Open Access
Add to BibSonomy
Abstract
An orbital angular momentum (OAM) fiber amplifier supporting 20 OAM modes based on a ring-core Yb-doped fiber (RC-YDF) is proposed and demonstrated. The RC-YDF we designed and fabricated has two successive Yb-doped annular layers in the ring-core and can support the amplification of OAM (|l|=1, 2, 3, 4, 5) modes at the wavelength of 1064 nm. With a core pump configuration, we characterize the amplification performance of the RC-YDF based amplifier by simulation and experiments. The amplification of each supported OAM mode is proved by the achieved gain of more than 8 dB and a low differential modal gain less than 1dB with an input signal power of about 5dBm. This is the first experimental demonstration, as far as we know, of the amplification of the OAM mode from 1- to 5-order in aYb-doped fiber.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Structured light, especially beams carrying orbital angular momentum (OAM), has gained much interest for its unique phase and amplitude structure [1,2]. The OAM beams are also known as vortex beams due to their spiral phase front and donut-shaped intensity profiles. The spiral or twisting helical phase front is described by exp(ilφ), where l is the number of 2π phase shifts around the center of the phase profile of beam. The beam with different l carries an OAM of lћ per photon. Benefit from these unique properties, the OAM as a new degree of freedom of light has attracted much attention in various application scenarios, such as optical trapping and manipulation of particle [3,4], material processing [5], nonlinear four-wave mixing [6], optical free space and fiber-based communications [7–9], super-resolution imaging [10], atomtronics [11] and ultrahigh-density data storage [12] and other fields. OAM beams are typically generated by imposing a helical phase front on a Gaussian beam using spatial light modulator (SLM), phase plate and so on in free space. These approaches are relatively easy to implement and the generated OAM beam is often coupled into optical fibers to facilitate application. However, the efficient power of OAM mode in the fiber is limited by relatively low power for the low conversion efficiency and the coupling efficiency. To cope with these issues, optical amplification in fiber is an effective approach. The amplification of OAM mode in fiber has captured a great attention recently [13–15]. In the band of 1.0 µm, the OAM mode is widely used in many fields including optical trapping and manipulation of particles, nonlinear four-wave mixing and other fields. Driven by these applications, the amplification of the OAM modes based on Yb-doped material also captured many interests, because the Yb-doped amplifiers can provide broad-gain bandwidth, high output power, excellent power conversion efficiency and good beam characteristics in the band of 1.0 µm [16].
The power amplification of OAM beam in two flash-lamp-pumped Nd:YAG amplifier stages has demonstrated using a bulk solid-state amplifier [17]. However, the bulk amplifier is rather challenging because it is difficult to achieve good overlap efficiency between the pump and the donut-shaped laser mode. The amplification of OAM mode based on Yb-doped fiber (YDF) has been realized by stressing a large-mode-area double-clad YDF amplifier [18,19], but the order of the OAM is limited to the first order (l=±1). Recently, the amplification of first and second order (l=±1, ±2) OAM mode is realized in a commercially available few-mode large mode area YDF [20]. In ring-core (RC) fibers, the stability of the supported OAM modes is higher, which have similar mode intensity profile and higher overlap with ring-type pump mode. In terms of the characteristics of the amplification of OAM, a ring-core YDF (RC-YDF) has a high efficiency for the high spatial overlap between its signal mode and core pump mode [21]. The RC-YDF has been proposed for the adaptive modal gain control theory of linear polarization (LP) mode [22] and realizing the amplification of cylindrical vector and LP mode with high purity [22,23]. In the amplification of higher-order OAM mode at 1064 nm, Li et al. realized the generation and amplification of 3 OAM modes (l=±1, ±2, ±3) employing a helical Yb-doped three-core microstructure fiber [24]. However, in this three-core method, the fiber must be twisted and has a relatively rigorous requirement for the environment. How to realize the amplification of multiple higher-order OAM modes to meet the rapid development of the variety of applications is still a crucial problem up to now.
In this work, to realize a multiple OAM modes fiber amplifier, we first design and fabricate a RC-YDF with two successive annular Yb-doped layers, which can support the amplification of 20 OAM modes (topological charge |l|=1, 2, 3, 4, 5 with different polarization) at 1064 nm. Then, we built a RC-YDF based optical amplifier. A core pumped implementation is adopted and a SLM is employed to generate input OAM signals with the required spiral phase front in the OAM fiber amplifier experiments. The amplification of OAM modes is demonstrated by the modal intensity, phase distribution and the modal gain. The measured gain of each mode is about 8 dB with input signal power of about 5 dBm.
2. Design and fabrication of ring-core Yb-doped fiber
Figure 1 shows the schematic cross section of the designed RC-YDF with two successive annular Yb-doped layers in the ring core. It consists of a centeral region, a Yb-doped ring core, a trench, and an outer cladding. The ring core has a high refractive index ncore, and the inner and outer radii are 7.5 and 13.0 µm, respectively. The centeral region and outer cladding are pure fused silica with nclad denoting its refractive index. The trench layer has a relatively low refractive index ntrench, and its inner and outer radii are 13 and 17.5 µm, respectively. It can increase the modal confinement and reduce the impact of bending and environments perturbation. Compared with the centeral region, the refractive index differences between the nclad, ncore, and ntrench are about 0, 0.0044 and −0.0004, respectively. The modal characteristic of this RC-YDF is theoretically analyzed by the full vector finite element method. Figure 2(a) shows the intensity and spatial phase distributions of the supported OAM modes in this fiber. Figure 2(b) shows the simulated effective indices of the OAM modes (i. e. OAMl, |l|=1, 2, 3, 4, 5) guided in this RC-YDF in the wavelength range of 960–1110nm. These simulation results make clear that this fiber can support 5 OAM mode groups (OAM1 to OAM5) at 1064 nm. The overlaps of the normalized mode intensity and the fiber refractive index profile (RIP) are shown in Fig. 2(c). One can see that the intensity distribution between the pump and signal modes is highly coincident, especially in the low order signal modes. To reduce the difference of the mode gain and taking the manufacturing process of optical fiber into consideration, the designed Yb-doped region cover the core region with different concentration, as shown in Fig. 1. Here, the concentration ratio between the lower- and high-doped layer is 3:4, three boundaries of the two-layer, r1, r2 and r3 are 7.5 µm, 9.5 µm and 13.0 µm, respectively. These structural parameters guarantee that there is a high overlapping distribution among the signal modes, pump mode and Yb3+ ions, which implies that each OAM mode will obtain almost identical amplification when they switched among the 20 OAM modes with a same input energy.
Fig. 2. (a) Intensity profiles and spatial phase distributions of different OAM modes. (b) Effective refractive index of different OAM modes of designed RC-YDF as a function of wavelength. (c) Overlap of RIP and normalized intensity profiles. (d) The simulated modal gains of different OAM modes as a function of the pump power.
When Yb3+ ion transition is considered as a two-level system, and a set of rate equations and power propagation equations presented in Ref. [25] and Ref. [26] can be modified and used to describe the transverse mode competition (between the pump mode and signal OAM mode) in the RC-YDF based amplifier. The modified equations can be expressed by the following space-dependent and time-independent steady rate equations:
Assuming that the amplified spontaneous emission (ASE), coupling loss of signal and pump light, the cross-coupling between modes, the propagation loss of pump and signal are neglected, the length of the RC-YDF is 1 m, the pump mode is fundamental mode at 976 nm and forward propagation, the signal wavelength is 1064 nm and input power in each OAM mode is 4 mW, we calculated the simulated modal gain of different OAM modes under different pump powers respectively, as shown in Fig. 2(d). We can see that the gain of each OAM mode increases with the pump power increasing in exactly the same way, and all the gain can reach to the 20 dB with increasing the pump power.
Based on the designed structure, we fabricated the RC-YDF using a modified chemical vapor deposition (MCVD) and an all-gas-phase high-temperature evaporation deposition process. Benefitting from the advanced all-gas-phase process, the uniform co-doping of Yb3+ ions and diverse co-doping agents was implemented, and a low-loss and high-gain core rod of YDF preform was manufactured. In order to satisfy the designed YDF with high performance, the core rod and the high-purity quartz sleeve were combined, and low-loss fusion was realized to make a high-performance RC-YDF preform. The process parameters of the drawing platform, such as furnace temperature, curing temperature, and annealing temperature are reformed continuously until a RC-YDF with high performance is fabricated. The cross section of the fabricated RC-YDF is shown in Fig. 3(a), which is consistent with the design. The outer radii of central region, ring-core, trench layer and cladding layer are 7.5, 13.1, 17.4 and 62.5 µm, respectively. The RIP of the fabricated RC-YDF shown in Fig. 3(b) is well matched to the designed RIP. These matched RIP and the simulation results suggest that the fabricated RC-YDF can support the 20 OAM modes at 1064 nm. The Yb-doped profile (YDP) of the fabricated RC-YDF along with designed are plotted in Fig. 3(c). Black solid square is the measured relative concentration of the Yb-doped at the corresponding radial positions. It has some deviation from the design data may because the ion diffusion during the fiber production process. The small-signal absorption spectrum of the fabricated RC-YDF is measured by the cutback method using a white light source with the output port of single-mode fiber (SMF) and an optical spectrum analyzer (OSA). Figure 3(d) shows the absorption spectrum of the fiber with a truncation length of ∼9.9 cm. Because the multimode interference of the light source within the spectrum band, it differs from the absorption cross sections for Yb3+ ions, but there is still a very clear spectral absorption peak around 976 nm. The corresponding absorption coefficient at 976 nm is ∼130 dB/m. The absorption coefficient of the OAM mode from first to fifth order is about 1.289,1.329,1.307,1.293,1.339 dB/m at1064 nm, respectively, which is measured using a narrow band laser and the cutback method.
Fig. 3. (a) Microscopy image of the RC-YDF. (b) designed (red line) and measured (black dots) RIP of the RC-YDF. (c) YDP (red line is designed data; the black solid square points are the test data.) (d) Result of sample transmission (black line is test data, red line is data after multiband smooth and envelope processing.)
3. Experimental results and discussion
To confirm that the amplification of 20 OAM modes can be realized with the fabricated RC-YDF, a core-pumped OAM mode amplifying system was built as shown in Fig. 4(a). In order to generate an OAM mode with the desired topological charge l, a reflective phase-only SLM is introduced at the input-end of the amplifier. One seed OAM mode is formed by a forked diffraction grating, which is a combination of a helical phase and a grating phase and can transform the incident Gaussian beam into an OAM beam at its first-order diffraction direction. Figure 4(b) shows the phase patterns of the forked diffraction grating which was loaded on the SLM for generating OAM modes with topological charge l = 1, 2, 3, 4, 5. The generated OAM mode, as shown in Fig. 4(c), passes through an isolator (prevents the SLM damage and undesired parasitic lasing), then is coaxial with a 976 nm single-mode pump beam by a dichroic mirror (DM) for coupling together into the RC-YDF. Here, the RC-YDF 80 cm long is used as the active fiber to provide the gain. The pump power was measured at the input end of the RC-YDF. The coaxial beams (signal and pump) are coupled into the RC-YDF by a 16× objective lens (NA = 0.25). At the other end of the RC-YDF, a 25 × objective lens is used to collect the output beam. Another DM is used to filter out residual pump energy. The amplified OAM mode is split into two branches by a beam splitter (BS), and one is passing a filter and the other is collected by a collimator and coupled into an OSA using a few-mode fiber. The modal intensity distribution and helical interference pattern of the branch after the filter were recorded by a charge-coupled device (CCD), in which the filter was used to strip away ASE. The branch coupled into the OSA is used to measure and analyze the amplified light spectrum.
Fig. 4. (a) Experimental configuration of the fabricated RC-YDF assisted OAM fiber amplifier. SLM, spatial light modulator; PC, polarization controller; ISO, isolator; DM, dichroic mirror; Obj., objective lens; RC-YDF, ring-core Yb-doped fiber; BS, beam splitter; OSA, optical spectrum analyzer; CCD, charge-coupled device. (b) Phase masks with different topological charge. (c) The intensity distribution and helical interference fringes of OAM beam that injected onto RC-YDF.
Based on the experimental system, as a validation demonstration, the modal gain properties of the 5 OAM modes (l=+1, +2, +3, + 4, +5) were characterized by activating separately. In the experiments, after considering the absorption loss of each OAM mode, we tested the amplification performance of different OAM modes at different signal powers. Figure 5 shows the modal intensity distribution and helical interference fringes of different OAM modes when the signal power was about −10 dBm and pump powers were 0 mW and 667 mW, respectively. The number of spiral arms and their rotation directions in each interference pattern indicate the order of the OAM mode (the number of independent spiral arms indicates absolute value of order of OAM mode, clockwise rotation means the order is positive, counterclockwise rotation means the order is negative.). The energy distribution and the interference pattern of the OAM modes were enhanced when pump light was coupled into the RC-YDF, which indicates that each OAM mode was amplified obviously. The distinct interference patterns almost did not change after amplification, which illustrates that the vortex phase of each mode is well preserved in the amplification process.
Fig. 5. The modal intensity distribution (a) and (c), and helical interference fringes (b) and (d), of different OAM modes at the 1064 nm wavelength under 0 mW and 667 mW total pump power, respectively.
After removing the right DM, we can obtain the total spectra in the wavelength band of 960–1070 nm. The spectrum of each mode individually under the pump power of 0 mW (shown in Fig. 6(a)) and 1037 mW (shown in Fig. 6(b)) was recorded, respectively, in which the input signal power was about 5 dBm. Comparing the spectra of these two states, we can find that each OAM mode is effectively amplified and all the modes have similar gain. The slight differences among the curves recorded by the OSA originate from the different coupling efficiency of the few-mode fiber under receiving the different modes. After considering various losses from the output of the RC-YDF to the input of few-mode fiber, we obtained the gain curve of each OAM mode with changing the pump power. Two seed OAM mode powers, −10 and 5dBm as two examples, are selected, and the gains of each OAM in the five modes were measured as functions of the pump power, as shown in Fig. 6(c) and Fig. 6(d), respectively. With the increase of the pump power, the gains are increased gradually. The gain of each OAM in the five representative modes are all about 9 dB and 8 dB, when the input signal power is about −10 or 5 dBm, respectively. We can found that each OAM mode have similar gain, differential modal gain (DMG) is less than 1dB. Low DMG means that the RC-YDF can support amplification of multiple modes and the gain does not decrease significantly when the mode is switched. These test results indicate that the gain is not saturated with the increase of pump power to 1037 mW. It is believed that with the further increase in pump power, the gain of the amplifier in each OAM mode will be further improved. On the other hand, one can see that the gain of each OAM mode under the 1037 mW pump power has not decreased significantly (the maximum decrease is only about 1 dB) with the signal power increases from about −10 dBm to ∼5 dBm. This result means that the output amplified OAM mode power can be further boosted by optimizing the signal power and increasing the pump power.
Fig. 6. (a) Spectrum of different OAM modes without pump. (b) Spectrum of different OAM modes with 1037 mW pump power. (c) The modal gain curves of different OAM modes as a function of the pump power when signal power is about −10 dBm. (d) The modal gain curves of different OAM modes as a function of the pump power when signal power is about 5 dBm.
There are some differences between experimental results and the simulation results, these differences can be attributed to the coupling loss of the pump light and the fluctuation of the light source. Due to the large absorption coefficient, the coupling loss of pump light wasn’t measured.
4. Conclusion
In summary, we have proposed and experimentally demonstrated the amplification of 20 OAM modes (|l| = 1, 2, 3, 4, 5) using the home-made RC-YDF. To the best of our knowledge, this is the first demonstration of effective amplification of five OAM mode groups (from 1st to 5th order) in YDF. The gain of more than 8 dB in each OAM mode has been achieved by the core pumped system under the 1037mW pump power with input signal power about 5 dBm. The effective gain of the system is limited by the input pump power and it can be further scaled by increasing the power and coupling efficiency of pump light. We expect that this RC-YDF based OAM amplifier will find more applications in the areas that require various OAM beams working at the band of 1.0 µm.
Funding
Key-Aera Research and Development Program of Guangdong Province (2020B0101080002); National Key Research and Development Program of China (2019YFA0706300); National Natural Science Foundation of China (61875076, 61935013, 62035018, U2001601); Guangzhou Science and Technology Program key projects (201904020048); Basic and Applied Basic Research Foundation of Guangdong Province (2021A1515011837).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011). [CrossRef]
2. H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017). [CrossRef]
3. M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011). [CrossRef]
4. N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22(1), 52–54 (1997). [CrossRef]
5. K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012). [CrossRef]
6. X. Liu, E. N. Christensen, K. Rottwitt, and S. Ramachandran, “Nonlinear four-wave mixing with enhanced diversity and selectivity via spin and orbital angular momentum conservation,” APL Photonics 5(1), 010802 (2020). [CrossRef]
7. A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015). [CrossRef]
8. J. Liu, S. Li, J. Du, C. Klitis, C. Du, Q. Mo, M. Sorel, S. Yu, X. Cai, and J. Wang, “Performance evaluation of analog signal transmission in an integrated optical vortex emitter to 3.6-km few-mode fiber system,” Opt. Lett. 41(9), 1969–1972 (2016). [CrossRef]
9. H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. A. Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5(1), 14931 (2015). [CrossRef]
10. L. Yan, P. Kristensen, and S. Ramachandran, “Vortex fibers for STED microscopy,” APL Photonics 4(2), 022903 (2019). [CrossRef]
11. S. Franke-Arnold, “Optical angular momentum and atoms,” Phil. Trans. R. Soc. A 375(2087), 20150435 (2017). [CrossRef]
12. X. Ouyang, Y. Xu, M. Xian, Z. Feng, L. Zhu, Y. Cao, S. Lan, B. Guan, C. Qiu, M. Gu, and X. Li, “Synthetic helical dichroism for six-dimensional optical orbital angular momentum multiplexing,” Nat. Photonics 15(12), 901–907 (2021). [CrossRef]
13. J. Liu, S. Chen, H. Wang, S. Zheng, L. Zhu, A. Wang, L. Wang, C. Du, and J. Wang, “Amplifying Orbital Angular Momentum Modes in Ring-Core Erbium-Doped Fiber,” Research 2020, 1–12 (2020). [CrossRef]
14. T. Wen, S. Gao, W. Li, J. Tu, C. Du, J. Zhou, Z. Ao, B. Zhang, W. Liu, and Z. Li, “Third- and fourth-order orbital angular momentum multiplexed amplification with ultra-low differential mode gain,” Opt. Lett. 46(21), 5473–5476 (2021). [CrossRef]
15. X. Zhang, J. Liu, S. Chen, W. Li, C. Du, and J. Wang, “Amplification of 14 orbital angular momentum modes in ring-core erbium-doped fiber with high modal gain,” Opt. Lett. 46(22), 5647–5650 (2021). [CrossRef]
16. R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33(7), 1049–1056 (1997). [CrossRef]
17. X. Chen, C. Chang, Z. Lin, P. Ding, and J. Pu, “High-Energy Nanosecond Optical Vortex Output From Nd:YAG Amplifiers,” IEEE Photonics Technol. Lett. 28(12), 1271–1274 (2016). [CrossRef]
18. Y. Tanaka, M. Okida, K. Miyamoto, and T. Omatsu, “High power picosecond vortex laser based on a large-mode-area fiber amplifier,’,” Opt. Express 17(16), 14362–14366 (2009). [CrossRef]
19. M. Koyama, T. Hirose, M. Okida, K. Miyamoto, and T. Omatsu, “Power scaling of a picosecond vortex laser based on a stressed Yb-doped fiber amplifier,” Opt. Express 19(2), 994–999 (2011). [CrossRef]
20. D. Lin, J. Carpenter, Y. Feng, Y. Jung, S.-U. Alam, and D. J. Richardson, “High-power, electronically controlled source of user-defined vortex and vector light beams based on a few-mode fiber amplifier,” Photonics Res. 9(5), 856–864 (2021). [CrossRef]
21. H. Li, Y. Zhang, Z. Dong, J. Lv, C. Gu, P. Yao, L. Xu, R. Zhang, J. Su, W. Chen, Y. Zhu, and Q. Zhan, “A High-Efficiency All-Fiber Laser Operated in High-Order Mode using Ring-Core Yb-Doped Fiber,” Ann. Phys. 531(10), 1900079 (2019). [CrossRef]
22. W. T. Fang, R. X. Tao, Y. M. Zhang, H. X. Li, P. J. Yao, and L. X. Xu, “Adaptive modal gain controlling for a high-efficiency cylindrical vector beam fiber laser,” Opt. Express 27(22), 32649–32658 (2019). [CrossRef]
23. J. Lv, H. Li, Y. Zhang, L. Deng, X. Ma, C. Gu, P. Yao, L. Xu, and Q. Zhan, “Tailoring the spectrum and spatial mode of Yb-doped random fiber laser,” Opt. Express 30(5), 8345–8355 (2022). [CrossRef]
24. B. Li, G. Zhou, J. Liu, C. Xia, and Z. Hou, “Orbital-angular-momentum-amplifying helical vector modes in Yb3+-doped three-core twisted microstructure fiber,” Opt. Express 28(14), 21110–21120 (2020). [CrossRef]
25. I. Kelson and A. A. Hardy, “Strongly pumped fiber lasers,” IEEE J. Quantum Electron. 34(9), 1570–1577 (1998). [CrossRef]
26. M. Gong, Y. Yuan, C. Li, P. Yan, H. Zhang, and S. Liao, “Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers,” Opt. Express 15(6), 3236–3246 (2007). [CrossRef]
