Influence of perturbative phase noise on active coherent polarization beam combining system Pengfei Ma,1 Pu Zhou,1,2 Xiaolin Wang,1 Yanxing Ma,1 Rongtao Su,1 and Zejin Liu1,* 1
College of Opticelectric Science and Engineering, National University of Defense Technology, Changsha 410073, China 2 [email protected] * [email protected]
Abstract: In this manuscript, the influence of perturbative phase noise on active coherent polarization beam combining (CPBC) system is studied theoretically and experimentally. By employing a photo-detector to obtain phase error signal for feedback loop, actively coherent polarization beam combining of two 20 W-level single mode polarization-maintained (PM) fiber amplifiers are demonstrated with more than 94% combining efficiency. Then the influence of perturbative phase noise on active CPBC system is illustrated by incorporating a simulated phase noise signal in one of the two amplifiers. Experimental results show that the combining efficiency of the CPBC system is susceptible to the frequency or amplitude of the perturbative phase noise. In order to ensure the combining efficiency of the unit of CPBC system higher than 90%, the competence of our active phase control module for high power operation is discussed, which suggests that it could be worked at 100s W power level. The relationship between residual phase noise of the active controller and the normalized voltage signal of the photo-detector is developed and validated experimentally. Experimental results correspond exactly with the theoretically analyzed combining efficiency. Our method offers a useful approach to estimate the influence of phase noise on CPBC system. ©2013 Optical Society of America OCIS codes: (140.3298) Laser beam combining; (140.3425) Laser stabilization.
References and links 1. 2. 3. 4. 5. 6.
7. 8. 9.
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, and C. P. J. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Express 16(17), 13240–13266 (2008). Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007). J. Bourderionnet, C. Bellanger, J. Primot, and A. Brignon, “Collective coherent phase combining of 64 fibers,” Opt. Express 19(18), 17053–17058 (2011). C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, and T. Y. Fan, “Coherent combining of a 4 kW, eight-element fiber amplifier array,” Opt. Lett. 36(14), 2686–2688 (2011). P. Zhou, Z. J. Liu, X. J. Xu, and Z. L. Chen, “Numerical analysis of the effects of aberrations on coherently combined fiber laser beams,” Appl. Opt. 47(18), 3350–3359 (2008). G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, Jr., M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007). T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14(25), 12015–12021 (2006). P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combination of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009). X. L. Wang, P. Zhou, Y. X. Ma, J. Y. Leng, X. J. Xu, and Z. J. Liu, “Active phasing a nine-element 1.14 kW allfiber two-tone MOPA array using SPGD algorithm,” Opt. Lett. 36(16), 3121–3123 (2011).
#198522 - $15.00 USD Received 30 Sep 2013; revised 8 Nov 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029666 | OPTICS EXPRESS 29666
10. C. J. Corcoran and F. Durville, “Experimental demonstration of a phase—locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86(20), 201118 (2005). 11. E. J. Bochove and S. A. Shakir, “Analysis of a spatial-filtering passive fiber laser beam combining system,” IEEE J. Sel. Top. Quantum Electron. 15(2), 320–327 (2009). 12. J. Lhermite, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Passive phase locking of an array of four fiber amplifiers by an all-optical feedback loop,” Opt. Lett. 32(13), 1842–1844 (2007). 13. P. B. Phua and Y. L. Lim, “Coherent polarization locking with near-perfect combining efficiency,” Opt. Lett. 31(14), 2148–2150 (2006). 14. L. H. Tan, C. F. Chua, and P. B. Phua, “Preserving a diffraction-limited beam in Ho:YAG laser using coherent polarization locking,” Opt. Lett. 37(22), 4621–4623 (2012). 15. R. Uberna, A. Bratcher, and B. G. Tiemann, “Power scaling of a fiber master oscillator power amplifier system using a coherent polarization beam combination,” Appl. Opt. 49(35), 6762–6765 (2010). 16. R. Uberna, A. Bratcher, and B. G. Tiemann, “Power scaling of a fiber master oscillator power amplifier system using a coherent polarization beam combination,” Appl. Opt. 49(35), 6762–6765 (2010). 17. P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photon. Technol. Lett. 25(19), 1936–1938 (2013). 18. P. F. Ma, P. Zhou, R. T. Su, Y. X. Ma, and Z. J. Liu, “Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique,” Laser Phys. Lett. 9(6), 456–458 (2012). 19. D. C. Jones, C. D. Stacey, and A. M. Scott, “Phase stabilization of a large-mode-area ytterbium-doped fiber amplifier,” Opt. Lett. 32(5), 466–468 (2007). 20. S. J. Augst, T. Y. Fan, and A. Sanchez, “Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers,” Opt. Lett. 29(5), 474–476 (2004). 21. H. Tünnermann, Y. Feng, J. Neumann, D. Kracht, and P. Weßels, “All-fiber coherent beam combining with phase stabilization via differential pump power control,” Opt. Lett. 37(7), 1202–1204 (2012). 22. M. Tröbs, S. Barke, T. Theeg, D. Kracht, G. Heinzel, and K. Danzmann, “Differential phase-noise properties of a ytterbium-doped fiber amplifier for the Laser Interferometer Space Antenna,” Opt. Lett. 35(3), 435–437 (2010). 23. G. D. Goodno, C. C. Shih, and J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18(24), 25403–25414 (2010). 24. Z. Li, J. Zhou, B. He, Y. Xue, P. Zhou, C. Liu, Y. Qi, Q. Lou, and X. Xu, “Impact of phase perturbation on passive phase-locking coherent beam combination,” IEEE Photon. Technol. Lett. 24(8), 655–657 (2012). 25. S. H. Xu, Z. M. Yang, W. N. Zhang, X. M. Wei, Q. Qian, D. D. Chen, Q. Y. Zhang, S. X. Shen, M. Y. Peng, and J. R. Qiu, “400 mW ultrashort cavity low-noise single-frequency Yb³⁺-doped phosphate fiber laser,” Opt. Lett. 36(18), 3708–3710 (2011). 26. Y. Ma, X. Wang, J. Leng, H. Xiao, X. Dong, J. Zhu, W. Du, P. Zhou, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination of 1.08 kW fiber amplifier array using single frequency dithering technique,” Opt. Lett. 36(6), 951–953 (2011).
1. Introduction Fiber lasers and amplifiers have attracted intensively attention due to their great potential in scaling to high power level with near diffraction-limited beam quality. However, the output power of the monolithic amplifier/laser will be ultimately limited by several obstacles, including high brightness pump diodes, fiber damage, thermal effects and non-linear effects [1, 2]. Coherent beam combination (CBC) technique provides a prominent approach to break through the limitations above-mentioned. Nowadays, active CBC of continuous-wave configuration had been extended to multi-channel [3] and the 4 kW combined output power had been demonstrated by Massachusetts Institute of Technology (MIT) [4]. Nevertheless, in most of the general CBC configurations, all the emitters were tiled into an array, which induced a portion of power encircled into the side-lobes in the far-field pattern [3–12], thus inevitably degrades the beam quality and power concentration of the coherently combined beam [5]. As a new technique to overcome the insufficiency of side-lobes in CBC system, coherent polarization beam combining (CPBC) was proposed and validated both in passive and active phasing techniques [13–18]. By passive phasing technique, Phua et al. demonstrated CPBC of two watt-level Nd:YVO4 laser with near-perfect combining efficiency (>99%) [13]. Tan et al. reported CPBC of two Ho: YAG lasers to overcome thermal issues and preserve beam quality, and 10 W-level output power was produced with 96% combining efficiency [14]. As for active phasing technique, Uberna et al. validated the feasibility of CPBC technique in four fiber lasers and scaled the output power to 25 W with the combining efficiency of 94% by heterodyne phase control technique [15, 16]. Recently, active CPBC of two 200 W-level PM fiber amplifiers were presented by our group with more than 90% combining efficiency by single-frequency dithering method [17].
#198522 - $15.00 USD Received 30 Sep 2013; revised 8 Nov 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029666 | OPTICS EXPRESS 29667
Due to the influence of some factors, such as thermal effects, ambient vibrations and nonlinear effects, the optical phases in fiber lasers and amplifiers are continuously changed along with time [19–22]. As for active and passive phasing CBC architectures, the property of perturbative phase noise plays a significant impact on the phase locking effect and the power encircled in the central-lobe [23, 24]. In the previous publications, the phase noise properties of amplifier chains in active CBC configurations were measured [4, 19–21], and differential pump power control method was proposed to mitigate its adverse effect [21]. Recently, Goodno et al. theoretically examined the phase noise influence on the actively aperture-filled CBC configuration by perturbative analytical method [23]. Li et al. clarified the impact of phase noise on a specific passive CBC architecture experimentally [24]. However, as far as we known, the inefficiency of phase noise on CPBC system has not been studied up to now. Therefore, it is necessary to clarify the influence of perturbative phase noise on the combining efficiency of the CBPC system theoretically and experimentally. In this manuscript, the impact of perturbative phase noise on the active CPBC system is investigated theoretically and experimentally by active CPBC of two 20 W-level PM single mode amplifiers. By utilizing a phase modulator and a signal generator to generate an artificial phase noise, the influence of perturbative phase noise on the combining efficiency of the CPBC system is studied. Without artificial phase noise, the combining efficiency of the two-channel CPBC system can be higher than 94%. When the artificial phase noise is implemented, the combining efficiency of the system decreases with the increase of the frequency or amplitude of the artificial noise. In order to ensure the combining efficiency of the unit of CPBC system higher than 90%, the competence of our active phase control module for high power operation is also discussed in the end of the manuscript. The relationship between residual phase noise of the active controller and the normalized voltage signal of the photo-detector is developed and validated experimentally, which offers an approach to estimate the influence of phase noise on the combining efficiency of CPBC system. 2. Principle and Experimental Setup In principle, the fulfillment of active CPBC can be illustrated as follows. Generally, when two linearly polarized beams are injected into a polarization beam combiner (PBC), the polarization state of the combined beam is not linearly polarized and fluctuates along with time due to phase difference between the two beams is uncertain, as is a mixture of the polarization state of two orthogonally polarized beams (as shown in Fig. 1(a)). However, when the phase difference (δ) between the two orthogonal polarizations is locked and set to δ = nπ, where n is an integer, the combined beam is a new pure linear-polarized one (see Fig. 1(b)), thus it can be completely transmitted through the next PBC by using a half wavelength plate (HWP) to rotate the polarization direction of the combined beam. Due to the linear property of the coherently combined beam, it can be further combined with another linearly polarized beam by a PBC, so multi-channel beams can be coherently combined straightforwardly by phase locking [15].
Fig. 1. The polarization state of combined beam for (a) without phase control and (b) phase locked.
The experimental setup to perform CPBC of two 20 W-level single mode PM fiber amplifier chains is demonstrated in Fig. 2. The seed is a linear-polarized and single-frequency (line-width t P0
(4)
Where
< Pc (t ) >=
ξ1 (t ) =
∞ ∞
1 1 2 2 −∞ ψ 1 ( x, y ) +ψ 2 ( x, y ) d x d y + 2T 2 −∞
∞ ∞
ψ 1 ( x, y )ψ 2 ( x, y ) cos δ (t )d x d y ξ2 =
−∞ −∞
P0 =
∞ ∞
ψ
−∞ −∞
2 1
∞ ∞
ψ
−∞ −∞
2 1
T
4ξ 21 + ξ 2 2 d t
(5)
0
( x, y ) −ψ 2 2 ( x, y ) d x d y (6)
( x, y ) + ψ 2 2 ( x, y ) d x d y
(7)
Defining that θ is the polarization angle of the linear polarizer (P), the relationship between the residual phase noise of the active phase control module and the normalized energy (denoted by voltage V(t)) in the PD can be expressed by
#198522 - $15.00 USD Received 30 Sep 2013; revised 8 Nov 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029666 | OPTICS EXPRESS 29670
cos δ (t ) =
V (t ) − κ1 cos2 θ − κ 2 sin 2 θ 2 κ1κ 2 sin(θ ) cos(θ )
(8)
Where Pb1 P κ 2 = b2 (9) P0 P0 In general operation, without phase control, by rotating the polarization angle of the linear polarizer (P), the peak-vale fluctuation energy collected in the PD can be maximized. This state is more advantageous for the active phase control system to demodulate the actual phase difference between the two amplifier chains. The active phase control module can lock the transformed voltage in either maximum state or minimum state, and the combining efficiency difference of the CPBC system in these two states can be negligible in the previous experiment. As a special case that the output power of the first beam (Pb1) is approximately equal to the scaled power of second beam (Pb2), Eq. (4) can be simplified by
κ1 =
1 T phase locking at maximum state V (t )d t T 0 η= T 1 1 − V (t ) d phase locking at minimum state ]t T [ 0
(10)
By the analysis aforementioned, we established the relationship between the residual phase noise of the active controller and the normalized voltage signal of the photo-detector, which offers an approach to estimate the influence of phase noise on the combining efficiency of the CPBC system experimentally. 4. Experimental Results and Discussions
4.1 Experimental results and discussions without artificial phase noise As shown in Fig. 2, after two collimators, the output powers of the two channels are scaled to 17.9 W and 18.2 W, respectively. The extinction ratios of the two amplifier chains are measured to be 26.4 dB and 25.4 dB respectively by a HWP and a PBC, and both of the M2 factors of the two amplifier chains are measured to be within 1.1. As mentioned above, the phase noise properties of the amplifier chains are crucial for active phasing effect. Therefore, in front of phase locking process, the spectral density of power of the phase noise in the two amplifier chains in 3 W level and 20 W level are measured based on coherent detection technique (as similar in Ref [19, 20].), which is shown in Fig. 4. From the measurement phase noise information, we conclude that the characteristic frequencies of the two 3 W and 20 W level amplifier chains are below 260 Hz and 400 Hz, respectively. By investigation, the envelopes of the spectral density of power below 260 Hz are mainly induced by cooling fans inserted into the commercial amplifiers. When the 20 W level amplifiers performed, some relative small (compared with frequency below 260 Hz) envelopes emerged between 260 Hz and 400 Hz, which is mainly induced by the influence of implementation of water tank in the main amplifiers.
#198522 - $15.00 USD Received 30 Sep 2013; revised 8 Nov 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029666 | OPTICS EXPRESS 29671
Fig. 4. The spectral density of power of phase noise in the two amplifier chains. (a) First amplifier in 3 W level. (b) First amplifier in 20 W level. (c) Second amplifier in 3 W level. (d) Second amplifier in 20 W level.
The active CPBC of the two amplifier chains is implemented based on our singlefrequency dithering algorithm processor [26]. The mathematical principle of single frequency dithering technique can be found in Ref [26]. and it is not repeated here to save place. The metric function of the phasing algorithm is related to the amplitude of the voltage signal transformed by the PD. The voltage signal transformed by the PD incorporates the information of phase difference between the two channels, which can be used to generate the phase control signal by modulation and demodulation technique. In the presented experimental system, each iteration cycle of the algorithm works as follows. Assuming that t denotes time, and t0, t1 and t2 denote different moment. In the experiment, a 1MHz sine wave phase modulation signal is employed in the phase control module. In the interval of t0 to t1, the phase modulation signal and control signal S1 is added to the phase modulator in the first channel, while the phase control signal of the second channel remains zero. By calculation, the control signal S1 is proportional to sin(δ), as is similarly described in Ref [26]. except for the proportional coefficient. At the interval of t1 to t2, the phase control signal S2 (proportional to sin(-δ)) are applied to the phase modulator in the second channel. During this period, the modulation signal of the first channel becomes zero, and the control signal retains the value at t = t1. Provided that the interval T = t2-t0 is short enough so that the phases of two channels experience negligible fluctuations but long enough for the feedback process to be operative, the phase difference between the two channels will be compensated by repeating the aboveoperations in turns. Finally, the phase difference between the two channels can be compensated to be zero by selecting the appropriate feedback gain in the phase control module. Before utilizing the artificial phase noise in the experimental setup, we investigate the active phase control process and phase noise suppression process of the two amplifier chains. The phase control and phase noise suppression process are shown in Fig. 5. Without the phase control module, the normalized energy collected by the PD fluctuates randomly due to that the phase difference between two amplifier chains continuously changes with the influence of thermal effects, experimental vibrations and so forth (shown in Fig. 5(a)). However, when the
#198522 - $15.00 USD Received 30 Sep 2013; revised 8 Nov 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029666 | OPTICS EXPRESS 29672
phase control module performed, the normalized energy in the PD can be locked effectively, which indicates that the phase difference between two amplifier chains is locked to be nπ. From Fig. 5(b), we conclude that the spectral density of power of the phase noise below 400 Hz is efficiently suppressed in the closed loop, and no significant phase noise increases compared to the spectral density of power in single amplifier chains.
Fig. 5. Time series signals and spectral density of energy encircled in the pinhole in open loop and closed loop. (a) Time series signals. (b) Spectral density.
The phase control process of the experimental CPBC system can also be reflected by the change of intensity profiles collected by the camera. In the experiment, when the CPBC system is in the open loop, the intensity profile at the camera is changed along with time and the encircled power values in P1 and P2 are unsteady due to the undefined phase difference between two beams. Figure 6(a) plots three snapshots of the intensity pattern when the system is in the open loop. When the single-frequency dithering algorithm is implemented and the whole system is in the closed loop, the intensity profile and the combined output power is steady. The intensity profile in closed loop is shown in Fig. 6(b). The power meter values of P1 and P2 are 34.1 W and 1.9 W, respectively. Due to the limited polarization extinction ratios of the two amplifier chains, a small portion of the power (86.2 mW in the experiment) is leaked out in the other port of the PBC1. Considering that the output power of the two amplifier chains are 36.1 W, so the combining efficiency of the whole system is more than 94.4%.
Fig. 6. The intensity profiles with the system in open loop and closed loop. (a) Three intensity profiles in open loop. (b) Intensity profiles in closed loop with phase locking to minimum (left) and maximum (right) state.
In the present CPBC system, inefficiency induced by some imperfections is about 5.6%. By Eq. (10), we estimated that inefficiency caused by phase noise is 3.5%. Inefficiency induced by other factors, such as polarization extinction ratio, beam size error, beam quality of the injected beams, and coaxial error, is 2.1%. Specifically, due to that the polarization extinction ratios of the two beams are 26.4 dB and 25.4 dB, so its influence on combining efficiency is within 0.4%. According to the M2 factor data, the beam widths of two amplifier
#198522 - $15.00 USD Received 30 Sep 2013; revised 8 Nov 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029666 | OPTICS EXPRESS 29673
chains are 7.4 mm and 7.8 mm, respectively. By calculation using previous theoretical analysis, the beam size error induced inefficiency is 0.9%. The residual inefficiency (
College of Opticelectric Science and Engineering, National University of Defense Technology, Changsha 410073, China 2 [email protected] * [email protected]
Abstract: In this manuscript, the influence of perturbative phase noise on active coherent polarization beam combining (CPBC) system is studied theoretically and experimentally. By employing a photo-detector to obtain phase error signal for feedback loop, actively coherent polarization beam combining of two 20 W-level single mode polarization-maintained (PM) fiber amplifiers are demonstrated with more than 94% combining efficiency. Then the influence of perturbative phase noise on active CPBC system is illustrated by incorporating a simulated phase noise signal in one of the two amplifiers. Experimental results show that the combining efficiency of the CPBC system is susceptible to the frequency or amplitude of the perturbative phase noise. In order to ensure the combining efficiency of the unit of CPBC system higher than 90%, the competence of our active phase control module for high power operation is discussed, which suggests that it could be worked at 100s W power level. The relationship between residual phase noise of the active controller and the normalized voltage signal of the photo-detector is developed and validated experimentally. Experimental results correspond exactly with the theoretically analyzed combining efficiency. Our method offers a useful approach to estimate the influence of phase noise on CPBC system. ©2013 Optical Society of America OCIS codes: (140.3298) Laser beam combining; (140.3425) Laser stabilization.
References and links 1. 2. 3. 4. 5. 6.
7. 8. 9.
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, and C. P. J. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Express 16(17), 13240–13266 (2008). Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007). J. Bourderionnet, C. Bellanger, J. Primot, and A. Brignon, “Collective coherent phase combining of 64 fibers,” Opt. Express 19(18), 17053–17058 (2011). C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, and T. Y. Fan, “Coherent combining of a 4 kW, eight-element fiber amplifier array,” Opt. Lett. 36(14), 2686–2688 (2011). P. Zhou, Z. J. Liu, X. J. Xu, and Z. L. Chen, “Numerical analysis of the effects of aberrations on coherently combined fiber laser beams,” Appl. Opt. 47(18), 3350–3359 (2008). G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, Jr., M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solidstate laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007). T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14(25), 12015–12021 (2006). P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combination of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009). X. L. Wang, P. Zhou, Y. X. Ma, J. Y. Leng, X. J. Xu, and Z. J. Liu, “Active phasing a nine-element 1.14 kW allfiber two-tone MOPA array using SPGD algorithm,” Opt. Lett. 36(16), 3121–3123 (2011).
#198522 - $15.00 USD Received 30 Sep 2013; revised 8 Nov 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029666 | OPTICS EXPRESS 29666
10. C. J. Corcoran and F. Durville, “Experimental demonstration of a phase—locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86(20), 201118 (2005). 11. E. J. Bochove and S. A. Shakir, “Analysis of a spatial-filtering passive fiber laser beam combining system,” IEEE J. Sel. Top. Quantum Electron. 15(2), 320–327 (2009). 12. J. Lhermite, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Passive phase locking of an array of four fiber amplifiers by an all-optical feedback loop,” Opt. Lett. 32(13), 1842–1844 (2007). 13. P. B. Phua and Y. L. Lim, “Coherent polarization locking with near-perfect combining efficiency,” Opt. Lett. 31(14), 2148–2150 (2006). 14. L. H. Tan, C. F. Chua, and P. B. Phua, “Preserving a diffraction-limited beam in Ho:YAG laser using coherent polarization locking,” Opt. Lett. 37(22), 4621–4623 (2012). 15. R. Uberna, A. Bratcher, and B. G. Tiemann, “Power scaling of a fiber master oscillator power amplifier system using a coherent polarization beam combination,” Appl. Opt. 49(35), 6762–6765 (2010). 16. R. Uberna, A. Bratcher, and B. G. Tiemann, “Power scaling of a fiber master oscillator power amplifier system using a coherent polarization beam combination,” Appl. Opt. 49(35), 6762–6765 (2010). 17. P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photon. Technol. Lett. 25(19), 1936–1938 (2013). 18. P. F. Ma, P. Zhou, R. T. Su, Y. X. Ma, and Z. J. Liu, “Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique,” Laser Phys. Lett. 9(6), 456–458 (2012). 19. D. C. Jones, C. D. Stacey, and A. M. Scott, “Phase stabilization of a large-mode-area ytterbium-doped fiber amplifier,” Opt. Lett. 32(5), 466–468 (2007). 20. S. J. Augst, T. Y. Fan, and A. Sanchez, “Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers,” Opt. Lett. 29(5), 474–476 (2004). 21. H. Tünnermann, Y. Feng, J. Neumann, D. Kracht, and P. Weßels, “All-fiber coherent beam combining with phase stabilization via differential pump power control,” Opt. Lett. 37(7), 1202–1204 (2012). 22. M. Tröbs, S. Barke, T. Theeg, D. Kracht, G. Heinzel, and K. Danzmann, “Differential phase-noise properties of a ytterbium-doped fiber amplifier for the Laser Interferometer Space Antenna,” Opt. Lett. 35(3), 435–437 (2010). 23. G. D. Goodno, C. C. Shih, and J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18(24), 25403–25414 (2010). 24. Z. Li, J. Zhou, B. He, Y. Xue, P. Zhou, C. Liu, Y. Qi, Q. Lou, and X. Xu, “Impact of phase perturbation on passive phase-locking coherent beam combination,” IEEE Photon. Technol. Lett. 24(8), 655–657 (2012). 25. S. H. Xu, Z. M. Yang, W. N. Zhang, X. M. Wei, Q. Qian, D. D. Chen, Q. Y. Zhang, S. X. Shen, M. Y. Peng, and J. R. Qiu, “400 mW ultrashort cavity low-noise single-frequency Yb³⁺-doped phosphate fiber laser,” Opt. Lett. 36(18), 3708–3710 (2011). 26. Y. Ma, X. Wang, J. Leng, H. Xiao, X. Dong, J. Zhu, W. Du, P. Zhou, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination of 1.08 kW fiber amplifier array using single frequency dithering technique,” Opt. Lett. 36(6), 951–953 (2011).
1. Introduction Fiber lasers and amplifiers have attracted intensively attention due to their great potential in scaling to high power level with near diffraction-limited beam quality. However, the output power of the monolithic amplifier/laser will be ultimately limited by several obstacles, including high brightness pump diodes, fiber damage, thermal effects and non-linear effects [1, 2]. Coherent beam combination (CBC) technique provides a prominent approach to break through the limitations above-mentioned. Nowadays, active CBC of continuous-wave configuration had been extended to multi-channel [3] and the 4 kW combined output power had been demonstrated by Massachusetts Institute of Technology (MIT) [4]. Nevertheless, in most of the general CBC configurations, all the emitters were tiled into an array, which induced a portion of power encircled into the side-lobes in the far-field pattern [3–12], thus inevitably degrades the beam quality and power concentration of the coherently combined beam [5]. As a new technique to overcome the insufficiency of side-lobes in CBC system, coherent polarization beam combining (CPBC) was proposed and validated both in passive and active phasing techniques [13–18]. By passive phasing technique, Phua et al. demonstrated CPBC of two watt-level Nd:YVO4 laser with near-perfect combining efficiency (>99%) [13]. Tan et al. reported CPBC of two Ho: YAG lasers to overcome thermal issues and preserve beam quality, and 10 W-level output power was produced with 96% combining efficiency [14]. As for active phasing technique, Uberna et al. validated the feasibility of CPBC technique in four fiber lasers and scaled the output power to 25 W with the combining efficiency of 94% by heterodyne phase control technique [15, 16]. Recently, active CPBC of two 200 W-level PM fiber amplifiers were presented by our group with more than 90% combining efficiency by single-frequency dithering method [17].
#198522 - $15.00 USD Received 30 Sep 2013; revised 8 Nov 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029666 | OPTICS EXPRESS 29667
Due to the influence of some factors, such as thermal effects, ambient vibrations and nonlinear effects, the optical phases in fiber lasers and amplifiers are continuously changed along with time [19–22]. As for active and passive phasing CBC architectures, the property of perturbative phase noise plays a significant impact on the phase locking effect and the power encircled in the central-lobe [23, 24]. In the previous publications, the phase noise properties of amplifier chains in active CBC configurations were measured [4, 19–21], and differential pump power control method was proposed to mitigate its adverse effect [21]. Recently, Goodno et al. theoretically examined the phase noise influence on the actively aperture-filled CBC configuration by perturbative analytical method [23]. Li et al. clarified the impact of phase noise on a specific passive CBC architecture experimentally [24]. However, as far as we known, the inefficiency of phase noise on CPBC system has not been studied up to now. Therefore, it is necessary to clarify the influence of perturbative phase noise on the combining efficiency of the CBPC system theoretically and experimentally. In this manuscript, the impact of perturbative phase noise on the active CPBC system is investigated theoretically and experimentally by active CPBC of two 20 W-level PM single mode amplifiers. By utilizing a phase modulator and a signal generator to generate an artificial phase noise, the influence of perturbative phase noise on the combining efficiency of the CPBC system is studied. Without artificial phase noise, the combining efficiency of the two-channel CPBC system can be higher than 94%. When the artificial phase noise is implemented, the combining efficiency of the system decreases with the increase of the frequency or amplitude of the artificial noise. In order to ensure the combining efficiency of the unit of CPBC system higher than 90%, the competence of our active phase control module for high power operation is also discussed in the end of the manuscript. The relationship between residual phase noise of the active controller and the normalized voltage signal of the photo-detector is developed and validated experimentally, which offers an approach to estimate the influence of phase noise on the combining efficiency of CPBC system. 2. Principle and Experimental Setup In principle, the fulfillment of active CPBC can be illustrated as follows. Generally, when two linearly polarized beams are injected into a polarization beam combiner (PBC), the polarization state of the combined beam is not linearly polarized and fluctuates along with time due to phase difference between the two beams is uncertain, as is a mixture of the polarization state of two orthogonally polarized beams (as shown in Fig. 1(a)). However, when the phase difference (δ) between the two orthogonal polarizations is locked and set to δ = nπ, where n is an integer, the combined beam is a new pure linear-polarized one (see Fig. 1(b)), thus it can be completely transmitted through the next PBC by using a half wavelength plate (HWP) to rotate the polarization direction of the combined beam. Due to the linear property of the coherently combined beam, it can be further combined with another linearly polarized beam by a PBC, so multi-channel beams can be coherently combined straightforwardly by phase locking [15].
Fig. 1. The polarization state of combined beam for (a) without phase control and (b) phase locked.
The experimental setup to perform CPBC of two 20 W-level single mode PM fiber amplifier chains is demonstrated in Fig. 2. The seed is a linear-polarized and single-frequency (line-width t P0
(4)
Where
< Pc (t ) >=
ξ1 (t ) =
∞ ∞
1 1 2 2 −∞ ψ 1 ( x, y ) +ψ 2 ( x, y ) d x d y + 2T 2 −∞
∞ ∞
ψ 1 ( x, y )ψ 2 ( x, y ) cos δ (t )d x d y ξ2 =
−∞ −∞
P0 =
∞ ∞
ψ
−∞ −∞
2 1
∞ ∞
ψ
−∞ −∞
2 1
T
4ξ 21 + ξ 2 2 d t
(5)
0
( x, y ) −ψ 2 2 ( x, y ) d x d y (6)
( x, y ) + ψ 2 2 ( x, y ) d x d y
(7)
Defining that θ is the polarization angle of the linear polarizer (P), the relationship between the residual phase noise of the active phase control module and the normalized energy (denoted by voltage V(t)) in the PD can be expressed by
#198522 - $15.00 USD Received 30 Sep 2013; revised 8 Nov 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029666 | OPTICS EXPRESS 29670
cos δ (t ) =
V (t ) − κ1 cos2 θ − κ 2 sin 2 θ 2 κ1κ 2 sin(θ ) cos(θ )
(8)
Where Pb1 P κ 2 = b2 (9) P0 P0 In general operation, without phase control, by rotating the polarization angle of the linear polarizer (P), the peak-vale fluctuation energy collected in the PD can be maximized. This state is more advantageous for the active phase control system to demodulate the actual phase difference between the two amplifier chains. The active phase control module can lock the transformed voltage in either maximum state or minimum state, and the combining efficiency difference of the CPBC system in these two states can be negligible in the previous experiment. As a special case that the output power of the first beam (Pb1) is approximately equal to the scaled power of second beam (Pb2), Eq. (4) can be simplified by
κ1 =
1 T phase locking at maximum state V (t )d t T 0 η= T 1 1 − V (t ) d phase locking at minimum state ]t T [ 0
(10)
By the analysis aforementioned, we established the relationship between the residual phase noise of the active controller and the normalized voltage signal of the photo-detector, which offers an approach to estimate the influence of phase noise on the combining efficiency of the CPBC system experimentally. 4. Experimental Results and Discussions
4.1 Experimental results and discussions without artificial phase noise As shown in Fig. 2, after two collimators, the output powers of the two channels are scaled to 17.9 W and 18.2 W, respectively. The extinction ratios of the two amplifier chains are measured to be 26.4 dB and 25.4 dB respectively by a HWP and a PBC, and both of the M2 factors of the two amplifier chains are measured to be within 1.1. As mentioned above, the phase noise properties of the amplifier chains are crucial for active phasing effect. Therefore, in front of phase locking process, the spectral density of power of the phase noise in the two amplifier chains in 3 W level and 20 W level are measured based on coherent detection technique (as similar in Ref [19, 20].), which is shown in Fig. 4. From the measurement phase noise information, we conclude that the characteristic frequencies of the two 3 W and 20 W level amplifier chains are below 260 Hz and 400 Hz, respectively. By investigation, the envelopes of the spectral density of power below 260 Hz are mainly induced by cooling fans inserted into the commercial amplifiers. When the 20 W level amplifiers performed, some relative small (compared with frequency below 260 Hz) envelopes emerged between 260 Hz and 400 Hz, which is mainly induced by the influence of implementation of water tank in the main amplifiers.
#198522 - $15.00 USD Received 30 Sep 2013; revised 8 Nov 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029666 | OPTICS EXPRESS 29671
Fig. 4. The spectral density of power of phase noise in the two amplifier chains. (a) First amplifier in 3 W level. (b) First amplifier in 20 W level. (c) Second amplifier in 3 W level. (d) Second amplifier in 20 W level.
The active CPBC of the two amplifier chains is implemented based on our singlefrequency dithering algorithm processor [26]. The mathematical principle of single frequency dithering technique can be found in Ref [26]. and it is not repeated here to save place. The metric function of the phasing algorithm is related to the amplitude of the voltage signal transformed by the PD. The voltage signal transformed by the PD incorporates the information of phase difference between the two channels, which can be used to generate the phase control signal by modulation and demodulation technique. In the presented experimental system, each iteration cycle of the algorithm works as follows. Assuming that t denotes time, and t0, t1 and t2 denote different moment. In the experiment, a 1MHz sine wave phase modulation signal is employed in the phase control module. In the interval of t0 to t1, the phase modulation signal and control signal S1 is added to the phase modulator in the first channel, while the phase control signal of the second channel remains zero. By calculation, the control signal S1 is proportional to sin(δ), as is similarly described in Ref [26]. except for the proportional coefficient. At the interval of t1 to t2, the phase control signal S2 (proportional to sin(-δ)) are applied to the phase modulator in the second channel. During this period, the modulation signal of the first channel becomes zero, and the control signal retains the value at t = t1. Provided that the interval T = t2-t0 is short enough so that the phases of two channels experience negligible fluctuations but long enough for the feedback process to be operative, the phase difference between the two channels will be compensated by repeating the aboveoperations in turns. Finally, the phase difference between the two channels can be compensated to be zero by selecting the appropriate feedback gain in the phase control module. Before utilizing the artificial phase noise in the experimental setup, we investigate the active phase control process and phase noise suppression process of the two amplifier chains. The phase control and phase noise suppression process are shown in Fig. 5. Without the phase control module, the normalized energy collected by the PD fluctuates randomly due to that the phase difference between two amplifier chains continuously changes with the influence of thermal effects, experimental vibrations and so forth (shown in Fig. 5(a)). However, when the
#198522 - $15.00 USD Received 30 Sep 2013; revised 8 Nov 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029666 | OPTICS EXPRESS 29672
phase control module performed, the normalized energy in the PD can be locked effectively, which indicates that the phase difference between two amplifier chains is locked to be nπ. From Fig. 5(b), we conclude that the spectral density of power of the phase noise below 400 Hz is efficiently suppressed in the closed loop, and no significant phase noise increases compared to the spectral density of power in single amplifier chains.
Fig. 5. Time series signals and spectral density of energy encircled in the pinhole in open loop and closed loop. (a) Time series signals. (b) Spectral density.
The phase control process of the experimental CPBC system can also be reflected by the change of intensity profiles collected by the camera. In the experiment, when the CPBC system is in the open loop, the intensity profile at the camera is changed along with time and the encircled power values in P1 and P2 are unsteady due to the undefined phase difference between two beams. Figure 6(a) plots three snapshots of the intensity pattern when the system is in the open loop. When the single-frequency dithering algorithm is implemented and the whole system is in the closed loop, the intensity profile and the combined output power is steady. The intensity profile in closed loop is shown in Fig. 6(b). The power meter values of P1 and P2 are 34.1 W and 1.9 W, respectively. Due to the limited polarization extinction ratios of the two amplifier chains, a small portion of the power (86.2 mW in the experiment) is leaked out in the other port of the PBC1. Considering that the output power of the two amplifier chains are 36.1 W, so the combining efficiency of the whole system is more than 94.4%.
Fig. 6. The intensity profiles with the system in open loop and closed loop. (a) Three intensity profiles in open loop. (b) Intensity profiles in closed loop with phase locking to minimum (left) and maximum (right) state.
In the present CPBC system, inefficiency induced by some imperfections is about 5.6%. By Eq. (10), we estimated that inefficiency caused by phase noise is 3.5%. Inefficiency induced by other factors, such as polarization extinction ratio, beam size error, beam quality of the injected beams, and coaxial error, is 2.1%. Specifically, due to that the polarization extinction ratios of the two beams are 26.4 dB and 25.4 dB, so its influence on combining efficiency is within 0.4%. According to the M2 factor data, the beam widths of two amplifier
#198522 - $15.00 USD Received 30 Sep 2013; revised 8 Nov 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029666 | OPTICS EXPRESS 29673
chains are 7.4 mm and 7.8 mm, respectively. By calculation using previous theoretical analysis, the beam size error induced inefficiency is 0.9%. The residual inefficiency (
