Open Access
Add to BibSonomy
Abstract
We demonstrate two critical rules of designing photonic lanterns for applications in adaptive spatial mode control: (1) optimized input fiber arrangements to effectively control modes; (2) appropriate input fiber core-cladding ratio to expand the optional range of the output fiber. The 3×1 and 5×1 photonic lanterns according to above design requirements have been fabricated. Using stochastic parallel gradient descent algorithm, the phases of the inputs are actively modulated to stabilize the output of novel 5×1 photonic lantern with 30/125 µm output fiber. When the control target is the fundamental mode, the M2 factor of output beam is below 1.2 stably, which will provide a possible technical solution to increase the mode instability threshold in large mode area fiber laser systems. Furthermore, we obtain single orbital angular momentum mode (OAM01 or OAM02 mode) and high order linearly polarized mode (LP11 or LP21 mode) with the purity of the corresponding modes over 0.85 by altering evaluation function, which will be of benefit in optical communication and atomic optics.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Specific spatial profile laser beams are desired in many applications. For example, fundamental mode beams with high beam quality are required for high energy industrial applications [1,2]; high-order linearly polarized (LP) mode beams used in optical fiber communication can overcome “capacity crunch” based on space-division multiplexing [3,4]; vortex beams with special propagation characteristic are used in atomic optics, free space optical communications, optical trapping of particles [5,6], and so on.
In order to obtain specific output modes, various methods have been demonstrated. Some attempts by using cylindrical lens mode converters, phase plates or spatial light modulators [7–9] have been carried out, which are often limited by the performance of the device itself. In 2016, Aksenov et al. suggested a technique for generation of synthesized orbital angular momentum (OAM) mode beams based on a fiber laser array [10]. But the smoothed phase distributions and intensity fluctuation dispersion decrease require contradictory conditions, which will be a dilemma in practical applications [11]. In 2017, a switchable LP01 or LP11 mode beam was achieved by controlling the input polarization state of the seed laser at output power of 500 W level [12]. However, it is difficult for this device to generate higher order modes.
Photonic lanterns (PL), as shown in Fig. 1(a), allow for a low-loss mode evolution from a bundle of discrete single-mode waveguides into a multimode waveguide [13]. In 2012, Nicolas K. Fontaine et al. proposed geometric requirements for photonic lanterns which can be used as both the spatial multiplexer and the spatial demultiplexer in communication systems [14]. In recent years, photonic lanterns have been explored in adaptive optics system to achieve spatial mode control. In 2016, Montoya et al. used a 3×1 photonic lantern to achieve fundamental mode with a high beam quality in a few-mode fiber with a core diameter of 20 µm [15]. That same year, Wittek et al. demonstrated a mode-selective amplification in large mode area ytterbium-doped fiber using a 3×1 photonic lantern and the three lowest linearly polarized modes (LP01, LP11a and LP11b) were obtained [16].
Fig. 1. The geometrical structure of a photonic lantern. (a) a schematic of a 5×1 photonic lantern; (b) geometrical arrangements of the input fiber bundles: fibers arranged according to regular polygons with a hollow center; (c) a diagram showing the definition of the core-cladding ratio.
In this paper, we propose and demonstrate two design rules to improve the beam control effect of PL-based fiber laser systems. The first design rule is to renew how the input fiber bundles should be arranged, as shown in Fig. 1(b). The second design rule is about the core-to-cladding ratio (as shown in Fig. 1(c)), which is proved to be an important parameter to optimize in order to achieve a stable single mode in large mode area (LMA) output fiber while minimizing the number of input fibers. The novel photonic lanterns according to above requirements are fabricated by tapering the bundle of input fibers inside a low-index tube. And the 3×1 photonic lantern with 30 µm output fiber is used in an adaptive spatial mode control system to verify the importance of core-to-cladding ratio experimentally. Furthermore, novel 5×1 PL has been used to achieve stable mode control in the large mode area fiber output. The fundamental mode (LP01), LP11a,b, LP21a,b, OAM0±1 and OAM0±2 modes with high purity have been obtained respectively at the output multimode fiber with a core diameter of 30 µm.
2. Novel photonic lanterns for mode control
Photonic lantern, as a linear optical device, can effectively solve the problems of mode energy coupling and mode quality degradation between a set of single-mode waveguide and a multimode waveguide [13]. The photonic lantern used here should not only have low transmission loss, but also satisfy the needs of the adaptive spatial mode control. Thus, a series of optimized input fiber arrangements of photonic lantern are proposed and compared with the traditional ones. Besides, to expand the optional range of the output fiber, the core-to-cladding ratio requirements for different photonic lanterns are found out.
2.1 Optimized input fiber arrangements
To analyze the mode evolution in photonic lantern, the light field distribution on the cross section at different locations are calculated using modal analysis and beam propagation method (BPM). Take a 5×1 photonic lantern as an example, as shown in Fig. 2(a)-(c), five independent fundamental modes with specific amplitude and phase are set at input single-mode fiber (SMF) end (A). As the cores of the SMF are approaching and thinning (B to D), energy coupling occurs between different cores, and the beam evolves into a supermode [17]. After entering the waist region (D to E), it finally evolves to the corresponding mode form in large mode area (LMA) fiber (F). Figure 2(b) and Fig. 2(c) show the evolution process of LP01 mode and OAM0+1 mode respectively.
Fig. 2. The process of mode evolution in a 5×1 photonic lantern. (a) slit diagram of a 5×1 photonic lantern; (b), (c) the evolution process to form LP01 mode and OAM0+1 mode respectively: the upper patterns show the intensity distribution at different locations, while the lower patterns show the phase distribution (Note that 0 and 2π are the same phase); (d) the transmission matrix of a 5×1 photonic lantern.
Transmission matrix is used mathematically to describe these processing from the input fundamental mode combinations to the multimode output. In this N×N matrix, every column corresponds to the input information of a SMF (the corresponding SMFs are highlighted in red in the bottom diagrams of Fig. 2(d)), and every row corresponds to an input combination that evolves to an output mode. Each element is the complex amplitude of the input light field, in the form A·eiφ (A is the amplitude of the fundamental mode and φ is its phase). For example, Fig. 2(d) indicates the 5×1 photonic lantern transmission matrix. The first row indicates the input combination for LP01 mode, that is, five fundamental mode beams with equal amplitude and same phase, which corresponds to Fig. 2(b). The second row indicates the input combination for OAM0+1 mode, that is, five fundamental mode beams with equal amplitude and 0.4π phase difference between two adjacent paths, which corresponds to Fig. 2(c).
If the tapper area of the photonic lantern is long enough so that the mode evolution is slow enough, such PLs can be regarded as an adiabatic linear mode converter. In this case, the one-to-one correspondence between the input and output fields entirely depends on the geometric arrangement of the SMFs of the photonic lantern. The appropriate geometric arrangement can make the input combination corresponding to the single output mode easier to obtain.
In 2012, Fontaine et al. proposed a series core arrangement for different photonic lanterns [14]. Though these core geometries minimize losses and suitable for space-division multiplexing system, it brings some difficulties to mode control in adaptive control system. As an example, we compare the traditional (5 + 1)×1 photonic lantern and the optimized 5×1 photonic lantern to gain LP01, OAM0±1 and OAM0±2 modes. Ideally, if the taper angles of above two photonic lanterns are small enough, 0 dB coupling losses and 0 dB mode-dependent losses would be achieved (rounded to within 0.1 dB numerical error) [14].
Figure 3 shows the transmission matrix of traditional (5 + 1)×1 photonic lantern. To achieve the LP01 mode, the intensity of the middle channel and the intensity of the side channel are calculated to be about 4:1, which will significantly reduce the control bandwidth [18]. On the other hand, as shown in the transmission matrix of optimized 5×1 photonic lantern (Fig. 2(d)), pure fundamental mode in MMF can be obtained if the input amplitudes and phases are the same. Such geometry helps the evaluation function of the control algorithm converge to the optimal value quickly. Besides, the output field can be conveniently tuned to other mode (such as OAM mode shown in Fig. 2(c)) by actively modulating input phase without altering intensity. Therefore, for mode control purpose, it is better to arrange the input fibers according to regular polygons without the center one.
Furthermore, we extend the optimized geometric arrangements to photonic lanterns with more channels (7, 9 core lanterns). Figure 4 summarizes the optimized arrangements of the photonic lanterns and the modes they can achieve. The 7 core pattern is the novel arrangement for obtaining LP01, LP11a,b, OAM0±1, LP21a,b and OAM0±2 mode and LP31a,b, OAM0±3 mode. The 9 core pattern is the novel arrangement for obtaining above 13 modes and LP41a,b, OAM1±4 mode. One great advantage from such arrangement is that LP01 and OAM modes can be conveniently obtained by inserting beams of the same amplitudes to every SMF.
Fig. 4. Novel arrangements of input fibers and the modes they can achieve. (a) arrangements of different photonic lanterns; (b) and (c) the LP modes and OAM modes generated by photonic lanterns with 3, 5, 7, 9 cores are framed in yellow, purple, green and pink respectively.
2.2 Core-to-cladding ratio requirement
Traditional photonic lanterns need to meet the mode matching requirement, that is, the number of input SMF fiber core should be equal to the number of the modes supported by the output fiber [19]. This requirement theoretically guarantees the invertibility of the transmission matrix, but the optional range of the output fiber is greatly limited. In 2016, MIT Lincoln Laboratory broke through this design requirement and used a 3×1 photonic lantern to achieve fundamental mode output in the multimode fiber with a core diameter of 20 µm which supports six modes [15].
To further extend the upper limit of the core diameter of the output fiber, we have simulated the influence of different core-cladding ratio (as defined in the Fig. 1(c)) of input fibers on the mode evolution results of the photonic lantern with different output fibers. For example, the LP01 mode evolution in 5×1 and 3×1 photonic lanterns are simulated. M2 factor is selected to evaluate the LP01 mode purity (the smaller the M2 factor, the higher the proportion of the LP01 mode).
The mode evolutions of photonic lanterns with different core-cladding ratios of the input SMFs (the core diameter is 10 µm) have been simulated based on beam propagation method. These photonic lanterns have the same tapering length of 15,000 µm to satisfy the adiabatic condition. The M2 factor of the output light field is calculated by second moment of light intensity. Figure 5 shows that the M2 factor varies with core-cladding ratio of the input SMFs (the core diameter is 10 µm) for output fibers with different core diameters. To ensure M2 factor of the output beam below 1.1, the general observation is that the core-cladding ratio needs to become smaller for larger core diameters. For example, to obtain the quasi-fundamental mode at the 30 µm output end of a 5×1 photonic lantern (Fig. 5(a), green), the cladding of the input fiber should be less than 72 µm (the core-cladding ratio should be more than 0.138); if the core diameter of the output fiber is 35 µm, the cladding diameter of the input fiber should be less than 80 µm (the core-cladding ratio should be more than 0.125). For 3×1 photonic lantern, to obtain the quasi-fundamental mode at the 30 µm output end (Fig. 5(b), orange), the cladding of the input fiber should be less than 98 µm (the core-cladding ratio should be more than 0.102); if the core diameter of the output fiber is 35 µm, the cladding diameter of the input fiber should be less than 105 µm (the core-cladding ratio should be more than 0.095). Moreover, in the actual fabrication processing, fiber cladding is etched by immersing the input SMF in hydrofluoric acid solution to increase its core-cladding ratio, which will be shown in detail in the next section.
Fig. 5. M2 - core-cladding ratio curves of different photonic lanterns. (a) 5×1 photonic lanterns with the core diameter of the output fiber at 30 um, 35 um, and 40 um; (b) 3×1 photonic lanterns with the core diameter of the output fiber at 25 um, 30 um, and 35 um. (Each curve corresponds to the same output fiber diameter.)
3. Experimental results
3.1 Fabrication
3×1 and 5×1 photonic lanterns are fabricated respectively with optimized core arrangements and appropriate core-to-cladding ratio. The fabrication process of photonic lantern includes bundling the SMFs into the capillary tube, fusing and tapering them to match the size of the output fiber for cutting and splicing [20]. Firstly, SMF is used as input fiber, a certain length of coating layer of each input fiber is peeled off. Secondly, these ends of input fibers are inserted into hydrofluoric acid solution to partially corrode the cladding layer, so that the core-cladding ratio reaches the set value. Next, all the input fibers are arranged according to the proposed geometry and inserted into the capillary tube with low refractive index. The fiber-tube bundle is then tapered under the condition of the adiabatic approximation. The end of the fiber bundle is finally cut flat and spliced with certain output multimode fiber.
For the 3×1 photonic lantern, 10/110 µm (NA=0.06) single-mode fiber as the input end and 25/125 µm (NA=0.08) few-mode fiber as the output end are chosen. The SMF bundle is inserted into a low-folding glass tube (510/1000 µm) and tapered into 25/45 µm (the outer diameter of the fiber bundle/capillary tube). By means of fiber cutting, we access clean fiber end face. The optical microscope of its end face is shown in the Fig. 6(a). This end is finally spliced with output fiber. For the 5×1 photonic lantern, 10/70 µm (NA=0.06) single-mode fiber as the input end and 30/125 µm (NA=0.08) few-mode fiber as the output end are chosen. The fiber-tube bundle is tapered into 30/60 µm to be cut (Fig. 6(b)) and spliced with the output fiber (Fig. 6(c)).
Fig. 6. The optical microscope of the fiber-tube bundle end face of 3×1 (a) and 5×1 (b) photonic lanterns; (c) splicing point image.
3.2 Adaptive spatial mode control results
As mentioned above, the ideal photonic lantern can be regarded as a linear optical element. However, in the actual optical laser system, the fluctuation of phase difference between different channels and polarization disturbances has a great influence on the results of mode evolution, resulting in unstable and irregular light spots at the output end of the photonic lantern. In order to lock the desired mode output, the idea of adaptive optics (AO) technology is used. The detected output light field should be actively fed back to the controller to control the state of each input beam.
Firstly, the importance of core-to-cladding ratio on mode evolution is studies by using of 3×1 photonic lantern with 30 µm output fiber. The experimental structure is shown in Fig. 7 [21]. The fundamental mode generated by the seed laser with a wavelength of 1064 nm is split into a set of SMFs. The stochastic parallel gradient descent (SPGD) algorithm [22] is selected, and it actively controls the phase modulators at the input ends according to the evaluation function fed back by the detector. CCD is used to collect the real-time near-field light spots and transmit the collected data to the computer for mode decomposition by using computer-generated hologram (CGH)-based correlation filters [23]. A comparative experiment on input fibers corroded to the proper size and input fibers uncorroded have been carried out in this system. When the input fibers do not meet the requirement of core-cladding ratio, the M2 factor of the output beam is above 2, as shown in Fig. 8(a). But when the requirement is met, stable quasi-fundamental mode has been obtained at the output end with M2 below 1.18, as shown in Fig. 8(b) [24].
Fig. 7. Spatial mode control system based on photonic lantern. PM– phase modulators. PL– photonic lantern. CGH– computer-generated hologram. MO–microscope objectives. L1, L2– imaging lenses. FL– Fourier lens. (Reference [21], Fig. 6)
Fig. 8. Experimental comparison on 3×1 photonic lantern with input fibers uncorroded and input fibers corroded to the proper size (see Visualization 1). (a) Output spot of 3×1 photonic lantern with input fibers uncorroded. (b) Output spot of 3×1 photonic lantern with corroded input fibers (95 µm) that meet the core-cladding ratio requirement [24].
Secondly, novel 5×1 photonic lantern with 30 µm output fiber is used in the above-mentioned mode control system to verify its mode control capability. When the target mode is the fundamental mode, the power in the bucket is selected as the evaluation function. Figure 9 shows the M2 changes of the output beam (blue curve) and the purity of LP01 mode before and after the control loop closed (orange curve). As shown in the figure, under the SPGD off condition, the energy is coupled between different modes, and the beam quality is poor. While, in the closed-loop control situation, the output beam is stable in the quasi-fundamental mode pattern. According to the mode decomposition calculation, at this time, the purity of the LP01 mode is over 0.85, and the M2 factor is stable below 1.2.
Fig. 9. M2 (blue curve) and cLP01 (orange curve) of the output beam before and after the control loop closed. cLP01 represents the purity of the LP01 mode (see Visualization 2).
When the target mode is high order modes or OAM modes, the purity of corresponding mode is accordingly selected as evaluation function. Figure 10 illustrates the simulation and experimental results of achieving stable LP11, LP21, OAM01, and OAM02 outputs using this system. The mode purities were 0.96, 0.89, 0.93 and 0.91 respectively. Besides, it is easy to tune different modes or generate specific modes combination output for this system, as long as the appropriate evaluation function is switched.
Fig. 10. Simulation and experimental results of achieving LP11, LP21, OAM01 or OAM02 mode. cLP11, cLP21, cOAM01 and cOAM02 represent the purity of LP11, LP21, OAM01 and OAM02 respectively (see Visualization 3 and Visualization 4).
4. Conclusion
We have shown an adaptive spatial mode control system based on photonic lantern for obtaining specific spatial modes output. Novel photonic lantern with optimized input fibers arrangements and appropriate core-to-cladding ratio have been proposed to realize mode control in large mode area fiber laser system with low coupling losses and low mode-dependent losses. To verify the simulation results, we have fabricated 3×1 photonic lantern with 25/125 µm output fiber and 5×1 photonic lantern with 30/125 µm output fiber as an example. And quasi-fundamental mode output has been obtained with M2 below 1.2 based on the above 5×1 photonic lantern.
Our results based on 25 µm or 30 µm few-mode fiber are potentially scalable to larger diameter if the photonic lantern owns more input channel. Especially, in traditional optical system, suppression of nonlinear effects and increase of mode-instability threshold are dilemmas, which can be solved expediently by using photonic lantern in the adaptive spatial mode control system. Further research will be devoted to splice photonic lantern output fiber with a master oscillator power amplifier (MOPA) configuration to increase the mode-instability threshold in high power laser systems.
Besides, single OAM mode or higher order LP mode have been obtained with corresponding purity over 0.85, which will have important applications in optical fiber communication, specific shape laser processing and optical trapping of particles. In particular, as the input channel increases higher OAM modes can be generated and tuned efficiently, which can realize the space division multiplexing technology and make good use of the advantages of OAM mode on propagation through atmosphere or other turbulent environments.
Funding
Science and Technology Program of Hunan Province (2021RC3083); National Natural Science Foundation of China (12074432, 61905281).
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
References
1. K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express 21(2), 1944–1971 (2013). [CrossRef]
2. W. Shi, Q. Fang, X. Zhu, R. A. Norwood, and N. Peyghambarian, “Fiber lasers and their applications [Invited],” Appl. Opt. 53(28), 6554–6568 (2014). [CrossRef]
3. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004). [CrossRef]
4. J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012). [CrossRef]
5. H. Ye, C. Wan, K. Huang, T. Han, J. Teng, Y. S. Ping, and C.-W. Qiu, “Creation of vectorial bottle-hollow beam using radially or azimuthally polarized light,” Opt. Lett. 39(3), 630–633 (2014). [CrossRef]
6. A. P. Porfirev and R. V. Skidanov, “Dark-hollow optical beams with a controllable shape for optical trapping in air,” Opt. Express 23(7), 8373–8382 (2015). [CrossRef]
7. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef]
8. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993). [CrossRef]
9. W. M. Lee, X. C. Yuan, and W. C. Cheong, “Optical vortex beam shaping by use of highly efficient irregular spiral phase plates for optical micromanipulation,” Opt. Lett. 29(15), 1796–1798 (2004). [CrossRef]
10. V. P. Aksenov, V. V. Dudorov, and V. V. Kolosov, “Fiber-array-based vortex beams propagation through a turbulent atmosphere,” in 2016 International Conference Laser Optics, (2016), R4-21.
11. M. A. Vorontsov and S. L. Lachinova, “Laser beam projection with adaptive array of fiber collimators. I. Basic considerations for analysis,” J. Opt. Soc. Am. A 25(8), 1949–1959 (2008). [CrossRef]
12. R. Su, B. Yang, X. Xi, P. Zhou, X. Wang, Y. Ma, X. Xu, and J. Chen, “500 W level MOPA laser with switchable output modes based on active control,” Opt. Express 25(19), 23275–23282 (2017). [CrossRef]
13. S. G. Leon-Saval, A. Argyros, and J. Bland-Hawthorn, “Photonic lanterns,” Nanophotonics 2(5-6), 429–440 (2013). [CrossRef]
14. N. K. Fontaine, R. Ryf, J. Bland-Hawthorn, and S. G. Leon-Saval, “Geometric requirements for photonic lanterns in space division multiplexing,” Opt. Express 20(24), 27123–27132 (2012). [CrossRef]
15. J. Montoya, C. Aleshire, C. Hwang, N. K. Fontaine, A. Velázquez-Benítez, D. H. Martz, T. Y. Fan, and D. Ripin, “Photonic lantern adaptive spatial mode control in LMA fiber amplifiers,” Opt. Express 24(4), 3405–3413 (2016). [CrossRef]
16. S. Wittek, R. Bustos Ramirez, J. Alvarado Zacarias, Z. Sanjabi Eznaveh, J. Bradford, G. Lopez Galmiche, D. Zhang, W. Zhu, J. Antonio-Lopez, L. Shah, and R. Amezcua Correa, “Mode-selective amplification in a large mode area Yb-doped fiber using a photonic lantern,” Opt. Lett. 41(10), 2157–2160 (2016). [CrossRef]
17. J. A. Besley and J. D. Love, “Supermode analysis of fibre transmission,” IEE Proceedings - Optoelectronics 144(6), 411–419 (1997). [CrossRef]
18. M. A. Vorontsov, G. W. Carhart, M. Cohen, and G. Cauwenbergs, “Adaptive optics based on analog parallel stochastic optimization technique,” in Conference on Lasers and Electro-Optics (CLEO 2000). Technical Digest. Postconference Edition. TOPS Vol.39 (IEEE Cat. No.00CH37088)605 (2000).
19. T. A. Birks, I. Gris-Sánchez, S. Yerolatsitis, S. G. Leon-Saval, and R. R. Thomson, “The photonic lantern,” Adv. Opt. Photonics 7(2), 107–167 (2015). [CrossRef]
20. S. 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]
21. Y. Lu, Z. Jiang, W. Liu, Q. Zhou, M. Jiang, and K. Xie, “Orbital angular momentum mode generation system based on photonic lantern,” J. Opt. 21(12), 125702 (2019). [CrossRef]
22. P. Zhou, Y. Ma, X. Wang, H. Ma, X. Xu, and Z. Liu, “Coherent beam combination of three two-tone fiber amplifiers using stochastic parallel gradient descent algorithm,” Opt. Lett. 34(19), 2939–2941 (2009). [CrossRef]
23. T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express 17(11), 9347–9356 (2009). [CrossRef]
24. Y. Lu, Z. Jiang, W. Liu, Z. Chen, M. Jiang, Q. Zhou, and J. Zhang, “Laser mode control in fiber with core diameter of 30µm based on 3×1 photonic lantern,” Acta Optica Sinica 41(17), 1736001 (2021). [CrossRef]
