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Beam cleanup of a multimode fiber seeded by an off-center single-mode laser source
Optik 124 (2013) 2501–2503
Contents lists available at SciVerse ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Beam cleanup of a multimode fiber seeded by an off-center single-mode laser source Jie Li ∗ , Hai-Chuan Zhao, Zi-Lun Chen, Xiao-Jun Xu College of Opto-Electronic Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
a r t i c l e
i n f o
Article history: Received 5 March 2012 Accepted 13 July 2012
Keywords: Multimode fiber laser Spatial light modulators Beam cleanup Off-center single mode laser
a b s t r a c t We study the beam cleanup of a multimode (MM) fiber with different output energy pattern following injection from a single-mode fiber laser source. The experimental research is based on a stochastic parallel gradient descent (SPGD) algorithm. The output beam intensity profile from the MM fiber varies via the change of the offset when the input single mode fiber spliced to the MM fiber. This is a consequence of diverse high-order modes excited in the MM fiber where the off-center single mode laser inject into. The experiment system is setup by using phase only liquid crystal spatial light modulators (LC-SLM). It is shown that the beam cleanup of the multimode fiber is depressed when the offset are relative large. © 2012 Elsevier GmbH. All rights reserved.
1. Introduction Fiber laser has become increasingly popular due to its advantages of good beam quality, high efficiency and high reliability [1–3]. IPG Photonics Corporation has developed a single mode fiber with 9.6 kW output power [1]. However, the power upscaling of the fiber laser is limited by the thermal damage and the nonlinear effects. It had been predicted that the theoretical maximal output power of a single-mode fiber laser is 36 kW [4]. Multimode fiber presents an effective solution to get even higher output, more than 50 kW multimode fiber laser system has become commercial [5]. Due to the large mode area of multimode fiber, many laser modes are excited and the beam quality degrades seriously, which is not expected in many application fields, i.e., long-range energy delivering. Beam cleanup technique seems an effective way to improve the beam quality, especially after the stochastic parallel gradient descent (SPGD) algorithm is introduced into adaptive optics (AO) [6]. Zhao has presented multimode fiber laser beam cleanup based on the SPGD algorithm [7,8]. It should be noted that in Ref. [7], the received MM fiber is injected into the center of the fiber core by the single-mode fiber laser which is assumed to be Gaussian. Because of the azimuthally symmetry of the input Gaussian beam, only m = 0 modes can be excited in the multimode fiber [9,10]. The quality evaluation function is increased to 10.5, more than 10 times higher than before cleanup. Moreover, in Ref. [8], there only one high-order mode of TEM20 is transformed with SPGD algorithm.
∗ Corresponding author. E-mail address: [email protected] (J. Li). 0030-4026/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2012.08.031
The results show that the far-field energy centrality of TEM20 mode is advanced and the evaluation function increases more than a factor of 6 after transformation. Accordingly, Zhao indicates that the beam with high-power and high beam quality can be realized by multimode fiber laser beam cleanup. However, if there exist more than one high-order modes in the multimode fiber or the mode components excited in the multimode fiber are not symmetric, i.e., off-center incident, what will happen after the beam cleanup? Is it still effective on improving beam quality by adaptive optics when the injected beam source is offset from the multimode fiber core axis? This paper tries to demonstrate the beam cleanup capability of the multimode fiber with off-axis incident based on SPGD algorithm. Section 2 introduces the experiment system and the principle of the beam cleanup. Section 3 is the results and discussion. And Section 4 is the conclusion.
2. Experiment setup A basic configuration for the beam cleanup system of a multimode fiber seeded by an off-center single-mode laser is presented in Fig. 1. A standard single mode fiber laser (Corning HI1060, 6.2 m MFD, 0.14 NA) was fused to a multimode fiber (Corning, 50/125, 0.22 NA). When the wavelength is 1064 nm, the corresponding normalized frequency V of the multimode fiber is about 65. Therefore, the multimode fiber can not only support the fundamental mode but also many high-order modes. After collimating, expanding and splitting, the multimode laser excited in the multimode fiber is divided into two parts. One incidents on the LC-SLM (BNS company, 256 × 256 with 24 m × 24 m pixels, 8 bit). And another beam is focused on the surface of a CCD (AVT company, 1032 × 778 with
2502
J. Li et al. / Optik 124 (2013) 2501–2503
Fig. 1. Schematic of the beam cleanup system.
Fig. 3. Experimental result of multimode fiber laser with 5 m offset. (a) Captured image of far-field intensity distribution before cleanup; (b) captured image of farfield intensity distribution after cleanup and (c) the quality evaluation function curve.
Then the perturbation is applied on the control signals in the other direction and the metric is obtained as (m)
J−
(m)
= (a1
{m}
(m)
− ıa1 , a2
{m}
(m)
− ıa2 , ..., an
{m}
− ıan )
(2)
The difference between two evaluations of the metric function is Fig. 2. Experimental result of multimode fiber laser with zero offset. (a) Captured image of far-field intensity distribution before cleanup; (b) captured image of farfield intensity distribution after cleanup and (c) the quality evaluation function curve.
4.65 m × 4.65 m pixels, 8 bit), which is used to capture the far field intensity distribution. By processing the images from the CCD camera, the phase distribution of the LC-SLM is controlled by the SPGD algorithm which was implemented in Matlab. The far field intensity distribution can evolve into the expected one by running the algorithm iteratively. In an adaptive optics system based on direct system performance metric optimization, J is defined as the quality evaluation function, and J is a function of the control parameters a = {a1 , a2 , . . ., an }. The voltage signals are applied to the LC-SLM. If the aberrations of the system are compensated, the system performance metric can be optimized. The SPGD algorithm follows the following procedure to optimize the metric. At nth iteration of the algorithm, the independent random perturbations (m) (m) (m) {ıa1 , ıa2 , . . . , ıan }, are applied simultaneously to the control (m)
(m)
(m)
parameters a(m) = {a1 , a2 , . . . , an }, and the perturbed system performance metric is obtained as (m)
J+
(m)
= (a1
{m}
(m)
+ ıa1 , a2
{m}
(m)
+ ıa2 , . . . , an
{m}
+ ıan )
(1)
(m)
ıJ (m) = J+
(m)
− J−
(3)
The stochastic parallel gradient descent algorithm for the wave front control method based on direct system performance metric optimization as (m+1)
ai
(m)
= ai
(m)
− ıJ (m) ıai
(4)
where is the update gain, and then next step circulation begins. 3. Experimental results When the single mode fiber is spliced to the MM fiber, the two fibers’ axes offset can be realized by adjusting the fiber clamp. The principle of the fiber device can be describes as follows: the fundamental LP0,1 mode of the SM fiber is coupled to the MM fiber, where LPm,n modes are excited. The field at the output facet of the MM fiber is the superposition of multiple modes. Firstly, make the offset parameter between the single-mode fiber and MM fiber to be zero, that is to say, the single-mode laser are injected from the center of the MM fiber core, the experimental results are shown in Fig. 2. The insets are far-field intensity distribution of the beam before and after one typical correction trial. Before close loop the intensity is distributed in many symmetric modes (LP0,n modes) which results in widening beam divergence
J. Li et al. / Optik 124 (2013) 2501–2503
2503
From the results all above, it is indicated that with the offset between the single-mode fiber and MM fiber increasing, the capability of beam cleanup based on SPGD becomes depressed. The reason is that the superposition wave-fronts at the output facet, especially of the asymmetric high-order modes, is distributed very complicatedly and exceeds the correction capability. Even if a faster modulation is applied, the difficulty and cost of the controlling process will be increased greatly for phase compensation in time. 4. Conclusion We have presented the beam cleanup of multimode fiber seeded by off-center single-mode laser source using a LC-SLM with control based on the SPGD algorithm. The LC-SLM is used to compensate the wave-front adaptively and the circulation rate is greatly expedited by optimizing the coefficients of the Zernike polynomials. The output beam profile of the MM fiber is the superposition of multiple modes. Each mode has a wave-front itself. Therefore, the output wave-fronts vary according to the incident position. Only when the single mode fiber laser is injected into the MM fiber along the axis or near the axis, the wave-fronts can be corrected effectively and the laser beam with high beam quality can be realized by multimode fiber laser beam cleanup, otherwise, the wave-fronts cannot be compensated due to many asymmetrical higher-order modes and the output beam energy cannot be centralized yet. In conclusion, this approach is not always appreciated for beam cleanup. It is better to put forward novel methods to improve beam quality of the multimode fiber. Fig. 4. Experimental result of multimode fiber laser with 10 m offset. (a) Captured image of far-field intensity distribution before cleanup; (b) captured image of far-field intensity distribution after cleanup and (c) the quality evaluation function curve.
and degenerating beam quality. A clear and stable spot is obtained when the loop is closed using the SPGD algorithm. The quality evaluation function after 1000 iterations is 10.5 and is increased by more than a factor of 10. In this case, the energy is centralized can be advanced evidently and multimode fiber laser beam cleanup can be well achieved by an AO system in this case. Then, we increase the offset to be 5 m. The typical results are shown in Fig. 3. The output beam of the MM fiber before cleanup comprises a lot of asymmetric high-order modes due to the offcenter incident. Comparing to the output beam of the zero offset, the beam divergence becomes wider and the beam quality gets worse. Although the spot after using SPGD algorithm is stable and the energy is also able to be centralized, the quality evaluation function after 1000 iterations is 6 and is increased by more than a factor of 6. Therefore, the effect of beam cleanup is weaker than that of zero offset. Next, continue to increase the offset parameter to be 10 m, the results are shown in Fig. 4. The output beam can be decomposed by higher-order modes and the intensity is dispersed. Even after using the SPGD algorithm, the energy is still disorder and the quality evaluation function is ruleless. Here, we can say that the system of beam cleanup has almost no effect on improving the beam quality.
Acknowledgements Project supported by the National Natural Science Foundation of China (Grant No. 61007073), the Natural Science Foundation of Hunan Province, China (Grant No. 12JJ4061) and the Advanced Research Foundation of National University of Defense Technology, China (Grant No. JC12-07-02) References [1] http://news.thomasnet.com/fullstory/562108. [2] J. Limpert, A. Liem, H.A. Zellmer, Tünnermann, 500 W continuous-wave fibre laser with excellent beam quality, Electron. Lett. 39 (2003) 645–647. [3] http://www.ipgphotonics.com. [4] J.W. Dawson, M.J. Messerly, R.J. Beach, M.Y. Shverdin, E.A. Stappaerts, A.K. Sridharan, P.H. Pax, J.E. Heebner, C.W. Siders, C.P.J. Barty, Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power, Opt. Express 16 (2008) 13240–13266. [5] http://www.ipgphotonics.com/apps mat multi YLR.htm. [6] V.I. Polejaev, M.A. Vorontsov, Proc. SPIE 3126 (1997) 216–220. [7] H.-C. Zhao, H.-T. Ma, P. Zhou, X.-L. Wang, Y.-X. Ma, X. Li, X.-J. Xu, Y.-J. Zhao, Multimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm, Opt. Commun. 284 (2011) 613–615. [8] H.-C. Zhao, X.-L. Wang, P. Zhou, H.-T. Ma, Y.-X. Ma, S.-H. Wang, X.-J. Xu, Y.-J. Zhao, Experimental explorations of the high-order Gaussian mode transformation based on blind-optimization adaptive optics, Opt. Commun. 284 (2011) 4654–4657. [9] A. Mafi, P. Hofmann, C.J. Salvin, A. Schülzgen, Low-loss coupling between two single-mode optical fibers with different mode-field diameters using a gradedindex multimode optical fiber, Opt. Lett. 36 (2011) 3596–3598. [10] X. Zhu, A. Schülzgen, H. Li, H. Wei, J.V. Moloney, N. Peyghambarian, Coherent beam transformations using multimode waveguides, Opt. Express 18 (2010) 7506–7520.
Contents lists available at SciVerse ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Beam cleanup of a multimode fiber seeded by an off-center single-mode laser source Jie Li ∗ , Hai-Chuan Zhao, Zi-Lun Chen, Xiao-Jun Xu College of Opto-Electronic Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
a r t i c l e
i n f o
Article history: Received 5 March 2012 Accepted 13 July 2012
Keywords: Multimode fiber laser Spatial light modulators Beam cleanup Off-center single mode laser
a b s t r a c t We study the beam cleanup of a multimode (MM) fiber with different output energy pattern following injection from a single-mode fiber laser source. The experimental research is based on a stochastic parallel gradient descent (SPGD) algorithm. The output beam intensity profile from the MM fiber varies via the change of the offset when the input single mode fiber spliced to the MM fiber. This is a consequence of diverse high-order modes excited in the MM fiber where the off-center single mode laser inject into. The experiment system is setup by using phase only liquid crystal spatial light modulators (LC-SLM). It is shown that the beam cleanup of the multimode fiber is depressed when the offset are relative large. © 2012 Elsevier GmbH. All rights reserved.
1. Introduction Fiber laser has become increasingly popular due to its advantages of good beam quality, high efficiency and high reliability [1–3]. IPG Photonics Corporation has developed a single mode fiber with 9.6 kW output power [1]. However, the power upscaling of the fiber laser is limited by the thermal damage and the nonlinear effects. It had been predicted that the theoretical maximal output power of a single-mode fiber laser is 36 kW [4]. Multimode fiber presents an effective solution to get even higher output, more than 50 kW multimode fiber laser system has become commercial [5]. Due to the large mode area of multimode fiber, many laser modes are excited and the beam quality degrades seriously, which is not expected in many application fields, i.e., long-range energy delivering. Beam cleanup technique seems an effective way to improve the beam quality, especially after the stochastic parallel gradient descent (SPGD) algorithm is introduced into adaptive optics (AO) [6]. Zhao has presented multimode fiber laser beam cleanup based on the SPGD algorithm [7,8]. It should be noted that in Ref. [7], the received MM fiber is injected into the center of the fiber core by the single-mode fiber laser which is assumed to be Gaussian. Because of the azimuthally symmetry of the input Gaussian beam, only m = 0 modes can be excited in the multimode fiber [9,10]. The quality evaluation function is increased to 10.5, more than 10 times higher than before cleanup. Moreover, in Ref. [8], there only one high-order mode of TEM20 is transformed with SPGD algorithm.
∗ Corresponding author. E-mail address: [email protected] (J. Li). 0030-4026/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2012.08.031
The results show that the far-field energy centrality of TEM20 mode is advanced and the evaluation function increases more than a factor of 6 after transformation. Accordingly, Zhao indicates that the beam with high-power and high beam quality can be realized by multimode fiber laser beam cleanup. However, if there exist more than one high-order modes in the multimode fiber or the mode components excited in the multimode fiber are not symmetric, i.e., off-center incident, what will happen after the beam cleanup? Is it still effective on improving beam quality by adaptive optics when the injected beam source is offset from the multimode fiber core axis? This paper tries to demonstrate the beam cleanup capability of the multimode fiber with off-axis incident based on SPGD algorithm. Section 2 introduces the experiment system and the principle of the beam cleanup. Section 3 is the results and discussion. And Section 4 is the conclusion.
2. Experiment setup A basic configuration for the beam cleanup system of a multimode fiber seeded by an off-center single-mode laser is presented in Fig. 1. A standard single mode fiber laser (Corning HI1060, 6.2 m MFD, 0.14 NA) was fused to a multimode fiber (Corning, 50/125, 0.22 NA). When the wavelength is 1064 nm, the corresponding normalized frequency V of the multimode fiber is about 65. Therefore, the multimode fiber can not only support the fundamental mode but also many high-order modes. After collimating, expanding and splitting, the multimode laser excited in the multimode fiber is divided into two parts. One incidents on the LC-SLM (BNS company, 256 × 256 with 24 m × 24 m pixels, 8 bit). And another beam is focused on the surface of a CCD (AVT company, 1032 × 778 with
2502
J. Li et al. / Optik 124 (2013) 2501–2503
Fig. 1. Schematic of the beam cleanup system.
Fig. 3. Experimental result of multimode fiber laser with 5 m offset. (a) Captured image of far-field intensity distribution before cleanup; (b) captured image of farfield intensity distribution after cleanup and (c) the quality evaluation function curve.
Then the perturbation is applied on the control signals in the other direction and the metric is obtained as (m)
J−
(m)
= (a1
{m}
(m)
− ıa1 , a2
{m}
(m)
− ıa2 , ..., an
{m}
− ıan )
(2)
The difference between two evaluations of the metric function is Fig. 2. Experimental result of multimode fiber laser with zero offset. (a) Captured image of far-field intensity distribution before cleanup; (b) captured image of farfield intensity distribution after cleanup and (c) the quality evaluation function curve.
4.65 m × 4.65 m pixels, 8 bit), which is used to capture the far field intensity distribution. By processing the images from the CCD camera, the phase distribution of the LC-SLM is controlled by the SPGD algorithm which was implemented in Matlab. The far field intensity distribution can evolve into the expected one by running the algorithm iteratively. In an adaptive optics system based on direct system performance metric optimization, J is defined as the quality evaluation function, and J is a function of the control parameters a = {a1 , a2 , . . ., an }. The voltage signals are applied to the LC-SLM. If the aberrations of the system are compensated, the system performance metric can be optimized. The SPGD algorithm follows the following procedure to optimize the metric. At nth iteration of the algorithm, the independent random perturbations (m) (m) (m) {ıa1 , ıa2 , . . . , ıan }, are applied simultaneously to the control (m)
(m)
(m)
parameters a(m) = {a1 , a2 , . . . , an }, and the perturbed system performance metric is obtained as (m)
J+
(m)
= (a1
{m}
(m)
+ ıa1 , a2
{m}
(m)
+ ıa2 , . . . , an
{m}
+ ıan )
(1)
(m)
ıJ (m) = J+
(m)
− J−
(3)
The stochastic parallel gradient descent algorithm for the wave front control method based on direct system performance metric optimization as (m+1)
ai
(m)
= ai
(m)
− ıJ (m) ıai
(4)
where is the update gain, and then next step circulation begins. 3. Experimental results When the single mode fiber is spliced to the MM fiber, the two fibers’ axes offset can be realized by adjusting the fiber clamp. The principle of the fiber device can be describes as follows: the fundamental LP0,1 mode of the SM fiber is coupled to the MM fiber, where LPm,n modes are excited. The field at the output facet of the MM fiber is the superposition of multiple modes. Firstly, make the offset parameter between the single-mode fiber and MM fiber to be zero, that is to say, the single-mode laser are injected from the center of the MM fiber core, the experimental results are shown in Fig. 2. The insets are far-field intensity distribution of the beam before and after one typical correction trial. Before close loop the intensity is distributed in many symmetric modes (LP0,n modes) which results in widening beam divergence
J. Li et al. / Optik 124 (2013) 2501–2503
2503
From the results all above, it is indicated that with the offset between the single-mode fiber and MM fiber increasing, the capability of beam cleanup based on SPGD becomes depressed. The reason is that the superposition wave-fronts at the output facet, especially of the asymmetric high-order modes, is distributed very complicatedly and exceeds the correction capability. Even if a faster modulation is applied, the difficulty and cost of the controlling process will be increased greatly for phase compensation in time. 4. Conclusion We have presented the beam cleanup of multimode fiber seeded by off-center single-mode laser source using a LC-SLM with control based on the SPGD algorithm. The LC-SLM is used to compensate the wave-front adaptively and the circulation rate is greatly expedited by optimizing the coefficients of the Zernike polynomials. The output beam profile of the MM fiber is the superposition of multiple modes. Each mode has a wave-front itself. Therefore, the output wave-fronts vary according to the incident position. Only when the single mode fiber laser is injected into the MM fiber along the axis or near the axis, the wave-fronts can be corrected effectively and the laser beam with high beam quality can be realized by multimode fiber laser beam cleanup, otherwise, the wave-fronts cannot be compensated due to many asymmetrical higher-order modes and the output beam energy cannot be centralized yet. In conclusion, this approach is not always appreciated for beam cleanup. It is better to put forward novel methods to improve beam quality of the multimode fiber. Fig. 4. Experimental result of multimode fiber laser with 10 m offset. (a) Captured image of far-field intensity distribution before cleanup; (b) captured image of far-field intensity distribution after cleanup and (c) the quality evaluation function curve.
and degenerating beam quality. A clear and stable spot is obtained when the loop is closed using the SPGD algorithm. The quality evaluation function after 1000 iterations is 10.5 and is increased by more than a factor of 10. In this case, the energy is centralized can be advanced evidently and multimode fiber laser beam cleanup can be well achieved by an AO system in this case. Then, we increase the offset to be 5 m. The typical results are shown in Fig. 3. The output beam of the MM fiber before cleanup comprises a lot of asymmetric high-order modes due to the offcenter incident. Comparing to the output beam of the zero offset, the beam divergence becomes wider and the beam quality gets worse. Although the spot after using SPGD algorithm is stable and the energy is also able to be centralized, the quality evaluation function after 1000 iterations is 6 and is increased by more than a factor of 6. Therefore, the effect of beam cleanup is weaker than that of zero offset. Next, continue to increase the offset parameter to be 10 m, the results are shown in Fig. 4. The output beam can be decomposed by higher-order modes and the intensity is dispersed. Even after using the SPGD algorithm, the energy is still disorder and the quality evaluation function is ruleless. Here, we can say that the system of beam cleanup has almost no effect on improving the beam quality.
Acknowledgements Project supported by the National Natural Science Foundation of China (Grant No. 61007073), the Natural Science Foundation of Hunan Province, China (Grant No. 12JJ4061) and the Advanced Research Foundation of National University of Defense Technology, China (Grant No. JC12-07-02) References [1] http://news.thomasnet.com/fullstory/562108. [2] J. Limpert, A. Liem, H.A. Zellmer, Tünnermann, 500 W continuous-wave fibre laser with excellent beam quality, Electron. Lett. 39 (2003) 645–647. [3] http://www.ipgphotonics.com. [4] J.W. Dawson, M.J. Messerly, R.J. Beach, M.Y. Shverdin, E.A. Stappaerts, A.K. Sridharan, P.H. Pax, J.E. Heebner, C.W. Siders, C.P.J. Barty, Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power, Opt. Express 16 (2008) 13240–13266. [5] http://www.ipgphotonics.com/apps mat multi YLR.htm. [6] V.I. Polejaev, M.A. Vorontsov, Proc. SPIE 3126 (1997) 216–220. [7] H.-C. Zhao, H.-T. Ma, P. Zhou, X.-L. Wang, Y.-X. Ma, X. Li, X.-J. Xu, Y.-J. Zhao, Multimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm, Opt. Commun. 284 (2011) 613–615. [8] H.-C. Zhao, X.-L. Wang, P. Zhou, H.-T. Ma, Y.-X. Ma, S.-H. Wang, X.-J. Xu, Y.-J. Zhao, Experimental explorations of the high-order Gaussian mode transformation based on blind-optimization adaptive optics, Opt. Commun. 284 (2011) 4654–4657. [9] A. Mafi, P. Hofmann, C.J. Salvin, A. Schülzgen, Low-loss coupling between two single-mode optical fibers with different mode-field diameters using a gradedindex multimode optical fiber, Opt. Lett. 36 (2011) 3596–3598. [10] X. Zhu, A. Schülzgen, H. Li, H. Wei, J.V. Moloney, N. Peyghambarian, Coherent beam transformations using multimode waveguides, Opt. Express 18 (2010) 7506–7520.