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Abstract
A broadband tunable orbital angular momentum (OAM) mode converter based on a helical long-period fiber grating (HLPFG) inscribed in a conventional single-mode fiber (SMF) is experimentally demonstrated. The proposed all-fiber OAM mode converter is based on the core-cladding mode dual resonance near the dispersion turning point (DTP). The converter can operate with a bandwidth of 303.9 nm @ −3 dB and 182.2 nm @ −10 dB, which is, as far as we know, the widest bandwidth for a conventional SMF. Furthermore, the bandwidth of the OAM mode can be dynamically tuned within a large dynamic range (>80 nm) by simply twisting the fiber clockwise (CW) or counterclockwise (CCW). The dynamic tunability of the bandwidth of the proposed OAM mode generator may find vital applications in large-capacity optical fiber communication systems.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Tremendous efforts have been made in countering the optical fiber network “capacity crunch” during the past decades, such as Dense Wavelength Division Multiplexing (DWDM), Space Division Multiplexing (SDM) and Mode Division Multiplexing (MDM) techniques [1–3]. In recent years, large attentions have been drawn on orbital angular momentum (OAM) modes due to its helical phase, which can carry a lot of information in a unique dimension and thus is attractive in optical communication systems [4] as well as in other fields such as optical tweezer [5] and nanoscale microscope [6]. For OAM mode generation in free space, plenty of schemes, such as spiral phase plate [7], spatial light modulators [8], q-plate [9] and metamaterials phase plates [10] have been reported. However, additional coupling system is critical to integrate the free space OAM modes with the existing optical fiber communication systems.
All-fiber versatile OAM mode generator have been reported in recent years and the most popular is helical long-period fiber grating (HLPFG) [11–13], which possess advantages of high mode conversion efficiency, low insertion loss, and simplicity in structure. The HLPFG can be inscribed by CO2 laser [11–18], arc discharge [19], and even oxyhydrogen-flame [20]. Various fiber types, such as conventional single-mode fibers (SMFs) [13,21], few-mode fibers (FMFs) [14–16], polarization-maintained fibers [17], as well as photonic crystal fiber (PCFs) [18] have been reported for HLPFG inscription and OAM mode generation. However, the bandwidth of conventional HLPFG-based OAM converter is narrow (several tens of nanometer @−10 dB), which limits the potential wavelength multiplexing abilities.
More recently, dual resonance effect has been employed for generating broadband OAM modes. In 2019, Guo et al. reported a broadband OAM mode generator based on a dual-resonant two-mode LPFG [16], a bandwidth of 118.2 nm @ −10 dB is demonstrated. In 2020, Zhao et al. reported a CO2-laser-inscribed dual-resonant HLPFG in a two-mode fiber, the obtained bandwidth is 297 nm @ −10 dB [15]. Compared with specific fibers, conventional SMF is more popular and compatible with the existing fiber-optic system. Although the cladding mode cannot propagate for a long distance, one can simply fusion splice it with a custom-made fiber for OAM mode transmissions. The feasibility of conventional SMF for broadband OAM generating has been theoretically demonstrated by Ren et. al. in 2020, and the obtained bandwidth is 287 nm @ −3 dB [22]. However, the experimental demonstration has not been reported as yet.
In this paper, we reported on a conventional SMF-based dual-resonance HLPFG for broadband (303.9 nm @ −3 dB and 182.2 nm @ −10 dB) tunable OAM mode generation. The oxyhydrogen-flame setup is adopted in preparing the HLPFG, which is the first experimental demonstration of SMF-based broadband OAM mode generator. The achieved OAM mode bandwidth is, as far as we know, the broadest with a conventional SMF. More importantly, the proposed OAM mode converter exhibits an excellent dynamic tunability of bandwidth, which is attractive in large-capacity optical fiber communication systems.
2. Dual-resonance principle and HLPFG preparation setup
2.1 Dual-resonant effect
In order to depict the dual-resonant principle, a Finite-Element-Method (FEM) is employed to calculate the total dispersion (including material and waveguide dispersion) of the core and several cladding modes of a conventional SMF. Within the simulation, the core/cladding diameters and the refractive index (RI) difference between the core and cladding are set as 8.2/125 µm and 0.0054, respectively. The resonant equation of a LPFG can be expressed by
where ${\lambda _{res}}$ and $\Lambda $ denote the resonance wavelength and grating pitch, respectively. $n_{co}^{eff}$ and $n_{cl,m}^{eff}$ represent the effective RIs of the core and cladding modes, respectively. By taking the obtained effective RIs into Eq. (1), the resonant wavelengths of cladding modes with orders from 9 to 11 versus the grating pitch $\Lambda $ is obtained and plotted in Fig. 1, where the white dots with a black edge denotes the DTP. Obviously, the DTPs represents the maximum grating pitch for each cladding mode resonance and the corresponding grating pitch of the LP 1, 9, LP 1, 10, LP1, 11 modes are about 172.4, 205.3, and 251.3 µm, respectively. As shown in Fig. 1, the slopes of the cladding modes LP 1, 9, LP 1, 10, LP1, 11 switch the signs from positive to negative with wavelength increasing, while at the DTP, $\textrm{|}d{\lambda _{res}}/d{\lambda _{res}}|\to \infty$. When the grating pitch is set at the DTP, there exists only one resonant dip and when the grating pitch $\Lambda $ decreases, two resonant dips will arise. In special, if the grating pitch $\Lambda $ is slightly smaller than the DTP, the two resonance dips can be overlapped, forming a broadband resonant dip. It is worth noting that, the two overlapped resonant dips are the same cladding mode (i.e. with the same order). As such, the broadband resonant dip has an excellent mode purity. This is the basic principle for generating broadband core-cladding modes resonance.
Fig. 1. Calculated resonant wavelength versus grating pitch $\Lambda $ for different cladding modes (Mode orders from $m = 9$ to 11, the DTPs are highlighted with hollow dots with black edge.)
2.2 Oxyhydrogen-flame setup for HLPFG inscription
In addition, for generating helical phase modulation and OAM modes, the helical structure of the fiber is necessary. Figure 2(a) depicts our homemade HLPFG preparation system, where an oxyhydrogen flame is used to fuse the fiber and a rotation motor is employed to twist the softened fiber, introducing helical phase modulation. In Fig. 2(a), ${V_1}$ (mm/s) and ${V_2}$ (mm/s) are the velocities of the stage-1 and stage-2, respectively. A little velocity difference between ${V_1}$ and ${V_2}$ (${V_1}$<${V_2}$) is applied to the fiber to introduce a constant stress along the axial direction, which ensures a stretched state of the fiber. The length L of HLPFG is determined by ${V_2}$ and the time T according to
The grating pitch $\Lambda $ can be written as
Fig. 2. (a) Schematic diagram of the homemade hydrogen-oxygen flame HLPFG preparation setup; (b) Schematic illustration of the helical modulation of the HLPFG; (c) Side view SEM image of a prepared HLPFG (i.e. S1).
where $\Omega $ (rpm) is the rotation speed of the rotator. Figure 2(b) schematically illustrates the helical phase modulation of the HLPFG. By tuning the rotation rate of the motor and the translation rate of the stages, the grating pitch $\Lambda $ can be precisely turned to the DTP. Scanning Electronic Microscope (SEM) image of a prepared HLPFG (S1) at the DTP of LP1, 10 mode is shown in Fig. 2(c), where the measured outer diameter of fiber (121 µm) is a little smaller than of the standard SMF (125 µm). It is worth noting that, Fig. 2(b) is merely a schematic diagram of the stress modulation of the HLPFG, in practice, the fiber shows no geometric change but thinning. As a result, no helical structure can be observed from the SEM image. Transmission spectrum of S1 is measured and shown in Fig. 3(a), where the resonant bandwidth are 230.1 nm @ −3 dB and 145.4 nm @ −10 dB, respectively. The mode field image at the center of resonant dip (1450.0 nm) is shown in Fig. 3(b), where we can see that the excited cladding mode at ∼1450.0 nm is LP1, 10. As such, both the grating pitch $\Lambda $ and resonant wavelength of the experiments exhibit a little deviation from the calculated results shown in Fig. 1. We believe that, the little deviation can be attributed to the thinning (from 125 to 121 µm) of the fiber during HLPFG preparation, which modifies the dispersion curve of the core and cladding modes slightly. In order to verify the helical phase of the generated LP1, 10 mode, a Mach-Zehnder interferometric (MZI) system is constructed for OAM phase characterization, details of the setup are available in [13]. Figure 3(c) shows the measured OAM mode profile by the MZI system, where the order of topological charge is 1. The experimental observation convinces the efficient generation of the OAM mode by the HLPFG.
Fig. 3. (a) Transmission spectrum of a prepared HLPFG (S1) working at the DTP. (b) Mode field profile within the center of resonant dip (i.e. 1450.0 nm); (c) OAM mode profile obtained by the MZI system.
3. Broadband HLPFG preparation and OAM mode characterization
3.1 Preparation and transmission spectra of the broadband HLPFG
We further prepare some HLPFGs (S2-S5) with gradually decreased grating pitch $\Lambda $ to obtain a broader resonance bandwidth. Figure 4(a) depicts the transmission spectra of the five prepared HLPFGs, where the grating pitch of S1 is at the DTP (198.8 µm) and the grating pitch of S2 (198.3 µm), S3 (197.9 µm), S4 (197.5 µm), and S5 (196.7 µm) decrease gradually. With the decreasing of grating pitch $\Lambda $, the single resonant dip splits and shifts toward the opposite directions. This observation agrees well with the calculations shown in Fig. 1. The resonant bandwidth of S1-S5 at −3 and −10 dB are measured and plotted in Fig. 4(b), respectively, where an approximate linear relationship between the bandwidth of −3 dB and grating pitch $\Lambda $ is presented, the linearities are 99.94%.
Fig. 4. (a) Transmission spectra of five prepared HLPFGs (S1-S5) with decreasing grating pitch $\Lambda $. (b) Measured −3 dB and −10 dB bandwidth versus the grating pitch $\Lambda $.
3.2 OAM mode characterization
The phase property of the generated OAM mode is characterized by employing a tunable laser source (1450–1650 nm) and the aforementioned MZI observation system. The HLPFG S2 is employed for observation and both the mode field and interference field is shown in Fig. 5(b). Within the wavelength range of 1450–1540 nm, OAM mode with a topological charge number of 1 is clearly observed, convincing the generation of broadband OAM mode. Unfortunately, limited by the wavelength range (1450–1650 nm) of the employed tunable laser, the interference field as well as the mode field distribution at a shorter wavelength range of 1357.4–1450 nm is not measured in the experiment. While, according to the transmission spectra evolution with the grating pitch $\Lambda $ that shown in Fig. 4(a), together with the calculated dispersion relationships that shown in Fig. 1, the mode at wavelength of 1357.4–1450 nm is convinced as the same LP 1,10 mode. As such, the mode properties within 1357.4–1450 nm will be all the same as observed in Fig. 5(b). As observed in Fig. 5(a), the OAM mode bandwidth of S2 is 257.6 nm @ −3 dB and 182.2 nm @ −10 dB, respectively. It is worth noting that, the bandwidth of generated OAM mode can be broadened further by reducing the grating pitch $\Lambda $ further, at the cost of OAM mode conversion efficiency. As shown in Fig. 4(a), a broader OAM mode bandwidth renders a shallower resonant dip, i.e. a lower conversion efficiency. To our best knowledge, this is the first experimental demonstration of broadband OAM mode generation based on a conventional SMF and oxyhydrogen-flame approach.
Fig. 5. (a) Transmission spectrum of a prepared HLPFG (S2) with grating pitch $\Lambda $ of 198.3 µm; (b) Measured mode field distribution and interference patterns within the broadband resonant dip (from 1450 to 1540 nm).
4. Dynamical tunability of the OAM mode
4.1 Wavelength and bandwidth tunability by torsion
As described above, precise controlling of the grating pitch $\Lambda $ is crucial to the OAM mode bandwidth. Alternatively, we find a more flexible and convenient way to tuning the bandwidth of the OAM mode dynamically, i.e. twisting the prepared HLPFG. The twisting equipment is schematically depicted in Fig. 6, where the two pigtails of the prepared HLPFG are fixed to a rotation stage and a stationary stage by a pair of fiber holders, respectively. The pigtails of the HLPFG are connected to a supercontinuum light source and Optical Spectrum Analyzer (OSA), respectively, to monitor the transmission spectra of the HLPFG during the twisting. The two HLPFGs (S1 and S2) are twisted from 0 to 360° (CW) and −360° (CCW) with a step of 60°, respectively. At each step, the transmission spectra are recorded and plotted in Fig. 7(a) and 8(a), respectively. All the tests are performed in a stable room temperature of 25 °C. It is worth noting that the CW direction is defined as the helix directions of the HLPFG while the CCW direction is opposite. A twist rate parameter $\gamma$ that defined as
is employed to quantitatively characterize the twist-induced stress per unit length. Here, $\theta$ and $L^{\prime}\textrm{ = }12.6$ cm are the twisting angle and the fiber length between the two fiber holders, respectively.Fig. 7. (a) Evolution of the transmission spectrum of S1 with varying torsion angles. (b) The −3 dB and −10 dB bandwidth of OAM mode versus the twist rate $\gamma$.
Fig. 8. (a) Evolution of the transmission spectrum of S2 with varying torsion angles. (b) The −3 dB and −10 dB bandwidth of OAM mode versus the twist rate $\gamma$.
The blackline in Fig. 7(a) is the initial transmission spectrum of S1. With the increasing of $\theta$ in the CW direction (the helix direction of HLPFG), the single resonant dip splits and shift toward the opposite directions, rendering a wider OAM mode bandwidth at both −3 and −10 dB. While, the resonance gets shallower when twisting the HLPFG in the CCW direction (opposite to the HLPFG helix). The −3 dB and −10 dB bandwidth of the OAM mode versus the twist rate $\gamma$ in both CW and CCW directions are shown in Fig. 7(b), where the −3 dB and −10 dB bandwidth can be dynamically tunned from 210.1 and 102.1 nm to 260.4 and 182.8 nm, respectively. For S2, the experimental results are presented in Fig. 8, where the −3 dB and −10 dB bandwidth can be tuned from 235.7 nm and 148.0 nm to 280.7 nm and 207.5 nm, respectively.
4.2 Discussion
Here, two points are worth noting. Firstly, by twisting the HLPFG with a larger angle $\theta$ or further reducing the $L^{\prime}$, the bandwidth of OAM mode can be tuned in a wider range. The principle of torsion tunability can be considered to a combined effect of grating pitch changing and the photo-elastic effect, which together brings about the wavelength and bandwidth change. Secondly, the mode field images of the OAM mode of S1 and S2 didn’t given repeatedly since the mode fields have been detailed analyzed in the previous section. As such, the dynamical tunability of the bandwidth of the OAM mode is verified.
Table 1 displays some typical results from previously reported all-fiber OAM mode converters. Compared with other types of all-fiber OAM mode converter, the oxyhydrogen-flame-induced HLPFG in this work has a simple structure, a broader bandwidth and a dynamic tunability of bandwidth.
Table 1. Comparison of several all-fiber OAM mode converters
5. Conclusion
We proposed and demonstrated a new approach for broadband tunable OAM mode generation based on oxyhydrogen-flame-induced HLPFG in a conventional SMF. The −3 dB and −10 dB bandwidth of the OAM mode are 303.9 nm and 182.2 nm, respectively. The dynamical tunability of the bandwidth is also reported. The proposed method and device may find vital applications in large-capacity optical fiber communications systems.
Funding
National Key Research and Development Program of China (2018YFF01010202); National Natural Science Foundation of China (61905164, 61905165); China Postdoctoral Science Foundation (2020M683184); Chongqing Municipal Education Commission (KJZD-M2000602); Natural Science Foundation of Guangdong Province (2018KQNCX219).
Disclosures
The authors declare no conflicts of interest.
Data Availability
The datasets are available from the corresponding author on reasonable request
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