1. Introduction

Orbital angular momentum (OAM), also called twist light, has helical phase front of exp(ilφ), comprising an OAM of lℏ per photon (where φ is the azimuth angle, l corresponds to the topological number) [1–5]. Owing to these attracting features, many researches for twist light applications such as optical manipulation [6–8], imaging [9,10], quantum communication [11,12], and optical communication systems [13–16] have been carried out since it was demonstrated by Allen in 1992 [1]. For optical communication, twisted lights are orthogonal with each other, having the potential to tremendously increase the capacity of communication systems [17–22].

In addition to these areas, all-fiber devices of twist light have attracted increasing attention in optical fiber communications recently [23–27]. All-fiber OAM devices convert the fundamental mode to higher order modes to produce OAM modes in fiber by fiber coupling. In recent years, many people have proposed various methods to achieve mode coupling transitions in optical fibers. Zeinab et al. propose to use photonic lantern to produce broadband orbital angular momentum mode multiplexer, in 2018 [28]. Kun Zhang et al. use tapered side-polished fibers to make broadband mode-selective couplers, in 2021 [29]. In 2018, Ya Han et al. propose the use of long period fiber gratings to generate the circularly polarized OAM beams [30]. Laipeng Shao et al. generate higher-order OAM mode (up to ±3 order) by using a helical long-period fiber grating in 2021 [31]. Compared with traditional approaches for manipulating twisted lights in free space paths such as Q-plates [32–34], spiral phase plates (SPPs) [35–37], and spatial light modulators (SLMs) [38–40] that are usually affected by diffraction effect and imperfect alignment between different optical components, all-fiber devices are more stable and suitable for twist lights processing and transmission. This is because the all-fiber devices can maintain the shape of the lights without causing beam divergence and manipulate twist lights in an enclosed environment, immune to external disturbance. In order to satisfy application requirements for optical fiber communications, high performance all-fiber devices of twist lights such as generator, mode-division-multiplexer, wavelength-division-multiplexer, beam splitter, and optical amplifier should be designed [41–46].

In this paper, we design, fabricated, and package a relatively full set of all-fiber devices [47] for twist light including all-fiber broadband OAM generator, OAM (de)multiplexer, OAM & wavelength-division-multiplexing (WDM) coupler, and OAM 1 × 2 coupler based on standard single mode fiber (SMF) and multi-mode fiber (MMF). Four OAM modes with large working bandwidth (1480-1620 nm), high purity (> 95%) and low insert loss (< 3 dB) are successfully generated and (de)multiplexed using proposed OAM generator and (de)multiplexer, respectively. Besides, we also demonstrated 980/1550 nm and 1455/1550 nm all-fiber OAM & WDM couplers with large working bandwidth (C bandwidth) and low insert loss (< 2 dB), which has potential use in erbium doped fiber amplifiers (EDFAs) and fiber Raman amplifier (FRA), respectively. Moreover, we demonstrate all-fiber OAM 1 × 2 coupler that can achieve a splitting ratio of 90:10 and 50:50 for twisted light with large working bandwidth (C bandwidth) and low insertion loss (< 0.1 dB).

2. Concept and principle

The concept diagram of general all-fiber optical communication system using twisted lights is displayed in Fig. 1(a). At the transmitter (TX) side, each independent data information is respectively added on the light beam with different wavelength. After amplified by the EDFAs, all these channels with different wavelength are combined by the all-fiber OAM & WDM coupler, which can successively convert fundamental Gaussian modes into OAM modes (OAM-1), generating multiple OAM modes of the same topological charge number with different wavelength. Then the generated WDM signals of OAM-1 is followed by a proposed all-fiber 1 × 2 OAM coupler, which can split the twisted lights into two paths with a custom power ratio. The upper path is connected to a twisted light monitor. The lower path is followed by a proposed OAM multiplexer that can multiplex generated twisted lights carrying different OAM. The WDM and OAM multiplexed signals will produced at the output side of the OAM multiplexer. To realize optical amplification, the OAM multiplexer is then followed by multiple cascaded all-fiber OAM & WDM couplers that combines the WDM and OAM multiplexed signals with multiple pump light with the same wavelength (λ_p). For example, the m-th OAM & WDM coupler will convert the pump light m in SMF into corresponding OAM mode (OAM-m, λ_p). After passing through the OAM amplifier, the WDM and OAM multiplexed signals will be amplified by the pump lights (OAM-1 of λ_p, …, OAM-m of λ_p). At the receiver (RX) side, the demultiplexing of WDM and OAM multiplexed signals can also be implemented by the proposed all-fiber OAM multiplexer and OAM & WDM coupler using the reverse process.

 

Fig. 1. (a) Concept of general all-fiber optical communication system using twisted lights carrying OAM at transmitter side. Concept of all-fiber functional devices for twist light including (b) OAM generator, (c) OAM (de)multiplexer, (d) OAM & WDM coupler, and (e) OAM 1 × 2 coupler. Inserts are photos of packaged all-fiber devices.

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Therefore, the key to the all-fiber OAM-based communication system is the realization of all-fiber components of broadband OAM generator, OAM (de)multiplexer, OAM & WDM coupler, and OAM 1 × 2 coupler. Figures 1(b) to (e) respectively show the proposed four all-fiber devices as mentioned above. The OAM generator is composed of a tapered SMF and a tapered MMF, as shown in Fig. 1(b). Using the mechanism of mode matching, the circularly polarized (CP) fundamental Gaussian mode in SMF can transform into the OAM mode in MMF. The OAM & WDM coupler is based on cascaded fiber tapers, as shown in Fig. 2(c). Each fiber taper can be seen as an OAM generator that can turn CP mode of specific wavelength into OAM mode. After passing through cascaded fiber tapers, multiple OAM modes with the same order but different wavelength are generated. The structure of OAM multiplexer is similar to that of OAM & WDM coupler, as shown in Fig. (d). The main difference is that each fiber taper has different mode matching parameters, leading to the production of various OAM modes. The OAM 1 × 2 coupler can be realized by utilizing two taper MMFs, as shown in Fig. 2(e). Based on these basic principles, we design, fabricate, and package of these all-fiber twisted light devices, whose photos are displayed in Figs. 1(b) to (e), respectively.

 

Fig. 2. (a)(b) Simulated effective index of different modes in SMF (LP₀₁) and OM3 (OAM _± 11, OAM _± 21) as functions of fiber cladding radius. Inserts are details of effective index of modes in OM3 near the phase matching points. (c)(d) Simulated effective index of different modes in pre-tapered SMF (LP₀₁) and OM3 (OAM _+ 11, OAM _+ 21) as functions of fused-taper ratio. (e) Measured refractive index profile of OM3 fiber. (f) Schematic diagram of proposed all-fiber OAM generator to generate OAM _± 11. LCP: left circularly polarized, RCP: right circularly polarized. (g) Microscopic image of pre-tapered SMF and MMF.

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We first investigate the proposed all-fiber OAM generator, whose mode properties are displayed in Fig. 2. Twisted lights in MMF with l = ±1 can be represented as linear combinations of the eigenmodes $\textrm{HE}_{\textrm{21}}^\textrm{e}$ and $\textrm{HE}_{\textrm{21}}^\textrm{o}$ with a π/2 phase difference, which can be expressed as $\textrm{OA}{\textrm{M}_{\mathrm{\ \pm 11}}}\textrm{ =HE}_{\textrm{21 }}^\textrm{e}\mathrm{\ \pm \ iHE}_{\textrm{21}}^\textrm{o}$ (for l = ±2, $\textrm{OA}{\textrm{M}_{\mathrm{\ \pm 21}}}\textrm{ =HE}_{\textrm{31}}^\textrm{e}\mathrm{\ \pm \ iHE}_{\textrm{31}}^\textrm{o}$). Here we use standard SMF (SMF-28, core/cladding diameter = 9.2/125 µm, refractive index difference $\Delta \textrm{ = 0}\textrm{.36\%}$) and conventional graded-index MMF (OM3, core/cladding diameter = 50/125 µm, as shown in Fig. 2(e)) to design the all-fiber OAM generator. According to coupled mode theory, in order to generate specific CP higher order OAM modes in the MMF, the diameters of the SMF and MMF need to be reduced to make LP₀₁ in SMF phase match with selected higher order OAM modes in the MMF. The simulated effective refractive indices of propagating modes as functions of fiber cladding radius (the length ratio of cladding and core radii remains constant) at 1550 nm is showed in Figs. 2(a) and (b), respectively. One can see that if the cladding radius of SMF is smaller than that of MMF, one can find the points at which the effective refractive indices of the modes in the two fibers are the same. The dotted lines in Figs. 2(a) indicate the radii in the two fibers required to achieve phase matching, where the effective refractive index differences between $\textrm{HE}_{\textrm{21}}^\textrm{e}$ ($\textrm{HE}_{\textrm{21}}^\textrm{o}$) and $\textrm{T}{\textrm{M}_{\textrm{01}}}$($\textrm{T}{\textrm{E}_{\textrm{01}}}$) are all above $\mathrm{1\ \times 1}{\textrm{0}^{\textrm{ - 3}}}$. And mode separation is guaranteed as long as the refractive index difference is greater than $\mathrm{1\ \times 1}{\textrm{0}^{\textrm{ - 4}}}$. In this case, $\textrm{HE}_{\textrm{21}}^\textrm{e}$ and $\textrm{HE}_{\textrm{21}}^\textrm{o}$ mode can be respectively excited by x-polarized and y-polarized LP₀₁ mode in SMF, while the excited $\textrm{T}{\textrm{M}_{\textrm{01}}}$ and $\textrm{T}{\textrm{E}_{\textrm{01}}}$ mode are in a very low level. Therefore, the input CP fundamental mode in SMF can generate the corresponding OAM (LCP → OAM _+ 11, RCP → OAM_-11) modes in MMF, as shown in Fig. 2(f). The dotted lines in Figs. 2(b) reveal the fiber parameters need to generate OAM _± 21. To fabricate the desired fibers with specially designed cladding radius ratio shown in Figs. 2(a) and (b), the cladding radii of SMF need to be respectively pre-tapered to 77 um and 55 um to generate OAM _± 11 and OAM _± 21, while the structures of the MMF remain unchanged, as shown in Fig. 2(g). Then we place the pre-tapered SMF and MMF together and continue to taper to the appropriate structural parameters. Figures 2(c) and (d) show the simulated effective refractive indices of propagating modes as functions of fused-taper ratio (ratio of fiber radius after and before tapering) at 1550 nm (see Supplement 1 for more details). One can see that the best fused-taper ratios are all about 0.049 to generate OAM _± 11 and OAM _± 21.

3. Experiment setup and results

Figure 3(a) shows the experiment setup to verify the generated twisted lights carry OAM using designed all-fiber OAM generator. A beam of 1550-nm laser is split into two arms by an optical coupler (OC). The upper arm is used for reference SMF. The lower arm is split into two paths, combined by an polarizing beam splitter (PBS). The linear polarized modes in two paths can be adjusted to synthesize CP modes by tuning polarization controllers (PCs). Then the OAM mode in MMF (blue fiber) can be excited by the CP fundamental modes in SMF. Two output beams from the reference SMF and OAM generator are collimated and then interfere by using a beam splitter (BS). The measured intensity profiles of the generated OAM modes (OAM _± 11, OAM _± 21) and their coaxial/tilted interferograms are recorded by a camera, as shown in Fig. 3(b). One can see that the doughnut shape with null intensity at the beam center of OAM modes are successfully generated, whose orders are verified by the number of spiral arms and forks in their corresponding interference patterns. In order to further characterize the quality of the generated OAM beams, we focus on the evaluation of the phase purity of the modes by using the Fourier transform method (see Supplement 1) to reconstruct the phase profiles of the generated OAM beams by measuring their tilted interferogram. After spherical correction (see Supplement 1), one can clearly see that the reconstructed spiral phase structure with azimuthal phase change from 0 to 2π, indicating the successfully generation of OAM _± 11, OAM _± 21 mode, whose phase purity are 97.44%, 97.17%, 90.90%, and 92.70%, respectively. Furthermore, we test the bandwidth performance of the all-fiber OAM generator such as intensity profiles, corresponding interferograms, and insertion loss, as shown in Figs. 2(c) and (d). The results indicate that the device has a favorable broadband performance ranging from 1480 to 1620 nm with very low loss below 2.2 dB for OAM _+ 11 and 3.2 dB for OAM _+ 21. Finally, we verify the generated OAM _+ 11 and OAM_-21 are respectively LCP and RCP as shown in Figs. 3(e) and (f). A polarizer (P1) is connected to the output port of MMF of the OAM generator to verify the CP state, and a quarter-wave plate (QWP) followed by a polarizer (P2) is then connected to the output port to determine if it is LCP or RCP. The results in the upper row of Figs. 3(e) and (f) show that after rotating the spindle of P1 from 0 to 180 degrees, the difference between maximum and minimum power is only 0.88 dB for OAM_-11 and 1.04 dB for OAM _+ 21, respectively, proving the CP state of generated OAM beams. Then the orientation angle of P2 is rotated to detect the rotation direction of CP state, as depicted in the lower row of Figs. 3(e) and (f). The approximate sinusoids and cosines indicate that the generated OAM_-11 is LCP and OAM _+ 21 is RCP.

 

Fig. 3. (a) Experiment setup for testing all-fiber OAM generator. OC: optical coupler. PC: polarization controller. VOA: variable optical attenuator. PBS: polarizing beam splitter. Col: collimator. OL: objective lens. BS: beam splitter. (b) Measured beam profiles of the generated OAM modes. (c) Received power of the generated OAM modes as functions of wavelength. (d) Measured intensity profiles and corresponding interferograms of the generated OAM modes with various wavelength. (e) (f) Measured polarization properties of generated OAM modes.

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On the basis of all-fiber OAM generator, we further design and fabricate a kind of all-fiber OAM (de)multiplexer. As shown in Fig. 4(a), two cascaded all-fiber OAM generators are used for OAM (de)multiplexing. Light from a 1550-nm laser source is split into six arms using one 1 × 3 and three 1 × 2 OCs. The PC array (PC1) can make the polarization states of linearly polarized lights in adjacent two arms orthogonal with each other, simultaneously combined by three PBSs (PBS1) to generate fundamental CP modes (CP1, CP2, CP3) in SMFs. Then by adjusting the PC array (PC2), the fundamental CP modes in SMFs become LCP or RCP to excite their corresponding OAM modes. CP1 mode in SMF is directly sent to a MMF that generate the fundamental mode OAM _± 01 (CP1 = OAM _± 01). CP2 mode is sent to the first all-fiber OAM generator to generate OAM1 mode, while CP3 mode is sent to the second all-fiber OAM generator to generate OAM2 mode. At the output port of the OAM multiplexer, there will exist three OAM modes at the same time in the MMF (CP1, OAM1, OAM2), realizing OAM multiplexing, as shown in Fig. 4(a). At the demultiplexing side, the all-fiber OAM demultiplexer is followed by three PCs (PC4) and PBSs (PBS2), where the power of modes is measured by six power detectors (PDs). The all-fiber OAM demultiplexer is the reverse construction of all-fiber OAM multiplexer. Figure 4(b) shows measured crosstalk matrix of three kinds of OAM modes (de)multiplexing (OAM _± 01, OAM _± 11, OAM _± 21) after back-to-back transmission in the experiment. One can see that the crosstalk between different OAM modes is less than -8.8 dB.

 

Fig. 4. (a) Experiment setup for testing all-fiber OAM (de)multiplexer. PD: power detector. (b) Measured crosstalk matrix of six OAM modes (de)multiplexing after back-to-back MMF transmission.

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Based on the principle of all-fiber OAM generator and OAM (de)multiplexer, we design and fabricate all-fiber OAM & WDM couplers, as shown in Fig. 5(a). Two cascaded all-fiber OAM generators are used to assemble the OAM & WDM coupler. The former operates at λ1 = 1550 nm to generate corresponding OAM mode (OAM-λ1), while the latter operates at λ2 = 980 or 1455 nm to generate the OAM modes with the same order as the former (OAM-λ2). Thence, the MMF at the output port of OAM & WDM coupler contains two OAM modes with the same order but different wavelengths (OAM-λ1, OAM-λ2). Figures 5(b) and (d) show the measured intensity profiles and interferograms of isolated 980, 1455, 1550 nm OAM modes. Figures 5(f) and (g) show the measured intensity profiles after WDM. To further investing the bandwidth of the OAM & WDM coupler, we investigate insertion loss, intensity profiles, and corresponding interferograms at different wavelength, as shown in Figs. 5(c) and (e). The measured insertion loss of generated twist light is ranging from 1.48 to 2.86 dB for 980/1550 nm OAM & WDM coupler and 0.88 dB to 1.30 dB for 1455/1550 nm OAM & WDM coupler, respectively. The measured intensity profiles and interferograms also indicate the successfully generation of OAM beams covering the entire C-band. Moreover, due to the fact that multiple pump lights are usually applied in raman fiber amplifier (RFA) and erbium doped fiber amplifier (EDFA), we further test insertion loss and intensity profiles at different wavelength, as shown in Fig. 6(h). The measured insertion loss is 1.67, 1.54, 1.66, and 1.62 dB for 1425, 1452, 1465, and 1495 nm, respectively.

 

Fig. 5. (a) Experiment setup of all-fiber OAM & WDM couplers. Measured intensity profiles and interferograms of generated OAM beams using (b) 980/1550 nm and (d) 1455/1550 nm OAM & WDM coupler. Measure relative power of generated OAM beams as function of wavelength using (c) 980/1550 nm and (e) 1455/1550 nm all fiber OAM & WDM coupler. Inserts are measured intensity profiles and interferograms. Mixed mode fields after multiplexed output of (f) 980/1550 nm and (g) 1455/1550 nm. (h) Measured intensity profiles of generated OAM beams of other wavelengths.

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Fig. 6. (a) Schematic diagram of all-fiber OAM 1 × 2 coupler. Measured insertion loss, intensity profiles, and interferograms of generated OAM beams (OAM _+ 11) using OAM 1 × 2 coupler with power ratio of (b) 90:10 and (c) 50:50.

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By replacing the SMF in the proposed OAM generator with MMF, we designed and fabricated a kind of all-fiber OAM 1 × 2 coupler, as shown in Fig. 6(a). We investigate the insertion loss, intensity profiles, and corresponding interferograms of output beams of proposed couplers with different power ratio (90:10, 50:50), as shown in Figs. 6(b) and (c). One can see that the insertion loss (0.02 dB for 50:50 coupler, 0.03 dB for 90:10 coupler at 1550 nm) is relatively low, while the power ratio of the OAM 1 × 2 coupler is relatively stable throughout the C-band. Moreover, the measured intensity profiles and interferograms of OAM beam at the output ports of the all-fiber OAM couplers perfectly in line with expectations, verfying the favorable performance of the couplers.

4. Summarization and discussion

In conclusion, all-fiber broadband OAM generator, OAM (de)multiplexer, OAM & WDM coupler, and OAM 1 × 2 coupler with large working bandwidth, high mode purity, and low insertion loss are successfully demonstrated and fabricated, forming a relatively complete set of all-fiber devices for optical communication based on twisted light carrying OAM. By using fused-tapering methods and packaging technology, the devices have favorable performance and compact size, making them potentially applicable in the future. All-fiber OAM generator provides a promising and convenient way to generate OAM modes, which is also the basic element of other all-fiber twisted light devices. All-fiber OAM (de)multiplexer can be used for mode-division-multiplexing (MDM) to satisfy the exponentially increasing demand for transmission capacity. All-fiber OAM & WDM coupler can act as core component in OAM amplifier such as DRA or EDFA. All-fiber 1 × 2 coupler will complete the diversity of all-fiber devices for twist light carrying OAM. Although the proposed devices have not fully covered all-fiber devices yet such as VOA, optical isolator, and optical circulator and so on, it is still a good step for twisted lights applying in optical fiber communication.

Additionally, we test the repeatability and stability of these devices. In the initial testing, we first use a glass sleeve to encapsulate the coupling area. After the performance test is up to standard, we then further encapsulate the coupling area with metal sleeves and encapsulate the optical fiber with plastic sleeves. Finally, after testing, our devices can maintain usable performance for several months to half a year.

We also selecte several representative works of all-fiber OAM devices to compare with our devices, and the results are shown in the following Table 1. Comparing the results in the Table 1, we can see that fiber grating has a small insertion loss, but the device corresponds to a small bandwidth due to the method limitation. Mode selective coupler (including photonic lantern) has a very large bandwidth and a larger insertion loss. Our device is also a mode-selective coupler. So, it has a larger operating bandwidth and slightly higher insertion loss. However, our preparation process is the simplest. The fibers we used are the most common commercial multimode fibers, and the preparation method is also a simple fiber fusion taper. Commercial multimode fiber can be easily interfaced with existing fiber optic networks.

Table 1. Comparison of several all-fiber OAM devices

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Furthermore, we can try to adjust the parameters to improve the performance of these device, such as loss, bandwidth, stability, etc. For example, for broadband OAM generator, we can optimize the parameters to broad the bandwidth, such as fiber radius and the space between two cores. In this experiment, we use commercial multimode fiber (Corning) for better practicality. Therefore, the corresponding parameters design could not be adjusted much. However, we can choose a new design for multimode fiber to improve the performance.