Research on the transmission characteristics and fabrication process of photonic lanterns

Summary

As a waveguide device capable of realizing low-loss adiabatic transition from multiple single-mode fibers to a multimode fiber, the photonic lantern exhibits broad application prospects in fields such as mode division multiplexing communication, high-power laser manipulation, and astronomical observation. This paper systematically investigates the physical mechanism of mode evolution, numerical modeling methods, and transmission characteristic characterization of photonic lanterns. The full-process fabrication technology, including material pretreatment, bundle arrangement, tapering optimization, precision cleaving, and dissimilar splicing, is detailed, with key process factors analyzed. Comprehensive characterization shows transmission efficiency exceeding 98% at low power, while mode field tests verify mode evolution laws consistent with simulations, laying a theoretical foundation and technical support for the engineering application of photonic lanterns.

Graphical abstract

Highlights

• •Neural network model predicts transmission with high speed and accuracy
• •Fabrication process ensures high yield and consistent performance
• •Experimental results validate mode evolution simulations

Physics; Photonics; Applied sciences; Engineering

Introduction

The spatial mode of fiber lasers, as an independent physical dimension, is gaining increasing prominence.¹ In mode division multiplexing (MDM) systems, different spatial modes can serve as independent channels for information transmission, significantly increasing communication capacity.² In high-power fiber lasers, higher-order modes have higher nonlinear effect thresholds and better distortion resistance compared to the fundamental mode, which is of great significance for suppressing stimulated Brillouin scattering (SBS) and transverse mode instability (TMI).³ In the field of celestial detection, the wavefront information carried by the light field in free space is carried by different modes after entering the optical fiber. Analysis and calculation of mode field information can effectively help realize near-diffraction-limited imaging or even super-resolution imaging.^4,5 However, how to realize the mutual conversion between the fundamental mode and higher-order modes efficiently, with low loss and controllability, has always been a key technical problem in the field of fiber optics.

The photonic lantern (PL) offers a revolutionary solution. Comprising multiple single-mode fibers (SMFs) adiabatically transitioning into a single multimode fiber (MMF), it maps discrete fundamental-mode inputs at the entrance to orthogonal spatial-mode superpositions at the output. First proposed by Leon-Saval et al. in 2005,⁶ photonic lanterns have since evolved rapidly, spawning diverse structures—from three-dimensional integrated and multi-core fused-taper types to single-mode fiber bundle sleeve-taper configurations—and expanding into fiber amplifiers, free-space optical communication, wavefront sensing, and vortex beam generation.

Depending on their mode conversion characteristics, photonic lanterns fall into two categories. Non-mode-selective (conventional PL) lanterns employ identical input fibers, enabling arbitrary target-mode synthesis through amplitude and phase control, making them ideal for adaptive mode control. Montoya et al. first applied a 3 × 1 lantern to a high-power fiber laser, raising the mode instability threshold of a 25 μm core fiber to over 1.2 kW.⁷ Lu et al. subsequently built an adaptive spatial mode control system generating high-power fundamental-mode and vortex beams in a 50 μm core fiber.⁸ Mode-selective (MSPL) lanterns use input fibers with different core diameters or refractive indices, so each input port naturally maps to a specific higher-order output mode. Velázquez-Benítez et al. demonstrated multiplexing and demultiplexing of five LP mode groups using a 15-core MSPL,⁹ while Eznaveh et al. achieved selective excitation of orbital angular momentum modes with a 5-core lantern.¹⁰

Despite these advances, practical engineering faces two major challenges. First, rapid and accurate transmission-characteristic calculation remains difficult: conventional beam propagation method (BPM) simulations require approximately 1 h per run, precluding batch optimization and real-time control. Second, high-precision fabrication demands extremely tight process control—bundling symmetry, collapse uniformity, and splicing alignment critically affect performance and yield.

To address these challenges, this paper presents a systematic study spanning the full chain of “transmission characteristics-fabrication process-performance testing” for photonic lanterns. We employ BPM and mode expansion propagation method (MEPM) to elucidate the physical mechanisms of mode evolution and introduce neural network modeling to achieve high-precision, rapid prediction of transmission characteristics—accelerating computation by five orders of magnitude. For fabrication, we adopt capillary-sleeve tapering of single-mode fiber bundles, systematically analyzing how cleanliness control, bundling techniques, tapering parameters, and splicing alignment influence device performance. Efficiency and mode-field characterization tests on a fabricated lantern series validate the design criteria and simulation results, reveal the high-power thermal effect mechanism, and confirm the device’s application potential in mode control systems.

Results

Light field transmission characteristics in photonic lanterns

The core structure of a photonic lantern is a tapered waveguide where a bundle of multiple single-mode fibers smoothly transitions into a single multimode fiber, as shown in Figure 1. This transition region (taper region) has a longitudinally non-uniform refractive index distribution and belongs to a typical non-uniform waveguide. According to optical waveguide theory, there is no strict mode eigen-solution for non-uniform waveguides, i.e., no analytical solution in the form of e(x,y)e^-iβz.

Figure 1.

3D schematic of photonic lantern

(A) 3 × 1 mode-selective photonic lantern.

(B) 6 × 1 non-mode-selective photonic lantern.

However, in this case, we can find a certain uniform waveguide such that the field inside the non-uniform waveguide can be expanded into a sum of a series of modes of this uniform waveguide. This decomposition includes not only the discrete sum of guided modes but also the continuous sum of radiation modes (where radiation modes are the radial standing wave distribution formed by the superposition of incident and reflected light outside the core). At this time, the total power of light transmitted in the waveguide remains unchanged, but the power of each mode changes, a conversion called mode coupling.¹¹ The focus of studying the mode evolution process of photonic lanterns is the calculation of eigenmodes including guided modes and radiation modes, and the calculation of mode superposition and coupling between them.

The BPM is one of the most popular methods in the research and design of optical waveguide devices, often used to calculate waveguide modes, dispersion, birefringence, transmission loss, and helps analyze transmission, connection, and coupling characteristics in waveguides. In 1978, Fleck et al. proposed using the fast Fourier transform (FFT) to implement BPM calculation,¹² starting from the scalar wave equation and using the concept of equivalent lenses to determine the reference refractive index. Its basic idea is a recursive algorithm, i.e., calculating the optical field distribution at the z+Δz section continuously through the known optical field distribution at the Z section. This paper selects the Rsoft-BeamPROP software based on the FFT-BPM algorithm to numerically calculate the mode evolution process in the photonic lantern. Taking a 5 × 1 non-mode-selective photonic lantern (input: 5 single-mode fibers with 10/70 μm, NA = 0.08; taper length: 1.5 cm; output: multimode fiber with 30/130 μm, NA = 0.065) as an example, evolution process has been showed in our previous work.¹³ The beam evolves from five discrete single-mode fiber guided modes (fundamental modes) in the single-mode fiber bundle, enters the taper region to form a supermode morphology, and finally becomes a multimode fiber guided mode morphology (fundamental mode with larger mode field) after passing through the waist region and the multimode fiber region. By using the BPM method, the optical field distribution of any input optical field after passing through the photonic lantern and the numerical calculation results of the entire mode evolution process can be obtained. However, the disadvantages of this algorithm are mainly two points: first, the calculation error will accumulate continuously with the increase of calculation distance; second, the calculation efficiency is low. Even if the waveguide structure is fixed, for different input initial optical fields, separate and time-consuming calculations are required each time (calculating one transmission takes 1.5–2 h under the premise of ensuring accuracy).

Through numerical calculation of the mode evolution process of the N × 1 photonic lantern, it is found that there is a one-to-one correspondence between the input optical field and the output optical field of the photonic lantern. With the help of the transmission matrix idea, the relationship between the input and output optical fields of the photonic lantern is compactly expressed as:

$$u=M·v$$ (Equation 1)

where M is the transmission matrix of the photonic lantern, v is a column vector describing the optical field information at the single-mode end of the photonic lantern, $v^T=\left[v_1{e}^{j{\theta }_1},v_2{e}^{j{\theta }_2},v_3{e}^{j{\theta }_3}\right]$ (where v_i,θ_i represent the amplitude and phase of the fundamental mode optical field input from the i-th single-mode fiber, respectively), and u is a column vector describing the optical field information at the multimode end of the photonic lantern, $u^T=\left[u_1{e}^{j{\phi }_1},u_2{e}^{j{\phi }_2},u_3{e}^{j{\phi }_3}\right]$ (where u_i,φ_i represent the amplitude and phase of the i-th eigenmode in the output superposition field, respectively).

This paper selects the mode expansion propagation method (MEPM)¹⁴ to calculate the transmission matrix of the photonic lantern. The MEPM is an efficient algorithm for calculating the transmission characteristics of special optical waveguides. Its calculation principle is: divide the entire waveguide into several sections, treat each section as a uniform waveguide, and use Maxwell’s equations to solve the eigenmodes of this section of the waveguide, generally including several guided modes and infinite radiation modes. Since an infinite number of radiation modes cannot be processed, the discretization of radiation modes is achieved by adding a reflection boundary to the waveguide. Under the assumption of monochromatic harmonic waves, the mode field distributions of the above guided modes and radiation modes all follow the form:

$$\psi \left(x,y\right)e^{i{\beta }_{i}z}$$ (Equation 2)

These guided modes and radiation modes together form a complete basis, that is, any solution of Maxwell’s equations in this waveguide region can be expressed by linear superposition of forward and backward eigenmodes:

$$\psi \left(x,y,z\right)=\sum _{i=1}^N\left(C_i^f{\psi }_i\left(x,y\right)e^{i{\beta }_{i}z}+C_i^b{\psi }_i\left(x,y\right)e^{-i{\beta }_{i}z}\right)\text{,}$$ (Equation 3)

where (C^f,C^b) are the forward and backward field coefficients, respectively. When N (the number of eigenmodes) is large enough, the above representation is accurate enough, and once the eigenmodes are determined, the field is completely determined by the field coefficients (C^f,C^b). The field coefficients are determined by the joint scattering matrix M_J of two adjacent sections. Let the field coefficients of the previous section be (l^f,l^b) and the field coefficients of the latter section be (r^f,r^b), then they satisfy the equation:

$$\left(\begin{array}{l}{l}^b\\ r^f\end{array}\right)=M_J\left(\begin{array}{l}{l}^f\\ r^b\end{array}\right)$$ (Equation 4)

The joint scattering matrix M_J is composed of mode overlap integrals between the eigenmodes of the front and rear sections. Methods for calculating these overlap integrals include: complete overlap method, normal Fresnel overlap method, and oblique Fresnel overlap methods.

Since the eigenmodes are orthogonal, the joint scattering is a diagonal matrix. And when the joint scattering matrix between each section is calculated, the total transmission matrix M of the entire waveguide (total L sections) can be quickly obtained using matrix multiplication:

$$M=\prod _{l=1}^{L-1}{M}_{J,l}\text{.}$$ (Equation 5)

Compared with BPM, the mode expansion algorithm has several obvious advantages: it can obtain both forward and backward transmission matrices simultaneously; the calculation between each section is independent, and the error does not accumulate with the transmission distance; the calculation accuracy depends on the number of radiation modes participating in the calculation.

Taking a 3 × 1 mode-selective photonic lantern (as shown in Figure 1A one 15/90 μm and two 10/90 μm SMFs with NA = 0.08; taper length: 2 cm; a 20/130 μm MMF with NA = 0.065) as an example, the process of numerically calculating the transmission characteristics of the optical waveguide using the PhotonDesign-FIMMPROP software based on the mode expansion propagation method is implemented. The calculation results include the following parts: (1) field distribution information, including the electromagnetic field distribution (E_x,E_y,E_z,H_x,H_y,H_z, intensity) of each direction section (XY, XZ, and YZ), as shown in Figure 2 for the E_x distribution and intensity distribution in the entire waveguide after inputting the fundamental mode from the 15 μm core diameter; (2) loss situation, which can calculate the loss of each eigenmode with transmission distance under different input optical field conditions; (3) the transmission matrix of the entire waveguide, including the forward transmission matrix and backward transmission matrix. Equation 6 gives the forward transmission matrix of this example:

$$M_{\text{LP},3\times 1\text{MSPL}}=\left[\begin{array}{ccc}0.971& 0& 0\\ 0& 0.007e^{i\left(0.702\pi \right)}& 0.918e^{i\left(0.702\pi \right)}\\ 0& 0.922e^{i\left(-1.145\pi \right)}& 0.007e^{i\left(-0.542\pi \right)}\end{array}\right]$$ (Equation 6)

Figure 2.

E_x and intensity distribution in a 3 × 1 mode-selective photonic lantern

The length of the taper region is scanned to find the variation of power loss and mode loss with taper length. Figure 3 shows the variation curve of total power and power of eigenmode 1 with taper length in this example. After the taper length exceeds 17,000 μm, the loss is small. This result provides a reliable reference for the structural design of photonic lanterns.

Figure 3.

Variation of total transmitted power and power of eigenmode 1 with taper length for 3 × 1 mode-selective photonic lantern

Mode expansion propagation method can not only calculate the vector optical field transmission results but also set scanning-related structural parameters to provide references for waveguide structure design and parameter selection. In addition, its calculation efficiency is also very impressive (calculating a photonic lantern structure takes about 10 min under the premise of ensuring accuracy), and there is no need to repeat calculations for optical waveguides with the same structure to obtain the transmission of different input optical fields (each input of a different optical field only requires a matrix multiplication operation). Although the mode expansion algorithm significantly improves the calculation efficiency, the accuracy of its calculation of transmission characteristics depends on the accuracy of mastering structural parameters. For photonic lanterns as non-standard optical waveguides, due to the extremely slow variation of their transverse cross-sectional dimensions with the longitudinal direction, the structural parameter errors caused by fabrication cannot be ignored. Therefore, the mode expansion propagation method is also difficult to accurately calibrate the physical photonic lantern.

Although the mode expansion method significantly improves the calculation efficiency of photonic lantern transmission characteristics, its solution process still relies on precise numerical simulation of the waveguide structure. In recent years, neural networks have shown great potential in the field of photonic device modeling. Research by Sweeney et al. shows that a trained neural network can model the transmission characteristics of the photonic lanterns.¹⁵ A neural network is a computational model that simulates the connection method of human brain neurons. It approximates complex functions by constructing multi-layer nonlinear transformations. Its core lies in introducing nonlinear activation functions to convert linear combinations into nonlinear mappings. The universal approximation theorem points out that as long as the hidden layer is wide enough, the structure can approximate any continuous function on a compact domain with arbitrary precision, which lays a theoretical foundation for neural networks to handle nonlinear regression problems.

From a mathematical perspective, the transmission process of a photonic lantern can be represented as a nonlinear operator T, mapping the input optical field I_in to the output optical field I_out:

$$I_{\text{out}}=T\left(I_{\text{in}},\mathrm{\lambda }\right)$$ (Equation 7)

where λ represents relevant parameters such as wavelength. With its nonlinear mapping capability, the neural network can learn the approximate representation of this operator. Through multi-layer nonlinear transformations, it can approximate any continuous function, providing a mathematical guarantee for accurate modeling of the transmission characteristics of photonic lanterns.

From a physical essence perspective, the transmission process of the photonic lantern follows Maxwell’s equations and has a deterministic input-output mapping relationship. For given input optical field parameters, there is a unique output optical field distribution. This deterministic nonlinear mapping characteristic makes the photonic lantern very suitable for modeling using supervised learning.

This paper constructs a dropout network for modeling the transmission characteristics of photonic lanterns. The network input is the amplitude and phase of each input light, and the output is the complex coefficient of each eigenmode of the optical field at the output end. The network structure contains multiple hidden layers, with 2,000 neurons per layer, and the activation function uses LeakyReLU to alleviate the gradient disappearance problem. To prevent overfitting and improve generalization ability, dropout regularization technology is adopted, and the hyperparameter is set to 0.2, that is, the probability of each neuron being randomly discarded in each training iteration is 20‰.

During the training process, the network learning is driven by minimizing the loss function. For regression tasks, the loss function uses mean square error (MSE):

$$L\left(\theta \right)=\frac{1}{N}\sum _{i=1}^N{\parallel {\mathit{y}}_i-{\hat{\mathit{y}}}_i\parallel }^2$$ (Equation 8)

where y_i is the true output of the i-th sample (obtained by BPM simulation or experimental measurement), $\widehat{y_i}$ is the network prediction output, and θ is the network trainable parameter. The Adam optimizer is used for gradient descent optimization, and the parameter update rule is:

$${\theta }^{\left(t+1\right)}={\theta }^{\left(t\right)}-\eta {\nabla }_{\theta }L\left({\theta }^{\left(t\right)}\right)$$ (Equation 9)

where η is the learning rate. The calculation of the gradient relies on the backpropagation algorithm, which efficiently calculates the gradient by backpropagating the output error layer by layer to each parameter through the chain rule.¹⁶

A learning rate decay strategy is adopted to dynamically control the training process: the system continuously monitors the validation set loss. When its improvement magnitude is lower than 10^–6 in consecutive 1,000 rounds, the learning rate is decayed to 50% of the current one, and 5 × 10⁻⁷ is set as the lower limit of the learning rate. The batch size is set to 64, and the number of training rounds (epoch) is 25,000 rounds.

The training dataset contains 1,500 sets of original input and output optical field pairs of the 6 × 1 photonic lantern (as shown in Figure 1B: six 10/90 μm and SMFs with NA = 0.08 and a fiber without a core in the center; taper length: 2 cm; a 30/130 μm MMF with NA = 0.065), and 6,000 sets of training data are obtained after 4 times expansion using data augmentation technology. This 4-fold increase is determined by the phase symmetry of the photonic lantern structure designed in this paper and the six input fundamental modes. The test set consists of 300 sets of original optical field data not involved in training, which are generated by the same photonic lantern structure but using different combinations of random input light fields (different amplitude/phase distributions between the input ports). Figure 4 shows the training process and results of the dropout network. It can be seen from the figure that the network tends to converge after 25,000 rounds of training, and the predicted value is highly correlated with the true value. It is important to emphasize that the current experiment was conducted using the photonic lantern with a fixed geometric structure. To achieve generalization across different geometric structures, larger and more diverse datasets will be required, which will be the focus of future research.

Figure 4.

Training process and results of the dropout network

(A) Intensity prediction scatterplot.

(B) Phase prediction scatterplot.

(C) Training loss (MSE) curve.

(D) Learning rate variation.

Table 1 summarizes the performance of dropout networks with different numbers of hidden layers. The results show that the minimum MSE of light intensity can reach 9.793 × 10⁻⁵ (normalized units), and R² reaches 0.9973; the minimum MSE of phase can reach 3.772 × 10⁻³, and R² reaches 0.9551. The network architecture with three hidden layers (2,000 neurons/layer) achieves the best balance between accuracy and complexity.

Table 1.

Performance summary of the ideal photonic lantern transmission characteristic neural network based on dropout

Layers	Hidden Layer size	Training examples	Intensity MSE (norm. units)	Intensity R2 (norm. units)	Phase MSE (norm. units)	Phase R2 (norm. units)
3	2,000	6,000 (1,500)	9.793 × 10−5	9.973 × 10−1	4.063 × 10−3	9.516 × 10−1
5	2,000	6,000 (1,500)	1.167 × 10−4	9.967 × 10−1	3.814 × 10−3	9.546 × 10−1
9	2,000	6,000 (1,500)	1.196 × 10−4	9.967 × 10−1	4.529 × 10−3	9.461 × 10−1
15	2,000	6,000 (1,500)	1.219 × 10−4	9.966 × 10−1	4.267 × 10−3	9.492 × 10−1
21	2,000	6,000 (1,500)	1.203 × 10−4	9.966 × 10−1	3.772 × 10−3	9.551 × 10−1
27	2,000	6,000 (1,500)	1.230 × 10−4	9.966 × 10−1	4.640 × 10−3	9.448 × 10−1

Experiments show that the size of the dataset has a significant positive correlation effect on the accuracy of the neural network: the larger the amount of data, the smaller the MSE, and the closer the coefficient of determination is to 1. If the amount of data is further increased, the model accuracy can continue to be improved on the premise of ensuring that no overfitting occurs. In terms of calculation efficiency, the trained neural network model can output prediction results at a speed of 60.2807 ms/sample (CPU model: 13th Gen Intel Core i7-13700H), which is an improvement of more than 5 orders of magnitude compared to traditional BPM simulation (1.5–2 h/sample), providing a technical path for efficient batch processing of optical field data.

During simulation, by collecting optical field data from the input and output ends of the photonic lantern and training a neural network, a neural network model of the photonic lantern’s transmission characteristics is obtained. To obtain the output light field of the photonic lantern under given input light field conditions, this model can be used to efficiently generate a high-precision output light field, enabling rapid prediction rather than performing time-consuming simulations from scratch. This process effectively enables batch optimization of the photonic lantern. However, to perform design optimization across multiple geometric structures, the model must be retrained using new data.

More importantly, the neural network model can be trained directly based on the experimentally measured photonic lantern input and output optical field dataset, providing a new solution path for solving the finished product screening and precise calibration of new non-uniform optical waveguides such as photonic lanterns.

Fabrication of tapered single-mode fiber bundles photonic lanterns

According to different fabrication methods and structural forms, photonic lanterns are mainly divided into three categories: 3D integrated type, tapered multi-core fiber (MCF) type, and tapered single-mode fiber bundle in capillary type.

The 3D integrated photonic lantern is an integrated optical waveguide fabricated using ultrafast laser inscription (ULI).¹⁷ This technology uses a microscope objective to focus ultrashort laser pulses onto a glass sample. Since the pulse is very short, the peak electric field at the focal point can be high enough to induce nonlinear absorption, thereby causing a change in the local refractive index of the corresponding part. Combined with a 3D movable platform to control sample displacement, a specific 3D refractive index distribution is finally achieved, forming a new 3D optical waveguide. Due to the neat appearance of the substrate material and easy fixation, and the ability to achieve the transition of a large number of single-mode cores and multimode cores in the same substrate, this structure of photonic lantern has good applications in fields such as optical imaging. However, a serious shortcoming of integrated photonic lanterns is the relatively low efficiency, which is due to the continuous change in the core size of the required single-mode fiber bundle (non-uniform refractive index distribution), causing scattering and absorption during light transmission, which in turn brings non-negligible losses. Therefore, the key to realizing low-loss integrated photonic lanterns is to find a material with specific absorption, so that the waveguide has a high enough refractive index change with less scattering. To date, this remains an unsolved problem.

The emergence of tapered MCF photonic lanterns has extremely well met the demand for efficiency in practical applications.¹⁸ Its fabrication process involves confining the MCF in a fluorine-doped silica jacket, heating it with an oxy-butane flame or graphite resistance filament, and applying tension at both ends to gradually taper the MCF cladding structure until a tapered structure is formed. Such photonic lanterns are widely used in fields such as astronomical detection and spectroscopy. The tapered thin end (multimode end) is used to collect detection signals, while the untapered end (single-mode end) is etched with devices such as Bragg gratings to complete optical filtering and other functions. Such photonic lanterns have two non-negligible disadvantages: first, it is difficult to splice with common multimode fibers; second, its structure is relatively fixed, and the distance between the cores of the MCF is relatively close, making it difficult to couple light independently into one or several single-mode cores, let alone independently modulate the light in the single-mode cores.

In 2009, Noordegraaf et al. first proposed the tapered photonic lantern based on single-mode fiber bundles in capillaries.¹⁹ A group of separated single-mode fibers are closely arranged and inserted into a low refractive index glass capillary, and they are fused and tapered simultaneously. As the lateral dimension decreases, the cores in the single-mode fiber bundle approach each other and taper to form the core of the new waveguide structure, while the low-index glass capillary becomes the new cladding. Since the single-mode fibers at the single-mode end are separated, it is easy to achieve light field control at the single-mode end. In addition, the raw material for making such photonic lanterns is common step-index fiber, which ensures that it can adapt well to fiber systems such as fiber laser seed sources and amplification stages.

The fabrication of tapered photonic lanterns based on single-mode fiber bundles in capillaries mainly includes the following steps: material selection and pretreatment, single-mode fiber bundling, fused tapering, end face cleaving, and splicing. Due to the small cross-sectional size of the fiber and the reduced strength of the waveguide structure after fused tapering, the quality of process details has a great impact on the yield and performance of the photonic lantern. Vytran Glass Processor Workstation GPX3400 and Fujikura specialty fiber splicer FSM-100P+ are selected. Taking a 3 × 1 non-mode-selective photonic lantern as an example, the operation points and precautions in the fabrication process are introduced in detail.

Material selection and pretreatment

The raw materials for fabricating a 3 × 1 non-mode-selective photonic lantern include: about 1.5 m of multimode fiber with core/cladding diameter of 30/130 μm (NA = 0.06); three single-mode fibers with structural parameters of 10/130 μm (NA = 0.08), each 1.5 m long; and about 9 cm of low refractive index glass capillary with inner and outer diameters of 800 μm, and 1,500 μm, respectively.

Firstly, pretreat the single-mode fibers: strip the coating layer of length 4.5 cm from one end of the single-mode fiber, and wipe off the residual coating debris with alcohol. Immerse the stripped end in hydrofluoric acid solution for a period of time to etch the cladding until the cladding size decreases to meet the core-to-cladding ratio condition.²⁰

Secondly, pretreat the low refractive index glass capillary: in order for the single-mode fibers to be arranged tightly enough during “single-mode fiber bundling,” the glass tube with original dimensions of 800/1,500 μm needs to be pre-tapered so that its inner diameter is equal to or slightly larger than the diameter of the circumscribed circle of the three single-mode fiber bundles.

In addition, pretreat the output multimode fiber: strip about 3 cm of the coating layer from one end of the multimode fiber, wipe off the residual coating debris with alcohol, and cut its end face flat using a fiber cleaver for later use.

Single-mode fiber bundling and fused tapering

Insert the pretreated ends of the single-mode fiber bundle into the left end of the glass tube evenly and tightly in an equilateral triangle arrangement until the taper region at the left end of the glass tube just holds the unstripped cladding area of the fiber bundle. At this time, the entire waist region of the glass tube is filled with the single-mode fiber bundle and the fibers inside the glass tube are closely attached. Use a fiber operation platform to fuse and taper the glass capillary-single-mode fiber bundle (see Table 2 for tapering parameters). With the continuous discharge of the electrodes and the operation of the moving stretching platform, the three single-mode-fibers are fused tightly under the restriction of the glass capillary and scaled down to a size matching the output fiber.

Table 2.

Tapering parameters for glass capillary-single-mode fiber bundle

Parameter	Value	Parameter	Value
No. of electrodes	3	vacuum	3.20 PSIA
Initial tapering speed	80 μm/s	tapering time	217 s
Entry heat	725	waist heat	715
Entry size	400 μm	waist size	60 μm
Entry taper length	15,000 μm	waist length	10,000 μm
Exit heat	705	exit taper length	15,000 μm

Cleaving glass capillary-single-mode fiber bundle

Since the waist diameter of the tapered glass capillary-single-mode fiber bundle is relatively thin and its strength is significantly reduced after fused tapering, ordinary fiber cleavers cannot cleave it into a flat end face. Therefore, it is necessary to use the built-in cleaving function of the fiber operation platform (Vytran Glass Processor Workstation GPX3400) to cleave it. Select the center of the waist region as the cleaving point. The final cleaving angle and cross-section image of this example are shown in Figure 5.

Figure 5.

Micrographs of the waist area after cleaving

(A) Side view.

(B) Cross-sectional view.

Splicing

Since the two ends to be spliced are the glass capillary-single-mode fiber bundle and the multimode fiber respectively, and their splicing end face cladding sizes and strength properties are different, ordinary fiber splicers cannot meet the requirements. Therefore, Fujikura FSM-100P+ fusion splicer, which is capable of dissimilar fiber splicing with adjustable arc power and alignment sensitivity, is selected. Before splicing, special arc calibration is performed to determine the appropriate discharge position, set suitable splicing parameters (see Table 3), and splicing is performed after precise alignment. Based on our measurements, lateral misalignment beyond ±0.5 μm causes >0.65 dB excess loss, and angular tilt beyond ±0.3 degrades mode purity by > 3 dB.

Table 3.

Key splicing parameters for glass capillary-single-mode fiber bundle and multimode fiber

Parameter	Value	Parameter	Value
Main fusion power	standard-5 bit	main fusion time	3,800 ms
Prefuse power	standard-55 bit	prefuse time	20 ms
Push distance	32 μm	cleave limit	1.0

At this point, the fabrication process of the photonic lantern is basically completed. For convenient storage and use, the drawn photonic lantern is packaged with a custom fixture. The physical images of the finished photonic lantern before and after packaging are shown in Figure 6.

Figure 6.

Physical image of the finished photonic lantern before and after packaging

Key process details and analysis

In the process of fabricating photonic lanterns, the requirements for process details are extremely high. Here are several main process details and analysis of their impact.

• (1)Cleanliness: the cleanliness of fibers and glass tubes is very important throughout the process. Any stain or liquid residue will cause severe combustion during the fused tapering and splicing stages, resulting in a decrease in yield. Residual tiny dirty spots will also become the biggest factor introducing loss in the finished photonic lantern. In our fabrication practice, based on 60 independent tapering attempts under controlled cleanliness levels, the fabrication yield (defined as the percentage of devices with < 0.5 dB insertion loss and no visible fracture after tapering) decreased from ∼85% under standard cleanroom cleaning to ∼35% when minor contamination was intentionally introduced, and to below 10% under poor drying conditions. The combustion manifests as localized burning spots observed under the splicer microscope, which act as scattering centers and cause catastrophic failure. Therefore, critical steps including fiber stripping, cleaning, drying, and splicing are recommended to be carried out in a class 1,000 cleanroom, and the tapering step in a laminar-flow hood. In our experiments, particles > 5 μm deposited on the taper waist were observed to cause localized absorption and thermal runaway at powers > 2 W, significantly reducing device reliability.
• (2)Bundling technique: the uniform arrangement of the single-mode fiber bundle will greatly affect the mode transmission characteristics of the photonic lantern, and even cause it to lose its original mode evolution capability. Figure 7 shows a comparison of failed and successful bundling of photonic lanterns with different numbers of channels. According to the design rules of photonic lanterns, single-mode fibers have lower losses and better mode evolution performance when arranged in regular polygons.²⁰ To avoid bundling failure, there are two main bundling techniques: (1) strictly control the pre-tapered inner diameter of the glass capillary to help the fiber bundle arrange tightly and uniformly and (2) customize special molds to help achieve specific geometric arrangements. In particular, for photonic lanterns with large gaps in the middle, a coreless fiber can be used to fill the central area first, and then the coreless fiber can be extracted before tapering to ensure that the fiber bundle is arranged in a regular polygon.
• (3)Selection of fused tapering parameters: the heat intensity and tapering speed of fused tapering will affect the collapse effect, that is, changing the size of the air holes between single-mode fibers or determining whether the size of the glass capillary and the fiber bundle decreases proportionally. Actual tests have found that the size of the air holes between single-mode fiber bundles has little effect on the mode evolution performance of the photonic lantern, but the uniformity of their distribution seriously affects the mode transmission properties of the photonic lantern. We conducted tapering experiments with controlled variations in heat intensity and pulling speed to obtain residual air-hole diameters ranging from ∼1 to ∼5 μm. For devices with symmetric air-hole distribution, the insertion loss varied by < 0.2 dB and mode purity by < 0.5 dB across this range. In contrast, asymmetry in air-hole distribution—rather than absolute hole size—was found to be the dominant factor, introducing > 1 dB loss and > 3 dB mode purity degradation. In addition, whether the glass capillary and fiber bundle decrease proportionally can determine the success rate of the splicing step, so it is very important to select appropriate fused tapering parameters. Based on cross-sectional microscopy of more than 40 splicing attempts, we define “proportional decrease” as the condition where the outer diameter of the tapered capillary is 1.8–2.2 times the circumscribed circle diameter of the fiber bundle at the cleaving plane. Within this range, the splicing success rate (splice loss < 0.3 dB and tensile strength > 1.5 N) reaches ∼90%; outside this range (ratio < 1.5 or > 2.5), the success rate drops to below 50%. Figure 8 presents four typical collapse conditions formed. Figure 8A: over-collapsed—capillary and bundle shrink non-uniformly, causing splicing failure. Figure 8B: excessive heat—glass capillary collapses too much, fiber bundle is distorted. Figure 8C (optimal): central air hole nearly collapsed, three surrounding air holes uniformly distributed, capillary diameter ≈2× bundle circumscribed circle diameter. This ensures uniform mode coupling and high splicing success rate. Figure 8D: insufficient heat—air holes remain large and irregular. The third configuration (as shown in Figure 8C) achieves the best balance: the central air hole is nearly eliminated, the three surrounding air holes are uniformly distributed (ensuring symmetric mode coupling), and the capillary diameter remains approximately twice the circumscribed circle diameter of the fiber bundle (ensuring high splicing yield).
• (4)Alignment of splicing: theoretically, the degree of misalignment in splicing between the glass capillary-single-mode fiber bundle and the multimode fiber will cause the correlation between the mode evolution result of the photonic lantern and the ideal result to decrease exponentially. Experimentally, the function of measuring the morphology and loss near the fusion point in the splicer can be used to initially screen for misalignment splicing. The screening is performed using the built-in side-view imaging system of the Fujikura FSM-100P+ splicer during the pre-fusion alignment phase. The system captures orthogonal side-view images and calculates lateral offset and angular tilt. Based on correlation analysis of 50 splicing trials, we established rejection thresholds: lateral offset > 0.5 μm or angular tilt > 0.3 were found to correlate with > 0.65 dB excess loss and > 3 dB mode purity degradation. Only splices meeting these criteria are accepted for further testing.

Figure 7.

Comparison of failed and successful bundling of photonic lanterns

Figure 8.

Collapse conditions formed under different tapering parameters

Efficiency testing of photonic lanterns

A 1,064 nm single-frequency fiber laser is used as the signal source. After being divided into equal parts by a beam splitter, the input power of each channel is first tested, and then they are spliced to the input arms of the photonic lantern, respectively. The output power after transmission through the photonic lantern is tested under single-arm input or multi-arm input conditions with micro-channel water cooling, water temperature maintained at 20°C ± 1°C. Taking the 3 × 1 non-mode-selective photonic lantern drawn in the previous section as an example, the test results of its light transmission are shown in Table 4. When the single-channel input power is below 1.5 W, the efficiency is maintained above 98%. However, when the single-channel input power exceeds 1.5 W, the loss increases significantly with the increase of power, and the efficiency decreases significantly. When the single-channel input is 3 W, the efficiency drops to about 62%. The variation trend is shown in Figure 9. Tests show that the efficiency of finished photonic lanterns drawn according to the process flow in the previous section conforms to this law. The observed nonlinear efficiency degradation at high power is attributed to thermal effects in the fused taper (waist) region. This effect is reversible: efficiency recovers when input power is reduced. No permanent damage to the lantern was observed at the tested power levels (≤ 5 W under water cooling).

Table 4.

Efficiency test data of 3 × 1 non-mode-selective photonic lantern

Single input power/W	Output power/W arm 1	Output power/W arm 2	Output power/W arm 3
0.38	0.37	0.38	0.37
0.63	0.59	0.62	0.58
0.81	0.78	0.78	0.81
1.00	0.99	1.00	0.99
1.22	1.20	1.16	1.19
1.41	1.39	1.39	1.34
1.91	1.70	1.71	1.64
2.50	2.00	2.05	1.93
3.00	2.25	2.31	2.19
4.00	2.80	2.88	2.76
5.00	3.14	3.20	3.09

Figure 9.

Single-arm efficiency test of photonic lantern

Mode field characteristic testing of non-mode-selective photonic lanterns

Mode field characteristic testing is performed on non-mode-selective photonic lanterns with the same input fiber core diameter. The schematic diagram of the test optical path is shown in Figure 10, where the seed source is a 1,064 nm single-frequency single-mode fiber laser. The beam splitter is used to divide the input beam equally and connect it to the arm under test of the photonic lantern by fusion splicing. The output fiber of the photonic lantern is angle-cleaved (flat). The external optical path consists of a 4F system composed of two lenses, allowing the beam profiler to measure the magnified near-field spot.

Figure 10.

Schematic diagram of photonic lantern mode field characteristic test optical path

Figure 11 shows the test results of the 3 × 1 non-mode-selective photonic lantern with single-arm input. A single-mode laser is injected into arms 1–3 shown in Figure 11A, respectively. The near-field spot obtained at the pigtail end is the superposition morphology of the LP₀₁ mode and the LP₁₁ mode in three different directions, as shown in Figures 11B–11D. This measured result is basically consistent with the numerical calculation result in section 2.2.3. The mode overlap integrals between the measured near-field intensity distributions and the simulated distributions all exceed 0.965. Single-arm tests were performed on 5 × 1, (5 + 1) × 1, and 7 × 1 non-mode-selective photonic lanterns using this method, and the obtained output results were also basically consistent with the numerical calculation results (overlap integrals exceed 0.934).

Figure 11.

Measured output optical field of 3 × 1 non-mode-selective photonic lantern with single-arm input

Next, the multi-arm input case is tested. When the beam splitter output fibers are spliced to multiple input fibers of the photonic lantern respectively, the spot morphology obtained at the output end of the photonic lantern changes continuously, and energy is converted between modes, with a transformation frequency within 100 Hz. This is because affected by environmental disturbances, the phase difference between the input optical fields of the photonic lantern changes continuously with time, making the final mode evolution result change continuously. Figure 12 shows the variation of the output spot morphology with time when the three arms of the 3 × 1 non-mode-selective photonic lantern are input simultaneously. This test result experimentally proves that if one wants to use a non-mode-selective photonic lantern to achieve beam mode control, it must be placed in an adaptive control system, and phase locking must be achieved through a control algorithm to finally stabilize the output spot on the target mode.

Figure 12.

Variation of output spot pattern with time for 3 × 1 non-mode-selective photonic lantern with three arms input simultaneously

Mode field characteristic testing of mode-selective photonic lanterns

The single-arm test results of mode-selective photonic lanterns are different from those of non-mode-selective photonic lanterns. Since the core diameters of their input single-mode fibers are different, the output modes obtained by inputting single-mode optical fields to different arms are also different.

Figure 13 shows the single-arm test situation of the 3 × 1 mode-selective photonic lantern. When the fundamental mode optical field is injected from the number 1 arm with a core diameter of 15 μm, a fundamental mode with a larger mode field area is obtained at the output end with a core diameter of 30 μm; when the fundamental mode optical field is injected from the number 2 arm with a core diameter of 10 μm, a LP_11o-like mode is obtained at the output end; when the fundamental mode optical field is injected from the number 3 arm with a core diameter of 10 μm, a LP_11e-like mode is obtained at the output end. This test result is consistent with the numerical simulation result, proving the mode selection capability of this type of photonic lantern.

Figure 13.

Single-arm input mode field test of 3 × 1 mode-selective photonic lantern

Using correlation filter method mode decomposition,²¹ we decomposed the output beam obtained from single-arm input. Because the output MMF of this photonic lantern supports first six LP modes (LP₀₁, LP_11o, LP_11e, LP_21o, LP_21e, and LP₀₂ mode), the decomposition was performed using these 6 modes as a basis, yielding a crosstalk matrix with quantitative crosstalk values in dB, given in Equation 10:

$$\text{Crosstalk}\left(\text{dB}\right)=\left[\begin{array}{ccc}-0.24& -27.0& -21.3\\ -5.9& -1.04& -16.8\\ -12.6& -12.1& 0.74\end{array}\right]$$ (Equation 10)

For the output beam obtained from arm 1 input, the fundamental mode purity reaches 94.6% (−0.24 dB), and the main crosstalk is into LP₀₂ mode with a crosstalk level of −13.4 dB. For the output beam obtained from arm 2 input, the LP_11o mode purity is 78.6% (−1.04 dB), with a crosstalk of −5.9 dB to LP₀₁ and –16.8 dB to LP_11e. For the output beam obtained from arm 3 input, the LP_11e mode purity is 84.3% (−0.74 dB), with crosstalk levels of −12.6 and −12.1 dB to LP₀₁ and LP_11o, respectively.

Figure 14 shows the single-arm test results of the (5 + 1) × 1 mode-selective photonic lantern. Analyzing the mode selection capability of the 6 arms at the input end to achieve the first 6 LP modes at the output end respectively, it is found that when the number 1 arm with 15 μm core diameter transmits light, the obtained LP₀₁-like mode has a small amount of LP₀₂ mode component; when the number 2 and 3 arms with 10 μm core diameter transmit light, the obtained LP₁₁-like mode contains a part of LP₂₁ mode; when the number 4 and 5 arms with 8 μm core diameter transmit light, the light intensity distribution of the four lobes of the obtained LP₂₁-like mode is not perfectly uniform; when the nmuber 6 arm with 6 μm core diameter transmits light, the obtained LP₀₂-like mode contains a small amount of LP₀₁ mode. In this case, the fundamental mode purity of the output beam obtained from arm 1 input is 71.01% (−1.49 dB), and the main crosstalk is into LP₀₂ mode. It can be seen that although the (5 + 1) × 1 photonic lantern has a certain mode selection capability, there is indeed some mode crosstalk in the actual testing and application of the finished product.

Figure 14.

Single-arm input mode field test of (5 + 1) × 1 mode-selective photonic lantern

Discussion

This paper has carried out a systematic study on the transmission characteristics, fabrication process, and performance testing of photonic lanterns. A complete analysis framework covering the beam propagation method, mode expansion propagation method, and neural network modeling has been established. Among them, neural network modeling has achieved high-precision and fast prediction of transmission characteristics, increasing the calculation speed by more than 5 orders of magnitude, with light intensity prediction MSE reaching 9.793 × 10⁻⁵ and phase prediction MSE reaching 3.772 × 10⁻³. A high-precision fabrication process system for tapered photonic lanterns based on single-mode fiber bundles in capillaries has been established, detailing the full-process technology of material pretreatment, bundle arrangement, tapering parameter optimization, precision cleaving, and dissimilar splicing. The influence mechanisms of key process details such as cleanliness control, bundling symmetry, collapse uniformity, and splicing alignment were systematically analyzed. Comprehensive performance characterization was conducted on the fabricated photonic lanterns. Efficiency tests showed that the transmission efficiency exceeded 98% at low power, revealed the thermal effect mechanism at high power, and supported 5 W single-arm input under water-cooled conditions. Mode field characteristic tests verified the mode evolution laws of non-mode-selective and mode-selective photonic lanterns, and the experimental results matched well with the numerical simulations.

In the future, aiming at the efficiency degradation problem of the current fabrication process under high-power conditions, it is suggested to further optimize the heat dissipation structure. One effective strategy is to use double-clad structured fibers as input to reduce the expansion ratio of the mode field diameter in the taper region, thereby shortening the required adiabatic length and reducing loss. Another optimization direction is to introduce a photonic crystal structure to reduce the effective refractive index of the cladding. The latest patent from Changchun Institute of Optics,²² Fine Mechanics and Physics proposes periodically arranging capillaries around the single-mode fiber bundle to form a photonic crystal structure after tapering, which can further avoid light leakage during the beam combining process, reduce transmission loss, and improve laser coherent beam combining efficiency.

Limitations of the study

The neural network model and fabrication process have been validated under specific laboratory conditions; their generalizability to other device geometries, material systems, or large-scale manufacturing environments requires further investigation.

Resource availability

Lead contact

Requests for further information and resources should be directed to and will be fulfilled by the lead contact, Yao Lu (lybenben1@163.com).

Materials availability

This study did not generate new unique reagents.

Data and code availability

• •Data reported in this paper will be shared by the lead contact upon request.
• •Code reported in this paper will be shared by the lead contact upon request.
• •Any additional information required to reanalyze the data reported in this paper are available from the lead contact upon request.

Acknowledgments

National Natural Science Foundation of China (62405378); National Key Laboratory of Space Target Awareness (STA2025ZCA0404).

Author contributions

Conceptualization, Y.L. and Z.J.; methodology, Y.L. and Z.C.; software, Z.S. and X.L.; validation, Y.L., Z.C., and T.L.; resources, Z.S., X.L., Y.L., and Z.C.; writing – original draft preparation, Y.L.; writing – review and editing, T.L. and Z.J.; visualization, Y.L., Z.S., and X.L. All authors have read and agreed to the published version of the manuscript.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Software and algorithms
Python 3	Python Software Foundation	RRID:SCR_008394
BeamGage	Ophir-Spiricon (MKS Instruments)	https://www.ophiropt.com/photonics

Experimental model and study participant details

This study does not involve any animal models, human participants, cell lines, microbial strains, or plant materials.

Method details

The fabrication process of the photonic lanterns, the optical characterization setup, and the numerical simulation procedures are described in detail in the sections “light field transmission characteristics in photonic lanterns” and “fabrication of tapered single-mode fiber bundles photonic lanterns”. Briefly, the photonic lanterns were fabricated by tapering single-mode fiber bundle in capillary type, with tapering parameters as listed in Table 2 and key splicing parameters as listed in Table 3. For full step-by-step process, please referred to the main text.

Quantification and statistical analysis

All data were processed using Python 3.

Additional resources

This study does not involve any additional resources such as protocol registries or external databases.