Air-Hole-Assisted Photonic Lanterns

Abstract

Exploring innovative approaches to enhance the performance of photonic lanterns is greatly valuable. In this paper, we first propose an air-hole-assisted pure silica-based capillary (AHC), featuring a single ring of embedded air holes. As a result, the PL based on the AHC exhibits good performance, successfully exciting LP₀₁, LP_11a & LP_11b, LP_21a & LP_21b, LP₀₂, and LP_31a & LP_21b modes. The average mode loss, mode-dependent loss, and maximum crosstalk are 0.08 dB, 0.04 dB, and −27.2 dB, respectively. In fact, the overall performance of the proposed AHC-based PL is on par with that of the traditional PL. Furthermore, an error analysis is provided to confirm the feasibility of our approach. The AHC-based PLs possess high numerical apertures and are expected to enable high spatial resolution imaging in optical imaging.

1. Introduction

Photonic lanterns (PLs) [1] play a key role in optical communication [2,3,4], astronomy [5], light detection and ranging (LiDAR) [6], micro-endoscopy [7], and spectroscopy [8]. The nonlinear Shannon limit has become a critical constraint for single-mode fiber (SMF) systems due to the escalating growing traffic demands. To overcome the intrinsic physical constraint, mode-division multiplexing utilizing few-mode fibers (FMFs) has gained traction among researchers and witnessed rapid development in the last few years [9,10]. Researchers have explored a few kinds of mode (de)multiplexers, such as PLs, multi-plane light converters (MPLCs) [11,12], mode selective couplers (MSCs) [13,14], and mode-selective converters using long-period fiber gratings [15]. Although MPLCs have demonstrated high mode selectivity, they exhibit relatively high insertion losses due to diffraction in free space, scattering on the phase plates inside, and mismatch with fibers. All-fiber mode converters are preferable due to their direct compatibility with transmission fibers. Typical all-fiber mode converters include PLs and MSCs. MSCs are realized by cascading several single-mode couplers, which can result in higher losses and reduced bandwidth. In contrast, PLs, characterized by a low insertion loss, a low mode-dependent loss (MDL), and wide bandwidth, are considered promising candidates for mode (de)multiplexers [1,16].

Generally, all-fiber PLs are fabricated using tapering techniques. A group of SMFs or FMFs is positioned into a fluorine-doped glass capillary tube with a low refractive index and subsequently tapered down [17,18,19]. Fluorine-doped capillaries (FDCs) with a high refractive index difference are necessary to ensure adiabatic evolution of light, especially when the number of mode channels increases. For the above-mentioned reasons, Neethu et al. have recently proposed and successfully fabricated PLs with outer capillary tubes that can be omitted [20,21,22]. Although FDCs were eliminated for the first time, simplifying the fabrication process, other challenges have arisen, such as how to deal with a tip with a diameter of tens of microns [23]. Exploring innovative approaches to enhance the performance of photonic lanterns is greatly valuable. In optical imaging, PLs possess high numerical apertures (NAs), enabling high spatial resolution imaging [7]. Silica-based fibers typically exhibit NAs below 0.4, while air–silica fibers can achieve NAs as high as 0.9 [24]. In fact, some progress has been made in the postprocessing technique for photonic crystal fibers (PCFs) in the past ten years [25,26]. Furthermore, PCF-type devices have been used to fabricate tapered mode converters [25,26,27]. Within these mode converters, the air hole arrays embedded in pure silica substrates serve as outer claddings, meaning that utilizing a pure silica-based tube with air holes as a capillary for PLs could be a feasible solution. The air-hole-assisted PL can be fabricated by pressurizing the nitrogen gas at the end of the PL during the tapering process [25].

In this paper, we propose a novel type of air-hole-embedded silica-based capillary (AHC) as an alternative to the FDC, featuring only one ring of air holes embedded inside. The PL based on the AHC exhibits excellent performance in terms of losses and crosstalks (XTs) after optimization, with LP₀₁, LP_11a & LP_11b, LP_21a & LP_21b, LP₀₂, and LP_31a & LP_{31 b} modes selectively excited. The performance of the AHC-based PL is comparable to that of the FDC-based PL. For the AHC-based PL, the average mode loss, MDL, and maximum XT are 0.08 dB, 0.04 dB, and −27.2 dB, respectively. Compared to the recently proposed eight-mode elliptical-core PL [28], the loss and XT of the air-hole-assisted PL can be even lower. Furthermore, an error analysis is provided to confirm the feasibility of the AHC-based PL.

2. Design Principle and Optimization Process

Generally, a PL is made up of a low refractive index capillary tube and a bundle of fibers, which are tapered together as a whole. Initially, light is guided in the fundamental mode within the core of each inserted fiber. As the tapering process progresses adiabatically, the core sizes of the fibers become too small to effectively guide the light. Simultaneously, the pitches between the cores are reduced to such an extent that the bundle of input fibers forms an equivalent core, while the capillary tube acts as the new cladding. In addition, supermodes emerge due to core-to-core coupling and subsequently evolve into the eigenmodes of the newly formed waveguide following further tapering. If the transition is sufficiently smooth to ensure adiabaticity, light initially in an input core would evolve into one of the output modes and vice versa. Here, the lowest refractive index in the outer region of the PL originates from the air holes in AHCs. We assume that the transverse scale of the PL’s refractive index distribution decreases in proportion to the taper ratio in simulation [1]. Based on the beam propagation method, the final parameters used for the PLs are determined through parameter scanning [29].

The AHC-based PL, as shown in Figure 1a, features an AHC with only one ring of 12 embedded air holes and a set of untapered input fibers. The cores (red region) have GeO₂-doped step-index (SI) profiles. Note that the fundamental modes in the input fibers, labeled with numbers 1, 2/3, 4/5, 6, and 7/8 in Figure 1b, would gradually evolve into LP₀₁, LP_11a & LP_11b, LP_21a & LP_21b, LP₀₂, and LP_31a & LP_31b modes, respectively. Figure 1c shows the front view of the capillary tube, where Λ and d are the air-hole pitch and air-hole diameter, respectively.

Through parametric scanning, the optimal SI input fiber diameters have been found to be 17 μm, 15 μm, 15 μm, 13 μm, 13 μm, 10 μm, 10 μm, and 8 μm. The cladding diameters (CDs) of all fibers are 52 μm, except for the 6th fiber, which has a CD of 68 μm. All input fibers are designed with a core refractive index of 1.449 and cladding index of 1.444 at 1550 nm. The modal losses and inter-mode XTs are quantitatively evaluated to assess the device performance. Here, XT_i-j represents mode coupling from the desired mode, i, to another mode, j (where i ≠ j). Then, we optimize the number, size, and positions of the air holes. We find good results when 12 air holes are used in a circular arrangement (CA), called PL Type I, with the parameters satisfying Λ = 91.1 µm and d = 66 µm. Additionally, a hexagonal arrangement (HA), as PL Type II, is also considered for comparison, where Λ = 91.3 µm and d = 66 µm, as shown in Figure 2a. Figure 2b illustrates the average mode losses and the maximum XTs as functions of d/Λ for these two arrangements, of which the air-hole pitch is 91.1 µm for PL Type I and 91.3 µm for PL Type II and the hole diameter is the variable. Both PL Type I and the PL Type II in Figure 2 have identical lengths of 12 cm. As we can see, the overall performance of PL Type I is significantly better than that of PL Type II. Specifically, for PL Type I, the average mode losses and the maximum XT values are within the ranges of 0.07–0.18 dB and −27.4–−26.6 dB, respectively, as d/Λ varies from 0.60 to 0.84. The best results, with a maximum XT of −23.5 dB and an average loss of 0.79 dB, are achieved at d/Λ = 0.72 for PL Type II. Furthermore, it is evident that PL Type I exhibits lower sensitivity to the air-filling ratio across a wide fluctuation range, while PL Type II is highly sensitive to it. These results indicate that PL Type I has a higher tolerance for fabrication errors in the air hole diameters. In contrast, the XT of PL Type II behaves non-monotonically with respect to d/Λ because the approximately circular guided modes are likely more suitable for transmission in CA structures. As a result, as the d/Λ further increases, the XT of PL Type I decreases, while the XT of PL Type II increases. Overall, PL Type I performs better. We also compared the performance of circular and square air-hole PLs. When setting the air-hole radius of the circular air hole and the side length of the square air hole to be equivalent (while keeping other parameters such as air-hole pitch the same), the average mode loss and maximum crosstalk are slightly different. Considering the fabrication feasibility, we only focus on the type with a circular air hole arranged in a circular pattern, i.e., PL Type I.

Then, we investigate the effect of the number of air holes on the performance of PL Type I. Also, we vary the hole size to determine the optimal configuration. Figure 2c compares the performance for 6, 12, 15, and 18 air holes, with 12 holes having the best results. The optimized Λ = 204.6 μm, 91.1 μm, 70.9 μm, and 51.6 μm, corresponding to the optimized air-hole diameter d = 160.6 μm, 66.0 μm, 49.5 μm, and 38.5 μm, respectively. As the number of holes varies from 12 to 18, the average mode losses and maximum XTs remain within 0.07–0.08 dB and −27.4–−27.1 dB, respectively. However, when the number of air holes is reduced to six, these values increase to 0.31 dB for the average mode loss and −26.9 dB for the maximum XT. This increase is attributed to the decreasing air-filling ratio in the capillary as the number of air holes decreases.

Then, we compare the proposed AHC with the traditional FDC, as illustrated in Figure 3a. The input fiber parameters for FDC-based PLs are the same as those for AHC-based PLs. Both the FDC and AHC have inner and outer diameters of 337.8 µm and 1.375 mm, while the FDC has a uniform refractive index of 1.435 at 1550 nm. The capillary is tapered down to an outer diameter of 125 μm to match a 1 cm-long FMF, which is connected to the output end of the PL. The 1 cm length of the FMF is sufficient for the simulation of PLs, and the parameters of this 1 cm-long FMF are described as follows: For the PL with an air-hole-embedded pure silica-based capillary, the 1 cm-long fiber has an air-hole-embedded silica-based structure with 12 air holes (8.3 μm air-hole pitch and 6-μm air-hole diameter); for the conventional PL with a fluorine-doped capillary, the 1 cm-long fiber has a silica-based fiber without air holes, with core/cladding diameters of 24/125 μm and refractive indices of 1.444/1.453 at 1550 nm. Note that both types of fibers connected at the end of the PL can achieve comparable performance.

We calculate the average mode losses, XTs, and MDLs of PL Type I and FDC-based PLs with different taper lengths, as shown in Figure 3b,c. As we can see, the average mode losses, XTs, and MDLs decrease with increasing taper length. At a length of 12 cm, the optimal PL Type I exhibits an average mode loss of 0.08 dB and a maximum XT of −27.2 dB, whereas the FDC-based PLs show values of 0.04 dB and −27.4 dB, respectively. When comparing AHC-based PLs to FDC-based PLs, the average mode losses and maximum XTs are comparable and low enough, with PL Type I being slightly higher by 0.04 dB and 0.2 dB, respectively. The MDL for PL Type I is 0.04 dB, which is lower than that for the FDC-based PL. These results indicate that PL Type I and FDC-based PLs have nearly equivalent performance. Additionally, the mode profiles are monitored at the output ends, proving that different modes are selectively excited, as shown in Figure 3d.

The spectral properties of the air-hole-assisted PL are presented in Figure 4. Over the 1530–1570 nm wavelength range, the average mode loss exhibits minimal variation of 0.02 dB, while XT fluctuation is confined to 0.2 dB, confirming excellent wavelength insensitivity.

3. Error Analysis

If the air holes (colored white) are rotated relative to the core arrangement with an angle of α, which are represented as solid circles in Figure 5a, the performance may vary. Since the input fibers are different, the effect of air hole rotation on the performance of PL Type I needs to be studied. Firstly, the range of α should be determined. Due to the geometric symmetry of the proposed PL Type I, considering α as the variation parameter, a range spanning a minimum period of 30° could be enough to represent all possible cases. As α increases from 0° to 30°, the fluctuations in average mode losses and maximum XTs are only 0.001 dB and 0.01 dB, respectively, which could be ignored, as shown in Figure 5b. Thus, the rotation of air holes relative to the core arrangement has a slight influence on the performance of PL Type I. In practical applications, attention can be focused solely on the relative positions of the input fibers rather than their absolute positions.

In addition, the schematic and results for the displacement of air holes from their optimal positions are presented in Figure 6, where ∆R denotes the radial displacement distance. For each air hole, ∆R is set within a range of ±3% of the air-hole diameter. The worst-case average mode loss and maximum XT are only 0.013 dB and 0.21 dB higher, respectively, compared to the pervious values.

Here, a 3% maximum parameter variation relative to theoretical designs is employed. We randomly generate 20 sets of parameters to examine the mode losses and XTs for PL Type I. As shown in Figure 7, the average mode losses vary from 0.07 to 0.08 dB, and the maximum XTs range from −26.9 to −27.4 dB. The variations for average mode losses and maximum XTs are minimal, i.e., 0.01 dB and 0.5 dB, respectively. The minor degradation in the performance of PL Type I is attributed to the high refractive index contrast between the fiber cladding and the air–silica capillary. These results indicate that the variations in the average mode loss and the maximum XT due to fabrication errors are relatively small and acceptable, thereby demonstrating the excellent and stable performance of the proposed PL Type I.

4. Conclusions

For the first time, we propose an AHC-based PL featuring a simple structure and excellent performance. The average mode loss, MDL, and maximum XT are 0.08 dB, 0.06 dB, and −27.2 dB, respectively. The AHC-based PLs demonstrate insensitivity to both wide fluctuations in air-filling ratio and the rotations of air holes relative to the core arrangement. Additionally, an error analysis was conducted to validate the feasibility of the proposed PLs. Furthermore, the overall performance of AHC-based PLs is comparable to that of traditional FDC-based PLs, indicating that our work introduces new PL structures, enhancing production diversity.