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Coherent beam combination of an optical array using adaptive fiber optics collimators
Optics Communications 284 (2011) 5531–5536
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Coherent beam combination of an optical array using adaptive fiber optics collimators Chao Geng a, b,⁎, Xinyang Li a, Xiaojun Zhang a, Changhui Rao a a b
The Key Laboratory on Adaptive Optics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China Graduate University of Chinese Academy of Sciences, Beijing 100049, China
a r t i c l e
i n f o
Article history: Received 1 April 2011 Accepted 26 August 2011 Available online 12 September 2011 Keyword: Fiber laser Coherent beam combination Adaptive fiber optics collimator Stochastic parallel gradient descent
a b s t r a c t A novel adaptive-fiber-optics-collimator (AFOC) compensating both piston-type and tip/tilt-type phase errors of output beam is introduced, and has been employed in experiments of coherent beam combination (CBC) of a delta distributed fiber array. Feedback control is realized using stochastic parallel gradient descent (SPGD) algorithm. Excellent CBC effect has been achieved when piston and tip/tilt errors among beamlets corrected. The necessity of wavefront tip/tilt control in CBC is verified. Experimental results exhibit great potential applications of this kind of AFOC in fiber amplifier arrays. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Coherent beam combination (CBC) of fiber amplifier arrays based on a master oscillator power amplifier (MOPA) configuration is an efficient way to generate high power and high quality laser beams. To achieve this, many approaches, such as heterodyne detection technique [1], multi-dithering technique [2,3], and stochastic parallel gradient descent (SPGD) algorithm technique [4,5], have been reported. The MOPA system using SPGD algorithm needs only one photoelectric detector and is easy to realize, which is widely researched. The key to CBC is to achieve phase-locking state of multiple element optical arrays. In lots of current CBC systems, phase locking is the only consideration, where LiNbO3 phase modulators are employed to compensate piston-type errors. In fact, laser beam propagation through turbulent atmosphere generates tip/tilt-type phase errors. During adjustment process of optical arrays, still comes with residual tip/tilt errors. Moreover, the adjusting mechanism leads to a huge optical system. All of these impact CBC seriously. So, to improve CBC effect, wavefront phase tip/tilt should be compensated [6]. A phased array correcting piston and tip/ tilt errors simultaneously was reported [7], where the phase locking device was still LiNbO3 PM and a wavefront tip/tilt control device named adaptive-fiber-optics-collimator (AFOC) [8] was introduced. The simplicity and compactness of AFOC make it suitable for a densely packed optical array system. In this paper, we present very recent research work of AFOC in the Key Laboratory on Adaptive Optics, CAS. A novel AFOC compensating
⁎ Corresponding author. Tel.: + 86 028 85100348. E-mail address: [email protected] (C. Geng). 0030-4018/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2011.08.069
both piston-type and tip/tilt-type phase errors of output beam is introduced. An experimental setup of CBC of a three-element fiber array using AFOCs is established. The CBC in 632.8 nm wavelength using SPGD algorithm is successfully demonstrated. 2. Development and mechanism of AFOC Fiber optics collimator is an optical passive device which collimates fiber tip emissive laser, and is widely produced for commerce. In 2005, L. A. Beresnev of U.S. Army Research Laboratory designed a fiber optics collimator which could control the deviation of output beam and was named adaptive fiber optics collimator (AFOC) according to its active feature in Adaptive Optics (AO). Compared with conventional fast-steering mirror (FSM), the AFOC drives fiber tip directly with advantages of precise control, small inertia, high resonance-frequency, compact structure and easiness for integration. But this AFOC can only compensate tip/tilt-type phase errors and is helpless with piston-type errors among beamlets. So, it needs to work with phase-locking device (like LiNbO3 PM) in CBC systems. But the high price and short operating life of LiNbO3 PM limit its applications. A novel AFOC compensating both piston-type and tip/tilt-type phase errors is developed in the Key Laboratory on Adaptive Optics, CAS. It consists of phase-locking module and tip/tilt-control module, as depicted in Fig. 1(a). The tip of fiber optics output is fixed in the central hole of the cross beam, deviated in the focal plane (X–Y) of the collimating lens. The design of the phase-locking module is based on three piezoelectric actuators, which operate under the same electric field along Z-direction. When piezoelectric actuators work, the micro stretches of actuators force the collimator to move along the same direction and change the optical path of the collimated output. The design of the tip/tilt-control module is based on four
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a)
3. Experimental configuration using AFOCs 3.1. The platform
b)
The experimental configuration of CBC is illustrated in Fig. 2. The single-mode fiber is employed in optical circuit. The seed laser is a single-mode linear polarized He–Ne laser of 632.8-nm wavelength with 5-mW output power. The optical power from the seed laser is coupled into a single-mode fiber before split into eight channels. Three employed channels are connected with three AFOCs, respectively. The AFOC array aligned in a ‘delta’ shape is used to correct both piston-type and tip/tilt-type phase errors among beamlets. The collimated output beams emitted from the AFOC array are focused by a lens with 1000-mm focus length. Then, the combined beams are sampled by a polarization beam-splitter prism into horizontal and vertical polarizations, one is sent to CCD for observation, another is sent to a photoelectric detector (PD) with a pinhole. The electric signal from the PD is defined as the cost function J and will be used in SPGD control. The SPGD algorithm generates three phase-locking signals and six tip/tilt-control signals which will be delivered to the AFOC array. Filling factor of near-field optical array is defined as the singlebeam aperture divided by the distance of adjacent beamlets. In our experiments, the collimated beam aperture is 12-mm, and the distance of adjacent beamlets is 38-mm. So the filling factor here is 0.32. The diameter of main lobe of ideal interference pattern is calculated to be 28-μm and a pinhole of 15-μm diameter is selected. 3.2. Control strategy
c)
The SPGD algorithm [4–7] is employed to maximize the cost function J, that is, to maximize the photocurrent detected by PD. J is defined as the power circled in the pinhole of a diameter of 15-μm. ⇀ ⇀ ⇀ J ¼ J U; V , where U ¼ fu1; u2 ; u3 g is three phase-locking signals ⇀ y and V ¼ vx1 ; v1 ; vx2 ; vy2 ; vx3 ; vy3 is six tip/tilt-control signals. Different operation rates between phase-locking module and tip/tilt-control module are considered. Here, we use the same algorithm-iteration speed of 200-Hz for simplicity. The steps for CBC using SPGD algorithm can be briefly described as follows: (1) Generate a group of random voltage perturbations: ⇀ ⇀ Δ U ¼ fΔu1 ; Δu2 ; Δu3 g and Δ V x y x y x y ¼ Δv1 ; Δv1 ; Δv2 ; Δv2 ; Δv3 ; Δv3 ;
Fig. 1. A novel AFOC compensating both piston and tip/tilt phase errors. (a) mechanism; (b) frequency response curve of phase-locking module; (c) frequency response curve of tip/tilt-control module.
bimorph actuators, two of them drive the X-direction and another two drive the Y-direction. The bimorph actuator consists of two piezoelectric sheets glued on both sides of a metal sheet. The applied voltage induces the contraction of one sheet and the expansion of another, actuators bend and force the cross beam with the fiber tip to translate Δx in the focus plane. The direction of the collimated output is deviated on angle Δx / f, where f is the focal length of the lens. The abilities of AFOC used in following experiments are tested. Optical path differences of the collimated output are in range 1-μm, the beam deviations are in range 1-mrad (75 μm/f = 1 mrad) for a chosen focal length of 75 mm. First resonance-frequencies of phase-locking module and tip/tilt-control module are about 1.8 kHz and 800 Hz, respectively, as depicted in Fig. 1(b) (c).
where |Δu1| = |Δu2| = |Δu3| and |Δv1x| = |Δv1y| = |Δv2x| = |Δv2y| = |Δv3x| = |Δv3y|. ⇀ ⇀ ⇀ ⇀ ⇀ ⇀ (2) Apply U þ ¼ U þ Δ U and V þ ¼ V þ Δ V on phase-locking module and tip/tilt-control respectively and get the cost ⇀module ⇀ ⇀ ⇀ ⇀ function from PD, Jþ U þ ; V þ ; then apply U − ¼ U−Δ U and ⇀ ⇀ ⇀ ⇀ ⇀ V − ¼ V−Δ V to get the cost function J− U − ; V − . (3) Update the control–voltage signals: ⇀ ⇀ ⇀ ⇀ ⇀ ⇀ ⇀ γ t Δ V Jþ −J− ; U ¼ U þ γ p Δ U Jþ −J− ; V ¼ V þ ⇀ n o γ t ¼ fγt ; γt ; γt ; γt ; γt ; γt g are where ⇀ γ p ¼ γp ; γp ; γp and ⇀ gains of SPGD algorithm. ⇀ ⇀ (4) Apply the renewed U and V on the AFOC array and get the renewed cost function J.
C. Geng et al. / Optics Communications 284 (2011) 5531–5536
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a) The scheme for coherent beam combination of a 3-element fiber array
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Fig. 2. Experimental configuration of coherent beam combination based on AFOCs.
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normalized power in the circle
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4. Experimental results 4.1. Without turbulence Experiments were carried out in a silent environment. Phase noises were induced by mechanical vibrations of equipments, airconditions, thermal expansion of the fiber, tip/tilt assembly errors, etc. By the way, compensation of piston-type errors is the only consideration in most of current CBC systems with MOPA configuration, but the following experiments will prove that compensation of wavefront phase tip/tilt is more important in systems with tip/tilt errors. Fig. 3 shows the 250-s long-time exposure patterns of CBC of a 3element array in open and closed loops acquired by CCD. Fig. 3(a) is the 2-D far-field interference pattern in open loop. The pattern is obscure with low fringe contrast and the peak of grey level is only 83.65.
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Fig. 3(b) is the 2-D far-field pattern with phase-locking only. The pattern is still dispersive but interference fringes can be found with good contrast. The peak of grey level is up to 129.53 and certain initial tip/tilt errors among beamlets can be seen. Fig. 3(c) is the 2-D farfield pattern with tip/tilt-control only. The contrast is not high but the pattern is intensive. The peak of grey level is up to 151.20 and initial tip/tilt errors were corrected. Fig. 3(d) is the 2-D far-field pattern with phase-locking and tip/tilt-control simultaneously. The contrast is very high and the peak of grey level is up to 253.95 which are nearly triple of open loop. Fig. 3(e) is the 3-D pattern with phase-locking and tip/tilt-control simultaneously. Fig. 3(f) is the ideal pattern. White curves are central section lines of patterns along X and Y directions. After AFOC array corrected piston and tip/ tilt errors, the brightness, contrast and beam quality of CBC promote greatly. The contrast between Fig. 3(b) and (d) tells the necessity of tip/tilt compensation in CBC. Based on Fig. 3(a–d), the centroidals of four experimental patterns are calculated. Four curves of Power-in-Circle are drawn with circle centers of centroidals and radiuses of pixels (from 0 to 150), as shown in Fig. 4. Experiments of CBC of 2-element fiber arrays were carried out when closing any element of three beamlets. Fig. 5 is the 250-s long exposure patterns of far field acquired by CCD. Fig. 5(a) (b) (c) represent open loop and Fig. 5(d) (e) (f) are with phase-locking and tip/ tilt-control simultaneously. Four operation modes of CBC of the 3-element fiber array, including open loop, phase-locking only, tip/tilt-control only, and phaselocking and tip/tilt-control simultaneously, are compared. 5000 iteration data are acquired in each mode, which are combined in the sequences of A, B, C and D, as shown in Fig. 6. In mode ‘A’, metrics dither between 0.2 and 0.3, which is induced by random phase noises among beamlets. In mode ‘B’, the curve is plane, metrics lie around 0.36 but are not high. In mode ‘C’, metrics promote to 0.6 to 0.9, initial tip/tilt errors among beamlets were corrected, but the curve oscillates
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Fig. 5. Long exposure patterns of CBC of 2-channel fiber arrays in far field. (a) (b) (c) represent open loop; (d) (e) (f) represent phase-locking and tilt-control simultaneously.
C. Geng et al. / Optics Communications 284 (2011) 5531–5536
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greatly because of random piston-type noises and tiny tip/tilt-voltage perturbations in SPGD control. In mode ‘D’, metrics maintain up to 0.9, the curve dithering is caused by tiny tilt-voltage perturbations in SPGD control. The contrast between ‘B’ and ‘D’ also tells the necessity of wavefront phase tip/tilt compensation in CBC. Run the program of CBC of the 3-element array for 10 times under the phase-locking and tip/tilt-control mode. Fig. 7 is the iteration curves of metrics, where 10 iteration curves are denoted as thin lines. The broad line represents mean values of ten iteration curves and about 200 iterations can promote the metric to 0.85. Fig. 8 shows control–voltage curves generated by SPGD algorithm under phase-locking and tip/tilt-control mode. Fig. 8(a) is three ⇀ ⇀ phase-locking signals U. Fig. 8(b) is six tip/tilt-control signals V, where the curves become flat after the correction of initial tilt errors.
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A cup of hot water was placed in the optical path to simulate turbulences. Dynamic experiments of CBC of the 3-element array were carried out. Four iteration courses, including open loop in turbulence, phase-locking and tip/tilt-control in turbulence, open loop without turbulence, and phase-locking and tip/tilt control without turbulence, were completed respectively. Fig. 9 shows the contrast of metrics in different environments, Fig. 9(a) with turbulence and Fig. 9(b) without turbulence. The results indicate that the effects of CBC decrease with the existence of turbulences, but our system still has certain capabilities to correct piston and tip/tilt errors. Fig. 10 is the control–voltage curves of SPGD algorithm under phase-locking and tip/tilt-control mode with turbulences. Fig. 10(a) is three phase-locking signals and Fig. 10(b) is six tip/tilt-control
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In summary, a new-style AFOC correcting piston and tip/tilt errors simultaneously was developed. The capabilities of this kind of AFOC in coherent beam combination were demonstrated. The brightness, contrast and beam quality of the far-field patterns were promoted noticeably after the corrections of piston and tip/tilt errors among beamlets with the help of the AFOC array. The necessity of wavefront phase tip/tilt compensation was proved by the obvious promotion of CBC effects. This system has certain abilities of dynamic corrections, but the first resonance-frequency of the AFOC and the speed of SPGD control need to be improved. In the future, we will develop the AFOC with higher first resonance-frequency and dynamic capability, improve the filling factor of fiber arrays and verify the high-power CBC system based on fiber amplifiers and more elements of AFOC. We believe this kind of AFOC can be widely used in coherent beam combination and beam transmission of high-power optical phased arrays through atmosphere.
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Acknowledgements
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This work is supported by the National Natural Science Foundation of China (Grant No. 60978050).
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References
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[1] G.D. Goodno, S.J. McNaught, J.E. Rothenberg, T.S. McComb, P.A. Thielen, M.G. Wickham, M.E. Weber, Optics Letters 35 (2010) 1542. [2] T.M. Shay, V. Benham, J.T. Baker, B. Ward, A.D. Sanchez, M.A. Culpepper, D. Pilkington, J. Spring, D. Nelson, C. Lu, Optics Express 14 (2006) 12015. [3] V. Jolivet, P. Bourdon, B. Bennai, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouen, B. Moreau, O. Vasseur, IEEE Journal of Selected Topics in Quantum Electronics 15 (2009) 257. [4] X.L. Wang, Y.X. Ma, P. Zhou, B. He, H. Xiao, Y.H. Xue, C. Liu, Z. Li, X.J. Xu, J. Zhou, Z.J. Liu, Y.J. Zhao, Optics Communication 284 (2011) 2198. [5] P. Zhou, Z.J. Liu, X.L. Wang, Y.X. Ma, H.T. Ma, X.J. Xu, Applied Physics Letters 94 (2009) 231106. [6] C. Geng, X.Y. Li, X.J. Zhang, C.H. Rao, Acta Phys. Sin. (To be published). [7] M.A. Vorontsov, T. Weyrauch, L.A. Beresnev, G.W. Carhart, L. Liu, K. Aschenbach, IEEE Journal of Selected Topics in Quantum Electronics 15 (2009) 269. [8] L.A. Beresnev, M.A. Vorontsov, Proceedings of SPIE 5895 (2005) 58950R.
-0.8 -1 -1.2
0
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
iteration number Fig. 10. Control–voltage curves generated by SPGD algorithm with turbulence.
signals. Compared with Fig. 8, the curves oscillate more greatly which exhibit the dynamic compensating abilities of the AFOCs.
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Coherent beam combination of an optical array using adaptive fiber optics collimators Chao Geng a, b,⁎, Xinyang Li a, Xiaojun Zhang a, Changhui Rao a a b
The Key Laboratory on Adaptive Optics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China Graduate University of Chinese Academy of Sciences, Beijing 100049, China
a r t i c l e
i n f o
Article history: Received 1 April 2011 Accepted 26 August 2011 Available online 12 September 2011 Keyword: Fiber laser Coherent beam combination Adaptive fiber optics collimator Stochastic parallel gradient descent
a b s t r a c t A novel adaptive-fiber-optics-collimator (AFOC) compensating both piston-type and tip/tilt-type phase errors of output beam is introduced, and has been employed in experiments of coherent beam combination (CBC) of a delta distributed fiber array. Feedback control is realized using stochastic parallel gradient descent (SPGD) algorithm. Excellent CBC effect has been achieved when piston and tip/tilt errors among beamlets corrected. The necessity of wavefront tip/tilt control in CBC is verified. Experimental results exhibit great potential applications of this kind of AFOC in fiber amplifier arrays. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Coherent beam combination (CBC) of fiber amplifier arrays based on a master oscillator power amplifier (MOPA) configuration is an efficient way to generate high power and high quality laser beams. To achieve this, many approaches, such as heterodyne detection technique [1], multi-dithering technique [2,3], and stochastic parallel gradient descent (SPGD) algorithm technique [4,5], have been reported. The MOPA system using SPGD algorithm needs only one photoelectric detector and is easy to realize, which is widely researched. The key to CBC is to achieve phase-locking state of multiple element optical arrays. In lots of current CBC systems, phase locking is the only consideration, where LiNbO3 phase modulators are employed to compensate piston-type errors. In fact, laser beam propagation through turbulent atmosphere generates tip/tilt-type phase errors. During adjustment process of optical arrays, still comes with residual tip/tilt errors. Moreover, the adjusting mechanism leads to a huge optical system. All of these impact CBC seriously. So, to improve CBC effect, wavefront phase tip/tilt should be compensated [6]. A phased array correcting piston and tip/ tilt errors simultaneously was reported [7], where the phase locking device was still LiNbO3 PM and a wavefront tip/tilt control device named adaptive-fiber-optics-collimator (AFOC) [8] was introduced. The simplicity and compactness of AFOC make it suitable for a densely packed optical array system. In this paper, we present very recent research work of AFOC in the Key Laboratory on Adaptive Optics, CAS. A novel AFOC compensating
⁎ Corresponding author. Tel.: + 86 028 85100348. E-mail address: [email protected] (C. Geng). 0030-4018/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2011.08.069
both piston-type and tip/tilt-type phase errors of output beam is introduced. An experimental setup of CBC of a three-element fiber array using AFOCs is established. The CBC in 632.8 nm wavelength using SPGD algorithm is successfully demonstrated. 2. Development and mechanism of AFOC Fiber optics collimator is an optical passive device which collimates fiber tip emissive laser, and is widely produced for commerce. In 2005, L. A. Beresnev of U.S. Army Research Laboratory designed a fiber optics collimator which could control the deviation of output beam and was named adaptive fiber optics collimator (AFOC) according to its active feature in Adaptive Optics (AO). Compared with conventional fast-steering mirror (FSM), the AFOC drives fiber tip directly with advantages of precise control, small inertia, high resonance-frequency, compact structure and easiness for integration. But this AFOC can only compensate tip/tilt-type phase errors and is helpless with piston-type errors among beamlets. So, it needs to work with phase-locking device (like LiNbO3 PM) in CBC systems. But the high price and short operating life of LiNbO3 PM limit its applications. A novel AFOC compensating both piston-type and tip/tilt-type phase errors is developed in the Key Laboratory on Adaptive Optics, CAS. It consists of phase-locking module and tip/tilt-control module, as depicted in Fig. 1(a). The tip of fiber optics output is fixed in the central hole of the cross beam, deviated in the focal plane (X–Y) of the collimating lens. The design of the phase-locking module is based on three piezoelectric actuators, which operate under the same electric field along Z-direction. When piezoelectric actuators work, the micro stretches of actuators force the collimator to move along the same direction and change the optical path of the collimated output. The design of the tip/tilt-control module is based on four
5532
C. Geng et al. / Optics Communications 284 (2011) 5531–5536
a)
3. Experimental configuration using AFOCs 3.1. The platform
b)
The experimental configuration of CBC is illustrated in Fig. 2. The single-mode fiber is employed in optical circuit. The seed laser is a single-mode linear polarized He–Ne laser of 632.8-nm wavelength with 5-mW output power. The optical power from the seed laser is coupled into a single-mode fiber before split into eight channels. Three employed channels are connected with three AFOCs, respectively. The AFOC array aligned in a ‘delta’ shape is used to correct both piston-type and tip/tilt-type phase errors among beamlets. The collimated output beams emitted from the AFOC array are focused by a lens with 1000-mm focus length. Then, the combined beams are sampled by a polarization beam-splitter prism into horizontal and vertical polarizations, one is sent to CCD for observation, another is sent to a photoelectric detector (PD) with a pinhole. The electric signal from the PD is defined as the cost function J and will be used in SPGD control. The SPGD algorithm generates three phase-locking signals and six tip/tilt-control signals which will be delivered to the AFOC array. Filling factor of near-field optical array is defined as the singlebeam aperture divided by the distance of adjacent beamlets. In our experiments, the collimated beam aperture is 12-mm, and the distance of adjacent beamlets is 38-mm. So the filling factor here is 0.32. The diameter of main lobe of ideal interference pattern is calculated to be 28-μm and a pinhole of 15-μm diameter is selected. 3.2. Control strategy
c)
The SPGD algorithm [4–7] is employed to maximize the cost function J, that is, to maximize the photocurrent detected by PD. J is defined as the power circled in the pinhole of a diameter of 15-μm. ⇀ ⇀ ⇀ J ¼ J U; V , where U ¼ fu1; u2 ; u3 g is three phase-locking signals ⇀ y and V ¼ vx1 ; v1 ; vx2 ; vy2 ; vx3 ; vy3 is six tip/tilt-control signals. Different operation rates between phase-locking module and tip/tilt-control module are considered. Here, we use the same algorithm-iteration speed of 200-Hz for simplicity. The steps for CBC using SPGD algorithm can be briefly described as follows: (1) Generate a group of random voltage perturbations: ⇀ ⇀ Δ U ¼ fΔu1 ; Δu2 ; Δu3 g and Δ V x y x y x y ¼ Δv1 ; Δv1 ; Δv2 ; Δv2 ; Δv3 ; Δv3 ;
Fig. 1. A novel AFOC compensating both piston and tip/tilt phase errors. (a) mechanism; (b) frequency response curve of phase-locking module; (c) frequency response curve of tip/tilt-control module.
bimorph actuators, two of them drive the X-direction and another two drive the Y-direction. The bimorph actuator consists of two piezoelectric sheets glued on both sides of a metal sheet. The applied voltage induces the contraction of one sheet and the expansion of another, actuators bend and force the cross beam with the fiber tip to translate Δx in the focus plane. The direction of the collimated output is deviated on angle Δx / f, where f is the focal length of the lens. The abilities of AFOC used in following experiments are tested. Optical path differences of the collimated output are in range 1-μm, the beam deviations are in range 1-mrad (75 μm/f = 1 mrad) for a chosen focal length of 75 mm. First resonance-frequencies of phase-locking module and tip/tilt-control module are about 1.8 kHz and 800 Hz, respectively, as depicted in Fig. 1(b) (c).
where |Δu1| = |Δu2| = |Δu3| and |Δv1x| = |Δv1y| = |Δv2x| = |Δv2y| = |Δv3x| = |Δv3y|. ⇀ ⇀ ⇀ ⇀ ⇀ ⇀ (2) Apply U þ ¼ U þ Δ U and V þ ¼ V þ Δ V on phase-locking module and tip/tilt-control respectively and get the cost ⇀module ⇀ ⇀ ⇀ ⇀ function from PD, Jþ U þ ; V þ ; then apply U − ¼ U−Δ U and ⇀ ⇀ ⇀ ⇀ ⇀ V − ¼ V−Δ V to get the cost function J− U − ; V − . (3) Update the control–voltage signals: ⇀ ⇀ ⇀ ⇀ ⇀ ⇀ ⇀ γ t Δ V Jþ −J− ; U ¼ U þ γ p Δ U Jþ −J− ; V ¼ V þ ⇀ n o γ t ¼ fγt ; γt ; γt ; γt ; γt ; γt g are where ⇀ γ p ¼ γp ; γp ; γp and ⇀ gains of SPGD algorithm. ⇀ ⇀ (4) Apply the renewed U and V on the AFOC array and get the renewed cost function J.
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a) The scheme for coherent beam combination of a 3-element fiber array
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normalized power in the circle
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4. Experimental results 4.1. Without turbulence Experiments were carried out in a silent environment. Phase noises were induced by mechanical vibrations of equipments, airconditions, thermal expansion of the fiber, tip/tilt assembly errors, etc. By the way, compensation of piston-type errors is the only consideration in most of current CBC systems with MOPA configuration, but the following experiments will prove that compensation of wavefront phase tip/tilt is more important in systems with tip/tilt errors. Fig. 3 shows the 250-s long-time exposure patterns of CBC of a 3element array in open and closed loops acquired by CCD. Fig. 3(a) is the 2-D far-field interference pattern in open loop. The pattern is obscure with low fringe contrast and the peak of grey level is only 83.65.
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Fig. 3(b) is the 2-D far-field pattern with phase-locking only. The pattern is still dispersive but interference fringes can be found with good contrast. The peak of grey level is up to 129.53 and certain initial tip/tilt errors among beamlets can be seen. Fig. 3(c) is the 2-D farfield pattern with tip/tilt-control only. The contrast is not high but the pattern is intensive. The peak of grey level is up to 151.20 and initial tip/tilt errors were corrected. Fig. 3(d) is the 2-D far-field pattern with phase-locking and tip/tilt-control simultaneously. The contrast is very high and the peak of grey level is up to 253.95 which are nearly triple of open loop. Fig. 3(e) is the 3-D pattern with phase-locking and tip/tilt-control simultaneously. Fig. 3(f) is the ideal pattern. White curves are central section lines of patterns along X and Y directions. After AFOC array corrected piston and tip/ tilt errors, the brightness, contrast and beam quality of CBC promote greatly. The contrast between Fig. 3(b) and (d) tells the necessity of tip/tilt compensation in CBC. Based on Fig. 3(a–d), the centroidals of four experimental patterns are calculated. Four curves of Power-in-Circle are drawn with circle centers of centroidals and radiuses of pixels (from 0 to 150), as shown in Fig. 4. Experiments of CBC of 2-element fiber arrays were carried out when closing any element of three beamlets. Fig. 5 is the 250-s long exposure patterns of far field acquired by CCD. Fig. 5(a) (b) (c) represent open loop and Fig. 5(d) (e) (f) are with phase-locking and tip/ tilt-control simultaneously. Four operation modes of CBC of the 3-element fiber array, including open loop, phase-locking only, tip/tilt-control only, and phaselocking and tip/tilt-control simultaneously, are compared. 5000 iteration data are acquired in each mode, which are combined in the sequences of A, B, C and D, as shown in Fig. 6. In mode ‘A’, metrics dither between 0.2 and 0.3, which is induced by random phase noises among beamlets. In mode ‘B’, the curve is plane, metrics lie around 0.36 but are not high. In mode ‘C’, metrics promote to 0.6 to 0.9, initial tip/tilt errors among beamlets were corrected, but the curve oscillates
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Fig. 5. Long exposure patterns of CBC of 2-channel fiber arrays in far field. (a) (b) (c) represent open loop; (d) (e) (f) represent phase-locking and tilt-control simultaneously.
C. Geng et al. / Optics Communications 284 (2011) 5531–5536
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greatly because of random piston-type noises and tiny tip/tilt-voltage perturbations in SPGD control. In mode ‘D’, metrics maintain up to 0.9, the curve dithering is caused by tiny tilt-voltage perturbations in SPGD control. The contrast between ‘B’ and ‘D’ also tells the necessity of wavefront phase tip/tilt compensation in CBC. Run the program of CBC of the 3-element array for 10 times under the phase-locking and tip/tilt-control mode. Fig. 7 is the iteration curves of metrics, where 10 iteration curves are denoted as thin lines. The broad line represents mean values of ten iteration curves and about 200 iterations can promote the metric to 0.85. Fig. 8 shows control–voltage curves generated by SPGD algorithm under phase-locking and tip/tilt-control mode. Fig. 8(a) is three ⇀ ⇀ phase-locking signals U. Fig. 8(b) is six tip/tilt-control signals V, where the curves become flat after the correction of initial tilt errors.
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A cup of hot water was placed in the optical path to simulate turbulences. Dynamic experiments of CBC of the 3-element array were carried out. Four iteration courses, including open loop in turbulence, phase-locking and tip/tilt-control in turbulence, open loop without turbulence, and phase-locking and tip/tilt control without turbulence, were completed respectively. Fig. 9 shows the contrast of metrics in different environments, Fig. 9(a) with turbulence and Fig. 9(b) without turbulence. The results indicate that the effects of CBC decrease with the existence of turbulences, but our system still has certain capabilities to correct piston and tip/tilt errors. Fig. 10 is the control–voltage curves of SPGD algorithm under phase-locking and tip/tilt-control mode with turbulences. Fig. 10(a) is three phase-locking signals and Fig. 10(b) is six tip/tilt-control
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In summary, a new-style AFOC correcting piston and tip/tilt errors simultaneously was developed. The capabilities of this kind of AFOC in coherent beam combination were demonstrated. The brightness, contrast and beam quality of the far-field patterns were promoted noticeably after the corrections of piston and tip/tilt errors among beamlets with the help of the AFOC array. The necessity of wavefront phase tip/tilt compensation was proved by the obvious promotion of CBC effects. This system has certain abilities of dynamic corrections, but the first resonance-frequency of the AFOC and the speed of SPGD control need to be improved. In the future, we will develop the AFOC with higher first resonance-frequency and dynamic capability, improve the filling factor of fiber arrays and verify the high-power CBC system based on fiber amplifiers and more elements of AFOC. We believe this kind of AFOC can be widely used in coherent beam combination and beam transmission of high-power optical phased arrays through atmosphere.
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Acknowledgements
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This work is supported by the National Natural Science Foundation of China (Grant No. 60978050).
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References
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[1] G.D. Goodno, S.J. McNaught, J.E. Rothenberg, T.S. McComb, P.A. Thielen, M.G. Wickham, M.E. Weber, Optics Letters 35 (2010) 1542. [2] T.M. Shay, V. Benham, J.T. Baker, B. Ward, A.D. Sanchez, M.A. Culpepper, D. Pilkington, J. Spring, D. Nelson, C. Lu, Optics Express 14 (2006) 12015. [3] V. Jolivet, P. Bourdon, B. Bennai, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouen, B. Moreau, O. Vasseur, IEEE Journal of Selected Topics in Quantum Electronics 15 (2009) 257. [4] X.L. Wang, Y.X. Ma, P. Zhou, B. He, H. Xiao, Y.H. Xue, C. Liu, Z. Li, X.J. Xu, J. Zhou, Z.J. Liu, Y.J. Zhao, Optics Communication 284 (2011) 2198. [5] P. Zhou, Z.J. Liu, X.L. Wang, Y.X. Ma, H.T. Ma, X.J. Xu, Applied Physics Letters 94 (2009) 231106. [6] C. Geng, X.Y. Li, X.J. Zhang, C.H. Rao, Acta Phys. Sin. (To be published). [7] M.A. Vorontsov, T. Weyrauch, L.A. Beresnev, G.W. Carhart, L. Liu, K. Aschenbach, IEEE Journal of Selected Topics in Quantum Electronics 15 (2009) 269. [8] L.A. Beresnev, M.A. Vorontsov, Proceedings of SPIE 5895 (2005) 58950R.
-0.8 -1 -1.2
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signals. Compared with Fig. 8, the curves oscillate more greatly which exhibit the dynamic compensating abilities of the AFOCs.