Characteristics of an Airy beam at a dielectric interface

A full analytical theory for the reflection and transmission of an Airy beam impinging on a dielectric surface is presented. Based on the plane-wave angular spectrum expansion, the analytical expressions for the reflected and transmitted fields comprising beam modes are derived. To improve the calculation accuracy, the actual beam field retains up to the second-order terms. The influences of decay factor and beam width on the intensity dis-tributions of the incident, reflected, and transmitted beams are studied. In addition, we investigate the effects of decay factor and beam width on the beam shift of the reflected beam near the Brewster angle. There is a giant negative lateral shift near the Brewster angle. Results show that the beam shift decreases and increases with increasing decay factor and beam width, respectively. A comparison with the beam shifts of Airy beams incident on the interface and dielectric slab at the Brewster angle is also discussed. The beam shift of the dielectric slab exists an abrupt increase. Finally, an Airy beam incident from air to the left-handed material (LHM) is consid-ered. Results indicate that the imaging position of the incident Airy beam in the LHM is affected by the incident angle and negative refractive index. Our results may provide some theoretical support for the applications of Airy beams in detection and imaging.