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Photonics Research

Photonics Research

| A joint OSA/Chinese Laser Press publication

  • Editor: Zhiping (James) Zhou
  • Vol. 1, Iss. 4 — Dec. 1, 2013
  • pp: 186–196

Coherent beam combination of fiber lasers with a strongly confined tapered self-imaging waveguide: theoretical modeling and simulation

Rumao Tao, Xiaolin Wang, Hu Xiao, Pu Zhou, and Lei Si  »View Author Affiliations

Photonics Research, Vol. 1, Issue 4, pp. 186-196 (2013)

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Coherent beam combination (CBC) of fiber lasers based on self-imaging properties of a strongly confined tapered waveguide (SCTW) is studied systematically. Analytical formulas are derived for the positions, amplitudes, and phases of the N self-images at the output of a SCTW, which are important for quantitative analysis of waveguide-based CBC. The formulas are verified with numerical examples by a finite difference beam propagation method (FDBPM) and the errors of the analytical expressions are studied. This study shows that the analytical formulas agree well with the FDBPM simulation results when the taper angle is less than 1.4° and the phase distortion is less than λ/10. The relative errors increase as the taper angle increases. Based on the theoretical model and the FDBPM, we simulated the CBC of fiber laser array and compared the CBC based on the tapered waveguide with that based on the nontapered one. The effects of input beam number, aperture fill factor, and taper angle on the combination performance have been studied. The study reveals that a beam which has near-diffraction limited beam quality (M21.41) and a single beam without side lobe in the far field can be achieved with tapered-waveguide-based CBC. It is shown that beam quality depends on input beam number, aperture fill factor, and taper angle. There exists a best fill factor which will increase as input beam number increases. The tolerance of the system on the fill factor and the taper angle is studied, which is 0.45<t<0.67 and θ<0.8°, respectively. The results may be useful for practical, high-power fiber laser systems.

© 2013 Chinese Laser Press

OCIS Codes
(140.3290) Lasers and laser optics : Laser arrays
(140.3510) Lasers and laser optics : Lasers, fiber
(140.3298) Lasers and laser optics : Laser beam combining

ToC Category:
Lasers and Laser Optics

Original Manuscript: August 20, 2013
Revised Manuscript: October 4, 2013
Manuscript Accepted: October 6, 2013
Published: November 8, 2013

Rumao Tao, Xiaolin Wang, Hu Xiao, Pu Zhou, and Lei Si, "Coherent beam combination of fiber lasers with a strongly confined tapered self-imaging waveguide: theoretical modeling and simulation," Photon. Res. 1, 186-196 (2013)

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  1. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber laser: current status and future perspectives,” J. Opt. Soc. Am. B 27, B63–B92 (2010). [CrossRef]
  2. J. R. Leger, J. Nilsson, J. P. Huignard, A. P. Napartovich, T. M. Shay, and A. Shirakawa, “Laser beam combining and fiber laser systems,” IEEE J. Sel. Top. Quantum Electron. 15, 237–239 (2009). [CrossRef]
  3. T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567–577 (2005). [CrossRef]
  4. T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zerinque, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High-power phase locking of a fiber amplifier array,” Proc. SPIE 7195, 71951M (2009). [CrossRef]
  5. B. He, Q. H. Lou, J. Zhou, J. Dong, Y. Wei, D. Xue, Y. Qi, Z. Su, L. Li, and F. Zhang, “High power coherent beam combination from two fiber lasers,” Opt. Express 14, 2721–2726 (2006). [CrossRef]
  6. J. Wang, K. Duan, and Y. Wang, “Experimental study of coherent beam combining of two fiber lasers,” Acta Phys. Sin. 57, 5627–5631 (2008).
  7. P. Zhou, Z. J. Liu, X. L. Wang, Y. X. Ma, H. T. Ma, X. J. Xu, and S. F. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009). [CrossRef]
  8. L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 6708K (2007).
  9. J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. J. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE 6306, 63060G (2006). [CrossRef]
  10. 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, 6537–6540 (2009). [CrossRef]
  11. 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, 354–356 (2008). [CrossRef]
  12. R. Uberna, A. Bratcher, and B. G. Tiemann, “Coherent polarization beam combination,” IEEE J. Quantum Electron. 46, 1191–1196 (2010). [CrossRef]
  13. S. E. Christensen and O. Koski, “2-Dimensional waveguide coherent beam combiner,” in Advanced Solid-State Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper WC1.
  14. R. Uberna, A. Bratcher, T. G. Alley, A. D. Sanchez, A. S. Flores, and B. Pulford, “Coherent combination of high power fiber amplifiers in a two-dimensional re-imaging waveguide,” Opt. Express 18, 13547–13553 (2010). [CrossRef]
  15. W. S. C. Chang, Fundamentals of Guided-Wave Optoelectronic Devices (Cambridge University, 2010).
  16. R. Ulrich and T. Kamiya, “Resolution of self-images in planar optical waveguides,” J. Opt. Soc. Am. 68, 583–592 (1978). [CrossRef]
  17. M. Bachmann, P. A. Besse, and H. Melchior, “General self-imaging properties in N×N multimode interference couplers including phase relations,” Appl. Opt. 33, 3905–3911 (1994). [CrossRef]
  18. S. He, X. Ao, and V. Romanov, “General properties of N×M self-images in a strongly confined rectangular waveguide,” Appl. Opt. 42, 4855–4859 (2003). [CrossRef]
  19. H. J. Baker, J. R. Lee, and D. R. Hall, “Self-imaging and high-beam-quality operation in multi-mode planar waveguide optical amplifiers,” Opt. Express 10, 297–302 (2002). [CrossRef]
  20. R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical technique for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000). [CrossRef]
  21. R. Scarmozzino and R. M. Osgood, “Comparison of finite-difference and Fourier-transform solutions of the parabolic wave equation with emphasis on integrated-optics applications,” J. Opt. Soc. Am. A 8, 724–731 (1991). [CrossRef]
  22. Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335–1339 (1990). [CrossRef]
  23. Y. Chung and N. Dagli, “Modeling of guided-wave optical components with efficient finite-difference beam propagation methods,” in Antennas and Propagation Society International Symposium (IEEE, 1992), pp. 248–251.
  24. C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).
  25. C. Vassallo, “Interest of improved three-point formulas for finite-difference modeling of optical devices,” J. Opt. Soc. Am. A 14, 3273–3284 (1997). [CrossRef]
  26. K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis (Wiley, 2001).
  27. C. Chen, Foundations for Guided-Wave Optics (Wiley, 2007).
  28. G. R. Hadley, “Transparent boundary condition for the beam propagation method,” Opt. Lett. 16, 624–626 (1991). [CrossRef]
  29. G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28, 363–370 (1992). [CrossRef]
  30. A. E. Siegman, “How to (maybe) measure laser beam quality,” in Diode Pumped Solid State Lasers: Applications and Issues, M. Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), paper MQ1.
  31. T. Poon and T. Kim, Engineering Optics with MATLAB (World Scientific, 2006).
  32. J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in MATLAB (SPIE, 2010).

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