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Abstract
In order to cover the bandwidth of optical fiber communication, a LP01-LP11 ultra-broadband mode converter based on triple superimposed long period grating in PCF is proposed and demonstrated. The transmission spectra of the D-SLPG with gratings pitches and the T-SLPG were simulated and analyzed. The simulation results on the D-SLPG indicate that the 3 dB bandwidth of the D-SLPG is more than 1.5 times than the 3 dB bandwidth of the independent LPG and the 3 dB bandwidth of T-SLPG approaches 2.6 times as much as the independent LPG. In the experiment, the mode converter based on PCF-T-SLPG covers the wavelength of S + C + L with 3 dB bandwidth of 121 nm from 1498 nm to 1619 nm. In addition, the mode converter based on PCF-T-SLPG can accomplish ultra-broadband transmission in any wavelength by adjusting the period of gratings.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Mode division multiplexing (MDM) has attracted lots of attention, which is proposed by S.Berdagué in 1982 [1]. MDM theoretically achieves orders of magnitude increase in communication capacity by using high-order linear polarization (LP) modes as transmission channels [2–4]. Mode converter is an important device in MDM, which can accomplish mode conversion from the fundamental mode to high-order modes. Many implement methods of mode converters have been reported, such as spatial light modulators [5], multi-core fiber [6], photonic lantern [7] and long period grating (LPG) [8–10]. The mode converter based on LPG possesses the merits of high coupling efficiency, small size, low loss and flexible fabrication. The fabrication methods of LPG have been reported including ultraviolet exposure method [11], femtosecond laser method [12], CO2 laser method [13–15,9,16,17]. In 2017, Liu Yunqi et al. [9] fabricated cascading two LPG with different grating pitches in few mode fiber by CO2 laser and realized mode conversion between LP01 mode and LP21 mode with a coupling efficiency of more than 99.5%. In 2020, Zuyao Liu et al. [16] fabricated LPG in an elliptical core few-mode fiber by CO2 laser and realized mode conversion between LP01 mode and LP21a mode with a coupling efficiency of more than 99%. The higher-order LP02 and LP31a mode can be generated successfully with different grating periods. Compared with LPG based on traditional optical fibers, the LPG based on photonic crystal fiber (PCF) with unique optical characteristics has gradually attracted more attention. In 2007, K. Lai et al. [17] proposed an LP01 to LP11 mode converter was made by the ferrule technique on a drawing tower, and an LP01 to LP02 mode converter was made by controlled hole inflation of an existing PCF on a tapering rig. In 2008, Lars Rindorf and Ole Bang [18] presented highly sensitive refractometers based on a long-period grating in a large-mode-area PCF. The maximum sensitivity is 1500 nm/refractive index unit at a refractive index of 1.33. In 2015, Gaetano Bellanca et al. [19] demonstrated a dual-core polymer holey fiber coupler for LP01 and LP11 mode multiplexing both numerically and experimentally for the first time. In 2017, Zejun Zhang et al. [20] provided an improved PC element. The polarization conversion efficiency is better than 99%, and the corresponding extinction ratio is better than −20 dB over a wavelength range of 310 nm. In 2018, Xiaohui Zhang et al. [21] proposed a mode converter based on LPG in a two-mode polarization-maintaining photonic crystal fiber, which realized mode conversions between the LP01 modes and LP11a modes with parallel polarization directions. The highest mode-conversion efficiency is more than 99%. In order to cover the bandwidth of optical fiber communication, the mode converters with wide bandwidth would be required. In 2019, Yange Liu et al. [22] proposed an ultra-broadband mode converter based on a cascade chirped long-period fiber grating (CLPFG) written in a two-mode fiber, which achieved the mode convision between LP01 and LP11 with 10 dB bandwidth of 170 nm from 1472 nm to 1642 nm. In 2021, Yang Cailong et al. [23] experimentally demonstrated a mode converter with C + L band coverage based on LPGs by the femtosecond laser. The mode converter implemented mode conversion between the LP01 mode and the LP11 mode with a coupling efficiency of more than 90% and insertion loss of less than 5 dB. In 2022, Quandong Huang et al. [24] reported an ultra-broadband LP11 mode converter with high purity based on LPG and an integrated Y-junction, which achieved a 10 dB bandwidth of 50 nm and 51 nm at resonance wavelengths of 1530 nm and 1570 nm, respectively.
In summary, the mode converters based on PCF are rarely reported. The reported mode converters based on PCF have disadvantage with less bandwidth compared to existing all-fiber mode converters. In this paper, a LP01-LP11 ultra-broadband mode converter based on triple superimposed long period grating (T-SLPG) in PCF is proposed and demonstrated. First, we investigate the mode characteristics of the PCF from simulation based on the finite element method. In the experiment, the double SLPG(D-SLPG) with different wavelength and the triple SLPG(T-SLPG) were fabricated. Experiment and simulation results indicate that the fabrication of the D-SLPGs with the decrease of wavelength need greater periodic interval, which provides experimental basis for the preparation of T-SLPG in order to cover the wavelength of optical communication. Both the D-SLPG and the T-SLPG have significantly achieved bandwidth expansion and the T-SLPG has a more prominent bandwidth expansion. The mode converter based on PCF-T-SLPG covers the wavelength of S + C + L with 3 dB bandwidth of 121 nm from 1498 nm to 1619 nm.
2. Principle and simulation
2.1 Principle
The fiber used is a total internal reflection PCF with pure silica core produced by YOFC Fiber. Figure 1(a) presents the cross section of PCF with the diameter of 125µm in scanning electron microscopy. Three rings of air holes with diameter d (6.39µm) are arrange along the radial direction spaced at equal intervals of S (8.06µm). It can be calculated by finite element method that the PCF supports two modes (LP01 and LP11). The electric field distribution of LP01 and LP11 modes at 1550 nm are shown in Fig. 1(b).
The mode conversion between LP01 and LP11 is realized by LPG with suitable grating period. The resonance wavelength of the LPG satisfies the phase-matching condition in accordance with coupled-mode theory.
Where λres is the resonance wavelength, and n01,eff are n11,eff the effective refractive index of LP01 and LP11 respectively, Λ is the grating period. We calculated the dispersion curves of LP01 and LP11 by using COMSOL Multiphysics based on the finite element method, as shown in Fig. 2(a) and the grating period corresponding to different resonance wavelength, as shown in Fig. 2(b).
Fig. 2. (a) Dispersion curves of LP01 and LP11; (b) Grating period corresponding to different resonance wavelength.
2.2 Simulation of D-SLPG mode converter
Figure 3 shows the schematic diagram of the D-SLPG mode converter, including two gratings with different periods in the same spatial position. Both the grating 1 and the grating 2 implement mode conversion between the LP01 and the LP11. When two resonance dips corresponding to the gratings are superimposed on each other, the spectra of the resonance dips will merge together as one dip to form the D-SLPG with much broader bandwidth.
We did the simulation of the transmission spectra of the D-SLPG with different grating pitches based on MATLAB. The periodic refractive index changes of SLPG was considered as a linear superposition of individual modulation of multiple gratings which were written at the same location. Then, the coupling coefficients and the coupled mode equation of SLPG can be derived from The periodic refractive index changes of SLPG. According to the coupled mode theory, the bandwidth decreases with the increase of the number of gratings. In order to emphasize the broadening ability of the SLPG, we set the number of gratings to 25. Figure 2(b) shows the grating period corresponding to different resonance wavelength, when the LP01 mode converts to LP11. The simulation results are shown in Fig. 4, which illustrates maximum grating pitches of two resonance dips with different resonance wavelength merged together as one dip. For example, When Λ1 is 243.4µm and Λ2 is at most 252.5µm, the resonance dips corresponding to LPG1 and LPG2 will merge together as one dip. The maximum grating pitches is the difference value between LPG1 and LPG2. The maximum grating pitches increases with the diminishing of the resonance wavelength. As shown in Table 1, the 3 dB bandwidth of the D-SLPG with different resonance wavelength is more than 1.5 times than the independent LPG. The conversion efficiency of the D-SLPG can be calculated by the following equation:
Where C is the value of the ordinate in the transmission spectrum. T is the conversion efficiency.Fig. 4. Simulation transmission spectra of the D-SLPG with different grating pitches: (a) D-SLPG-1 (b) D-SLPG-2 (c) D-SLPG-3 (d) D-SLPG-4
Table 1. 3 dB bandwidth of the D-SLPG with different grating pitches
2.3 Simulation of T-SLPG mode converter
Figure 5 shows the schematic diagram of the T-SLPG mode converter, including three gratings with different periods in the same spatial position. All the gratings accomplish mode conversion between the LP01 and the LP11. When three resonance dips corresponding to the gratings are superimposed on each other, the spectra of the resonance dips will merge together as one dip to form the T-SLPG with more broader bandwidth than the D-SLPG.
We did simulate the transmission spectra of the T-SLPG based on MATLAB with the program as shown in Code 1 [25]. The number of all the gratings are 25. Figure 6 indicates the maximum grating pitches of three resonance dips with different resonance wavelength merged together as one dip. The 3 dB bandwidth of independent LPG is approximately 57 nm. The mode converter based on PCF-T-SLPG covers the wavelength of S + C + L with 3 dB bandwidth of 151 nm from 1478 nm to 1629 nm, which approaches 2.6 times as much as the independent LPG. The maximum coupling efficiency is 15.2 dB. Furthermore, the bandwidth and coupling efficiency of mode converter is adjustable by changing the number of the gratings. As the number of gratings increases, the coupling efficiency enhances and the bandwidth decreases.
Fig. 6. Simulation transmission spectra of the T-SLPG with different grating Pitches: (a) T-SLPG-1 (b) T-SLPG-2 (c) T-SLPG-3.
3. Fabrication of D-SLPG and T-SLPG
In the experiment, we fabricated the D-SLPG and the T-SLPG based on PCF by CO2 laser (CO2-H10C, Han’s laser). The parameters of CO2 laser are shown in Table 2 and its maximum output power is 2 W. The schematic diagram of fabrication system is shown in Fig. 7. The SLED is used as an SC light source. Both sides of PCF were connected with single mode fiber (SMF) by the fusion splicer (FITEL,S178) in manual mode. It can be seen from Fig. 7 that the PCF has slight collapse, however, which do not impede the experimental results. The PCF were placed horizontally on the rotating device. A supercontinuum light source (working wavelength 470 nm-2400 nm) and a spectral analyzer (OSA, AQ6370C, YOKOGAWA) were used to monitor the transmission spectra of the D-SLPG and the T-SLPG.
Table 2. The parameters of CO2 laser
3.1 Fabrication of D-SLPG
According to the simulation results, firstly LPG1 was inscribed in PCF horizontally. Then rotate the PCF with 180° to inscribe the LPG2. The transmission spectra of the D-SLPG in the experiment are shown in Fig. 8. Figure 8(a) and Fig. 8(b) demonstrate the maximum grating pitches are 272µm-255.5µm and 252.4µm-243.4µm to fabricate the D-SLPG-3’ and the D-SLPG-1’, respectively. The contractible figure, which is inset into the Fig. 8(b), indicates when Λ1 is 243.4µm and Λ2 is 255.5µm, the resonance dips corresponding to LPG1 and LPG2 will exist exist on their own. Table. 3 illustrates the 3 dB bandwidth of the D-SLPG approximates 1.5∼2 times than the 3 dB bandwidth of the independent LPG and the maximum grating pitches increases with the diminishing of the resonance wavelength, which are well consistent with the simulation results. The transmission spectra of D-SLPG-1’ with the different number of the gratings are shown in Fig. 8(c). When the number of gratings is 25, the 3 dB bandwidth and coupling efficiency of the D-SLPG-1’ are 106 nm and 11.2 dB respectively. When the number of gratings is 35, the 3 dB bandwidth and coupling efficiency of the D-SLPG-1’ are 84 nm and 12.3 dB respectively. In conclusion, the bandwidth and coupling efficiency of the D-SLPG mode converter are adjustable by changing the number of the gratings.
Fig. 8. Transmission spectra of the D-SLPG: (a) D-SLPG-3’ (b) D-SLPG-1’ (c) The D-SLPG-1’ with the different number of the gratings
Table 3. The 3 dB bandwidth of the D-SLPG from experiment and simulation
3.2 Fabrication of T-SLPG
We fabricated the T-SLPG based on the D-SLPG. According to the simulation results, firstly LPG1 was inscribed in PCF horizontally. Then rotate the PCF with 120° to inscribe the LPG2. Finally rotate the PCF with 120° again to inscribe the LPG3. In order to verify the uniformity of the gratings, the T-SLPG was observed by microscope. As shown in Fig. 9, the length of the LPG1, LPG2 and LPG3 are uniformly distributed within measuring error.
Fig. 9. The length of the LPG1, LPG2 and LPG3: (a) Horizontal placement (b) Clockwise rotation with 120° based on horizontal placement
In terms of the simulation results, when the periods of LPG1, LPG2 and LPG3 are 248µm, 255µm, 263µm respectively, three resonance dips can merge together as one dip. The period of the gratings was fine-tuned in the experiment. The transmission spectra of the T-SLPG are shown in Fig. 10. The 3 dB bandwidth of LPG1 is 58 nm. The T-SLPG covers the wavelength of S + C + L with 3 dB bandwidth of 121 nm from 1498 nm to 1619 nm. The results indicates the 3 dB bandwidth of mode converter based on T-SLPG exceeds 2 times as much as the independent LPG and improves about 20 nm than the D-SLPG mode converter. The experimental results are in good agreement with simulation results. In addition, the mode converter based on T-SLPG can accomplish ultra-broadband transmission in any wavelength by adjusting the period of grating, like the mode converter based on D-SLPG. The bandwidth of mode converter is adjustable by changing the number of the gratings.
We observed the mode distribution of LP11 by the experimental system shown in Fig. 11. A tunable laser (TSL-770, Santec) was used as a light source to connect the mode converter. 40×Lens collimated the light emitted by the mode converter based on PCF-T-SLPG. Beam Profiler (CinCam CMOS 1202, Cinogy) collocated IR Module (IR01-4716-0014, Cinogy) to monitor the mode distribution at the output of the mode converter. The mode distribution of LP11 observed was shown in Fig. 10. The experimental results confirmed that the mode converter based on PCF-T-SLPG implemented mode conversion between LP01 and LP11.
4. Conclusion
In this paper, a LP01-LP11 ultra-broadband mode converter based on triple superimposed long period grating in PCF is proposed and demonstrated. First, we investigate the mode characteristics of the PCF from simulation based on the finite element method. The transmission spectra of the D-SLPG with gratings pitches and the T-SLPG were simulated and analyzed. The simulation results on the D-SLPG indicate that the 3 dB bandwidth of the D-SLPG is more than 1.5 times than the 3 dB bandwidth of the independent LPG and the maximum gratings pitches to form the D-SLPG increases with the diminishing of the resonance wavelength of the D-SLPG. The simulation results on the T-SLPG demonstrate the T-SLPG covers the wavelength of S + C + L with 3 dB bandwidth of 151 nm from 1478 nm to 1629 nm, which approaches 2.6 times as much as the independent LPG. Based on the simulation results, we fabricated the D-SLPG and the T-SLPG by CO2 laser. The mode converter based on PCF-T-SLPG covers the wavelength of S + C + L with 3 dB bandwidth of 121 nm from 1498 nm to 1619 nm. The results indicates the 3 dB bandwidth of mode converter based on T-SLPG exceeds 2 times as much as the independent LPG and improves about 20 nm than the D-SLPG mode converter. The experiment results are well consistent with simulation results. In addition, the mode converter based on PCF-T-SLPG can accomplish ultra-broadband transmission in any wavelength by adjusting the period of grating, like the mode converter based on D-SLPG and the bandwidth of mode converter is adjustable by changing the number of the gratings. The proposed ultra-broadband mode converter based on PCF-T-SLPG have a promising application in MDM system.
Funding
Hebei Provincial Central Leading Local Science and Technology Development Fund Project (226Z1702G); Hebei Province Key Laboratory of Special Optical Fiber and Fiber Sensing (4800007); National Natural Science Foundation of China (61475133).
Disclosures
The authors declare no conflicts interest.
Data availability
Data underlying the results presented in this paper are available in Code 1, Ref. [25]
References
1. S. Berdagué and P. Facq, “Mode division multiplexing in optical fibers,” Appl. Opt. 21(11), 1950–1955 (1982). [CrossRef]
2. 2. Nobutomo Hanzawa, Kunimasa Saitoh, Taiji Sakamoto, Takashi Matsui, Shigeru Tomita, and Masanori Koshiba, “Demonstration of mode-division multiplexing transmission over 10 km two-mode fiber with mode coupler,” Optical Fiber Communication Conference (2011) OSA Technical Digest (Optica Publishing Group, 2011), OWA4.
3. B. Puttnam, G. Rademacher, and R. Luis, “Space-Division Multiplexing for Optical Fiber Communications,” Optica 8(9), 1186–1203 (2021). [CrossRef]
4. D. Reza Mirzaei Nejad, K. Allahverdyan, P. Vaity, S. Amiralizadeh, C. Brunet, Y. Messaddeq, S. LaRochelle, and L. A. Rusch, “Mode Division Multiplexing Using Orbital Angular Momentum Modes Over 1.4-km Ring Core Fiber,” J. Lightwave Technol. 34(18), 4252–4258 (2016). [CrossRef]
5. J. von Hoyningen-Huene, R. Ryf, and P. Winzer, “LCoS-based mode shaper for few-mode fiber,” Opt. Express 21(15), 18097–18110 (2013). [CrossRef]
6. Y. Zhang, Y. Wang, S. Cai, M. Lan, S. Yu, and G. WanYi, “Mode converter based on dual-core all-solid photonic bandgap fiber,” Photonics Res. 3(5), 220–223 (2015). [CrossRef]
7. J. G. Leon-Saval, A. Argyros, and J. Bland-Hawthorn, “Photonic lanterns: A study of light propagation in multimode to single-mode converters,” Opt. Express 18(8), 8430–8439 (2010). [CrossRef]
8. L. Fang and H. Jia, “Mode add/drop multiplexers of LP02 and LP03 modes with two parallel combinative long-period fiber gratings,” Opt. Express 22(10), 11488–11497 (2014). [CrossRef]
9. Y. Zhao, Y. Liu, C. Zhang, L. Zhang, G. Zheng, C. Mou, J. Wen, and T. Wang, “All-fiber mode converter based on long-period fiber gratings written in few-mode fiber,” Opt. Express 42(22), 4708–4711 (2017). [CrossRef]
10. C. Fu, S. Liu, Z. Bai, J. He, C. Liao, Y. Wang, Z. Li, Y. Zhang, K. Yang, B. Yu, and Y. Wang, “Orbital Angular Momentum Mode Converter Based on Helical Long Period Fiber Grating Inscribed by Hydrogen-Oxygen Flame,” J. Lightwave Technol. 36(9), 1683–1688 (2018). [CrossRef]
11. S. Ramachandran, Y. Wang Z, and M. Yan, “Band-selection filters with concatenated long-period gratings in few-mode fibers,” Opt. Express 27(19), 1678–1680 (2002). [CrossRef]
12. T. Allsop, M. Dubov, A. Martinez, F. Floreani, I. Khrushchev, D. J. Webb, and I. Bennion, “Bending characteristics of fiber long-period gratings with cladding index modified by femtosecond laser,” J. Lightwave Technol. 24(8), 3147–3154 (2006). [CrossRef]
13. Y.-J. Rao, Y.-P. Wang, Z.-L. Ran, and T. Zhu, “Novel Fiber-Optic Sensors Based on Long-Period Fiber Gratings Written by High-Frequency CO 2 Laser Pulses,” J. Lightwave Technol. 21(5), 1320–1327 (2003). [CrossRef]
14. T. Zhu, K. S. Chiang, Y. J. Rao, C. H. Shi, Y. Song, and M. Liu, “Characterization of Long-Period Fiber Gratings Written by CO2 Laser in Twisted Single-Mode Fibers,” J. Lightwave Technol. 27(21), 4863–4869 (2009). [CrossRef]
15. B. Li, X. Zhan, M. Tang, L. Gan, L. Shen, L. Huo, S. Fu, W. Tong, and D. Liu, “Long-period fiber gratings inscribed in few-mode fibers for discriminative determination,” Opt. Express 27(19), 26307–26316 (2019). [CrossRef]
16. Z. Liu, X. Zhao, C. Mou, and Y. Liu, “Mode Selective Conversion Enabled by the Long-Period Gratings Inscribed in Elliptical Core Few-Mode Fiber,” J. Lightwave Technol. 38(6), 1536–1542 (2020). [CrossRef]
17. K. Lai, S. G. Leon-Saval, A. Witkowska, W. J. Wadsworth, and T. A. Birks, “Wavelength-independent all-fiber mode converters,” Opt. Lett. 32(4), 328–330 (2007). [CrossRef]
18. L. Rindorf and O. Bang, “Highly sensitive refractometer with a photonic-crystal-fiber long-period grating,” Opt. Express 33(6), 563–565 (2008). [CrossRef]
19. G. Bellanca, N. Riesen, A. Argyros, S. G. Leon-Saval, R. Lwin, A. Parini, J. D. Love, and P. Bassi, “Holey fiber mode-selective couplers,” Opt. Express 23(15), 18888–18896 (2015). [CrossRef]
20. Z. Zhang, Y. Tsuji, M. Eguchi, and C. Chen, “Design of polarization converter based on photonic crystal fiber with anisotropic lattice core consisting of circular holes,” J. Opt. Soc. Am. B 34(10), 2227–2232 (2017). [CrossRef]
21. X. Zhang, Y. Liu, Z. Wang, J. Yu, and H. Zhang, “LP01-LP11a mode converters based on longperiod fiber gratings in a two-mode polarization-maintaining photonic cry,” Opt. Express 26(6), 7013–7021 (2018). [CrossRef]
22. M. Feng, Y. Liu, Z. Wang, B. Mao, and H. Zhang, “Ultra-Broadband Mode Converter Using Cascading Chirped Long-Period Fiber Grating,” IEEE Photonics J. 11(6), 1–10 (2019). [CrossRef]
23. Y. Cailong, Z. Cong, F. Songnian, S. Lei, W. Yuncai, and Q. Yuwen, “Mode converter with C + L band coverage based on the femtosecond laser inscribed long period fiber grating,” Opt. Lett. 46(14), 3340–3343 (2021). [CrossRef]
24. Q. Huang, X. Wang, J. Dong, Z. Zheng, O. Xu, D. P. Songnian Fu, J. Li, and Y. Qin, “Ultra-broadband LP11 mode converter with high purity based on long-period fiber grating and an integrated Y-junction,” Opt. Express 30(8), 12751–12759 (2022). [CrossRef]
25. Pengfei Tian, “The simulation program of the T-SLPG,” figshare, (2022), https://doi.org/10.6084/m9.figshare.21308076
