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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 13 — Jun. 21, 2010
  • pp: 13547–13553
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Coherent combination of high power fiber amplifiers in a two-dimensional re-imaging waveguide

Radoslaw Uberna, Andrew Bratcher, Thomas G. Alley, Anthony D. Sanchez, Angel S. Flores, and Benjamin Pulford  »View Author Affiliations


Optics Express, Vol. 18, Issue 13, pp. 13547-13553 (2010)
http://dx.doi.org/10.1364/OE.18.013547


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Abstract

Four actively phase-locked beams produced by fiber amplifiers in a master oscillator power amplifier (MOPA) configuration were coherently combined in a glass capillary re-imaging waveguide producing more than 100 W of coherent output with 80% combining efficiency and excellent beam quality. The beam combiner components maintained a temperature below 30°C with no external cooling at >100 W of combined power.

© 2010 OSA

1. Introduction

Power scaling of a single laser module faces challenges associated with the thermal management of the lasing medium. At high output powers, thermal effects degrade the laser efficiency and beam quality. This thermal degradation can be prevented by operating the individual lasing modules at their optimum power levels. Coherent combination of multiple lasing modules, each operating at its optimum power level, with the phases of the individual beams actively controlled, is a promising approach to power scaling of single-mode lasers [1

1. T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005). [CrossRef]

12

12. A. Bratcher, and R. Uberna, “Optimization and power scaling of 2-dimensional re-imaging assisted phased array,” in Solid State and Diode Laser Technology Review Technical Digest, (Directed Energy Professional Society, 2009), pp. 32–36.

].

To date, free-space phased arrays incorporating multiple tiled emitters are the prevalent architectures for coherent combination [3

3. 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). [CrossRef] [PubMed]

6

6. P. Zhou, Y. Ma, X. Wang, H. Ma, J. Wang, X. Xu, and Z. Liu, “Coherent beam combination of a hexagonal distributed high power fiber amplifier array,” Appl. Opt. 48(33), 6537–6540 (2009). [CrossRef] [PubMed]

]. However, alternative solutions based on filled-aperture designs, where the multiple outputs overlap in both the near- and far-field, offer much better theoretical combining efficiencies and reduce or eliminate side-lobes compared to tiled-aperture designs. Examples of such filled-aperture coherent beam combination architectures include those based on diffractive optical elements (DOEs) [7

7. E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt. Lett. 33(4), 354–356 (2008). [CrossRef] [PubMed]

], coherent polarization beam combination (CPBC) [8

8. R. Uberna, A. Bratcher, and B. G. Tiemann, “Coherent polarization beam combination,” IEEE J. Quantum Electron. 46(8), 1191–1196 (2010). [CrossRef]

,9

9. R. Uberna, A. Bratcher, and B. G. Tiemann, Lockheed Martin Coherent Technologies, 135 S. Taylor Avenue, Louisville, Colorado 80027, are preparing a manuscript to be called “Power scaling of fiber laser system using coherent polarization beam combination.”

], and re-imaging assisted phased arrays (REAPAR) [10

10. S. E. Christensen, and O. Koski, “2-Dimensional waveguide coherent beam combiner,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper WC1.

12

12. A. Bratcher, and R. Uberna, “Optimization and power scaling of 2-dimensional re-imaging assisted phased array,” in Solid State and Diode Laser Technology Review Technical Digest, (Directed Energy Professional Society, 2009), pp. 32–36.

]. The REAPAR architecture was originally developed by Lockheed Martin Coherent Technologies for coherent beam combination in planar waveguides. Recently, the REAPAR technology has been extended to two-dimensional (2-D) waveguides and successfully implemented at low power levels (up to ~10 W) using commercial-off-the-shelf (COTS) glass capillary waveguides [11

11. A. Bratcher and R. Uberna, “Two-dimensional re-imaging assisted phased array architecture for coherent beam combination,” J. Directed Energy 3, 107–117 (2009).

,12

12. A. Bratcher, and R. Uberna, “Optimization and power scaling of 2-dimensional re-imaging assisted phased array,” in Solid State and Diode Laser Technology Review Technical Digest, (Directed Energy Professional Society, 2009), pp. 32–36.

]. The key benefits of the glass capillary waveguides include low cost, low weight, small size, and excellent thermal and mechanical properties.

In this paper, we present the experimental results of power-scaling the 2-D REAPAR technology to levels in excess of 100 W using a fused quartz capillary waveguide and a novel fiber array fabricated out of photonic crystal fiber (PCF). We demonstrated high-efficiency coherent combination of actively phase-locked beams produced by four fiber amplifiers in a master oscillator power amplifier (MOPA) configuration. The experimental work was performed at the Air Force Research Laboratory High Power Fiber Laser Testbed (Kirtland Air Force Base, Albuquerque, NM).

2. Experimental Setup

The operation principle of the 2-D REAPAR architecture, the waveguide beam combiner components, and the optimization techniques to improve the combiner efficiency have been discussed previously [10

10. S. E. Christensen, and O. Koski, “2-Dimensional waveguide coherent beam combiner,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper WC1.

12

12. A. Bratcher, and R. Uberna, “Optimization and power scaling of 2-dimensional re-imaging assisted phased array,” in Solid State and Diode Laser Technology Review Technical Digest, (Directed Energy Professional Society, 2009), pp. 32–36.

]. The four input beams were phase-locked using the Locking of Optical Coherence by Single-Detector Electronic Frequency Tagging (LOCSET) system [13

13. T. M. Shay, “Theory of electronically phased coherent beam combination without a reference beam,” Opt. Express 14(25), 12188–12195 (2006). [CrossRef] [PubMed]

,14

14. 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). [CrossRef] [PubMed]

], which has been developed at the Air Force Research Laboratory (AFRL).

Figure 1
Fig. 1 Schematic diagram of the four-beam waveguide beam combination system. The seed source, phase-lock electronics, electro-optic modulators, and fiber amplifiers were elements of the AFRL high power fiber laser testbed.
shows a schematic diagram of the high power beam combination system. The front end (a narrow-line seed source at 1064 nm) and the LOCSET phase-lock and control electronics as well as the fiber amplifiers were supplied by the AFRL. The pre-amplified narrow-line (<5 kHz) laser output was split into multiple seed beams. Prior to seeding the amplifier chain, each seed beam passed through a lithium niobate phase modulator whose function was to tag the beam with a unique dither frequency and to actuate its phase in response to the feedback signal.

The amplifiers were terminated with LMA 25/400 passive fibers equipped with high power endcaps. After passing through high power isolators, the collimated amplified beams travelled several meters through free-space and were coupled into the PCF transport fibers of the beam combiner. A set of optical attenuators made of half-wave plates combined with thin film polarizing beam splitters was used during the optical alignment to attenuate the beams.

The beam combiner assembly depicted in Fig. 1 consists of the capillary waveguide resting on an aluminum support, a microlens array, and four PCF transport fibers, which merge at the waveguide side to form a square 2 × 2 fiber array. The four beams emerging from the fiber array pass through an AR-coated fused silica microlens array, which focuses the beams into the combining waveguide. A small portion of the combined output (“the servo beam”) is picked off with a partial reflector and detected with a high-speed photodiode. The photodiode output is sent to the LOCSET electronics and used as a closed-loop feedback signal. The components of the beam combiner module are shown in Fig. 2
Fig. 2 Photograph of the high power beam combiner module. The combined length of the waveguide and fiber array is approximately 7 inches. The insert in the upper right corner shows the cross-section view of the 500 µm × 500 µm capillary waveguide.
. The hollow waveguide is a ~11.5 cm-long square capillary made of fused quartz. An insert in Fig. 2 shows the 500 µm × 500 µm cross-section of the capillary whose walls are ~200 µm thick. The waveguide support, the microlens array and the fiber array are mounted on separate multi-axis stages.

Since the beam combiner’s transport fibers could not be spliced directly to the fiber amplifiers, the collimated beams were free-space coupled to the transport fibers. The LMA-PM-15 polarization maintaining (PM) large mode area (LMA) PCF was chosen for the transport fibers because of its single-mode and polarization properties, relatively large mode area (~12 µm), and availability (LMA-PM-15 is a commercial product). Traditional LMA fibers are difficult to use in single mode operation, often requiring mode stripping though coiling. In applications where splicing to the fiber array is allowed, the fiber array could be constructed with the fiber type identical to that of the amplifiers and the PCF transport fibers would be unnecessary.

The LMA-PM-15 ends were thermally collapsed, polished and AR-coated to enable high power operation and to minimize back reflections. To provide additional protection of the fiber ends from overheating and thermal damage, we incorporated water cooled chucks to strip the light coupled into the cladding. The fiber ends were mounted into V-grooved blocks made of fused silica and secured with high index (n = 1.539) UV-cured epoxy (Epo-Tek OG142-112). The V-grooves were thermally contacted with the aluminum chucks using thermal heat sink grease (Chemtronics 9150PCT 40-5). With 30–50 watts being coupled into the fibers, the temperature of all the input fiber ends was less than 40°C.

Our earlier, low power beam combination results were produced using fiber arrays made of single-mode PM fibers cemented in a pair of V-groves made of glass. For the high power combination experiments, a new-generation fiber array with better thermal properties and more accurate fiber alignment needed to be developed. The new-design array, shown in Fig. 3
Fig. 3 Photograph of the high power fiber array (a); collapsed, polished, and AR-coated fiber ends mounted in the brass plate (b); and four fiber ends in a square configuration (c). The insert in (a) shows the internal structure of the LMA-PM-15 fiber.
, used thin brass plates with precision-drilled fiber mounting holes. The multiple brass plates were mounted on a glass support bar, with the individual fibers threaded through the holes and aligned. Figure 3(a) shows the fiber array, which is mounted inside a ~11 cm long tube for easy handling and strain relief. A brass plate with four aligned LMA-PM-15 fiber ends and the front surfaces of the fibers are shown in Fig. 3(b) and Fig. 3(c), respectively. Similar to the input fiber ends, the array fiber ends were thermally collapsed, polished and AR-coated for high power operation. The maximum pointing and position errors of the individual fibers in the array were, respectively, ~0.2° and ~5 µm. The effects of the fiber array imperfections on the combining efficiency and beam quality are beyond the scope of this paper and will be published separately.

3. Experimental Results

At the time of this experiment, the maximum power produced by the individual fiber amplifiers was ~50 W. Since the output powers varied from fiber to fiber and also fluctuated with time, full power balance between the four amplifiers was uncommon. These fluctuations were caused by the thermal response of external isolators, which were used to protect the amplifiers. The four beams were delivered to the fiber array via free space over a distance of up to ~10 m and coupled into PCF transport fibers. An AR-coated microlens array (MLA) made of fused silica was used to focus the beams into the fused quartz waveguide. The total power transmitted through the LMA-PM-15 fibers and delivered to the waveguide was determined by the coupling efficiency, which depended on the free space beam quality, room temperature, beam size, divergence, and pointing stability. To accommodate different beam diameters, we used different coupling lenses for different beams.

The results of the high power beam combination are shown in Fig. 4
Fig. 4 Two-dimensional (left) and three-dimensional images (right) of the 100 W output of the combiner with the phases of the individual beams random (unlocked).
and Fig. 5
Fig. 5 Two-dimensional (left) and three-dimensional images (right) of the 100 W output of the combiner with phase-locked of the input beams.
. After coupling the four beams into the transport fibers, we aligned the components of the beam combiner at low power level with the input beams attenuated, and acquired the near-field images of the combined output emerging from the waveguide. With random (unlocked) phases of the four input beams, the combined output consisted of a regular, 3 × 3 array of lobes, shown in the Fig. 4. The high degree of symmetry in the image reflects the quality of the alignment of the beam combiner components and provided a convenient tool for the alignment optimization. Upon activation of the closed-loop system (LOCSET), the phase modulators locked the phases of the four beams [13

13. T. M. Shay, “Theory of electronically phased coherent beam combination without a reference beam,” Opt. Express 14(25), 12188–12195 (2006). [CrossRef] [PubMed]

,14

14. 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). [CrossRef] [PubMed]

]. As a result, the optical power was transferred from the sidelobes to the central lobe. Figure 5 shows the 2-D and 3-D images of the combined output of the waveguide combiner with cophased input beams. The central lobe, which contains 83% of the combined power emerging from the waveguide, is remarkably symmetric. The total combined power transmitted by the waveguide was 101.2 W, as seen on the power meter display photo in Fig. 5.

The combining efficiency was defined as the ratio of the central lobe power to the total power emerging from the fiber array. The central lobe power was measured on the CCD camera by integrating the image of the combined beam inside a circle whose radius extended approximately to the minimum intensity between the central lobe and the closest side lobe (see center circle drawn in Fig. 5). The capillary transmission was typically measured prior to the beam combination experiment for a single beam and was a function of beam quality and the alignment of the system components. The coupling efficiency to the PCF transport fibers was not taken into account in the efficiency definition and measurement because of its strong dependence on the input beam and transport fiber characteristics. Ideally, the fiber coupling stages would not be included in a laser system because the beam combiner transport fibers would be spliced directly to the amplifier output fibers. The combining efficiency was measured by determining the fraction of the power in the central lobe and multiplying it by the transmission of the waveguide combiner (96%). The best combining efficiency was obtained with the total transmitted power of 101.2 W, with 83% of the transmitted power measured in the central lobe. This figure was then multiplied by the waveguide transmission to produce 80% efficiency. The remaining ~20% included contributions from the residual power in the sidelobes, the light scattered by surface imperfections inside the waveguide, and the lightwhich leaks into the capillary walls, about half of which re-enters the capillary.

The M 2 measurement of the combined beam using a Spiricon M2-200 Beam Propagation Analyzer produced a value of M 2 = 1.25. This measurement took place after optimized performance had deteriorated and the combined output developed significant sidelobes as a result of misalignment. The M 2 of the demonstrated 101.2 W combined beam (Fig. 5) is expected to be less than 1.25. The measured M 2 of the beams emerging from the PCF transport fibers is 1.17.

During the high power (100 W-level) demonstration, the temperature of the beam combiner module was maintained at or near room temperature even after several hours of operation. Figure 6
Fig. 6 FLIR image of the beam combiner module. With 116 W emerging from the waveguide, the temperature of the fiber array and the waveguide did not exceed 30°C .
shows a FLIR image of the beam combiner transmitting more than 116 W. The warmest spot in Fig. 6 is actually the center of the imaging lens, which was not a part of the beam combiner and was used to image the waveguide output on the CCD camera. Although all of the beam combiner components performed remarkably well during the high power demonstration, a number of “hot spots” developed on the surface of the PCF transport fibers. The hot spots were caused by black pen marks made on the fiber’s polymer jacket during the fiber array assembly. The residual light propagating in the fiber cladding was absorbed by the black ink that penetrated the protective polymer jacket. The heat generated by the absorbed light was sufficient to melt the jacket. Figure 7
Fig. 7 FLIR image of the PCF transport fibers with hot spots caused by ink marks.
shows a FLIR image of the fiber array with the hot spots clearly visible on each of the four transport fibers.

To protect the fibers from thermal damage, we built a cooling system using a pump submerged in ice water and a system of tubes and funnels to pour water directly over the hot spots. The cooling system effectively kept the temperature of the hot spots to a manageable level.

4. Conclusion

The high power demonstration at the AFRL High Power Fiber Laser Testbed produced the best to date results of coherent beam combination in a 2-D waveguide: 80% combining efficiency at the 100 W combined power level. The maximum combined power was limited by the available amplifier output and the varying efficiency of the free-space coupling to the PCF transport fibers.

The components of the beam combiner performed remarkably well, demonstrating low thermal sensitivity and high stability at 100 W combined power levels, with the exception of the PCF transport fibers, which developed hot spots at ink marks on their jackets. The combining waveguide and the fiber array maintained a temperature around 25°C over several hours with no active cooling. The high power combining efficiency was comparable to the efficiency we demonstrated earlier at low power levels. The 2D REAPAR waveguide architecture is expandable to higher fiber counts than the 2 × 2 demonstrated here by employing appropriate waveguides and larger arrays. Scaling the combiner to high beam counts could involve both increasing the number of beams combined in a single waveguide and combination of the outputs of multiple waveguides. The experimental and theoretical data indicate that the waveguide beam combiner is suitable for power scaling MOPA systems to multi-kilowatt-class power levels and beyond.

Acknowledgment

This effort was funded by the High Energy Laser Joint Technology Office (HEL-JTO).

References and links

1.

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005). [CrossRef]

2.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, 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 solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007). [CrossRef]

3.

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). [CrossRef] [PubMed]

4.

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31(9), 1247–1249 (2006). [CrossRef] [PubMed]

5.

S. J. Augst, J. K. Ranka, T. Y. Fan, and A. Sanchez, “Beam combining of ytterbium fiber amplifiers,” J. Opt. Soc. Am. B 24(8), 1707–1715 (2007). [CrossRef]

6.

P. Zhou, Y. Ma, X. Wang, H. Ma, J. Wang, X. Xu, and Z. Liu, “Coherent beam combination of a hexagonal distributed high power fiber amplifier array,” Appl. Opt. 48(33), 6537–6540 (2009). [CrossRef] [PubMed]

7.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt. Lett. 33(4), 354–356 (2008). [CrossRef] [PubMed]

8.

R. Uberna, A. Bratcher, and B. G. Tiemann, “Coherent polarization beam combination,” IEEE J. Quantum Electron. 46(8), 1191–1196 (2010). [CrossRef]

9.

R. Uberna, A. Bratcher, and B. G. Tiemann, Lockheed Martin Coherent Technologies, 135 S. Taylor Avenue, Louisville, Colorado 80027, are preparing a manuscript to be called “Power scaling of fiber laser system using coherent polarization beam combination.”

10.

S. E. Christensen, and O. Koski, “2-Dimensional waveguide coherent beam combiner,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper WC1.

11.

A. Bratcher and R. Uberna, “Two-dimensional re-imaging assisted phased array architecture for coherent beam combination,” J. Directed Energy 3, 107–117 (2009).

12.

A. Bratcher, and R. Uberna, “Optimization and power scaling of 2-dimensional re-imaging assisted phased array,” in Solid State and Diode Laser Technology Review Technical Digest, (Directed Energy Professional Society, 2009), pp. 32–36.

13.

T. M. Shay, “Theory of electronically phased coherent beam combination without a reference beam,” Opt. Express 14(25), 12188–12195 (2006). [CrossRef] [PubMed]

14.

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). [CrossRef] [PubMed]

OCIS Codes
(030.1670) Coherence and statistical optics : Coherent optical effects
(140.3298) Lasers and laser optics : Laser beam combining

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: April 16, 2010
Revised Manuscript: May 23, 2010
Manuscript Accepted: June 3, 2010
Published: June 9, 2010

Citation
Radoslaw Uberna, Andrew Bratcher, Thomas G. Alley, Anthony D. Sanchez, Angel S. Flores, and Benjamin Pulford, "Coherent combination of high power fiber amplifiers in a two-dimensional re-imaging waveguide," Opt. Express 18, 13547-13553 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-13-13547


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References

  1. T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005). [CrossRef]
  2. G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, 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 solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007). [CrossRef]
  3. 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). [CrossRef] [PubMed]
  4. G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31(9), 1247–1249 (2006). [CrossRef] [PubMed]
  5. S. J. Augst, J. K. Ranka, T. Y. Fan, and A. Sanchez, “Beam combining of ytterbium fiber amplifiers,” J. Opt. Soc. Am. B 24(8), 1707–1715 (2007). [CrossRef]
  6. P. Zhou, Y. Ma, X. Wang, H. Ma, J. Wang, X. Xu, and Z. Liu, “Coherent beam combination of a hexagonal distributed high power fiber amplifier array,” Appl. Opt. 48(33), 6537–6540 (2009). [CrossRef] [PubMed]
  7. E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt. Lett. 33(4), 354–356 (2008). [CrossRef] [PubMed]
  8. R. Uberna, A. Bratcher, and B. G. Tiemann, “Coherent polarization beam combination,” IEEE J. Quantum Electron. 46(8), 1191–1196 (2010). [CrossRef]
  9. R. Uberna, A. Bratcher, and B. G. Tiemann, Lockheed Martin Coherent Technologies, 135 S. Taylor Avenue, Louisville, Colorado 80027, are preparing a manuscript to be called “Power scaling of fiber laser system using coherent polarization beam combination.”
  10. S. E. Christensen, and O. Koski, “2-Dimensional waveguide coherent beam combiner,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper WC1.
  11. A. Bratcher and R. Uberna, “Two-dimensional re-imaging assisted phased array architecture for coherent beam combination,” J. Directed Energy 3, 107–117 (2009).
  12. A. Bratcher, and R. Uberna, “Optimization and power scaling of 2-dimensional re-imaging assisted phased array,” in Solid State and Diode Laser Technology Review Technical Digest, (Directed Energy Professional Society, 2009), pp. 32–36.
  13. T. M. Shay, “Theory of electronically phased coherent beam combination without a reference beam,” Opt. Express 14(25), 12188–12195 (2006). [CrossRef] [PubMed]
  14. 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). [CrossRef] [PubMed]

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