Introduction

Coherent and incoherent beam combining are techniques for improving laser system power delivery (or performance). Incoherent beam combining offers several advantages, as it eliminates the need for frequency, phase and polarization locking of individual lasers, allowing for scalable, compact, and reliable systems1. These systems are predominantly employed in free-space optics arrangements1,2,3 or fiber tapers4,5.

Two-dimensional (2D) VCSEL arrays are widely used as incoherent sources due to their wafer level fabrication ease. Coupling these independent sources into a multimode fiber (MMF) enables beam delivery for applications such as high-power fiber laser pumping and optical communications6,7. Typically, VCSEL sources are combined using a relay lens system that includes a micro-lens array (MLA) and a condenser lens to focus the light into the MMF (see Discussion). The MMF is generally a highly multimode fiber with a large core diameter (greater than 50 μm) having a high numerical aperture (NA >  0.22). These fibers support thousands of guided modes, enabling efficient light coupling.

However, beam brightness is a key factor for optical systems (see Discussion section). Brightness defined by the beam’s power, devide by its area and divergence8, is a physical property that cannot be increased beyond the source measure. Coupling light into a large-core high-NA multimode fiber increases the beam area, and the excitation of extensive modal content results in greater divergence, thereby diminishing the delivered brightness. A brightness-efficient approach involves coupling the energy into a fiber that supports the same number of spatial modes as the source, which corresponds to the maximum degrees of freedom of the system9.

Spatial multiplexers have wide-ranging applications in various light-related fields, such as high-capacity mode-division multiplexing (MDM) for fiber communication networks10,11,12, free-space optical communication13,14, coherent power combining15,16, adaptive optics17,18, and wavefront sensing19,20. Spatial mode multiplexers (and demultiplexers) convert individual, distinct sources (modes) into spatially overlapping and orthogonal modes, ideally with low losses and in compact form.

One prominent spatial mode multiplexer is the multi-plane light conversion (MPLC) multiplexer, which facilitates efficient spatial mode transformations through a series of discrete phase masks or refractive planes21,22,23. Incoherent and coherent laser beam combining has been demonstrated using MPLC24,25 yet for single mode source arrays. Another spatial multiplexer is the Photonic Lantern (PL), which consists of an adiabatic and continuous spatial transition from a multi-mode optical waveguide to a finite set of single-mode (SM) waveguides, converting between matching mode and waveguide counts26. Both MPLC and PL devices ideally convert from the multi-mode domain to the single-mode array domain and vice versa with minimal loss, making them key enablers of space division multiplexing (SDM)27. Photonic lanterns can be fabricated from single-mode fibers that merge into one28,29,30, through waveguide inscription in glass via direct laser writing31,32, often resulting in millimeter-scale devices, or via 3D nano-printing with polymer core/air cladding waveguides33,34,35,36, which enables the creation of micrometer scale PL devices using 3D nano-printing technology and high-index contrast waveguides (polymer vs. air). Moreover, 3D nano-printing technology allows fabrication on versatile surfaces and sources, making it an excellent platform for VCSEL integration37,38 and a wide range of microscale photonic systems.

Traditional PL and MPLC spatial multiplexers are typically designed to receive single-mode (SM) fibers or waveguides as inputs, with these designs being incompatible for beam combining from multiple multi-mode (MM) laser or VCSEL sources. In this manuscript, we introduce a novel 3D-printed micro-scale photonic lantern (PL) designed to multiplex multiple (7, 19, and 37) 6-mode beams into a multi-mode fiber (MMF) that supports the corresponding number of modes (i.e., 7 × 6 = 42, 19 × 6 = 114, and 37 × 6 = 222). We refer to this device as an N-MM PL, where N is the number of inputs. The manuscript presents the design, fabrication, and characterization of three scales of MM PL devices (7, 19, and 37 inputs). These devices were fabricated directly on a commercial multi-mode incoherent VCSEL array. The ability to 3D-print the PL device at high precision and with micrometer scale allows for efficient and compact integration, with direct coupling between VCSEL sources and the PL and finally with the collecting fiber. In addition to comprehensive characterization, including efficiency, modal content and beam quality assessment of the PL, we directly couple to a 50 μm core diameter, NA = 0.22 MMF, achieving coupling losses of  − 0.8 dB.

Results

Designing a multi-mode photonic lantern

The design of a PL supporting array count of MM sources, specifically, the design of a 7-MM PL that multiplexes seven 6-mode sources into a 42-mode waveguide, a 19-MM PL that combines nineteen 6-mode sources into a 114-mode waveguide, and a 37-MM PL that integrates thirty-seven 6-mode sources into a 222-mode waveguide is challenging due to scale and computational complexity. The incoherent MM VCSEL source used in this work (Vixar, model V0013239), lases at 940 nm has a source pitch of 44 μm and 10 μm mode field diameter for the fundamental mode. In this section we outline the methodology and the computational speed-ups we incorporated for their design. Figure 1a illustrates the targeted output fiber modes for these devices.

Fig. 1: Design and system description.
Fig. 1: Design and system description.
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a Output modes of the different devices, with each background color corresponding to a specific device (Blue: 7-MM PL, Blue + Yellow: 19-MM PL, Blue + Yellow + Black: 37-MM PL). Schematics of the (b) 7-MM PL, (c) 19-MM PL, and (d) 37-MM PL integrated with the VCSEL array chip. e Illustration of the input waveguide arrangement for the 37 sources with classification to symmetry waveguide groups ("A"–"D"). Evolution of the GA generations for (f) 7-MM PL, (g) 19-MM PL and (h) 37-MM PL, showing the average and best results for each generation.

The primary objective for MM-PL devices is to maximize transmission power while ensuring power confinement within the designated mode sets with no requirments over mode mixing. This approach minimizes the excitation of higher-order modes, reducing the M2 value of the output beam. Consequently, brightness is preserved, and coupling efficiency into a multimode fiber (MMF) having the same mode count is improved. Achieving power confinement within the target modes (42, 114, or 222) requires an adiabatic transition between the inputs (VCSEL sources) and the multimode waveguide. An ideal adiabatic transition would eliminate losses during this process, allowing the PL device to be represented as a unitary matrix. PL multiplexers can be classified as either mode-preserving or mode-mixing devices. In the mode-mixing case, injecting light into any input of the PL results in a linear superposition of the supported modes at the multimode output. Conversely, mode-preserving PLs are designed to target specific modes or mode groups from each input40. In this study, we focus on the mode-mixing PL, as our goal is to efficiently transfer power from the MM VCSEL sources to the MMF.

The PL device design relies on algorithmic convergence and numerical FDTD simulations to model light propagation within the guiding structure. These simulations are computationally intensive due to the MM-PL volume and source count, with individual runs taking anywhere from minutes to hours depending on mesh point density. Therefore, significant effort has been dedicated to optimizing computational efficiency and speed.

To evaluate the PL’s performance, the coupling matrix is computed, representing the connectivity between each input source mode and each output mode. From the coupling matrix, insertion loss (IL) and mode-dependent loss can be derived using singular value decomposition (SVD). Calculating the full coupling matrix requires 2 × N FDTD simulations, where N is the number of modes and the factor two accounts for polarization. This linear increase in computation time with the number of modes makes optimization challenging. To address this, an IL estimator was developed that significantly reduces the number of required simulations by leveraging the PL’s symmetry relative to the central waveguide and the fact that the PL is designed for mode mixing. Figure 1e depicts the PL input waveguide arrangements for the 7,19 and 37-waveguide configurations, where circles labeled “A” to “D” represent symmetrical waveguide groups. The 7-source PL utilizes groups “A” and “B”, while the 19-source PL comprises groups “A” “B”, and “C” and the 37-source PL uses all four waveguide groups. The IL estimator utilizes a single simulation per symmetry group, significantly reducing computational requirements. For instance, the 7-MM PL requires only two simulations per algorithm step, the 19-MM PL requires three, and the 37-MM PL requires four. This method ensures that computation time does not increase linearly with the number of modes.

Our IL estimator is defined by the weighted sum:

$$\widehat{IL}=\frac{1}{N}{\sum }_{i=1}^{S}{M}_{i}\cdot {P}_{i}\le IL\le 1$$
(1)

where N is the total number of PL modes, Pi represents the total power transmission from a selected input source from the i-th simulation to the output, S denotes the number of symmetry groups, and Mi is the number of modes in each symmetry group where \(N={\sum }_{i=1}^{s}{M}_{i}\). To address the more complex scenario of multimode inputs, which demands another simulation multiplier to account for each source mode, the estimator function is calculated based on the highest-order input source spatial mode only, which always experiences the lowest efficiency. This strategy reduces the required simulations per waveguide group from 2 × 6 to just one. The rationale is that if the structure can efficiently support the highest-order mode—associated with the highest transverse momentum and therefore is the most challenging to couple adiabatically—it is expected to perform better for lower-order input modes. As a result, the IL estimator consistently underestimates the actual IL and its maximization converges to well performing designs (maxmin optimization). Further details are provided in the supplementary materials section 1. This assumption is particularly valid for adiabatic devices but may not apply to other types of multiplexers, such as MPLC, which rely on discrete phase masks.

Using the IL estimator as the objective function, we utilized a genetic algorithm35 (GA) to optimize the designs of the 7-MM PL, 19-MM PL, and 37-MM PL. Each PL leg of groups A-D was defined by a set of 9 parameters, including 8 parameters that determine the waveguide curve shape and the waveguide tapering rate35. The the PL length is another parameter defined equally for all waveguide groups. Each unique parameter set corresponds to a distinct design. The GA aimed to identify the parameter set that maximized the IL estimator. Figure 1(f–h) illustrates the GA scores at each iteration for the three devices, demonstrating convergence to well performing designs.

After selecting the best design from the GA optimization, we evaluated its real IL by evaluating all input modes and sources. For the 7-MM PL, the best IL estimator was −0.8 dB, corresponding to the estimated loss using the highest-order spatial mode only. Since the estimator provides a lower bound for the insertion loss, the total efficiency is expected to be higher. Calculating the complete coupling matrix for the optimized device, an IL of −0.45 dB was obtained. Similarly, for the 19-MM PL, the best IL estimator was −1.55 dB, with an actual IL of −0.86 dB. For the 37-MM PL, the best IL estimator was  − 2 dB, with an actual IL of −1.4 dB, confirming the design methodology we adopted.

Both the 19-MM and 37-MM PLs, are designed to interface with a 0.22 NA, 50 μm step-index (Thorlabs model FG050UGA) multimode fiber, have total lengths of 425 μm and 470 μm, respectively, and terminate with an expansion taper of 52 μm diameter cross-section (Fig. 1c, d) which best matches the MM fiber according to simulations. The 7-MM PL has a total length of 345 μm only and terminates with a 10 μm diameter cross-section to expand the output beam and reduce the required NA of the measuring optical system (Fig. 1b).

PL on VCSEL 3D-printing

We utilized direct laser writing with a Nanoscribeⓒ Photonic Professional GT2 3D Printer for the fabrication of the PL devices. Tightly focused beam of the pulsed laser with the center wavelength of 780 nm was used to polymerize IP-S resin through a two-photon polymerization process. The writing was done using a 25 × objective. The system is calibrated to deliver 50 mW (CW equivalent) at 100% laser power. This fabrication technology enables fine resolution feature definition down to 200 nm. Fig. 2 shows SEM images of the three PL devices (a: 7-MM, b: 19-MM and c:37-MM) directly printed on a MM-VCSEL array corners.

Fig. 2: PL fabrication directly on multimode VCSELs.
Fig. 2: PL fabrication directly on multimode VCSELs.
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SEM images of (a) 7-MM PL. b 19-MM PL (c) 37-MM.

Transfer matrix analysis of a 7 source-six mode input PL

To accurately assess the performance and modal behavior of the fabricated MM-PL, the coupling matrix must be experimentally measured. This is normally done (in the SM input case) by exciting one input source at a time. Using the MM VCSEL array as the source, it is not possible to individually excite one VCSEL source in our device, let alone controllably radiate by a mode and polarization basis. Hence, for characterization purposes, we fabricated the PL on a glass substrate and operate it in reverse, serving as a mode demultiplexer. We excited the PL from the 10  μm output side with 42 LP modes, generated with a phase spatial light modulator (SLM) that converts an incident collimated Gaussian beam to each mode after two reflections from different SLM regions with applied phase patterns to generate each target mode. The PL demultiplexes each input mode to orthogonal states spanning the seven PL waveguides and six modes (as the PL mode mixes). Hence we must record the entire complex field emerging cumulatively from all PL legs, which we do with a digital holography (DH) setup that records the interferogram of light emerging from the PL legs with a reference collimated beam from the same input laser source, (setup in Fig. 3e). For this free-space coupling measurement, the PL was slightly modified for operation at 1550 nm wavelength, which better suits our communication-focused lab equipment. To reduce background light, we also gold-coated the glass substrate, leaving only an array of seven apertures matching the input waveguides’ position and size for PL printing. We recorded the interferograms from the seven 6-mode waveguides, extracted the complex electric field and assessed the PL transfer matrix in reverse, functioning as a demultiplexer. From these complex field measurements, we derived the modal content of each waveguide and relative phase and constructed the complete coupling matrix with the proper phase relationship between matrix elements, with each measurement contributing a row (Fig. 3b: The absolute squared matrix and c: The phase values). Fig. 3a illustrates the generated input LP mode, the measured output electric field, and its intensity for each measurement. Figure 3d presents the singular values of the measured transfer matrix. As illustrated, 7 out of the 42 singular values have power levels below  − 5 dB, indicating that the majority of the system’s modes are functioning effectively. The mode-dependent loss (MDL) is calculated as  − 5.1 dB using the standard deviation of the singular values (− 40 dB when assessed using the min-max metric). Based on the average of the singular values, the insertion loss (IL) is determined to be  − 1.6 dB, reflecting the fraction of transmitted optical power confined within the 42 target modes.

Fig. 3: MM-PL transfer matrix analysis.
Fig. 3: MM-PL transfer matrix analysis.
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a All measured output fields along with their corresponding excitation input mode generated by an SLM. The measured transfer matrix, (b) Absolute squared, (c) Phase. d Singular values of the complex transfer matrix. e A schematic of the DH measurment setup. M.O Microscope Objective, P.C Polarization Controller, Lens; f = 10mm.

Beam quality measurements

Understanding the modal content and beam quality of PL devices is essential for a complete analysis of the VCSEL+PL system. To achieve this, we employed a self-interference method to measure the complex electric field of the emitted light from VCSELs or PL devices41. The experimental setup is depicted in Fig. 4a.

Fig. 4: Beam quality measurement.
Fig. 4: Beam quality measurement.
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a Self-interference experimental setup. M.O microscope objective, ND neutral density filter, BS beam splitter. 7-MM PL, 19f-MM PL, and 37-MM PL: b measured intensity, complex field, (c) M2, and ideal fiber coupling at different currents per VCSEL source (6–11.2 mA).

The process begins by splitting the VCSEL beam using a beam splitter (BS) and recombining it on a camera sensor with another BS. The optical path lengths of the two beams were carefully matched to ensure the temporal coherence of the VCSEL source. The reference path includes spatial filtering to create a broad, Gaussian-like beam with flat phase fronts, which is then magnified to fully overlap with the second, multimode (MM) beam. The second BS is slightly tilted, introducing a small angle (~ 3°) between the two beams for fringe formation.

Subsequently, we apply an off-axis digital holography technique to reconstruct the electric field of the VCSEL beam. This method allows each lasing source to interfere with itself, on account of self-coherence, enabling wavefront reconstruction42. Finally, we perform a modal decomposition using the Laguerre-Gaussian (LG) mode basis. This decomposition identifies the spatial modes present in the VCSEL beam and determines the beam quality factor (M2) using the formula43:

$${M}^{2}={\sum }_{p=0}^{\infty }{\sum }_{l=-p}^{p}(2p+l+1)| {c}_{pl}{| }^{2}$$
(2)

Where, l, p are the LG modes indexing, and Cpl is the coupling coefficient of l, p mode to the measured electric field. Additionally, we estimated the coupling efficiency to a multimode fiber (MMF) by projecting the measured fields onto a step-index MMF modal basis. For each measured PL (7, 19, or 37), the simulated MMF was configured to support the same number of modes as those considered in the PL design (7 × 6 = 42, 19 × 6 = 114, and 37 × 6 = 222). This approach allows us to emulate the performance of ideal, mode count matched fiber coupling35. A characterization of the modal content and beam quality of a single VCSEL source is shown in the supplementary materials section 3. From the measurements, most of the power is concentrated in the first six LG modes, with a small fraction extending up to the 12th mode at higher injection currents. The VCSEL source M2 factor varies between 2.25 and 4.1, with lower values at lower current (see supplementary).

Beam quality measurement of a 7-MM PL and 42-mode fiber coupling estimation

The M2 and modal analysis were performed on the 7-MM PL printed on a VCSEL array using the self interference digital holography technique. Figure 4b shows the electric fields and intensity profiles of the PL output at various injection current levels. It also includes a plot of the measured M2 values and calculated fiber coupling efficiency for each current. Figure 4c shows the fiber coupling values range from −1 dB to −1.5 dB, closely matching the insertion loss (IL) estimated via digital holography, which was −1.6 dB for all 42 designed modes. The M2 values were found to range between 7.6 and 8.6.

Beam quality measurement of a 19-MM PL and 114-mode fiber coupling estimation

The M2 and field analysis were subsequently conducted on the 19-MM PL printed on a VCSEL array. Figure 4b illustrates the electric fields and intensity profiles of the PL output at different injection currents. Figure 4c shows the fiber coupling values, representing the power contained within the 114 target modes, range from −1.2 dB to −1.6 dB. The M2 values were observed to vary between 12.3 and 13.42.

Beam quality measurement of a 37-MM PL and 222-mode fiber coupling estimation

The M2 and field analysis were subsequently conducted on the 37-MM PL printed on a VCSEL array. Figure 4b illustrates the electric fields and intensity profiles of the PL output at different injection currents. Figure 4c shows the fiber coupling values, representing the power contained within the 114 target modes, range from −1 to −2.2 dB. The M2 values were observed to vary between 14.9 and 17.

Power transmission and fiber coupling

To assess the transmission efficiency of the MM-PL devices, we performed direct optical power measurements by imaging the PL output onto a large photodetector, using a spatial filter to suppress background light from adjacent VCSELs on the chip that are not attached to the PL. Additionally, the 19-MM PL and 37-MM PL were directly coupled to a step-index MMF with a 50 μm core diameter and NA = 0.22. The PL-to-fiber alignment was performed actively by measuring the fiber output power while precisely adjusting the VCSEL chip and PL using a piezo-actuated x, y, z, and tip/tilt stages. The PL was brought into direct contact with the fiber. Microscope images of the butt-coupled VCSEL+PL+MMF system are shown in Fig. 5c, f. Since the fiber supports approximately 677 spatial modes, efficient coupling is expected.

Fig. 5: Power transmission measurement.
Fig. 5: Power transmission measurement.
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a Raw transmission measurement of a single VCSEL source and the 7-MM PL device. b Loss curve of the 7-MM PL versus injection current. c Microscope image of the 19-MM PL directly butt-coupled to a multimode fiber (MMF). d Raw measured curves of the 19-MM PL with fiber coupling measurement. e Loss curves for the 19-MM PL. f Image of the 37-MM PL coupled to a fiber. g Raw measured curves of the 37-MM PL with fiber coupling measurement. h Loss curves for the 37-MM PL.

7-MM PL Power transmission

A measurement of the 7-MM PL device was conducted. Figure 5a presents the optical power measurement of the PL, alongside the power from a single VCSEL source. An additional curve, scaling by 7 × the single VCSEL power, illustrates the maximum potential power at the PL output, assuming all sources emit at approximately the same power. This assumption is valid as the VCSELs were operated with injection current above the threshold lasing current, and the reference VCSEL was measured on the same sources used for the PL (Prior to its fabrication). Furthermore, the reference VCSEL measurement was performed with a source filled with a 3D-printed photopolymer pillar to match lasing conditions to the PL itself. Figure 5b shows the PL power loss relative to the measurement of seven single VCSEL sources, with losses ranging from −1.5 dB to −0.8 dB as a function of current.

19-MM PL Power transmission and MM fiber coupling

A similar measurement was conducted for the 19-MM PL device. A microscope image of the VCSEL+19-MM PL+MM fiber is shown in Fig. 5f. Figure 5d shows the optical power measurement, while Fig. 5e presents the corresponding loss curves. The power loss for the 19-MM PL was found to range from −1.5 dB to −1.7 dB, following the same procedure used for the 7-MM PL. The figures also includes coupling results to a multimode fiber (MMF), performed with Thorlabs FG050LGA 50 μm core diameter step-index MMF (NA = 0.22). The transmitted power through the fiber is shown in Fig. 5d, and the loss is depicted in Fig. 5e, ranging from −2.1 dB to −2.3 dB. The fiber coupling efficiency (green curve in Fig. 5e) was calculated by subtracting the PL transmission curve from the fiber transmission curve, yielding a range of −0.8 dB to −0.5 dB, indicating efficient power transfer from the PL to the fiber.

37-MM PL Power transmission and MM fiber coupling

A similar measurement was also performed for the 37-MM PL device. A microscope image of the VCSEL+37-MM PL+MM fiber is shown in Fig. 5f. Figure 5g shows the optical power measurement, while the loss curves are presented in Fig. 5h. The power loss for the 37-MM PL was measured to range between −3.5 dB and −1.8 dB. The transmitted power through the fiber is shown in Fig. 5g, while the loss is depicted in Fig. 5h, ranging from −4 dB to −2.5 dB. The measured fiber coupling efficiency (green curve in Fig. 5h), which was calculated by subtracting the fiber transmission curve from the PL transmission curve, is around an average of  − 0.7 dB, demonstrating effective coupling and efficient power transfer from the 37-MM PL to the fiber.

Long duration operation measurement

To assess potential damage formation from long duration operation, long duration optical power measurements were performed at the PL output utilizing the 19-MM PL. The system was characterized at six distinct driving currents; each measurement duration was 1 h and 10 min, resulting in a total operational time of 7 h. To ensure stable lasing of the VCSEL sources, a backside thermal stabilization system was implemented. This setup included a cooling fan, a thermoelectric cooler (TEC) controller, a temperature sensor, and a PID (Thorlab’s TED4015) control loop (see Fig. 6a). The VCSEL surface temperature was stabilized at 25°. Fig. 6b illustrates the temperature deviation over the measurement period, showing a stability of approximately  ± 0.02°. The measured optical power versus time for different injection current levels is presented in Fig. 6c. The output power remained stable over time, with minor fluctuations attributed to intrinsic laser noise and potential mechanical instabilities within the laboratory setup. The measurement results for each current level-including mean power (μ), standard deviation (σ), and power stability—are summarized in Table 1. The stability metric is calculated as \(20{\log }_{10}(\sigma /\mu )\) and describes the fluctuation strength relative to the average power. For all tested current values, the stability was observed to be less than −50 dB. These results demonstrate a robust and stable PL-VCSEL system capable of continuous operation across a wide range of driving currents over extended periods.

Fig. 6: Long duration operation measurement.
Fig. 6: Long duration operation measurement.
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a Experimental setup. TEC Thermoelectric Cooler, TS Temperature sensor, PID Proportional, Integral, and Derivative, MO microscope objective, PD photo-detector. b Temperature vs time, showing the temperature fluctuations. c Measured PL output Power [mW] vs time for different injection current values.

Table 1 Optical Power Fluctuation Analysis
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Discussion

Many VCSEL-based applications require efficient coupling between an array of incoherent VCSEL sources and a MMF or a few-mode fiber (FMF). Most coupling methods involve using a microlens array to collimate each source, followed by a focusing lens to direct the beamlets to the MMF8,44,45. An essential aspect of this process is preserving the beam brightness8, defined as \(B=\frac{P}{A\Omega }\), where P is the output power, A is the spot area, and Ω is the solid angle. In radiometry, AΩ is referred to as the etendue. For a general Gaussian beam:

$$B=\frac{P}{{(\pi {\omega }_{0}\theta /2)}^{2}}=\frac{P}{{({M}^{2}\lambda )}^{2}}$$
(3)

Where θ is the divergence angle, M2 is beam divergence factor and λ is the wavelength. Coupling a large-étendue source, such as a VCSEL array, to a fiber with a small core diameter and numerical aperture (NA) using standard relay optics (e.g., microlens arrays and focusing lens) presents inherent limitations. For 100% coupling efficiency, the étendue of the target fiber must be equal to or greater than that of the source; otherwise, the étendue invariant will not be preserved. Efficient coupling with relay optics requires adjustments to both the NA and beam size. The NA of the lenses must be smaller than that of the fiber but large enough to magnify the beam to match the dimensions of the fiber modes. Consequently, large-core, high-NA fibers that support thousands of modes are commonly used for coupling to VCSEL sources. While these fibers enable efficient coupling, the brightness of the output beam is diminished and could be greater if a few-mode fiber, with the number of modes equal to the number of VCSEL sources modes, were employed with no or little IL.

To illustrate the limitations of a lens system, we conducted a numerical simulation of the setup depicted in Fig. 7a. The system consists of incoherent MM VCSEL sources arranged in a triangular grid, each simulated as a collection of Laguerre-Gaussian beams. The beams propagate through a microlens array (MLA) for collimation and are then focused toward an optical fiber by a second lens. Light propagation was simulated using the angular spectrum algorithm, and fiber coupling efficiency was evaluated by decomposing the field at the focal plane of the second lens onto the simulated fiber modes. Since the system involves incoherent beams, we simulated each source individually (specific location on the source array and specific mode) and calculated the total coupling efficiency as a weighted average. Further details are provided in the supplementary materials section 7. The focal lengths of the MLA and the focusing lens were optimized to maximize fiber coupling efficiency. For the target fiber, we simulated a 50 μm core fiber with a NA of 0.12, supporting approximately 37 × 6 = 222 modes, with each VCSEL source containing 6 LG spatial modes. Figure 7b shows the maximum coupling efficiency achieved when coupling different numbers of sources to the target fiber. We observed that coupling a small number of sources can be achieved with very high efficiency (higher than  − 0.5 dB). However, when attempting to couple the same number of sources as the number of fiber modes (fully utilizing the system’s degrees of freedom), an efficiency of  − 3.5 dB was obtained. It is important to note that the simulation does not account for the effects of misalignment or aberrations, which could result in further reduction to coupling efficiency.

Fig. 7: VCSEL and lens system.
Fig. 7: VCSEL and lens system.
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a An alternative fiber coupling system. b Best simulated fiber coupling efficiency for different sources to mode ratios.

Using space division multiplexing (SDM) techniques, an N-mode source can theoretically be converted into a different N-mode waveguide without any losses. This enables the coupling of a VCSEL array with N sources, where each source supports M modes (generalizing for a multimode array), to a target fiber with M × N modes. Simulation results presented in this manuscript demonstrate that the optimized 37-MM PL achieves an insertion loss (IL) of  − 1.4 dB, which is nearly 2 dB better than the theoretical lens based system.

Based on the measurements presented, we can qualitatively estimate the total power transmission of the VCSEL and PL-based system. Using the beam quality measurements, which calculate the estimated fiber coupling, we can determine the fraction of transmitted light remaining in the target modes. This, combined with the power transmission measurements that evaluate the PL’s total optical transmission, provides an overall assessment of the system’s efficiency.

Focusing on the 37-MM PL device, the average estimated fiber coupling (from Fig. 4c) is LCoupling = − 1.6 dB, and the average power transmission (from Fig. 5h) is LPower = − 2.2 dB. Therefore, the estimated total power coupling of the experimental system is LTotal = LPower + LCoupling = − 3.8 dB, which closely matches the results from the simulated lens system despite the simulation assuming ideal conditions without alignment errors, aberrations, or other practical imperfections.

It is important to highlight that in the VCSEL measurements, additional power is present in higher-order modes beyond the six simulated modes. This extra power contributes to higher-order modes in the PL device and is considered in the beam quality assessment. Furthermore, discrepancies between simulation results and measured devices may arise due to fabrication imperfections, including surface roughness, structural shrinkage after development, misalignment between the VCSEL array sources and the PL, and other factors.

In conclusion, we have presented the design, fabrication, and characterization of three PL devices engineered to accept 6-mode inputs and transform them into multimode outputs with varying mode numbers (7 × 6 = 42, 19 × 6 = 114, 37 × 6 = 222). We demonstrated direct integration with a multimode VCSEL array and efficient power delivery to a multimode fiber. The modal behavior of the 7-MM PL was thoroughly characterized through transfer matrix measurements and analysis, while the beam quality of all three devices was evaluated, showing that transmitted power is confined within the target modes with high efficiency (greater than  − 2 dB).

We have showcased a compact system for fiber coupling that requires minimal alignment effort to a multimode fiber in a diminutive scale. High coupling efficiencies were achieved with a 50 μm core MM fiber (NA = 0.22), with the 19-MM PL achieving coupling efficiency exceeding  − 0.6 dB and the 37-MM PL exceeding  − 0.8 dB. Optical transmission efficiencies greater than  − 3 dB were also measured. Furthermore, we demonstrate long-term operation measurements with stable power delivery over several hours at different drive currents. Since this work primarily focuses on power delivery applications-namely, efficient optical power transmission from a large VCSEL array via a multimode fiber-other use cases, such as short-reach optical fiber communication, can be realized by employing a VCSEL array designed for communication, as the photonic lantern can be readily optimized for different VCSEL platforms. The 3D-printed PL structures are mechanically robust and remain stable over extended periods in standard laboratory conditions, and for practical implementations, the device can be encapsulated to protect against dust, physical contact, and other environmental factors.

For improved robustness and higher power handling capability, it is also possible to employ alternative inorganic materials such as silica-rich sol-gel46, which have been shown to withstand significantly higher optical power levels compared to standard photoresists like IP-S.

The 3D nano printer we use is limited to writing transverse area of 400 × 400 [μm]2 with the 25 × objective and galvo scanning mirrors. Without this constraint, it would be possible to cover a large VCSEL array with hundreds of sources using the same design methodology. To scale the number of integrated VCSEL sources, two complementary approaches can be employed: First, by extending the photonic lantern optimization framework to higher-order modes, allowing efficient coupling of a larger number of input sources; and second, through modular integration, where the demonstrated 37-MM PL serves as a repetitive building block that can be interconnected to form larger assemblies. With modern 3D nanoprinting systems capable of multi-millimeter writing fields, such scaling can be achieved in a single fabrication step, enabling dense and compact integration of large VCSEL arrays with the photonic lantern.

Methods

Simulation tools

The electromagnetic simulations carried out using Ansys Lumerical solvers encompass the utilization of FDTD, EME, and FDE algorithms. The optimization and design process involves utilizing a Python API that has been developed in house for the Lumerical solver.

Digital holography and SLM mode generation

To measure the coupling matrix of the PL at a single wavelength (1.55 μm), we employed off-axis digital holography to capture the complex electric field at the device’s output. The experimental setup included the following equipment: a Yenista Optics model −1560 ECL (External Cavity Laser) source, Thorlabs MPC320 polarization controllers, and a Thorlabs TC25FC-1550 fiber collimator for collimating the reference beam and the signal beam before the SLM. To image the PL output beams onto the camera plane, we used a  × 20 Mitutoyo T1.1 LCD Plan Apo NIR (Near-Infrared) infinity-corrected objective paired with a 200 mm tube lens. The imaging system incorporated an Allied Vision Goldeye G-033 TECless InGaAs camera for capturing the beam.

Mode patterns were generated using a Holoeye PLUTO-2.1 TELCO SLM combined with a λ/2 waveplate to ensure proper polarization alignment on the SLM. The SLM phase patterns were optimized using a gradient descent algorithm (see Supplementary Information section 2) to maximize the quality of the generated LP modes. A f = 3 mm aspheric lens was used to focus the collimated light after passing through the SLM onto the PL input.

Beam quality measurement

The experimental setup is shown in Fig. 4a. A 60 × /0.85 Plan infinity-corrected microscope objective was used to collect light from the PL or VCSEL source. Two identical 4f systems with a magnification ratio of 1:5 (f1 = 10 mm, f2 = 50 mm) were employed to magnify the reference beam and demagnify the PL beam, ensuring uniform illumination of the reference beam on the measured beam. A pinhole with a 75 μm diameter was selected to produce a clean Gaussian beam with sufficient power. Adjustable neutral density (ND) filters, ranging from 0.1 to 4, were placed in the signal path to balance the intensities of the signal and reference beams. The setup utilized an iDS UI-148xLE CMOS camera for detection and a Thorlabs LDC4020 laser diode controller to operate the VCSELs.

Power transmission measurement

The setup incorporates an imaging system consisting of a 60 × /0.85 Plan infinity-corrected microscope objective and an f = 180 mm tube lens to focus the measured light onto a 1 mm2 HP-8153A optical power meter. To eliminate stray light from neighboring VCSEL sources, an adjustable iris was placed after the microscope objective. The imaged light was split by a beam splitter, directing it simultaneously to a camera and the power meter. The camera served to verify that the correct VCSEL or PL light was being accurately imaged onto the power detector.

3D nano-printing on a VCSEL array

The process of 3D nanoprinting on VCSELs is highly intricate and requires meticulous surface preparation. Initially, the VCSEL was submerged in acetone and subjected to ultrasonic cleaning in a 55 °C bath, just below acetone’s boiling point, for 1 h. This step removed contaminants, reducing the risk of issues such as explosions caused by residual particles. To enhance adhesion, a three-step process was employed: the VCSEL surface was silanized by immersing it in 30 mL of ethanol mixed with three drops of 3-(Trimethoxysilyl) propyl methacrylate for 30 min, introducing coupling agents and functionalizing the surface. A drop of material was then applied to the VCSEL and placed in a desiccator where air was evacuated for 20 min, ensuring the IP-S photopolymer filled the apertures without bubbles. A 2 μm-thick circular skirt, raised 3 μm above the waveguide bottom—aligned with the VCSEL’s gold contact surface—was added to increase the contact area between the polymer layer (PL) and the VCSEL top electrode without introducing additional optical losses.

Before printing, the VCSEL was carefully aligned relative to the printing direction to ensure precise coupling between the VCSEL and the waveguides. Each leg of the PL was positioned over its corresponding aperture, with alignment fine-tuned by activating the VCSEL and ensuring its beam center matched the waveguide center. The reflective nature of VCSEL surface materials, such as gold and GaAs, required a reduced laser power for the initial layers. The first 5 μm were printed near the polymerization threshold at 10% of maximum laser power, while subsequent layers were printed at 32% power with a Galvo scanning speed of 10, 000 μm/s. A 25 × objective lens and IP-S resin were used, and the structure was sliced into 100 nm increments in both vertical and horizontal planes to ensure a smooth and high-quality PL surface. The PL’s fine features, with widths as small as 2 μm, were reinforced against deformation during development by applying a 60-degree offset to the hatching angle.

The heights of the PLs were set to 345 μm, 425 μm, and 470 μm for the 7-MM, 19-MM, and 37-MM configurations, respectively. Since the piezo stage’s maximum longitudinal range is 300 μm, the structures were divided and stitched at 295 μm. Alignment of the upper and lower sections was performed atop the bottom part before continuing the print. To mitigate power losses from uncovered VCSEL apertures, unused apertures were sealed with 15 μm-high pillars, ensuring uniform lasing power distribution across the array.

After printing, the structures were cleaned in propylene glycol methyl ether acetate (PGMEA) for 20 min, rinsed in isopropanol (IPA) for 2 min, and dried in Novec 7100 for 1 min. Additional curing of potentially non-polymerized material in the apertures beneath the circular plate was completed using strong UV light to ensure full polymerization.