correctly biased, the dual-stage MZI matrix can simultaneously excite four OAM modes with equal intensity. A detailed description of the transfer function of the LOC is in Supplementary Information Section 3.

To compensate for fabrication errors of the routing waveguides and the splitting ratio deviations in the MZIs, 14 TOPSs and 14 VOAs are placed at the star coupler inputs to fine-tune the relative phase and intensity. Fabrication errors arise when the actual waveguide geometry deviates from the intended design due to sidewall roughness, sidewall angle variations, and thickness non-uniformity during lithography and etching processes29. Such geometric deviations modify the effective refractive index of the guided modes, leading to unwanted phase fluctuations. The impact of the fabrication errors can be mitigated by using wider silicon waveguides30 silicon waveguides or by employing rib waveguide structures31.

An additional 13 PSs within the MZIs adjust the splitting ratios for different LOC configurations. Due to the inherent geometry of the star coupler, the output intensities are not perfectly uniform; therefore, 14 VOAs are placed at the star coupler outputs for amplitude balancing. Likewise, 14 PSs at the outputs enable fine phase alignment between antennas.

The OAM-GC follows the design methodology described in ref. 20. In this device, the OAM multiplexer uses a nine-antenna ring emitter and supports 14 OAM modes up to the third order. The schematic of the OAM-GC is illustrated in Fig. 4c. Each antenna is a two-dimensional grating emitter with a vertical emission loss of 4 dB. Light from the 2 × 2 MMI is combined with a 90∘ relative phase shift, enabling direct generation of circularly polarized beams and fulfilling the requirement of Eq. (1).

Fig. 4: Experimental setup for mode generation and crosstalk characterization.
Fig. 4: Experimental setup for mode generation and crosstalk characterization.
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a photo of the experimental setup. b schematic of the experimental setup. The setup has three configurations. (1) intensity tuning of the OAM mode: inject the laser into one of the input channels of the chip and tune the variable attenuator at the other arm to the maximum, bias the LOC to generate OAM modes; (2) OAM interference: keep the setting of 1) and tune the variable attenuator to observe an interference pattern using the camera; (3) phase tuning of the OAM mode: inject 2nd order OAM generated with a vortex plate to calibrate the phase errors (using the chip as a demultiplexer). c Schematic of the OAM generator circuit. This diagram illustrates the example of generating \(OA{M}_{1}^{+}\) with the corresponding signal path highlighted in red. The star coupler imposes the required topological charge and imparts the appropriate phase-front rotation to its nine output ports. For \(OA{M}_{1}^{+}\), the desired phase progression across nine outputs is 0, 2π/9,..., 16π/9, as indicated in the figure. These outputs are then routed to an MMI array to produce the desired state of polarization. For LCP, the relative phase of the outputs at one of the MMIs is 0°and +90°. For RCP, the corresponding phases for the same ports become 0° and -90°.

The chip was fabricated using a CMOS-compatible silicon photonics process on a 220-nm-thick SOI wafer. As shown in Fig. 2a, the LOC is located in the middle-left region of the chip, with the input fiber array coupled via edge couplers. The OAM generator circuits are positioned along the top and bottom edges, producing LCP and RCP OAM modes, respectively. The emitter is located in the middle-right region.

Figure 2b shows the emitter, consisting of nine 2D antennas arranged in a circular configuration. A close-up of a single 2D antenna is presented in Fig. 2c. Figure 2d shows a micrograph of an MZI, where multiple waveguide crossings are also visible.

Chip calibration

The LOC and OAM-GC are calibrated separately. The dual-stage MZI matrix in the LOC determines the number of simultaneously excited OAM modes and their relative intensities and phases. To ensure proper biasing, 10% tap monitors are included at the output of both MZI stages.

The OAM-GC is calibrated for amplitude uniformity and phase error in both LCP and RCP configurations. The experimental setup is shown in Fig. 4b. A 4-f system is used to image the near field of the generated pattern, while on-chip VOAs adjust the antenna output power to improve uniformity. For phase calibration, a second-order OAM beam generated by a vortex plate is injected into the chip (operating in demultiplexer mode). A correctly calibrated phase suppresses 13 unwanted modes and maximizes power in the intended mode.

LCP and RCP OAM modes are calibrated independently. Crosstalk is measured by illuminating the emitter with a vortex-plate-generated OAM beam and recording the power at all outputs. A gradient descent algorithm is used to iteratively tune the VOAs and PSs to minimize the worst-case crosstalk. Detailed tuning steps are provided in ref. 10.

The side view of the measurement setup is shown in Fig. 4a. The optically and electrically packaged chip is mounted on a five-axis stage with a heat sink beneath. The vertically emitted beam propagates into the free-space optics assembly and is magnified by two lenses—one before and one after a beam-splitter cube. Intensity tuning is performed based on the beam profile captured by the camera. For phase correction, the vortex plate positioned above the beam-splitter converts the Gaussian input beam into an OAM mode.

After intensity and phase calibration, OAM mode generation is verified via interferometry. The right-hand lens of the beam splitter is removed, and the LOC is biased for OAM mode generation. A Gaussian reference beam is injected from the opposite port, with its polarization controlled by a quarter-wave plate and polarizer.

For LP mode generation, the relative intensity and phase between the four constituent OAM modes are optimized. The mode profile captured by the camera serves as the optimization criterion, with the algorithm described in Supplementary Information Section 4. The resulting VOA and PS settings are applied, and a polarizer is inserted before the camera to assess polarization. The polarizer is rotated to maximize SNR, with an angle θ corresponding to the desired LP mode polarization and θ + π/2 to the orthogonal polarization. The same tuning set applies to all degenerate LP modes.