[1] [1] Y. Huo and P. K. Cheo, “Analysis of transverse mode competition and selection in multicore fiber lasers,” J. Opt. Soc. Am. B 22, 2345–2349 (2005).

[2] [2] C. Xia, N. Bai, I. Ozdur, X. Zhou, and G. Li, “Supermodes for optical transmission,” Opt. Express 19, 16653–16664 (2011).

[3] [3] B. Zhu, T. F. Taunay, M. F. Yan, J. M. Fini, M. Fishteyn, E. M. Monberg, and F. V. Dimarcello, “Seven-core multicore fiber transmissions for passive optical network,” Opt. Express 18, 11117–11122 (2010).

[4] [4] K. S. Abedin, J. M. Fini, T. F. Thierry, V. R. Supradeepa, B. Zhu, M. F. Yan, L. Bansal, E. M. Monberg, and D. J. DiGiovanni, “Multicore erbium doped fiber amplifiers for space division multiplexing systems,” J. Lightwave Technol. 32, 2800–2808 (2014).

[5] [5] Y. Huo, P. Cheo, and G. King, “Fundamental mode operation of a 19-core phase-locked Yb-doped fiber amplifier,” Opt. Express 12, 6230–6239 (2004).

[6] [6] A. M. Rubenchik, E. V. Tkachenko, M. P. Fedoruk, and S. K. Turitsyn, “Power-controlled phase-matching and instability of CW propagation in multicore optical fibers with a central core,” Opt. Lett. 38, 4232–4235 (2013).

[7] [7] H.-J. Otto, A. Klenke, C. Jauregui, F. Stutzki, J. Limpert, and A. Tünnermann, “Scaling the mode instability threshold with multicore fibers,” Opt. Lett. 39, 2680–2683 (2014).

[8] [8] E. Kapon, J. Katz, and A. Yariv, “Supermode analysis of phaselocked arrays of semiconductor lasers,” Opt. Lett. 9, 125–127 (1984).

[9] [9] E. Yamashita, S. Ozeki, and K. Atauki, “Modal analysis method for optical fibers with symmetrically distributed multiple cores,” J. Lightwave Technol. LT-3, 341–346 (1985).

[10] [10] J. Zhou, “Analytical formulation of super-modes inside multicore fibers with circularly distributed cores,” Opt. Express 22, 673–688 (2014).

[11] [11] A. S. Kurkov, S. A. Babin, I. A. Lobach, and S. I. Kablukov, “Mechanism of mode coupling in multicore fiber lasers,” Opt. Lett. 33, 61–63 (2008).

[12] [12] P. J. Mosley, I. Gris-Sánchez, J. M. Stone, R. J. A. Francis-Jones, D. J. Ashton, and T. A. Birks, “Characterizing the variation of propagation constants in multicore fiber,” Opt. Express 22, 25689–25699 (2014).

[13] [13] S. Zheng, G. Ren, Z. Lin, and S. Jian, “Mode-coupling analysis and trench design for large-mode-area low-cross-talk multicore fiber,” Appl. Opt. 52, 4541–4548 (2013).

[14] [14] F. Y. M. Chan, A. P. T. Lau, and H.-Y. Tam, “Mode coupling dynamics and communication strategies for multi-core fiber systems,” Opt. Express 20, 4548–4563 (2012).

[15] [15] A. Amphawan, F. Payne, D. O’Brien, and N. Shah, “Derivation of an analytical expression for the power coupling coefficient for offset launch into multimode fiber,” J. Lightwave Technol. 28, 861–869 (2010).

[16] [16] P. K. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” J. Lightwave Technol. 13, 439–441 (2001).

[17] [17] K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh, and M. Koshiba, “A large effective area multi-core fiber with an optimized cladding thickness,” Opt. Express 19, B543–B550 (2011).

[18] [18] A. S. Jazi and G. Lamyip, “Cutoff conditions in three layer cylindrical dielectric waveguides,” IEEE Trans. MTT-26, 898– 903 (1978).

[19] [19] R. J. Black and R. Bourbonnais, “Core-mode cutoff for finitecladding lightguides,” Proc. IEE 133, 377–384 (1986).

[20] [20] J. Bures, Guided Optics: Optical Fibers and All-fiber Components (Wiley-VCH, 2009).

[21] [21] A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).

[22] [22] J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. I. Adiabaticity criteria,” Proc. IEE 138, 343–354 (1991).

[23] [23] K. Okamoto, Fundamentals of Optical Waveguides (Elsevier, 2006).

[24] [24] M. N. McLandrich, “Core dopant profiles in weakly fused singlemode fibers,” Electron. Lett. 24, 8–10 (1988).