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

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

http://dx.doi.org/10.1364/PRJ.1.000186

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### Abstract

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

© 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

**History**

Original Manuscript: August 20, 2013

Revised Manuscript: October 4, 2013

Manuscript Accepted: October 6, 2013

Published: November 8, 2013

**Citation**

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)

http://www.opticsinfobase.org/prj/abstract.cfm?URI=prj-1-4-186

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### References

- 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]
- 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]
- T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567–577 (2005). [CrossRef]
- 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]
- 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]
- J. Wang, K. Duan, and Y. Wang, “Experimental study of coherent beam combining of two fiber lasers,” Acta Phys. Sin. 57, 5627–5631 (2008).
- 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]
- 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).
- 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]
- 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]
- 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]
- R. Uberna, A. Bratcher, and B. G. Tiemann, “Coherent polarization beam combination,” IEEE J. Quantum Electron. 46, 1191–1196 (2010). [CrossRef]
- 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.
- 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]
- W. S. C. Chang, Fundamentals of Guided-Wave Optoelectronic Devices (Cambridge University, 2010).
- R. Ulrich and T. Kamiya, “Resolution of self-images in planar optical waveguides,” J. Opt. Soc. Am. 68, 583–592 (1978). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335–1339 (1990). [CrossRef]
- 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.
- C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).
- 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]
- K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis (Wiley, 2001).
- C. Chen, Foundations for Guided-Wave Optics (Wiley, 2007).
- G. R. Hadley, “Transparent boundary condition for the beam propagation method,” Opt. Lett. 16, 624–626 (1991). [CrossRef]
- G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28, 363–370 (1992). [CrossRef]
- 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.
- T. Poon and T. Kim, Engineering Optics with MATLAB (World Scientific, 2006).
- J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in MATLAB (SPIE, 2010).

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