The eigenwave functions of the general linear potential field and the tent-type linear potential field are solved, the free evolutions of these two Airy wave packets are analyzed, and the propagation properties of Airy wave packets used as optical information carriers are investigated in the media. Firstly, the core form of the solution of the intrinsic wave function in the general linear potential field can be expressed as the standard Airy function, and the characteristics of the soliton and self-accelerating properties of Airy wave packet propagating in free space are discussed. Then the eigenwave function of the bidirectional airy wave packet under the tent type linear potential is calculated and the accelerated interference diffusion behavior of the bidirectional Airy wave packet under different parameters is discussed. The solutions of the above two kinds of Airy wave packets are applied to the dielectric transmission problem of electromagnetic field. The accelerated transverse deflection and transverse interference of the electric field of Airy wave packets in the medium are discussed.