Self-Organized Coherence In Fiber Laser Arrays - Semantic Scholar
Self-Organized Coherence In Fiber Laser Arrays M. L. Minden∗a, Hans Bruesselbacha, J. L. Rogersa, M. S. Mangira, D. C. Jonesa, G. J. Dunninga, D. L. Hammon, A. J. Solis, L. Vaughanb a HRL Laboratories, LLC, 3011 Malibu Canyon Rd, Malibu, CA 90265 b Raytheon SAS, 2000 E. El Segundo Blvd., El Segundo, CA 90245 ABSTRACT Self-organized coherence between fiber lasers has been reported both via all-fiber 2x2 directional coupler trees and in spatially multi-core fibers. We have taken this a major step forward, coupling together a number of independent fiber lasers to obtain a spatially and spectrally coherent far field, with no active length, polarization, or amplitude control. The near field output comes from a spatial array rather than from a single fiber, making this approach scalable to extremely high power. Keywords: fiber lasers, self organization, coherent coupling
1. INTRODUCTION Lasers are nonlinear oscillators capable of complex dynamical behaviors1,2. This richness offers opportunities for interactions between them that would not be anticipated from classical laser theories. For example, groups of nonlinear oscillators can form same-frequency states even in the presence of a distribution of intrinsic frequencies among the array members. In laser terms, this means that identical resonator lengths and center wavelengths are not required to make an array of lasers coherent and inphase. Interpreting our and others’ coupling experiments3,4,5,6 as manifestations of nonlinear oscillator behavior allows us to relax some of our assumptions about lasers having to be identical in order to lock to each other. Utilizing both the proper inherent nonlinearities and appropriate interactions between array members, we have been able to spontaneously form stable coherent and inphase states. This talk reports our experimental confirmations that stable coherent and inphase states can spontaneously form (self-organize) in arrays of fiber lasers. In none of our experiments was active control used or any effort made to precisely match fiber lengths, as is the case in multicore fiber4,5. The practical advantage of our approach to laser coupling is that it frees us from the belief that lasers must be identical lengths in order to lock: There is no requirement that the oscillators start out at identical frequencies. So, although we can couple lasers and analyze the resulting system in conventional terms, using the description of injection seeding or a supermode, utilizing the inherent nonlinearity and imposing connectivity highlights the freedom from the rigid length constraints many of us have held sacrosanct. Starting with the same frequency is not essential. The lasers do not have to be the same optical length before the gain is turned on, neither within modulo 2, nor within large-scale lengths. The typical Nd fiber laser that we used ranged from 10 to 12 meters in length. What they do require is correct connectivity and a sufficiently large nonlinearity. But what is correct? And how large is large enough? These are all things we are still studying. All-to-all coupling is one case. It is one of the few cases amenable to a closed form solution7, but is not easy to realize in a laser system. A few examples exist: anti-guided diode structures are one; fibers with a common output port connected to star or laddered fiber couplers are another. Unfortunately, none of these lend themselves practically to the very large numbers and high powers that are of interest.
∗
Phone: 310-317-5535 Fax: 310-317-5840 email:[email protected]
Fiber Lasers: Technology, Systems, and Applications, edited by L. N. Durvasula, Proceedings of SPIE Vol. 5335 (SPIE, Bellingham, WA, 2004) · 0277-786X/04/$15 · doi: 10.1117/12.536444
89
2. EXPERIMENTS DEMONSTRATING SELF-ORGANIZATION The first experiments to be discussed are the concept demonstrations using simple 2x2 couplers, in which the laser output phases up into just one of the output ports. Among the most interesting experiments in this group are coupling between 5 Nd fiber lasers, between pairs of Yb lasers made from holey fibers, and DFB diode-and-EDFA hybrids. After these first experiments, we describe our results with spatial arrays in which there are multiple parallel emitting apertures. The potential scalability of these arrays to large numbers and high powers drives our interest in this work. Diode pumps (5)
standard fused fiber couplers (4)
Nd lasers(5)
50%50%
80%20% 50%50%
Laser output
WDM couplers (5) Fiber grating reflectors (5)
50%50%
1 x 5 coupler
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Figure 1. Experimental layout of 5 Nd fiber lasers coupling coherently. There is no active length or polarization control.
Our first experiment with coupling fiber lasers was with 5 low power (~15mW) Nd lasers coupled together in a 1x5 configuration using concatenated splitters (see Figure 1). Any one of the lasers can be operated independently, although with 80% of its output power lost via the 4 angle cleaves. If the lasers were still independent and incoherent with each other when all 5 were on, then we would still expect only 20% of the power to come out of the flat cleaved port. What actually happens, however, is that the lasers operate coherently with each other, spontaneously phasing up so that at each coupler the energy is directed towards the flat output port (see Figure 2).
Output from common flat-cleaved end
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Figure 2. Output power as a function of the number of laser pumps turned on. The dashed line, Linear projection, shows the power output if the lasers were all exactly equal power and combining incoherently. The dotted line, Quadratic projection, shows the N2 rise in power out of the cleaved fiber when the lasers are all coherent and all combining in phase.
Now, on first view, this does not seem to necessarily corroborate self-organization, or the need for a nonlinear component. After all, this can be considered a composite cavity whose lowest loss state occurs when there is no light in the angle-cleaved arms. However, this would not explain why active length and polarization control are not needed. One suggestion as to why active length control is not needed6 is that there is a wide set of longitudinal modes and for a few lasers, at least, there can be found at least one frequency, one spectral overlap, that allows all lengths to oscillate simultaneously. This would indicate that scaling to large numbers requires increasingly wide choice of longitudinal modes, and correspondingly increased bandwidth.
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However, the longitudinal mode overlap model does not explain the next result, in which we obtained coherent locking using a hybrid cavity with DFB diode lasers and EDFAs. DFB Diode Laser #1 1541 nm
Fiber Amplifiers
Fiber Grating
Lens
2 X 2 Coupler
Detector 2
Detector 1
Polarization Controller
DFB Diode Laser #2 1541 nm
Polarizer
Figure 3. Experimental demonstration of self-phased coupling between two DFB diode and fiber amplifier arms.
In this experiment (Figure 3) two inherently single longitudinal mode DFB diode lasers were connected via a 2x2 coupler, with one arm of the coupler chosen as the output port, and the other angle-cleaved for diagnostics. In this case we had an overconstrained system with 3 grating elements and 2 arms of fiber length, all of which would have had to be controlled in frequency and phase to add up coherently into the output arm (Detector 2). By adding fiber amplifiers in the arms, self-organization was free to do the phasing, and, when the gain was high enough, did so successfully (see Figure 4).
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Figure 4. Phased output with fiber amplifiers attached to each diode laser. In both plots the upper line is the Grating Output (i.e. Detector 2, which sees what is coming from the fiber with the grating), and the lower line is the Angled Output (i.e. Detector 1, which sees what is coming from the angle-cleaved fiber). On the Left: Gain eG= 7 dB (ErYb). On the Right: Gain eG= 40dB (Er).
This is the first time that passive self-organized locking between two single longitudinal mode lasers has been demonstrated. Finally we have an example of lasers made from holey fiber (see Figure 5). Here we were able to push the coherent power up to 7 W each arm (see Figure 6) (limited by SBS in the single-mode fiber from which the coupler is made). In this demonstration, the high reflectivity side of the laser was a dichroic mirror, demonstrating that having the limited and overlapping bandwidth of a grating reflector is not a requirement for self-organization. Hi Speed Det
Crystal Fiber Lasers
R=20% Pol. rotators
Power meter
Figure 5. Two Yb-doped Large Mode Area holey fiber lasers spliced to a 2x2 coupler to demonstrate self-organized coupling.
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Measured output, both lasers on, W Incoherent sum of individual powers, W Coherent sum of individual powers, W
Power through output grating, W
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20 25 30 35 40 45 Current, A (Both lasers turned up simultaneously) Figure 6. Coupler arm output through a 20% grating reflector. Lower curve (squares) sum of the intensity outputs (I1+I2) of the two lasers turned on individually. Upper curve (diamonds) Coherent sum of the two outputs (I11/2+I21/2)2. This is the maximum output possible when the two arms are coherent and in phase. The curve with the circles shows what was actually measured when the two lasers were turned on together. The curve is closer to the coherent sum line up to ~14.5 W.
3. ARCHITECTURE SUITABLE FOR POWER SCALING Coupling schemes with a single fiber output, however, are probably not suitable for high power scaling, >~1kW, even with damage mitigation efforts such as large mode area fibers and coreless endcaps. The problem is that nonlinear effects within the fiber (SBS, SPM, XPM) can not be avoided. In this case, a spatially distributed but nevertheless coherent output array is desired. Figure 7 shows the coupling approach we have now demonstrated. The output coupler is a cleaved bundle of evanescently coupled fibers; something like a star coupler that has been cleaved across the narrowest part. This cleaved face serves as the output reflector of the laser array.
COUPLER
GAIN BLOCKS
FIBER GRATINGS
Figure 7. Fiber laser concept combining gain blocks, fiber gratings, combination output and inter-fiber coupler.
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We have at this time coupled from 2 to 7 lasers in this configuration, using either Nd core-pumped or Yb claddingpumped lasers. The back reflector of each laser was a grating at 1064nm (Nd lasers) or at ~1070-1080nm(Yb lasers). One example of coherent output is shown in Figure 8. In this case, the tapered bundle consisted of 7 fibers connected to 7 Nd lasers, of which five (N=5) were found to create an in-phase state when turned on simultaneously. As the near field pattern shows, there was no symmetry in the coupler itself; it was made from a twisted bundle of fibers in random positions. The particular set of 5 that gave the single-lobed far field was discovered by trial and error.
Figure 8. Far-field and near-field patterns of a 5-laser coherent combination. The coupler was formed by cleaving a 7x7 tapered singlemode fiber bundle. The two near field images are approximately 70µm square. All far-field images are to the same scale, and the size of the far-field central lobe is consistent with it having diffracted from the near field;
The peak intensity of the far field pattern is 5 times what would have been expected from an incoherent sum (Figure 9); exactly what would be expected from a coherent and inphase (N2) to incoherent (N) ratio.
Figure 9. (Left:) Incoherent sum of measured far-field intensities; i.e. the lasers operating one at a time, and the five recorded contour plots summed. (Right:) Measured far-field intensity with all lasers turned on simultaneously.
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The optical spectra also support that the lasers are coherent. Figure 10 shows the optical spectra of 5 of those 7 lasers turned on individually, which are spread over ~0.5nm, compared with the coalesced peak when all 5 are turned on at the same time. A different coupler, same type of fabrication process, was used with 5 cladding-pumped Yb lasers. Once again, the experimental results show the robustness of self-organization when it occurs: Three of the lasers were single mode, unpolarized, with a grating line center of 1080 nm, and two were made of polarization-maintaining (PM) fiber, with a grating line center of 1075 nm. The result shown in Figure 11 is at very low power, ~200mW per laser.
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Figure 11. Far field pattern of 5 Yb lasers at low power, combined in a coupler cleaved from a randomly positioned fiber bundle.
A process for making symmetrical close-packed hexagonal output couplers was developed. Shown in Figure 12a is the near field output of a 19-element device attached to 19 Nd fiber lasers. Self-organization of the full set of 19 was not observed. Real-time observation of the pattern in Figure 12b shows an unstable pattern with no central hot spot.
Figure 12. 19 Nd lasers in an array formed by a 19-element coupler (12a, Left) Near field. (12b, Right) Far field.
Numerous subsets of 4 and 5 lasers, however, did lock up correctly in the 19-element array. One pattern of 4 connected lasers is shown in Figure 13. Once again, we show the near field and far field patterns of the array output as the lasers are turned on, one at a time. The figure shows that the resulting high-brightness far-field pattern does not depend at all on the sequence in which the lasers are turned on.
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Figure 13. Self-organization of 4 lasers in a 19-element array. Top and bottom sets are the same lasers but turned on in a different sequence. Near-field images are approximately 190 µm square.
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Figure 14. Temporal behavior of the self-organized spatial laser array, sampling the position of peak intensity.
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Temporally, the central spot of the coherent self-organized 4-laser array in Figure 13 has fewer long-period fluctuations than either the single fiber lasers or the full 19-element array. We picked up a sample of the central lobe and fed it into a high-speed (200ps) detector. As shown in Figure 14, the temporal behavior of the central lobe in the locked array is noisy on the small scale, possibly chaotic, but more stable on a longer scale than either a single laser or the full 19element set.
4. SUMMARY In summary, fiber lasers are an ideal testbed for self-organization concepts. They have extremely high gain and are flexible in layout. The engineering of fiber coupling components is well established. Although fibers have limited individual output power, the creation of high brightness, high power sources composed of fiber laser arrays is of great interest because of their superb efficiency and thermal advantages. Again, note that there are no active controls in our approach. The lengths of the fibers are not carefully matched, and have differed by at least 10% from each other. The gratings overlap spectrally but do not necessarily peak at the same wavelength. The self-organized coherence of the lasers grows out of the inherent laser dynamics and the connectivity between them. We grapple still with concept and predictions; the design of the perfect coupler and the perfect laser. Yet we have demonstrated numerous examples of locking of multiple lasers under completely passive conditions that we would not have tried without the impetus of the self-organization concept. We thank DARPA-TTO and L. N. Durvasula for supporting a large portion of this work.
REFERENCES 1. 2. 3. 4. 5.
6. 7.
R. Albert and A.-L. Barabasi, “Statistical mechanics of complex networks”; Rev. Mod. Phys., 74, 47 (2002). S. H. Strogatz, “Exploring complex networks”; Nature, 410, 268 (2001). V. A. Kozlov, J. Hernandez-Cordero, and T. F. Morse, “All-fiber coherent beam combining of fiber lasers”; Optics Lett. 24, 1814 (1999). E. J. Bochove, P. K. Cheo, G. G. King, “Self-organization in a multicore fiber laser array;” Optics letters, 28,14,(2003). Glas, P.; Wrage, M.; Fischer, D.; Leitner, M.; Napartovich, A.P.; Vysotsky, D.V.; Elkin, N.N., “Coherent coupling in circular fiber laser arrays with reduced radial divergence;” Technical Digest, Conference on Lasers and Electro-Optics, May 2002 Long Beach, CA, USA, v.1,pp 595-6. Shirakawa, A.; Saitou, T.; Sekiguchi, T.; Ueda, K., ‘Coherent addition of fiber lasers by use of a fiber coupler; ” Optics Express.10,21 Oct. 2002. Y.Kuramoto, “Chemical Oscillations, Waves, and Turbulence”, Springer, Berlin, 1984.
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1. INTRODUCTION Lasers are nonlinear oscillators capable of complex dynamical behaviors1,2. This richness offers opportunities for interactions between them that would not be anticipated from classical laser theories. For example, groups of nonlinear oscillators can form same-frequency states even in the presence of a distribution of intrinsic frequencies among the array members. In laser terms, this means that identical resonator lengths and center wavelengths are not required to make an array of lasers coherent and inphase. Interpreting our and others’ coupling experiments3,4,5,6 as manifestations of nonlinear oscillator behavior allows us to relax some of our assumptions about lasers having to be identical in order to lock to each other. Utilizing both the proper inherent nonlinearities and appropriate interactions between array members, we have been able to spontaneously form stable coherent and inphase states. This talk reports our experimental confirmations that stable coherent and inphase states can spontaneously form (self-organize) in arrays of fiber lasers. In none of our experiments was active control used or any effort made to precisely match fiber lengths, as is the case in multicore fiber4,5. The practical advantage of our approach to laser coupling is that it frees us from the belief that lasers must be identical lengths in order to lock: There is no requirement that the oscillators start out at identical frequencies. So, although we can couple lasers and analyze the resulting system in conventional terms, using the description of injection seeding or a supermode, utilizing the inherent nonlinearity and imposing connectivity highlights the freedom from the rigid length constraints many of us have held sacrosanct. Starting with the same frequency is not essential. The lasers do not have to be the same optical length before the gain is turned on, neither within modulo 2, nor within large-scale lengths. The typical Nd fiber laser that we used ranged from 10 to 12 meters in length. What they do require is correct connectivity and a sufficiently large nonlinearity. But what is correct? And how large is large enough? These are all things we are still studying. All-to-all coupling is one case. It is one of the few cases amenable to a closed form solution7, but is not easy to realize in a laser system. A few examples exist: anti-guided diode structures are one; fibers with a common output port connected to star or laddered fiber couplers are another. Unfortunately, none of these lend themselves practically to the very large numbers and high powers that are of interest.
∗
Phone: 310-317-5535 Fax: 310-317-5840 email:[email protected]
Fiber Lasers: Technology, Systems, and Applications, edited by L. N. Durvasula, Proceedings of SPIE Vol. 5335 (SPIE, Bellingham, WA, 2004) · 0277-786X/04/$15 · doi: 10.1117/12.536444
89
2. EXPERIMENTS DEMONSTRATING SELF-ORGANIZATION The first experiments to be discussed are the concept demonstrations using simple 2x2 couplers, in which the laser output phases up into just one of the output ports. Among the most interesting experiments in this group are coupling between 5 Nd fiber lasers, between pairs of Yb lasers made from holey fibers, and DFB diode-and-EDFA hybrids. After these first experiments, we describe our results with spatial arrays in which there are multiple parallel emitting apertures. The potential scalability of these arrays to large numbers and high powers drives our interest in this work. Diode pumps (5)
standard fused fiber couplers (4)
Nd lasers(5)
50%50%
80%20% 50%50%
Laser output
WDM couplers (5) Fiber grating reflectors (5)
50%50%
1 x 5 coupler
4% Reflector
Figure 1. Experimental layout of 5 Nd fiber lasers coupling coherently. There is no active length or polarization control.
Our first experiment with coupling fiber lasers was with 5 low power (~15mW) Nd lasers coupled together in a 1x5 configuration using concatenated splitters (see Figure 1). Any one of the lasers can be operated independently, although with 80% of its output power lost via the 4 angle cleaves. If the lasers were still independent and incoherent with each other when all 5 were on, then we would still expect only 20% of the power to come out of the flat cleaved port. What actually happens, however, is that the lasers operate coherently with each other, spontaneously phasing up so that at each coupler the energy is directed towards the flat output port (see Figure 2).
Output from common flat-cleaved end
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Figure 2. Output power as a function of the number of laser pumps turned on. The dashed line, Linear projection, shows the power output if the lasers were all exactly equal power and combining incoherently. The dotted line, Quadratic projection, shows the N2 rise in power out of the cleaved fiber when the lasers are all coherent and all combining in phase.
Now, on first view, this does not seem to necessarily corroborate self-organization, or the need for a nonlinear component. After all, this can be considered a composite cavity whose lowest loss state occurs when there is no light in the angle-cleaved arms. However, this would not explain why active length and polarization control are not needed. One suggestion as to why active length control is not needed6 is that there is a wide set of longitudinal modes and for a few lasers, at least, there can be found at least one frequency, one spectral overlap, that allows all lengths to oscillate simultaneously. This would indicate that scaling to large numbers requires increasingly wide choice of longitudinal modes, and correspondingly increased bandwidth.
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However, the longitudinal mode overlap model does not explain the next result, in which we obtained coherent locking using a hybrid cavity with DFB diode lasers and EDFAs. DFB Diode Laser #1 1541 nm
Fiber Amplifiers
Fiber Grating
Lens
2 X 2 Coupler
Detector 2
Detector 1
Polarization Controller
DFB Diode Laser #2 1541 nm
Polarizer
Figure 3. Experimental demonstration of self-phased coupling between two DFB diode and fiber amplifier arms.
In this experiment (Figure 3) two inherently single longitudinal mode DFB diode lasers were connected via a 2x2 coupler, with one arm of the coupler chosen as the output port, and the other angle-cleaved for diagnostics. In this case we had an overconstrained system with 3 grating elements and 2 arms of fiber length, all of which would have had to be controlled in frequency and phase to add up coherently into the output arm (Detector 2). By adding fiber amplifiers in the arms, self-organization was free to do the phasing, and, when the gain was high enough, did so successfully (see Figure 4).
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Figure 4. Phased output with fiber amplifiers attached to each diode laser. In both plots the upper line is the Grating Output (i.e. Detector 2, which sees what is coming from the fiber with the grating), and the lower line is the Angled Output (i.e. Detector 1, which sees what is coming from the angle-cleaved fiber). On the Left: Gain eG= 7 dB (ErYb). On the Right: Gain eG= 40dB (Er).
This is the first time that passive self-organized locking between two single longitudinal mode lasers has been demonstrated. Finally we have an example of lasers made from holey fiber (see Figure 5). Here we were able to push the coherent power up to 7 W each arm (see Figure 6) (limited by SBS in the single-mode fiber from which the coupler is made). In this demonstration, the high reflectivity side of the laser was a dichroic mirror, demonstrating that having the limited and overlapping bandwidth of a grating reflector is not a requirement for self-organization. Hi Speed Det
Crystal Fiber Lasers
R=20% Pol. rotators
Power meter
Figure 5. Two Yb-doped Large Mode Area holey fiber lasers spliced to a 2x2 coupler to demonstrate self-organized coupling.
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Measured output, both lasers on, W Incoherent sum of individual powers, W Coherent sum of individual powers, W
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3. ARCHITECTURE SUITABLE FOR POWER SCALING Coupling schemes with a single fiber output, however, are probably not suitable for high power scaling, >~1kW, even with damage mitigation efforts such as large mode area fibers and coreless endcaps. The problem is that nonlinear effects within the fiber (SBS, SPM, XPM) can not be avoided. In this case, a spatially distributed but nevertheless coherent output array is desired. Figure 7 shows the coupling approach we have now demonstrated. The output coupler is a cleaved bundle of evanescently coupled fibers; something like a star coupler that has been cleaved across the narrowest part. This cleaved face serves as the output reflector of the laser array.
COUPLER
GAIN BLOCKS
FIBER GRATINGS
Figure 7. Fiber laser concept combining gain blocks, fiber gratings, combination output and inter-fiber coupler.
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We have at this time coupled from 2 to 7 lasers in this configuration, using either Nd core-pumped or Yb claddingpumped lasers. The back reflector of each laser was a grating at 1064nm (Nd lasers) or at ~1070-1080nm(Yb lasers). One example of coherent output is shown in Figure 8. In this case, the tapered bundle consisted of 7 fibers connected to 7 Nd lasers, of which five (N=5) were found to create an in-phase state when turned on simultaneously. As the near field pattern shows, there was no symmetry in the coupler itself; it was made from a twisted bundle of fibers in random positions. The particular set of 5 that gave the single-lobed far field was discovered by trial and error.
Figure 8. Far-field and near-field patterns of a 5-laser coherent combination. The coupler was formed by cleaving a 7x7 tapered singlemode fiber bundle. The two near field images are approximately 70µm square. All far-field images are to the same scale, and the size of the far-field central lobe is consistent with it having diffracted from the near field;
The peak intensity of the far field pattern is 5 times what would have been expected from an incoherent sum (Figure 9); exactly what would be expected from a coherent and inphase (N2) to incoherent (N) ratio.
Figure 9. (Left:) Incoherent sum of measured far-field intensities; i.e. the lasers operating one at a time, and the five recorded contour plots summed. (Right:) Measured far-field intensity with all lasers turned on simultaneously.
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The optical spectra also support that the lasers are coherent. Figure 10 shows the optical spectra of 5 of those 7 lasers turned on individually, which are spread over ~0.5nm, compared with the coalesced peak when all 5 are turned on at the same time. A different coupler, same type of fabrication process, was used with 5 cladding-pumped Yb lasers. Once again, the experimental results show the robustness of self-organization when it occurs: Three of the lasers were single mode, unpolarized, with a grating line center of 1080 nm, and two were made of polarization-maintaining (PM) fiber, with a grating line center of 1075 nm. The result shown in Figure 11 is at very low power, ~200mW per laser.
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Figure 11. Far field pattern of 5 Yb lasers at low power, combined in a coupler cleaved from a randomly positioned fiber bundle.
A process for making symmetrical close-packed hexagonal output couplers was developed. Shown in Figure 12a is the near field output of a 19-element device attached to 19 Nd fiber lasers. Self-organization of the full set of 19 was not observed. Real-time observation of the pattern in Figure 12b shows an unstable pattern with no central hot spot.
Figure 12. 19 Nd lasers in an array formed by a 19-element coupler (12a, Left) Near field. (12b, Right) Far field.
Numerous subsets of 4 and 5 lasers, however, did lock up correctly in the 19-element array. One pattern of 4 connected lasers is shown in Figure 13. Once again, we show the near field and far field patterns of the array output as the lasers are turned on, one at a time. The figure shows that the resulting high-brightness far-field pattern does not depend at all on the sequence in which the lasers are turned on.
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Figure 13. Self-organization of 4 lasers in a 19-element array. Top and bottom sets are the same lasers but turned on in a different sequence. Near-field images are approximately 190 µm square.
Intensity at brightest far field spot V, uncal.
All 19 lasers 4 lasers, locked 1 laser 0.06
0.04
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Figure 14. Temporal behavior of the self-organized spatial laser array, sampling the position of peak intensity.
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Temporally, the central spot of the coherent self-organized 4-laser array in Figure 13 has fewer long-period fluctuations than either the single fiber lasers or the full 19-element array. We picked up a sample of the central lobe and fed it into a high-speed (200ps) detector. As shown in Figure 14, the temporal behavior of the central lobe in the locked array is noisy on the small scale, possibly chaotic, but more stable on a longer scale than either a single laser or the full 19element set.
4. SUMMARY In summary, fiber lasers are an ideal testbed for self-organization concepts. They have extremely high gain and are flexible in layout. The engineering of fiber coupling components is well established. Although fibers have limited individual output power, the creation of high brightness, high power sources composed of fiber laser arrays is of great interest because of their superb efficiency and thermal advantages. Again, note that there are no active controls in our approach. The lengths of the fibers are not carefully matched, and have differed by at least 10% from each other. The gratings overlap spectrally but do not necessarily peak at the same wavelength. The self-organized coherence of the lasers grows out of the inherent laser dynamics and the connectivity between them. We grapple still with concept and predictions; the design of the perfect coupler and the perfect laser. Yet we have demonstrated numerous examples of locking of multiple lasers under completely passive conditions that we would not have tried without the impetus of the self-organization concept. We thank DARPA-TTO and L. N. Durvasula for supporting a large portion of this work.
REFERENCES 1. 2. 3. 4. 5.
6. 7.
R. Albert and A.-L. Barabasi, “Statistical mechanics of complex networks”; Rev. Mod. Phys., 74, 47 (2002). S. H. Strogatz, “Exploring complex networks”; Nature, 410, 268 (2001). V. A. Kozlov, J. Hernandez-Cordero, and T. F. Morse, “All-fiber coherent beam combining of fiber lasers”; Optics Lett. 24, 1814 (1999). E. J. Bochove, P. K. Cheo, G. G. King, “Self-organization in a multicore fiber laser array;” Optics letters, 28,14,(2003). Glas, P.; Wrage, M.; Fischer, D.; Leitner, M.; Napartovich, A.P.; Vysotsky, D.V.; Elkin, N.N., “Coherent coupling in circular fiber laser arrays with reduced radial divergence;” Technical Digest, Conference on Lasers and Electro-Optics, May 2002 Long Beach, CA, USA, v.1,pp 595-6. Shirakawa, A.; Saitou, T.; Sekiguchi, T.; Ueda, K., ‘Coherent addition of fiber lasers by use of a fiber coupler; ” Optics Express.10,21 Oct. 2002. Y.Kuramoto, “Chemical Oscillations, Waves, and Turbulence”, Springer, Berlin, 1984.
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