Digital holography for coherent fiber beam combining with a co-propagative scheme Marie Antier,1,* Christian Larat,1 Eric Lallier,1 Jérôme Bourderionnet,1 Jérôme Primot,2 and Arnaud Brignon1 1
Thales Research & Technology, 1 avenue Augustin Fresnel, F-91767 Palaiseau cedex, France 2 ONERA, The French Aerospace Lab, BP80100, F-91123 Palaiseau cedex, France * [email protected]
Abstract: We present a technique for passive coherent fiber beam combining based on digital holography. In this method, the phase errors between the fibers are compensated by the diffracted phase-conjugated −1 order of a digital hologram. Unlike previous digital holography technique, the probe beams measuring the phase errors between the fibers are copropagating with the phase-locked signal beams. This architecture is compatible with the use of multi-stage isolated amplifying fibers. It does not require any phase calculation algorithm and its correction is collective. This concept is experimentally demonstrated with three fibers at 1.55μm. A residual phase error of λ/20 is measured. ©2014 Optical Society of America OCIS codes: (140.3298) Laser beam combining (090.1995) Digital holography; (140.3290) Laser beam combining.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
A. Brignon, ed., Coherent Laser Beam Combining (Wiley-Vch, 2013). N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng. 51(10), 104301 (2012). T. Y. Fan, “Laser beam combining for high-power, high radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005). 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). 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). S. Demoustier, C. Bellanger, A. Brignon, and J. P. Huignard, “Coherent beam combining of 1.5μm Er-Yb doped fiber amplifiers,” Fiber Int. Opt. 27(5), 392–406 (2008). L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront tip-tilt compensation,” Proc. SPIE 6708, 67080K, 67080K-12 (2007). M. Antier, J. Bourderionnet, C. Larat, E. Lallier, E. Lenormand, J. Primot, G. Mourou, and A. Brignon, “Highly scalable coherent fiber combining using interferometric technique,” in CLEO: Paper CW3M.4 (2013). 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). H. J. Kong, S. K. Lee, J. W. Yoon, and D. H. Beak, “Beam Combination using Stimulated Brillouin Scattering for the Ultimate High Power-Energy Laser System Operating at High Repetition Rate over 10 Hz for Laser Fusion Driver,” Opt. Rev. 13(3), 119–128 (2006). E. A. Stappaerts, “Holographic system for interactive target acquisition and tracking,” U.S. patent 5,378,888 (1995). U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005). E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38(34), 6994–7001 (1999). M. Gross and M. Atlan, “Digital holography with ultimate sensitivity,” Opt. Lett. 32(8), 909–911 (2007). C. Bellanger, A. Brignon, J. Colineau, and J. P. Huignard, “Coherent fiber combining by digital holography,” Opt. Lett. 33(24), 2937–2939 (2008).
Coherent beam combining of fiber amplifiers provides an attractive mean of reaching high power laser by scaling up the available energy while keeping the intrinsic advantages of fibers like beam quality, reliability, robustness and compactness [1]. The development of high
#212149 - $15.00 USD Received 14 May 2014; revised 2 Sep 2014; accepted 10 Sep 2014; published 16 Sep 2014 (C) 2014 OSA 22 September 2014 | Vol. 22, No. 19 | DOI:10.1364/OE.22.023310 | OPTICS EXPRESS 23310
brightness semiconductor diodes as pump sources allowed a rapid increase of the output power of fiber lasers. Even given these advantages, it is desirable to increase the emitted power beyond what is possible with a single-mode fiber laser [2]. Beam combining techniques are a promising route toward this goal. In this approach, all the emitters operate at the same wavelength and are phase locked for constructive field recombining. The different methods for coherent beam combining fall under two categories: passive and active phase locking. Active phase locking involves phase detection, calculation of the correction and compensation of the phase of each amplifier [3]. Well known phase detection methods include single-detector electronic-frequency tagging technique [4], heterodyne techniques [5,6], stochastic parallel gradient descent (SPGD) algorithm phase control technique [7] or interferometric phase measurement method [8]. As examples of passive approaches, an all optical feedback loop in a single ring cavity has been demonstrated [9], and a technique based on nonlinear phase conjugate mirror has also been proposed [10]. In this paper, we present a new technique of passive coherent fiber beam combining, based on digital holography [1114] with a co-propagative scheme. A previous demonstration was already done using digital holography [15]. However, the probe beams used to measure the phase errors between the fibers and the phase-locked signal beams were counter-propagating. This configuration forbade the use of multi-stage isolated amplifying fibers which is compulsory for high energy applications. The set up proposed in the present paper overcomes that limitation. After explaining the basic principles of this technique, we present our results with three fibers at the wavelength of 1.55µm.
Fig. 1. Principle of digital holography.
The general principle of digital holography is described in Fig. 1. A “writing” beam with phase φ interferes with a reference beam onto a camera. The recorded interference pattern is directly transferred to a Spatial Light Modulator (SLM) which acts as a programmable digital hologram. This hologram (“reading” beam) is read out and a phase conjugate beam with phase -φ is generated in order −1 of the diffraction pattern. Digital holography can be applied to coherent fiber beam combining. The order −1 of the digital hologram, we called signal, is used to compensate the phase differences between the fibers. The “writing” beam used to measure the phase errors of the fibers is called probe beam. Each fiber amplifier is injected with one probe beam and one signal beam. The co-propagating probe and signal beams are temporally separated with an optical switch placed before the SLM. The intensities of the probe beams and signal beams are adapted before the SLM to have the same intensity in the fiber amplifiers after their diffraction on the SLM. In this scheme, each amplifier sees a continuous intensity. Therefore, there is no dynamic effect in the amplifier. Only the signal beams have its phase corrected. Then, to avoid loss in the combined energy, the duty cycle of the probe should be low. The main advantages of this technique are that it does not require any phase measurement and have a collective correction modulator.
#212149 - $15.00 USD Received 14 May 2014; revised 2 Sep 2014; accepted 10 Sep 2014; published 16 Sep 2014 (C) 2014 OSA 22 September 2014 | Vol. 22, No. 19 | DOI:10.1364/OE.22.023310 | OPTICS EXPRESS 23311
Fig. 2. Experimental set up of coherent fiber combining using digital holography with a copropagative scheme.
The setup of fiber beam combining with digital holography with a co-propagative scheme is described in Fig. 2. The amplifying fibers are precisely positioned and collimated at both ends to form two identical fiber arrays. The first array is used for injection of the probe and signal beams. The probe beams are coupled in the 0 order of the SLM. The diffraction efficiency of the probe beam on the order 0 is 70%. Then they propagate through the fibers. We record on a camera the interferences between the probe beam issued from each fiber and a planar reference beam. For each fiber i, the recorded interference pattern consists of series of linear fringes whose positions are given by the relative dephasing φi between one fiber i and the reference beam. This dephasing φi comes from fixed length propagation differences and time varying phase perturbations. As time evolves, we can observe the scrolling of the fringes on the camera. The interference pattern recorded by the camera is then directly transferred to the phase-only SLM, creating a phase grating. This phase grating is then read by the signal beam. The angle of incidence of the signal beam onto the SLM is adjusted such as the order −1 of the diffracted signal beam is coupled into the fiber array. The diffraction efficiency of the signal beam is 12%, mainly due to the Gaussian envelope of the diffraction grating written on the SLM. Therefore, the phase of each signal beam is pre-compensated by an amount of φi before beam-injection in the related fibers. Then at the output of the second fiber array all the fiber beams are in-phase. The camera is trigged to measure only the probe beams. A proof of concept is realized with three single-mode polarization-maintaining fibers. In our experimental set up, a 1.55µm continuous-wave 1GHz linewidth master oscillator is used. The three fibers are placed at both ends into V-grooves, separated by 1.5mm, and collimated by microlens arrays. The linear fill factor of the collimated beams issued from the array is 70%. A 320 × 256 pixels InGaAs camera is used to record the interferences between the probe beams and the reference plane wave. The pixel size is 30µm. A typical interferogram pattern recorded by the camera is shown in Fig. 3. Our probe temporal duty cycle is set to 10%. The liquid crystal phase-only SLM has a high resolution of 1920 × 1080 pixels, with a pixel size of 8µm. The SLM works in reflection and its operating angle is set to 36°. The phase measurement sampling is limited to 30Hz due to the SLM characteristics. The difference of pixels size between the SLM and the camera requires a numerical resizing of the camera image before its transfer to the SLM. This resizing can be avoided with a SLM and a camera that have the same pixels size or by adjusting the two fiber array sizes.
#212149 - $15.00 USD Received 14 May 2014; revised 2 Sep 2014; accepted 10 Sep 2014; published 16 Sep 2014 (C) 2014 OSA 22 September 2014 | Vol. 22, No. 19 | DOI:10.1364/OE.22.023310 | OPTICS EXPRESS 23312
Fig. 3. Experimentally recorded hologram with the three fibers.
The left plot of Fig. 4 shows the far field pattern with or without correction. The far field intensity is integrated over 30s. Without correction, a speckle pattern is observed. With correction, the far field profile corresponds to the constructive interferences of 3 fibers arranged in a line. The right plot of Fig. 4 shows the central lobe far field intensity, normalized to the measured total near field intensity. The sampling rate of the far field intensity is set to 300S/s. The green dash plot represents the theoretical profile of the combined far field with the measured total near field intensity. The experimental difference between our experimental profile and the theoretical one is mainly due to optical aberrations on the measurement path.
Fig. 4. Left: experimental far field of the 3 fibers integrated over 30s. Right: evolution of the central lobe intensity over 60s. The correction is closed after 30s.
The residual phase shift error is measured to be λ/15rms, when the experimentally recorded hologram is written directly on the SLM. By adjusting the threshold level of the camera before writing the grating on the SLM, a residual phase shift error of λ/20rms can be achieved. This value is smaller than λ/10, which is sufficient for coherent beam combining [2]. This threshold level increases the contrast of the central fringes of the grating of each fiber and suppresses the snow like noise on the background of the hologram. To conclude, we coherently combine three passive fibers using a digital holography with a co-propagative scheme. The phase control proposed does not require any phase calculation algorithm and its architecture is collective. The previous results were done with a fringe period of the recorded hologram of 5.4 pixels. The fringe period is not an integer to avoid Moiré effect. Ideally if the signal to noise ratio is infinite, as long as the sampling of the sinusoidal pattern if higher than 2 pixels per fringe (Shannon theorem), we can precisely measure a phase shift of λ/20. In our experimental conditions, the same result is obtained with 3.6 pixels and 6.8 pixels per fringe. Below 3.6 pixels per fringe, the sampling of the hologram is too critical and does not permit the phase control. Over 7 pixels per fringe, the angle between the probe beam and the signal beam is too small and we didn’t succeed in aligning the signal. We also observed that below 5 fringes per hologram the diffraction efficiency of the order −1 decreases.
#212149 - $15.00 USD Received 14 May 2014; revised 2 Sep 2014; accepted 10 Sep 2014; published 16 Sep 2014 (C) 2014 OSA 22 September 2014 | Vol. 22, No. 19 | DOI:10.1364/OE.22.023310 | OPTICS EXPRESS 23313
Under our experimental conditions, the maximum number of fibers, Nmax, that could be combined by digital holography is limited by the number of pixels on our camera. At least 50 × 50 pixels per fiber are required for a residual phase shift error of λ/15rms, giving Nmax = 25. With a camera having a number of pixels larger than the one of the SLM, which is currently availed at 1µm with CMOS technology, Nmax is now fixed by the characteristics of the SLM. Our SLM has a size of 1920 × 1080 pixels. Therefore, Nmax can reach 400 fibers arranged in a square 20 × 20 fibers. For higher bandwidth correction, up to few kilohertz, a high speed camera and a fast SLM such as ferroelectric LC or micro-opto-electromechanical systems devices would be required. Indeed, a kilohertz phase sampling frequency is sufficient to compensate the typical phase noise of fiber amplifiers [5]. Coherent fiber beam combining by digital holography offers the opportunity to phase lock a high number of fiber amplifiers simultaneously and without any phase measurement and complex electronic feedback loop. In conclusion, we have proposed a new technique of coherent fiber amplifier beam combining based on digital holography with a co-propagative scheme. This new technique permits the use of multi-stage isolated fiber amplifiers thanks to the co-propagation of probe beams used to measure the phase errors and in-phase signal beams. The phase locking of three fibers has been experimentally demonstrated with a residual phase error of λ/20rms. Due to a high spatial resolution of existing SLMs and cameras, a large number of fiber amplifiers could be coherently combined with this technique. Further work will include the increase of the number of combined fibers.
#212149 - $15.00 USD Received 14 May 2014; revised 2 Sep 2014; accepted 10 Sep 2014; published 16 Sep 2014 (C) 2014 OSA 22 September 2014 | Vol. 22, No. 19 | DOI:10.1364/OE.22.023310 | OPTICS EXPRESS 23314
Thales Research & Technology, 1 avenue Augustin Fresnel, F-91767 Palaiseau cedex, France 2 ONERA, The French Aerospace Lab, BP80100, F-91123 Palaiseau cedex, France * [email protected]
Abstract: We present a technique for passive coherent fiber beam combining based on digital holography. In this method, the phase errors between the fibers are compensated by the diffracted phase-conjugated −1 order of a digital hologram. Unlike previous digital holography technique, the probe beams measuring the phase errors between the fibers are copropagating with the phase-locked signal beams. This architecture is compatible with the use of multi-stage isolated amplifying fibers. It does not require any phase calculation algorithm and its correction is collective. This concept is experimentally demonstrated with three fibers at 1.55μm. A residual phase error of λ/20 is measured. ©2014 Optical Society of America OCIS codes: (140.3298) Laser beam combining (090.1995) Digital holography; (140.3290) Laser beam combining.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
A. Brignon, ed., Coherent Laser Beam Combining (Wiley-Vch, 2013). N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng. 51(10), 104301 (2012). T. Y. Fan, “Laser beam combining for high-power, high radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005). 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). 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). S. Demoustier, C. Bellanger, A. Brignon, and J. P. Huignard, “Coherent beam combining of 1.5μm Er-Yb doped fiber amplifiers,” Fiber Int. Opt. 27(5), 392–406 (2008). L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront tip-tilt compensation,” Proc. SPIE 6708, 67080K, 67080K-12 (2007). M. Antier, J. Bourderionnet, C. Larat, E. Lallier, E. Lenormand, J. Primot, G. Mourou, and A. Brignon, “Highly scalable coherent fiber combining using interferometric technique,” in CLEO: Paper CW3M.4 (2013). 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). H. J. Kong, S. K. Lee, J. W. Yoon, and D. H. Beak, “Beam Combination using Stimulated Brillouin Scattering for the Ultimate High Power-Energy Laser System Operating at High Repetition Rate over 10 Hz for Laser Fusion Driver,” Opt. Rev. 13(3), 119–128 (2006). E. A. Stappaerts, “Holographic system for interactive target acquisition and tracking,” U.S. patent 5,378,888 (1995). U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005). E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38(34), 6994–7001 (1999). M. Gross and M. Atlan, “Digital holography with ultimate sensitivity,” Opt. Lett. 32(8), 909–911 (2007). C. Bellanger, A. Brignon, J. Colineau, and J. P. Huignard, “Coherent fiber combining by digital holography,” Opt. Lett. 33(24), 2937–2939 (2008).
Coherent beam combining of fiber amplifiers provides an attractive mean of reaching high power laser by scaling up the available energy while keeping the intrinsic advantages of fibers like beam quality, reliability, robustness and compactness [1]. The development of high
#212149 - $15.00 USD Received 14 May 2014; revised 2 Sep 2014; accepted 10 Sep 2014; published 16 Sep 2014 (C) 2014 OSA 22 September 2014 | Vol. 22, No. 19 | DOI:10.1364/OE.22.023310 | OPTICS EXPRESS 23310
brightness semiconductor diodes as pump sources allowed a rapid increase of the output power of fiber lasers. Even given these advantages, it is desirable to increase the emitted power beyond what is possible with a single-mode fiber laser [2]. Beam combining techniques are a promising route toward this goal. In this approach, all the emitters operate at the same wavelength and are phase locked for constructive field recombining. The different methods for coherent beam combining fall under two categories: passive and active phase locking. Active phase locking involves phase detection, calculation of the correction and compensation of the phase of each amplifier [3]. Well known phase detection methods include single-detector electronic-frequency tagging technique [4], heterodyne techniques [5,6], stochastic parallel gradient descent (SPGD) algorithm phase control technique [7] or interferometric phase measurement method [8]. As examples of passive approaches, an all optical feedback loop in a single ring cavity has been demonstrated [9], and a technique based on nonlinear phase conjugate mirror has also been proposed [10]. In this paper, we present a new technique of passive coherent fiber beam combining, based on digital holography [1114] with a co-propagative scheme. A previous demonstration was already done using digital holography [15]. However, the probe beams used to measure the phase errors between the fibers and the phase-locked signal beams were counter-propagating. This configuration forbade the use of multi-stage isolated amplifying fibers which is compulsory for high energy applications. The set up proposed in the present paper overcomes that limitation. After explaining the basic principles of this technique, we present our results with three fibers at the wavelength of 1.55µm.
Fig. 1. Principle of digital holography.
The general principle of digital holography is described in Fig. 1. A “writing” beam with phase φ interferes with a reference beam onto a camera. The recorded interference pattern is directly transferred to a Spatial Light Modulator (SLM) which acts as a programmable digital hologram. This hologram (“reading” beam) is read out and a phase conjugate beam with phase -φ is generated in order −1 of the diffraction pattern. Digital holography can be applied to coherent fiber beam combining. The order −1 of the digital hologram, we called signal, is used to compensate the phase differences between the fibers. The “writing” beam used to measure the phase errors of the fibers is called probe beam. Each fiber amplifier is injected with one probe beam and one signal beam. The co-propagating probe and signal beams are temporally separated with an optical switch placed before the SLM. The intensities of the probe beams and signal beams are adapted before the SLM to have the same intensity in the fiber amplifiers after their diffraction on the SLM. In this scheme, each amplifier sees a continuous intensity. Therefore, there is no dynamic effect in the amplifier. Only the signal beams have its phase corrected. Then, to avoid loss in the combined energy, the duty cycle of the probe should be low. The main advantages of this technique are that it does not require any phase measurement and have a collective correction modulator.
#212149 - $15.00 USD Received 14 May 2014; revised 2 Sep 2014; accepted 10 Sep 2014; published 16 Sep 2014 (C) 2014 OSA 22 September 2014 | Vol. 22, No. 19 | DOI:10.1364/OE.22.023310 | OPTICS EXPRESS 23311
Fig. 2. Experimental set up of coherent fiber combining using digital holography with a copropagative scheme.
The setup of fiber beam combining with digital holography with a co-propagative scheme is described in Fig. 2. The amplifying fibers are precisely positioned and collimated at both ends to form two identical fiber arrays. The first array is used for injection of the probe and signal beams. The probe beams are coupled in the 0 order of the SLM. The diffraction efficiency of the probe beam on the order 0 is 70%. Then they propagate through the fibers. We record on a camera the interferences between the probe beam issued from each fiber and a planar reference beam. For each fiber i, the recorded interference pattern consists of series of linear fringes whose positions are given by the relative dephasing φi between one fiber i and the reference beam. This dephasing φi comes from fixed length propagation differences and time varying phase perturbations. As time evolves, we can observe the scrolling of the fringes on the camera. The interference pattern recorded by the camera is then directly transferred to the phase-only SLM, creating a phase grating. This phase grating is then read by the signal beam. The angle of incidence of the signal beam onto the SLM is adjusted such as the order −1 of the diffracted signal beam is coupled into the fiber array. The diffraction efficiency of the signal beam is 12%, mainly due to the Gaussian envelope of the diffraction grating written on the SLM. Therefore, the phase of each signal beam is pre-compensated by an amount of φi before beam-injection in the related fibers. Then at the output of the second fiber array all the fiber beams are in-phase. The camera is trigged to measure only the probe beams. A proof of concept is realized with three single-mode polarization-maintaining fibers. In our experimental set up, a 1.55µm continuous-wave 1GHz linewidth master oscillator is used. The three fibers are placed at both ends into V-grooves, separated by 1.5mm, and collimated by microlens arrays. The linear fill factor of the collimated beams issued from the array is 70%. A 320 × 256 pixels InGaAs camera is used to record the interferences between the probe beams and the reference plane wave. The pixel size is 30µm. A typical interferogram pattern recorded by the camera is shown in Fig. 3. Our probe temporal duty cycle is set to 10%. The liquid crystal phase-only SLM has a high resolution of 1920 × 1080 pixels, with a pixel size of 8µm. The SLM works in reflection and its operating angle is set to 36°. The phase measurement sampling is limited to 30Hz due to the SLM characteristics. The difference of pixels size between the SLM and the camera requires a numerical resizing of the camera image before its transfer to the SLM. This resizing can be avoided with a SLM and a camera that have the same pixels size or by adjusting the two fiber array sizes.
#212149 - $15.00 USD Received 14 May 2014; revised 2 Sep 2014; accepted 10 Sep 2014; published 16 Sep 2014 (C) 2014 OSA 22 September 2014 | Vol. 22, No. 19 | DOI:10.1364/OE.22.023310 | OPTICS EXPRESS 23312
Fig. 3. Experimentally recorded hologram with the three fibers.
The left plot of Fig. 4 shows the far field pattern with or without correction. The far field intensity is integrated over 30s. Without correction, a speckle pattern is observed. With correction, the far field profile corresponds to the constructive interferences of 3 fibers arranged in a line. The right plot of Fig. 4 shows the central lobe far field intensity, normalized to the measured total near field intensity. The sampling rate of the far field intensity is set to 300S/s. The green dash plot represents the theoretical profile of the combined far field with the measured total near field intensity. The experimental difference between our experimental profile and the theoretical one is mainly due to optical aberrations on the measurement path.
Fig. 4. Left: experimental far field of the 3 fibers integrated over 30s. Right: evolution of the central lobe intensity over 60s. The correction is closed after 30s.
The residual phase shift error is measured to be λ/15rms, when the experimentally recorded hologram is written directly on the SLM. By adjusting the threshold level of the camera before writing the grating on the SLM, a residual phase shift error of λ/20rms can be achieved. This value is smaller than λ/10, which is sufficient for coherent beam combining [2]. This threshold level increases the contrast of the central fringes of the grating of each fiber and suppresses the snow like noise on the background of the hologram. To conclude, we coherently combine three passive fibers using a digital holography with a co-propagative scheme. The phase control proposed does not require any phase calculation algorithm and its architecture is collective. The previous results were done with a fringe period of the recorded hologram of 5.4 pixels. The fringe period is not an integer to avoid Moiré effect. Ideally if the signal to noise ratio is infinite, as long as the sampling of the sinusoidal pattern if higher than 2 pixels per fringe (Shannon theorem), we can precisely measure a phase shift of λ/20. In our experimental conditions, the same result is obtained with 3.6 pixels and 6.8 pixels per fringe. Below 3.6 pixels per fringe, the sampling of the hologram is too critical and does not permit the phase control. Over 7 pixels per fringe, the angle between the probe beam and the signal beam is too small and we didn’t succeed in aligning the signal. We also observed that below 5 fringes per hologram the diffraction efficiency of the order −1 decreases.
#212149 - $15.00 USD Received 14 May 2014; revised 2 Sep 2014; accepted 10 Sep 2014; published 16 Sep 2014 (C) 2014 OSA 22 September 2014 | Vol. 22, No. 19 | DOI:10.1364/OE.22.023310 | OPTICS EXPRESS 23313
Under our experimental conditions, the maximum number of fibers, Nmax, that could be combined by digital holography is limited by the number of pixels on our camera. At least 50 × 50 pixels per fiber are required for a residual phase shift error of λ/15rms, giving Nmax = 25. With a camera having a number of pixels larger than the one of the SLM, which is currently availed at 1µm with CMOS technology, Nmax is now fixed by the characteristics of the SLM. Our SLM has a size of 1920 × 1080 pixels. Therefore, Nmax can reach 400 fibers arranged in a square 20 × 20 fibers. For higher bandwidth correction, up to few kilohertz, a high speed camera and a fast SLM such as ferroelectric LC or micro-opto-electromechanical systems devices would be required. Indeed, a kilohertz phase sampling frequency is sufficient to compensate the typical phase noise of fiber amplifiers [5]. Coherent fiber beam combining by digital holography offers the opportunity to phase lock a high number of fiber amplifiers simultaneously and without any phase measurement and complex electronic feedback loop. In conclusion, we have proposed a new technique of coherent fiber amplifier beam combining based on digital holography with a co-propagative scheme. This new technique permits the use of multi-stage isolated fiber amplifiers thanks to the co-propagation of probe beams used to measure the phase errors and in-phase signal beams. The phase locking of three fibers has been experimentally demonstrated with a residual phase error of λ/20rms. Due to a high spatial resolution of existing SLMs and cameras, a large number of fiber amplifiers could be coherently combined with this technique. Further work will include the increase of the number of combined fibers.
#212149 - $15.00 USD Received 14 May 2014; revised 2 Sep 2014; accepted 10 Sep 2014; published 16 Sep 2014 (C) 2014 OSA 22 September 2014 | Vol. 22, No. 19 | DOI:10.1364/OE.22.023310 | OPTICS EXPRESS 23314
