1. Introduction

Orbital angular momentum (OAM) beams, also known as optical vortices, have shown significant potential for increasing transmission capacity in high-capacity fiber communication systems [1,2]. However, the transmission of OAM modes over long distances in few-mode fibers (FMFs) presents a notable challenge due to the coupling of degenerate modes of the same order during transmission [3]. To overcome this issue, ring-core fiber (RCF) has been developed to support and transmit OAM modes, making it a promising medium for future high-capacity fiber communication systems [4]. In the systems, the high-efficiency and low-loss generation of OAM modes is an urgent problem to be solved. Currently, OAM modes are primarily generated using spatial devices such as spatial light modulators [5], phase plates [6], and Q-plates [7], which can achieve accurate and efficient excitation of OAM modes. Nevertheless, the coupling of these spatial devices to the fiber can be challenging, resulting in high insertion loss [2]. Therefore, all-fiber mode converters such as long-period fiber gratings (LPFGs) have unparalleled advantages in terms of loss and integration.

Currently, most all-fiber OAM mode converters rely on traditional few-mode fibers. Long-period fiber gratings have been employed to achieve first to fourth-order mode conversion in FMFs [8–11], and broadband mode generation up to the third-order has been achieved using various methods such as chirping, cascading, and dual-resonance coupling [12–16]. However, in few-mode fibers, the degenerate modes cannot be separated, and the generated OAM modes cannot be transmitted stably. Therefore, the generation of OAM modes in RCFs is essential, but there are some coupling challenges. Due to the structural differences between single-mode fibers (SMFs) and RCFs, mode mismatch may occur during the coupling process, leading to problems in both mode generation and manipulation. Several approaches have been proposed to solve these coupling issues. Zhang et al. used a polarization-maintaining fiber to control the polarization state of the input light and achieved the excitation of first-order cylindrical vector (CV) modes based on LPFGs. Similarly, first-order OAM modes were generated using the same method, but with a 10 dB bandwidth of less than 5 nm [17,18]. In addition, Wu et al. reported a method for mode adiabatic evolution in a tapered RCF, which improved the coupling efficiency of the fundamental modes to 90% and achieved the generation of first to third-order modes by employing LPFGs. Nevertheless, the mode conversion is accompanied by an insertion loss of more than 2 dB and a 10 dB bandwidth of about 10 nm [19]. Another, Huang et al. generated second and third-order modes based on a chiral LPFG inscribed in RCF, with a conversion efficiency of 98.7% and insertion loss as low as 0.5 dB. However, the 10 dB bandwidth of the generated modes is still narrow, at about 10 nm [20]. Although some methods have been proposed to achieve higher-order mode generation in RCFs, the bandwidths of the modes remain narrow and are insufficient for many applications. To support and transmit OAM modes, RCFs are designed with a high contrast between the core and cladding refractive index, which increases the effective refractive index separation of the modes and thus reduces crosstalk of the radial mode. However, this design characteristic simultaneously leads to a larger difference in group refractive index, resulting in a narrow bandwidth. The reported 10 dB bandwidth for mode conversion on RCFs is typically about 5-10 nm, and there are no reports on broadband OAM modes in RCFs. Therefore, it is necessary to develop a broadband method suitable for RCF to achieve broadband higher-order mode generation in RCF.

In this paper, we demonstrate a multi-order broadband mode converter in a RCF for the first time, which is achieved by fabricating a multi-pitch chirped LPFG. The proposed mode converter successfully achieves simultaneous broadband generation of second-order and third-order OAM modes. Specifically, the second-order OAM mode operates at >90% (10 dB) conversion efficiency from 1456 nm to 1513 nm, with a bandwidth of 57 nm. Meanwhile, the third-order OAM mode operates from 1573 nm to 1624 nm at >90% (10 dB) conversion efficiency, with a bandwidth of 51 nm. The insertion loss is less than 0.8 dB, and the mode purity exceeds 90%. This is the first time that a multi-order broadband OAM mode generation has been implemented simultaneously in RCF, and LPFG employed on RCF will be an ideal OAM mode converter for future high-capacity fiber communication systems.

2. Simultaneous generation of second-order and third-order modes

The RCF used in our simulations and experiments has a step refractive index profile, and the fiber end surfaces were observed by a microscope (OLYMPUS, BXUCB), as illustrated in Fig. 1(a). The RCF consists of a cladding with a radius of 62.5 µm and a ring core with inner and outer radii of 3.75 µm and 8.25 µm, respectively, with a refractive index difference of 0.012, as shown in Fig. 1(b). At 1550 nm, the RCF supports transmission of OAM₀, OAM _± 1, OAM _± 2, and OAM _± 3 modes. Using the finite element method and commercial software (COMSOL), the effective refractive indices of the modes in the wavelength range of 1200-1700nm were calculated in Fig. 1(c). According to the phase-matching condition, the relationship between the resonant wavelength and period of the grating can be expressed as $\Lambda = q\frac{{{\lambda _{\textrm{res}}}}}{{|{{n_{\textrm{eff,}}}_l - {n_{\textrm{eff,0}}}} |}}$, where n_eff is the effective refractive index of the modes, l is the order of the mode, $\Lambda $ is the grating period coupling from the fundamental mode to the l-order OAM mode, ${\lambda _{\textrm{res}}}$ is the resonance wavelength, and q is the diffraction order of the grating. We calculated the grating period for the first diffraction order coupling from OAM₀ mode to OAM _± 2 mode and the second diffraction order coupling from OAM₀ mode to OAM _± 3 mode, as shown in Fig. 1(d). At 1550 nm, the period of the first diffraction order for the coupling from OAM₀ mode to OAM _± 2 mode is 576 µm, and the period of the second diffraction order coupling from OAM₀ mode to OAM _± 3 mode is 616 µm. The results show that it is feasible to generate second-order and third-order modes at different wavelengths simultaneously when the grating period is taken in the range of 576 µm and 616 µm.

 

Fig. 1. (a) The cross-section image of RCF captured by a microscope. (b) The transverse refractive index distribution of the RCF. (c) The dispersion curves of modes supported by the RCF in the wavelength range of 1200-1700nm. (b) Calculated grating pitch as a function of wavelength for the coupling from OAM₀ mode to OAM _± 2 mode and OAM _± 3 mode, considering the first and second diffraction orders.

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During the fabrication of the LPFG, a focused CO₂ laser (CO₂-H30, Han's laser) was utilized to periodically irradiate the RCF from one side, the experiment setup is same as that in our previous work [11]. A supercontinuum broadband source (BBS) and an optical spectrum analyzer (OSA) were used to monitor the transmission spectrum of LP₀₁ mode and two segments of SMF were core-align spliced with a section of RCF at both ends for linking the BBS and OSA. In the experiments, by using a grating period of 570 µm with a pitch number of 40, simultaneous generation of second-order and third-order modes can be achieved, with resonant coupling at 1514 nm and 1615 nm, respectively. The transmission spectrum is shown in Fig. 2(a), with 10 dB bandwidths of only 5 nm and 4 nm for the second-order and third-order modes, respectively. According to Ref. [21], the 20-dB bandwidth of a uniform grating of length L that offers 30-dB maximal coupling can easily be shown to be $\mathrm{\Delta \lambda } = \frac{{0.0955{\lambda _{\textrm{res}}}^2}}{{L\mathrm{\Delta }{n_g}}}$, where ${\lambda _{\textrm{res}}}$ is the resonant wavelength and $\mathrm{\Delta }$n_g is the corresponding difference in the group indices. For the same grating length and resonant wavelength, taking a step index four-mode fiber (4MF, Yangtze Optical Fibre and Cable, FM2011-B) as an example, the difference in effective indices between fundamental mode and the second-order mode is 0.0033, and $\mathrm{\Delta }$n_g is 0.0015, the bandwidth at a grating length of 5 cm is calculated to be 3.05 nm. However, for the RCF, the difference in effective indices is 0.0027 and $\mathrm{\Delta }$n_g is 0.0022, and the bandwidth is only 2.11 nm for the same grating length. In comparison, the $\mathrm{\Delta }$n_g of the RCF is about 1.46 times that of the 4MF, and the grating bandwidth is about 0.69 times that of the 4MF at the same length and resonant wavelength, which indicates that the bandwidth of the long-period fiber grating inscribed in the RCF is quite narrow. Figure 2(b) illustrates the 10 dB bandwidths for the 4MF and RCF as the pitch number is increased from 10 to 40 when coupling from the fundamental mode to the second-order mode. It can be observed that as the pitch number increases from 10 to 40, the 10 dB bandwidth corresponding to 4MF decreases from 62 nm to 12 nm. Conversely, the 10 dB bandwidth corresponding to RCF decreases from 14 nm to 5 nm. Such limited bandwidth is insufficient for high-capacity communication applications. Therefore, it is necessary to propose a broadband method specifically tailored for mode conversion in RCFs.

 

Fig. 2. (a) The transmission spectrum of LPFG in RCF with pitch number of 40 periods for the period of 570 µm in the experiment. (b) The 10 dB bandwidths for the 4MF and RCF as the pitch number is increased from 10 to 40 when coupling from the fundamental mode to the second-order mode.

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3. Broadband generation of multiple high-order OAM modes

A broadband method of multi-pitch chirped LPFG in ring-core fibers is proposed and demonstrated. In order to increase the bandwidth of the grating, the linear chirp with multiple pitches in LPFG was introduced. The schematic diagram is depicted in Fig. 3, where Λ_i (i = 1,2,3 ……n) is the period per chirp, n is the number of chirps, Δd denotes the chirp of LPFG, p denotes the number of pitches per chirp, and L_i (i = 1,2,3 ……n) is the length per chirp.

 

Fig. 3. The schematic diagram of the multi-pitch chirped LPFG.

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For the designed multi-pitch chirped grating, the transmission spectrum is primarily influenced by the number of chirps and the pitch number per chirp. The impact of these two parameters on the bandwidth is examined through simulations. As illustrated in Fig. 4(a), when the starting period Λ₁ is set to 590 µm and p is 1, the ending periods are 600 µm, 605 µm, 610 µm, and 615 µm when n is set to 10, 15, 20, and 25, respectively. The 10 dB bandwidths of the second-order modes are 14 nm, 24 nm, 32 nm, 40 nm, and the bandwidths of the third-order modes are 13 nm, 17 nm, 33 nm, 42 nm. The results demonstrate that the bandwidth increases as n is incremented from 10 to 25. However, as the wavelengths of the two modes are very close to each other, significant mode crosstalk occurs when n is further increased. Consequently, n is fixed at 25 to strike a balance. Subsequently, the effect of p on the bandwidth is simulated under the same starting and ending periods. As shown in Fig. 4(b), the bandwidths of the second-order modes are 40 nm, 47 nm, 52 nm, and 59 nm and the bandwidths of the third-order modes are 42 nm, 45 nm, 53 nm, and 62 nm when p is set to 1, 2, 3, and 4, respectively. The simulation results indicate that the bandwidth of the grating increases with an increasing pitch number when the starting and ending periods remain constant.

 

Fig. 4. (a) The simulated transmission spectra of multi-pitch chirped LPFGs with n of 10, 15, 20 and 25 when p is 1. (b) The simulated transmission spectra of multi-pitch chirped LPFGs with p of 1, 2, 3 and 4 when n is 25.

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In the experiments, the influence of the number of chirps and pitches on the bandwidth was investigated. Firstly, the effect of the number of chirps on the bandwidth was examined with the pitch number per chirp set to 1. The starting period was fixed at 570 µm, and n was varied from 10 to 25, resulting in ending periods of 560 µm, 555 µm, 550 µm, and 545 µm, respectively. As the number of chirps increased, the bandwidths of the second-order modes are 18 nm, 32 nm, 43 nm, and 47 nm, and the bandwidths of the third-order modes are 16 nm, 20 nm, 23 nm, and 37 nm, respectively (Fig. 5(a)). Then, the impact of the pitch number per chirp on the bandwidth was verified by keeping the starting and ending periods fixed at 545 µm and 570 µm, respectively, and increasing the pitch number from 1 to 4. The bandwidths of the second-order modes are 47 nm, 48 nm, 52 nm, and 57 nm, and the bandwidths of the third-order modes are 37 nm, 47 nm, 48 nm, and 51 nm, respectively (Fig. 5(b)). The experimental results are in good agreement with the simulations, and the results demonstrate that the bandwidth is influenced by both the number of chirps and pitches. Specifically, a larger number of chirps and a larger number of pitches contribute to a wider grating bandwidth. It is worth mentioning that the total length of the grating increases with the increase of the number of pitches per chirp. As a result, the conversion efficiency also increases with the increase of bandwidth. However, due to the limited radiation range of the CO₂ laser, the total length of the grating cannot be increased indefinitely. Therefore, the number of pitches per chirp segment is determined as 4.

 

Fig. 5. (a) The experimental transmission spectra of multi-pitch chirped LPFGs with n of 10, 15, 20 and 25 when p is 1. (b) The experimental transmission spectra of multi-pitch chirped LPFGs with p of 1, 2, 3 and 4 when n is 25.

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After optimization, when the number of chirps was set to 25 and the number of pitches was 4, the 10 dB bandwidth of the second-order mode extended from 1456 nm to 1513 nm, covering a range of 57 nm. Similarly, the 10 dB bandwidth of the third-order mode spanned from 1573 nm to 1624 nm, encompassing a range of 51 nm. Consequently, the generation of multiple high-order broadband OAM modes was finally achieved as illustrated in Fig. 6. Four typical wavelengths were uniformly selected in the 10 dB bandwidth range (corresponding to a conversion efficiency over 90%) for the second-order and third-order modes, respectively. For the second-order mode, the conversion efficiencies at 1460 nm,1475 nm,1490 nm, and 1505 nm are 96.0%, 97.8%, 97.9%, 94.8%, respectively. For the third-order mode, the conversion efficiencies at 1575 nm, 1590 nm, 1605 nm, and 1620 nm are 93.3%, 98.6%, 97.4%, 93.8%, respectively. What’s more, the insertion loss of the second-order mode at four typical wavelengths were measured to be 0.56 dB, 0.49 dB, 0.40 dB, and 0.63 dB, and the insertion loss of the third-order mode at four typical wavelengths were measured to be 0.64 dB, 0.53 dB, 0.77 dB, and 0.70 dB.

 

Fig. 6. The transmission spectrum of the broadband second-order and third-order mode converter.

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A tunable laser (KEYSIGHT 81600B, 1460 nm–1640 nm) and a CCD (Xi’an leading optoelectronic, LD-SW640171550-UC-G) were utilized to observe the distribution of the generated OAM modes. Highly efficient second-order and third-order OAM modes were observed by adjusting the wavelength and polarization of laser, and intensity distributions of the generated OAM _± 2 modes and OAM _± 3 modes at four typical wavelengths were recorded in Fig. 7. To confirm the order of the modes with donut shapes, we interfered the generated modes with a reference Gaussian mode. The interference patterns are also shown in Fig. 7. The interference patterns indicate that OAM _± 2 modes and OAM _± 3 modes were successfully generated at the output of the RCF. To evaluate the quality of the generated modes, the mode decomposition method of the intensity distribution was employed to measure the mode purity [22,23]. Based on the intensity distribution measured in Fig. 7, the components of the different modes can be recovered and the purity of a particular mode can be obtained. For the OAM _+ 2 and OAM_-2 mode, the purities at 1460 nm,1475 nm,1490 nm, and 1505 nm are 93.70%, 95.48%, 96.86%, 90.94%, and 96.14%, 93.92%, 95.82%, 90.48%, respectively. For the OAM _+ 3 and OAM_-3 mode, the purities at 1575 nm, 1590 nm, 1605 nm, and 1620 nm are 95.01%, 95.10%, 94.56%, 91.82%, and 95.65%, 95.93%, 92.72%, 94.28%, respectively. Based on the recovered mode components, the intensity distributions can be reconstructed as shown in Fig. 7, which are very similar to the intensity distributions obtained experimentally, ensuring the confidence and accuracy of the mode purities. The results demonstrate that the efficient generation of both OAM _± 2 and OAM _± 3 modes can be achieved over a wide wavelength range with low insertion loss and high mode purity.

 

Fig. 7. The mode profiles, interference patterns, recovered mode profiles and the purity of (a) OAM _± 2 modes and (b) OAM _± 3 modes at four typical wavelengths.

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4. Conclusion

In summary, we have proposed a multi-order broadband mode converter based on a multi-pitch chirped LPFG inscribed in a RCF using a CO₂ laser. The grating parameters have been optimized to achieve wider bandwidth and higher conversion efficiency by increasing the number of chirps and the number of pitches. The fabricated multi-order broadband mode converter proved to operate in second-order OAM mode within a 57 nm, ranging from 1456 nm to 1513 nm. Additionally, it operated in third-order OAM mode within a 51 nm bandwidth from 1573 nm to 1624 nm. The conversion efficiency is over 90%, the insertion loss is less than 0.8 dB, and the mode purity exceeds 90%. To the best of our knowledge, this is the first time that multiple orders of broadband OAM mode generation have been achieved simultaneously in a RCF, which is expected to find potential applications in OAM mode-division multiplexing systems.