Chirped Airy beams in strongly nonlocal media with focusing and defocusing nonlinearity

In this paper, we derive an analytical solution of linearly chirped Airy beams (CAB) propagating in strongly nonlocal media with focusing and defocusing nonlinearity. Our analytical results show the periodic evolution pattern of CAB supported by strongly nonlocal focusing nonlinearity is made to be gradually reshaped each other between Airy distribution and conventional standard Gaussian distribution. Meanwhile, we further disclose how initial chirp affects the periodic evolution of optical beam. It is found that we can change ballistic trajectory gradually from conventional parabolic to trigonometric shapes through increasing initial chirp; however the corresponding period is only determined by the degree of nonlocality but independent on the former. Moreover, another interesting property is that initial chirp will lead to a positive or negative transverse displacement of the resulting Gaussian distribution depending on the direction of input beam, but does not affect its shape and longitudinal location. On the other hand, for defocusing nonlinearity, CAB is found to exhibit the conventional nonperiodic self-accelerating behavior, which direction is decided by the initial chirp. Our analytical results agree with the existing results and can be confirmed by numerical prediction.