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3Ioffe Physico-Technical Institute of Russian Academy of Science, 194021 Politekhnicheskaya 26,. St. Petersburg, Russia. *Corresponding author: Andrei.

OPTICS LETTERS / Vol. 34, No. 22 / November 15, 2009

All-fiber coherent combining of Er-doped amplifiers through refractive index control in Yb-doped fibers Andrei A. Fotiadi,1,3,* Nikita Zakharov,1,2 Oleg L. Antipov,2 and Patrice Mégret1 1

Service d’Electromagnétisme et de Télécommunications, Université de Mons, 31 Boulevard Dolez, B-7000 Mons, Belgium 2 Institute of Applied Physics of Russian Academy of Science, 46 Uljanov Street, Nizhny Novgorod 603950, Russia 3 Ioffe Physico-Technical Institute of Russian Academy of Science, 194021 Politekhnicheskaya 26, St. Petersburg, Russia *Corresponding author: [email protected] Received August 18, 2009; revised October 15, 2009; accepted October 15, 2009; posted October 21, 2009 (Doc. ID 115898); published November 12, 2009 We propose a simple all-fiber solution for coherent beam combining of Er-doped fiber amplifiers. This method, which we believe to be a new method, employs the effect of refractive index changes in Yb-doped fibers induced at ⬃1.55 ␮m by optical pumping at ⬃980 nm, which is performed for an active phase control in the fiber configuration. An algorithm based on population inversion in a two-level system supports the straightforward implementation of the effect into a feedback loop. Combining two 500 mW Er-doped amplifiers in a single-mode fiber is successfully demonstrated with control by ⬃120 mW laser diode. The method is shown to operate against the acoustic phase noise within the range of ⬃␲ rad and with a rate of ⬃2.6␲ rad/ ms that potentially serves combining of at least 50 amplifiers similar to those used in practical work. © 2009 Optical Society of America OCIS codes: 140.3510, 060.2320, 140.3298.

Nonlinear effects reduce power levels available with standard single-mode cw fiber sources. The idea of coherent combining is to split a single coherent beam into many beams, which are then amplified by a parallel array of similar amplifiers and finally recombined to a high-power diffraction limited beam. To achieve constructive interference after amplification, i.e., to collect the power from all channels in one single-mode fiber, the fiber amplifiers must be phase locked together [1–5]. A straightforward infallible beam combining can be provided by the active control of each fiber amplifier by an attached phase modulator [6]. However, piezoelectrical or electro-optical modulators are not a perfect choice owing to obvious disadvantages of parasitic resonances or integrating bulk and fiber components. In our all-fiber solution [7] [Fig. 1(a)], the Er-doped fiber amplifiers (EDFAs) are supplied by the sections of Yb-doped fibers (YDFs) operating as optically controlled phase modulators. The principle of operation employs the effect of refractive index changes (RICs) induced in YDFs by optical pumping at 980 nm [8]. Importantly, the RIC effect is significant within the whole YDF transparency band, so it is appropriate for Raman, neodymium-, erbium-, thulium-, or holmium-doped fiber amplifier services [9–11]. In this Letter we verify the validity of our concept demonstrating the coherent combining of two 500 mW EDFAs. The two-level RIC model is developed to a simple algorithm enabling the natural implementation of the RIC effect into an active phase control loop. The ability of the method to operate again the acoustic phase noise with the rate of ⬃2.6␲ rad/ ms is experimentally confirmed. The experimental setup is shown in Fig. 1(b). A master laser diode in combination with a 15 dBm 0146-9592/09/223574-3/$15.00

preamplifier delivers single-mode radiation at ⬃1.55 ␮m with a coherence length of ⬃10 m. The first fiber coupler splits the laser emission into two arms, which are then amplified by two single-mode EDFAs specified with 500 mW output. No spectral broadening of the amplified radiation has been observed at such a power level. The EDFAs are supplied by thermoelectric controllers (TECs) used for low-frequency phase noise elimination. For fast phase adjustment, one of the arms is supplied by a 2 m length of the YDF directly spliced with the amplifier. The YDF has an independent input for 120 mW laser diode operating at 980 nm. The use of the highly doped aluminum silicate YDF (see fiber 2 in [8] for specifications) ensures maximal RIC effect owing to the total absorption of the pump radiation inside the fiber. Since the RIC is directly proportional to the population density of the excited Yb ions [8],

Fig. 1. (a) Multichannel laser system with coherent beam combining employing RIC in YDF. (b) Experimental setup. © 2009 Optical Society of America

November 15, 2009 / Vol. 34, No. 22 / OPTICS LETTERS

the phase shift induced in the fiber is determined by the laser diode power, which could be managed to maintain a constructive phase-matched coupling of two intense laser arms in a single-mode fiber (channel 1). The power emitted through channel 2 evaluates the phase mismatching, as explained in [8]. Figure 2 presents the operation of the laser configuration without active feedback. There are two classes of traces that highlight phase fluctuations associated with thermal variations [Fig. 2(a)] and environmental acoustic vibrations [Fig. 2(b)]. Two kinds of noise contribute to different time domains and show different scales of the phase excursion to be compensated. Thermally induced phase noise exhibits large fluctuations up to several ␲ rad attained for several seconds. The ordinary EDFA TEC connected with the feedback loop enable perfect suppression of this low-frequency noise. In contrast, acoustic phase noise, caused mainly by noisy equipment, dominates with excursion rates of ⬃1 ms and a much smaller excursion, typically of ⬃0.01␲ rad. This should be considered as a minimum requirement for active phase control since these measurements were taken in a quiet laboratory setting. Noisier environments would require an increase in the servo loop bandwidth, but we have checked that even a flick given on the amplifier causes a phase fluctuation no larger than ⬃0.2␲ rad attending with a rate of ⬃0.02␲ rad/ ms. To demonstrate the ability of the proposed method to operate against the acoustic noise the steady-state and dynamical characteristics of the electronic RIC have to be taken into account [Figs. 3(a) and 3(b)]. The steady-state characteristic ␸ = ␾共P兲 [Fig. 3(a)] is evaluated as a phase response to long 共⬃4 ms兲 rectangular pulses of different amplitudes P. One could adjust the phase in the range of up to ⬃3.75␲ rad by a simple tuning of the laser diode power. As an example, the phase switching from ␸1 = ␾共P1兲 to ␸2 = ␾共P2兲 is provided by a switch of the diode power from P1 to P2. However, this procedure requires several milliseconds to proceed. Fast dynamical switching is available within a part of the range covered by the steady-state curve ␸ = ␾共P兲, in particular, within the range of ⬃␲ rad marked in Fig. 3(a). The dynamical phase response to rectangular pulses [Fig. 3(b)] is perfectly described by the two-level population inversion model shown to be valid for different YDF geometries, ion concentrations, and test wavelengths ␭T [8]. In the general case

Fig. 2. Time series of the typical amplifier phase noise (after 2–3 min of operation with maximal power): (a) temperature noise; (b) acoustic noise: natural (black), caused by a flick given on the amplifier (gray).


Fig. 3. Experimental (a) steady-state and (b) dynamical phase characteristics. (c) Phase response on a double jump of (d) the diode power: positive (black) and inverted (gray). Curves 1–8 are for pulse amplitudes of 20–120 mW.

of total pump absorption and negligible spontaneous emission, i.e., within a linear part of the steady-state curve, the phase response ⌬␸共t兲 on a single positive or negative jump of the diode power ⌬P is expressed as

冋 冉 冊册

⌬␸共t兲 = K␶sp 1 − exp −





where ␶sp ⬇ 0.85 ms is the Yb-ion lifetime; K = 2␲FL2 ⌬p¯␩␳T共0兲␭P / n0hc␭T, ⌬p ⬇ 7.5⫻ 10−26 cm3 is the difference of Yb-ion polarizabilities in the ground and excited states, FL = 共n02 + 2兲 / 3 is the Lorentz factor, n0 is the unperturbed refractive index, h is the Plank constant, c is the light velocity, ␳T共r兲 is the normalized radial power distribution in the fiber at ␭T, and the factor ¯␩ ⬇ 0.7. For the YDF used in the experiment K ⬇ 0.056␲ rad ms−1 mW−1 at ␭T ⬇ 1.55 ␮m [8]. In accordance with Eq. (1) a fast phase tuning [Figs. 3(a), 3(c), and 3(d)] from ␸1 = ␾共P1兲 to ␸2 = ␾共P2兲 could be carried out by two consequent switches of the diode power; first, from the level P1 to a level P1 + ⌬P0 and then to the level P2, where ⌬P0 is the power jump (positive or negative) available with the laser diode within the used tuning range. Fortunately, the switching time now is equal to the time ␶ between two opposite jumps of the diode power, and for small phase steps it is expressed as ␶ = 共␸2 − ␸1兲 / K⌬P0 Ⰶ ␶sp from Eq. (1). The higher the ⌬P0, the faster the phase tuning. However, a higher ⌬P0 is available within smaller tuning ranges. For tuning within the range of ⬃␲ rad, ⌬P0 is limited by ⬃45 mW that corresponds to an adjustment rate of ⬃2.6␲ rad/ ms [Figs. 3(a) and 3(c)]. The task given to the feedback loop shown in Fig. 1(b) is to support the maximal power level emitted at ⬃1.55 ␮m through channel 1. Accordingly, the power recorded by the photodetector through channel 2 has to be kept as low as possible. This power is used for the operation with the feedback circuit synchronized by a 2.86 MHz acquisition card (NI PCI-6251, National Instruments). The period of data acquisition


OPTICS LETTERS / Vol. 34, No. 22 / November 15, 2009

␶ = 25 ␮s sets a semiperiod to the card output used as a pulse generator that forces the laser diode to emit a periodic meander signal with an amplitude of ⌬P0 = ± 45 mW and a controllable dc level Pav within the range of 45–75 mW [Fig. 4(a)]. The modulated diode power causes a saw-tooth modulation of the induced phase with a dc level of ␸av = ␾共Pav兲 and the excursion of ⌬␸0 = K⌬P0␶ ⬇ 0.06␲ rad [Figs. 4(b) and 4(d)]. Such a phase modulation leads to ⬃100% amplitude modulation of the power in channel 2 [Figs. 4(a) and 4(c)], while the modulation of the high-power radiation in channel 1 remains negligible 共⬃1%兲. Importantly, the signal at the photodetector is a result of the superposition between the phase noise and the periodic phase modulation. In the case of right phase matching (when the phase noise is completely compensated) the saw-tooth signal peaks associated with the positive and negative phase switches have the same amplitude [Fig. 4(a)]. In contrast, at the presence of uncompensated noise the signal peaks are spread in two series, highlighting the phase mismatching ⌬ to be directly proportional to the difference between neighboring peaks [Fig. 4(c)]. The error signal produced by a PC controls the phase ␸av, providing smooth corrections ␦Pav → −⌬ / K␶ to Pav. The coherent combining of two 500 mW Er-doped amplifiers resulting in ⬃1 W power decoupled through the single-mode fiber output has been successfully demonstrated with joint TEC and YDF phase control. Typical channel 2 power and phase traces [Figs. 5(a) and 5(b)] exhibit the features similar to those shown in Figs. 4(c) and 4(d). The absolute power variations are about 10–20 mW, i.e., ⬃1% – 2% of the total power emitted by two amplifiers. One can see how during the given time series the initial phase mismatch caused by a flick given on the amplifier is suppressed owing to the operation of the feedback loop: the peaks initially separated in two series join together, highlighting the constructive interference achieved in channel 1. The power characteristics of the combined system [Fig. 5(c)] give clear evidence that more than 95% of radiation generated in two fiber amplifiers is efficiently decoupled through the single-mode output.

Fig. 4. Simulated feedback loop operation for cases of (a),(b) compensated and (c),(d) uncompensated phase noise: (a),(c) laser diode (gray) and channel 2 (black) powers; (b),(d) the reconstructed phase deviation (gray) and reconstructed error signal (black); Pav ⬇ 60 mW.

Fig. 5. Experimental operation of two combined amplifiers against the noise: (a) the photodiode signal; (b) the reconstructed phase (gray) and generated error signals (black); (c) the system power without (gray) and with (black) active phase control averaged over thermal noise.

In conclusion, the reported result gives us the basis of the work toward the development of the multichannel system [Fig. 1(a)]. The method is proved to operate against the noise with a rate of ⬃2.6␲ rad/ ms that through time-division multiplexing potentially serves combining of ⬃50– 100 amplifiers like those used in the work. It opens the potential to produce high-power narrowband radiation through the complete near-infrared employing the YDF phase control in combination with various rareearth-doped or Raman fiber amplifiers, in particular, based on large-mode-area fibers. Attractions of these sources are their compactness, reliability, and allfiber integrated format. This research was supported by the Interuniversity Attraction Pole Program VI/10 of the Belgian Science Policy, and Program “Scientific and ResearchEducational Cadres for Innovation Russia” of Russian Federal Agency on Science and Innovation (contract 02.740.11.5093). References 1. T. Y. Fan, IEEE J. Sel. Top. Quantum Electron. 11, 567 (2005). 2. H. Bruesselbach, D. C. Jones, M. S. Mangir, M. Minden, and J. L. Rogers, Opt. Lett. 30, 1339 (2005). 3. C. Bellanger, A. Brignon, J. Colineau, and J. P. Huignard, Opt. Lett. 33, 2937 (2008). 4. Y. Huo and P. K. Cheo, J. Opt. Soc. Am. B 22, 2345 (2005). 5. B. W. Grime, W. B. Roh, and Th. G. Alley, Opt. Lett. 30, 2415 (2005). 6. S. J. Augst, T. Y. Fan, and A. Sanchez, Opt. Lett. 29, 474 (2004). 7. A. A. Fotiadi, N. G. Zakharov, O. L. Antipov, and P. Mégret, in Conference on Lasers and Electro-Optics (Optical Society of America, 2008), paper CWB2. 8. A. A. Fotiadi, O. L. Antipov, and P. Mégret, Opt. Express 16, 12658 (2008). 9. H. Bruesselbach, Sh. Wong, M. Minden, D. C. Jones, and M. Mangir, J. Opt. Soc. Am. B 22, 347 (2005). 10. G. D. Goodno, L. D. Book, and J. E. Rothenberg, Opt. Lett. 34, 1204 (2009). 11. L. Taylor, Y. Feng, and D. B. Calia, Opt. Express 17, 14687 (2009).