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1 Self-healing of Airy Beams Self-reconstructing Optical Airy Beams Perhaps one of the most remarkable properties of any diffraction-free beam is its very ability to self-reconstruct during propagation. This characteristic is of particular importance when such waves propagate in inhomogeneous media [48]. The question naturally arises whether Airy beams can self-heal and to what extent? If so, how does this process take place and how is it affected by the beam’s acceleration dynamics? For example, can an Airy beam negotiate adverse environments?

N. Christodoulides, Opt. Lett. 35, 4045 (2010) 39. I. K. N. Christodoulides, Opt. Lett. 36, 1890 (2011) 40. E. Greenfield, M. Segev, W. Walasik, O. Raz, Phys. Rev. Lett. 106, 213902 (2011) 41. G. K. N. Christodoulides, S. Tzortzakis, Opt. Lett. 36, 1842 (2011) 42. P. Zhang, J. Prakash, Z. Zhang, Y. Hu, N. K. Efremidis, V. Kajorndejnukul, D. N. Christodoulides, and Z. Chen, CLEO:QELS-Fundamental Science, paper QThS7 (2011) 43. W. Goodman, Introduction to Fourier Optics, 3rd edn. (Roberts & Company Publishers, Greenwood Village, CO, 2005) 44.

Under the self-defocusing nonlinearity, our numerical results show that the Airy beam is somewhat expanded at the beginning due to the self-defocusing nonlinearity but its shape is nearly unchanged (Fig. 32a). In contrast to the self-focusing case, the Airy beam persists in its intensity pattern and transverse acceleration during subsequent free-space propagation (Fig. 32b, d). Furthermore, its power spectrum reshapes into a diamond-like pattern and is concentrated unevenly on four spots (Fig.

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