Open Access
Add to BibSonomy
Abstract
1.6 µm high-order vortex modes carrying orbital angular momentums (OAMs) play significant roles in long-range Doppler lidars and other remote sensing. Amplification of 1.6 µm high-order vortex modes is an important way to provide high-power laser sources for such lidars and also enable the weak echo signal to be amplified so that it can be analyzed. In this work, we propose a four-pass Er:YAG vortex master-oscillator-power-amplification (MOPA) system to amplify 1.6 µm high-order vortex modes. In the proof-of-concept experiments, 1.6 µm single OAM mode (l = 3) is amplified successfully and the gain ranging from 1.88 to 2.36 is achieved. Multiplexed OAM mode (l=±3) is also amplified with favorable results. This work addresses the issue as the low gain of Er:YAG vortex MOPA, which provides a feasible path for 1.6 µm high-order vortex modes amplification.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
It has been proved that laser beams can carry orbital angular momentums (OAMs) [1,2]. Such an OAM-carried beam is also called vortex mode due to its doughnut-shaped intensity pattern and spiral wavefront. Its complexed amplitude comprises a helical phase term exp(ilφ), with l the topological charge, also the eigenvalue of OAM, and φ the azimuthal angle. Vortex modes show rotational Doppler effect which results from OAM and has great potentials on rotation detection [3–5]. When a vortex beam is incident on a spinning object, frequency shifts present for reflected echo beams and such frequency shift is determined by the OAM order l and the rotational angular velocity ω of the object. Locating at eye-safe band and atmospheric window, the 1.6 µm is always an ideal wavelength for long-range lidars and other remote sensing scenarios [6–8]. Introducing OAM for 1.6 µm laser opens a new era for lidars enabling more parameter probing through rotational Doppler effect [9].
For a rotational Doppler lidar, power amplification for 1.6 µm high-order vortex modes is of great significance. Such significance is reflected from two aspects. Firstly, it is an ideal and feasible solution to generate 1.6 µm high-power high-order vortex modes which can be employed as the source to achieve longer detection range and higher detection accuracy. It only needs a vortex seed beam with low power, which addresses the issue as output power limitation resulting from the low damage threshold of OAM-tailoring elements in current vortex source. Secondly, the weak echo OAM signals of rotational Doppler lidars need to be amplified with enough intensity to be analyzed. Therefore, studying the power amplification of 1.6 µm high-order vortex modes is benefit for the increase of detection range and accuracy of rotational Doppler lidars.
For power amplification in 1.6 µm band, Er3+-doped fiber amplification is usually employed [10–12]. However, the high loss of high-order vortex modes in commercial fibers and the high cost of special type fibers choke the OAM order in fiber amplification schemes. Hence current fiber amplifications usually work for ±1st order 1.6 µm vortex modes. Considering the divergence of high-order vortex modes and the system cost, solid-state master-oscillator-power-amplification (MOPA) scheme is more suitable for 1.6 µm vortex mode amplification. Current vortex MOPA schemes are often applied in 1 µm and 2 µm band [13–16]. In 1.6 µm band, the gain ion Er3+ has small emission cross section and strong reabsorption [17–19]. Thus, the gain of Er3+-based single-pass MOPA is always low. Power amplification of 1.6 µm high-order vortex modes with higher gain is still a great issue to be addressed.
Figure 1 gives the concept of the power amplification for 1.6 µm high-order vortex modes. Criterias that must be met during the whole amplification process is, the power is increased, while the mode distribution, namely, the OAM mode purity or OAM spectrum, shouldn’t be changed. To achieve these goal, in this paper, a four-pass Er:YAG vortex MOPA is demonstrated to amplify 1.6 µm high-order vortex modes, in which the mode matching between the pump beam and the seed beam should be adjusted well that the pump beam completely covers the seed beam and the optical elements are all placed in right position. The seed beam is converted from a 1645 nm single-frequency Gaussian mode, which is generated from an Er3+-doped non-planar ring oscillator (NPRO). In the proposed four-pass vortex MOPA system, a Faraday rotator (FR), thin film polarizers (TFPs), half wave plates (HWPs), and quarter wave plates (QWPs) are inserted, which enable the vortex seed beam to pass four times in sequence through an Er:YAG rod. The Er:YAG rod is the amplified medium and pumped by a 30 W 1532 nm fiber laser. Therefore, the vortex seed beam is amplified four times and finally emits with high power and good quality. In the experiment, the gain ranging from 1.88 to 2.36 for single OAM mode (l = 3) and up to 1.78 for two-fold multiplexed OAM mode (l=±3) have been achieved. To the best of our knowledge, this is the highest gain of power amplification of 1.6 µm high-order vortex modes that ever reported. Furthermore, the OAM mode purity and linewidths before and after power amplification are also evaluated as almost unchanged. The favorable results illustrate the good performance of four-pass Er:YAG vortex MOPA system and offer a feasible path for amplifying 1.6 µm high-order vortex modes.
2. Constructing 1.6 µm high-order vortex modes amplifier
The configuration of the proposed four-pass Er:YAG vortex MOPA is sketched as Fig. 2. The whole system consists of the seed laser and the four-pass MOPA. In the seed laser, the NPRO is prepared by cutting monolithic Er:YAG crystal and is coated with high-transmission at 1470 nm and high-reflection (much higher for s-polarization than for p-polarization) at 1645 nm on the incident plane. The NPRO is a compact and stable device to generate single-frequency laser output with narrow linewidth and low noise. Because it can achieve unidirectional operation of intra-cavity oscillating laser and eliminate spatial hole burning [20]. There are also other methods to generate single-frequency vortex beam [21,22], however, single-frequency vortex beam amplification is not our focus and the NPRO is employed here just for the reason that there is already an Er:YAG NPRO in our laboratory. The single-frequency Gaussian mode is converted into horizontally polarized vortex mode after passing through a quarter wave plate (QWP2), a q-plate (QP), and a polarized beam splitter (PBS2), respectively. Then the beam is injected as seed into the four-pass Er:YAG MOPA system. QP is a non-homogenous polarization optical element that can achieve photon spin-orbital angular momentum conversion [23]. It can transform the incoming circular polarization into opposite polarization (left circular polarization to right and right circular polarization to left). Meanwhile, the QP introduces OAMs with l = 2q or l = -2q, where q is the charge of the QP and the sign is decided by the incident polarization. Here, considering that the diameters of the Er:YAG rod and the Faraday rotator employed here are 5 mm, the OAM order of seed beam should not be so high that it can’t pass through the elements. Therefore, here a q = 3/2 order QP whose transmittance is 99.5% at 1645 nm is employed. In the four-pass Er:YAG MOPA, a 0.25 at.% (atomic fraction) doping Φ4 × 50 mm Er:YAG ceramic rod is pumped by a single mode 1532 nm fiber laser. Such a low doping concentration in Er:YAG ceramic is to alleviate energy transfer upconversion (ETU) [17]. Both sides of the rod are anti-reflection coated for pump (1532 nm) and seed (1645 nm) wavelength. M1 and M2 are 45° dichroic mirrors and are high-transmission coated at 1532 nm and high-reflection coated at 1645 nm, in order to couple the pump beam into the Er:YAG rod and filter the unabsorbed out. M3 is a concave end mirror with a radius of curvature of 300 mm. M4 is a flat mirror. Both M3 and M4 are coated with high-reflectivity at 1645 nm and placed to reflect the laser back. The lens L1 with focal length of 150 mm is employed to adjust the position and waist diameter of the incident vortex seed beam, which ensures the mode matching with pump beam in Er:YAG rod together with M3 and M4. Here, the incident vortex beam with |l|=3 before the L1 is near collimated and its diameter is 4 mm. Then through L1, it is focused in the center of the Er:YAG rod and its waist diameter is adjusted to about 600 µm. The waist diameter of pump beam is fixed at about 600 µm in the Er:YAG center. As both the curvature of M3 and the focal length of L1 are large enough compared with the spot size of the beam on them, the astigmatism introduced by L1 and M3 hardly affects the mode distribution and OAM purity of vortex beam as long as they are placed in right position in optical paths. A half wave plate (HWP1) and a Faraday rotator (FR) constitute an isolator showing different polarization modulation performance for different incident directions. If horizontal polarizations pass through the isolator respectively along opposite directions, one will be still horizontal polarization and the other will turn into vertical polarization. The four mirrors (M1-M4), quarter wave plate (QWP1), thin film polarizer (TFP2), and isolator collectively constitute a four-pass process, which make the incident horizontally polarized vortex mode be amplified four times.
Fig. 2. Configuration of the proposed four-pass Er:YAG vortex MOPA. In the dashed box: the seed laser. L1-L4: lenses; M1, M2, M5 and M6: 45° dichroic mirrors; M3-M4: end mirrors; HWP1 & HWP2: half wave plates; QWP1 & QWP2: quarter wave plates; FR: Faraday rotator; TFP1 & TFP2: thin film polarizers; NPRO: non-planar ring oscillator; PBS1 & PBS2: polarized beam splitter; QP: q-plate.
In the four-pass MOPA process, the p-polarized incident beam transmits through TFP1 and the isolator with the polarization unchanged. Then, it transmits through TFP2 and the Er:YAG rod for the first amplification. Later, it turns to s-polarization through QWP1 and M3 and is reflected into the Er:YAG rod for the second amplification. The double passed s-polarized beam is reflected by TFP2 and M4 and goes back to the Er:YAG rod for the third amplification. The s-polarized beam is transformed into p-polarized by QWP1 and M3 and goes back to the Er:YAG rod for the fourth amplification. The p-polarized four-pass amplified beam transmits through TFP2 and is turned into s-polarization by the isolator. Finally, the 1.6 µm high-power and high-order vortex mode outputs after being reflected by TFP1.
3. Results and discussions
In the experiment, to demonstrate the amplification performance of the proposed single OAM mode with l = 3 is selected as the seed. The maximum incident power only reaches 3 W because of the limited pump power for Er:YAG NPRO. The fast-axis arranged angle of QWP2 is 135°. The q value of QP is 3/2. Figure 3 shows the power amplification performance for single-pass, double-pass and four-pass cases. With a fixed seed power, the output power will increase as pump power increases at the beginning. Then it tends to be constant due to the pump absorption saturation when the pump power reaches ∼20 W or larger. Here, the pump power is fixed at 30 W directly to make the output stable and to get highest output for all cases. The maximal gains are calculated as about 1.24 for single-pass and 1.51 for double-pass. The four-pass gain dramatically improves compared with single-pass and double-pass gains. But drops with the increase of incident power due to gain saturation, which is caused by the low Er3+ ion density of the amplified medium and the strong reabsorption induced by ETU effect. By this regime, the gain ranging from 1.88 to 2.36 is achieved at various incident power from 320 mW to 3 W. The highest output is 5.65 W with 3 W incident seed laser.
Fig. 3. Power amplification performance of Er:YAG vortex MOPA for single OAM mode (l = 3) under various cases. (a) The input-output dependencies of single-pass, double-pass and four-pass. (b) The gain curves of single-pass, double-pass and four-pass cases.
Figures 4(a-b) give the intensity distributions of the incident vortex seed beam (l = 3) and the amplified output beam after four-pass. They are almost identical. The topological charges of OAM before and after power amplification are diagnosed separately through a tilted lens [24] as displayed in Figs. 4(c-d). The topological charges are determined by the numbers and direction of dashed nodal lines, Obviously, it is unchanged after the amplification. Furthermore, the OAM spectra before and after four-pass amplification are measured through OAM projection as encoding various anti-spiral phases on a liquid crystal spatial light modulator [25], as shown in Fig. 4(e). The OAM purity is 98.2% of the seed beam and is 91.1% of the amplified beam. There is a little degradation of OAM purity because of the slightly pitch and offset of optical elements and the thermal effect of Er:YAG.
Fig. 4. Intensity distributions and mode purity of single OAM mode (l = 3) before and after passing through the four-pass Er:YAG vortex MOPA. (a) Incident intensity pattern. (b) Output intensity pattern. (c) Incident topological charge. (d) Output topological charge. (e)The OAM spectra of incident and output beams.
The single-frequency characteristics before and after power amplification are also evaluated through monitoring the beat frequency signal, where the setup is given in Fig. 5(a). A spiral phase plate (SPP) is employed to transform the single OAM mode into a Gaussian mode. Then the Gaussian mode is coupled into two fibers. One introduces time delay through a length of Fiber delay line and the other introduces frequency shift through an acousto-optic modulator (AOM). The two beams in the two fibers are then mixed and detected by a InGaAs detector. Finally, the beat signal is analyzed by a spectral analyzer. Figures 5(b) and (c) display the optical RF spectra of the heterodyne signals of vortex modes before and after power amplification, which are measured by the delayed self-heterodyne method. The 3 dB bandwidth of both the incident vortex seed beam and the output beam are measured as 25 kHz, which illustrates that the linewidths of both the incident and output beams are 12.5 kHz. Obviously, the proposed four-pass vortex MOPA system doesn’t affect the single-frequency characteristic. In addition, it should be emphasized that multi-longitudinal modes can also be amplified by this scheme, as long as the longitudinal modes are located in the range of the gain curve of Er3+.
Fig. 5. Linewidth evaluation. (a) Setup for measuring linewidth of vortex modes, where AOM is the acousto-optic modulator, SPP is a spiral phase plate. (b) and (c) are optical RF (radio frequency) spectra of the self-heterodyne signal of vortex modes before and after power amplification through the proposed four-pass Er:YAG vortex MOPA.
Furthermore, the power amplification performance for multiplexed vortex mode is also carried out. Two-fold multiplexed OAM mode (l=±3) is selected as the seed for demonstration. In this occasion, QWP2 is 0° fast-axis-arranged while the other elements in Fig. 2 remain unchanged. After passing through the QP, the generated beam is transformed into vortex mode containing two OAM modes (l=±3) with orthogonal circular polarizations. PBS2 achieves polarization transformation and generates horizontally polarized two-fold multiplexed OAM mode, which shows lobe pattern as presented in Fig. 6(a). After four-pass amplification, the gains for 37 mW and 135 mW seed beams reach 1.78 and 1.67, respectively. The intensity distribution of amplified beam is given as Fig. 6(b), showing good consistence with the incident beam. The OAM spectra are also evaluated as Fig. 6(c), illustrating the OAM mode purity remains well after amplification. The purity of the 3rd order OAM channel is 51.2% for the seed beam and is 46.7% for the amplified beam, and the purity of the −3rd order OAM channel is 46.0% for seed beam and is 41.5% for the amplified beam. Such good performance indicates the efficiency and robustness of the four-pass Er:YAG vortex MOPA system. Notably, the gain and mode purity slightly decrease compared to single OAM mode amplification. It’s mainly because the multiplexed vortex mode has lobe-like mode distribution, which is more complicated and half smaller than annular distribution of single OAM mode, making the overlapping area between the seed and pump beams even smaller.
Fig. 6. The amplification performance for two-fold multiplexed vortex mode (OAM mode l=±3) through four-pass Er:YAG vortex MOPA. (a, b) Intensity patterns before and after four-pass power amplification. (c) The OAM spectra before and after power amplification.
To be noted, the overlapping between the seed and pump beams largely affects the amplification performance. The gain will be higher if the mode matching is adjusted well. In our experiment, the pump beam is in Gaussian mode and the large energy density in its center is not used as the vortex seed beam is annular, which means the amplified gain could be improved further by shaping the pump beam. For instance, one can shape the pump beam into a flap-top beam or annular beam with adjustable ring width and diameter, to achieve mode matching as well as it can. While such path is sometimes difficult since it is not easy to tailor pump beam to meet perfectly the mode matching requirements with different vortex seed beams, especially the seed with multiplexed OAM modes. Besides, the intensity profile of pump beam will affect the thermal profile inside the Er:YAG crystal, further the mode distribution of amplified beam, especially when the pump power reaches a much higher level than it is in our work. Hence, the purity of OAM modes will be affected. In this case, the precise adjustment of this four-pass MOPA system is of higher requirement.
4. Conclusion
In summary, we have proposed a four-pass Er:YAG vortex MOPA system to achieve the power amplification of 1645 nm high-order vortex modes. An Er:YAG NPRO, a QP, and a series of wave plates are employed to provide low power vortex seed beams. The vortex seed beams are injected into the four-pass MOPA system and amplified successfully with good performance. In our experiment, the gain for single OAM mode with l = 3 ranges from 1.88 to 2.36. The maximal output power reaches 5.65 W with 3 W incident seed laser. The output beam remains high OAM purity of 91.1% with narrow linewidth in the meantime. Besides, the two-fold multiplexed OAM beam with l=±3 is also incident to be amplified with the gain of 1.78 and the mode purity of 88.2% is achieved. The results show the efficiency and robustness of the system. By this scheme, 1.6 µm vortex modes with high OAM orders are expected to be amplified in a simple and universal way, which paves the path for various scenarios of OAM-based rotational Doppler lidars.
Funding
National Natural Science Foundation of China (62375014, 11834001, 61905012); National Key Research and Development Program of China (2022YFB3607700); National Defense Basic Scientific Research Program of China (JCKY2020602C007); Beijing Municipal Natural Science Foundation (1232031); Special Fund for Basic Scientific Research of Central Universities of China (2022CX11006); National Postdoctoral Program for Innovative Talents (BX20190036).
Disclosures
The authors declare no competing financial interests.
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. L. Allen, M. W. Beijersbergen, R. J. Spreeuw, et al., “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef]
2. S. Fu and C. Gao, Optical Vortex Beams, (Springer, 2023). [CrossRef]
3. M. P. J. Lavery, F. C. Speirits, S. M. Barnett, et al., “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013). [CrossRef]
4. M. P. J. Lavery, S. M. Barnett, F. C. Speirits, et al., “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optcia 1(1), 1–4 (2014). [CrossRef]
5. L. Fang, M. J. Padgett, and J. Wang, “Sharing a Common Origin Between the Rotational and Linear Doppler Effects,” Laser Photonics Rev. 11(6), 1700183 (2017). [CrossRef]
6. R. C. Stoneman, R. Hartman, A. I. R. Malm, et al., “Coherent laser lidar using eyesafe YAG laser transmitters,” Proc. SPIE 5791, 167 (2005). [CrossRef]
7. S. W. Henderson and S. M. Hannon, “Advanced coherent lidar system for wind measurements,” Proc. SPIE 5887, 58870I (2005). [CrossRef]
8. M. Chen, W. J. Rudd, J. Hansell, et al., “Er:YAG methane lidar laser technology,” Proc. SPIE 11005, 110050Q (2019). [CrossRef]
9. Y. Zhai, S. Fu, J. Zhang, et al., “Remote detection of a rotator based on rotational Doppler effect,” Appl. Phys. Express 13(2), 022012 (2020). [CrossRef]
10. J. Lin, S. Chen, H. Wang, et al., “Amplifying Orbital Angular Momentum Modes in Ring-Core Erbium-Doped Fiber,” Research 2020, 7623751 (2020). [CrossRef]
11. Y. Jung, Q. Kang, R. Sidharthan, et al., “Optical Orbital Angular Momentum Amplifier Based on an Air-Hole Erbium-Doped Fiber,” J. Lightwave Technol. 35(3), 430–436 (2017). [CrossRef]
12. Q. Kang, P. Gregg, Y. Jung, et al., “Amplification of 12 OAM modes in an air-core erbium doped fiber,” Opt. Express 23(22), 28341 (2015). [CrossRef]
13. H. Sroor, I. Litvin, D. Naidoo, et al., “Amplification of higher order Poincaré sphere beams through Nd:YLF and Nd:YAG crystals,” Appl. Phys. B 125(3), 49 (2019). [CrossRef]
14. Y. Li, W. Li, Z. Zhang, et al., “Concentric vortex beam amplification: experiment and simulation,” Opt. Express 24(2), 1658 (2016). [CrossRef]
15. S. H. Noh, D. J. Kim, and J. W. Kim, “High power generation of adaptive laser beams in a Nd:YVO4 MOPA system,” Chin. Opt. Lett. 15, 120801 (2017). [CrossRef]
16. D. J. Kim, J. W. Kim, and W. A. Clarkson, “High-power master-oscillator power-amplifier with optical vortex output,” Appl. Phys. B 117(1), 459–464 (2014). [CrossRef]
17. J. W. Kim, J. I. Mackenzie, and W. A. Clarkson, “Influence of energy-transfer-upconversion on threshold pump power in quasi-three-level solid-state lasers,” Opt. Express 17(14), 11935–11943 (2009). [CrossRef]
18. J. W. Kim, D. Y. Shen, J. K. Sahu, et al., “Fiber-laser-pumped Er:YAG lasers,” IEEE J. Select. Topics Quantum Electron. 15(2), 361–371 (2009). [CrossRef]
19. J. W. Kim, D. Y. Shen, J. K. Sahu, et al., “High-power in-band pumped Er:YAG laser at 1617 nm,” Opt. Express 16(8), 5807–5812 (2008). [CrossRef]
20. K. Wang, X. Zhang, S. Fu, et al., “1645 nm single longitude-mode vortex laser from an ErYAG nonplanar ring oscillator,” Opt. Lett. 48(2), 331 (2023). [CrossRef]
21. T. H. Kim, J. S. Park, J. W. Kim, et al., “Direct Generation of a Laguerre-Gaussian-Mode Optical Vortex Beam in a Single-Frequency Nd:YVO4 Unidirectional Ring Laser,” J. Korean Phys. Soc. 75(8), 557–560 (2019). [CrossRef]
22. D. J. Kim and J. W. Kim, “Direct generation of an optical vortex beam in a single-frequency Nd:YVO4 laser,” Opt. Lett. 40(3), 399–402 (2015). [CrossRef]
23. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006). [CrossRef]
24. P. Vaity, J. Banerji, and R. P. Singh, “Measuring the topological charge of an optical vortex by using a tilted convex lens,” Phys. Lett. A 377(15), 1154–1156 (2013). [CrossRef]
25. S. Fu, S. Zhang, T. Wang, et al., “Measurement of orbital angular momentum spectra of multiplexing optical vortices,” Opt. Express 24(6), 6240 (2016). [CrossRef]
