附加球面相位引致Airy光束在单轴晶体传输时的两次镜像演化

Dual mirror evolutions of Airy beams propagating through uniaxial crystals induced by added spherical phase

利用单轴晶体光束传输理论,求得了具有附加球面相位Airy光束在单轴晶体中的传输公式.数值模拟计算结果表明,线偏振附加球面相位Airy光束在晶体中传输时仍为线偏振,但不是传输不变的.粗略地讲,具有附加球面相位的Airy光束在晶体中传输时,近场是传输不变的;而在由晶体寻常与非寻常折射率和球面半径共同确定的两个特定传输距离处,传输光束转换成了取向不同的Gaussian-Airy光束,且高斯依赖的束宽度敏感地与截断因子相关;而当光束依次穿过此两位置时光斑花样先后相对于两横向轴平面做镜像演化,且镜像演化顺序也与晶体寻常和非寻常折射率相对大小密切相关,其总的效果是远场强度花样能恢复原样但花样取向产生了关于对过横平面二、四象限平分平面的镜像演化.这些结果表明,通过恰当选择晶体材料(即折射率)和附加球面相位的半径R,可以调控光束花样的形状、取向及表征各向异性材料的相关性质.

Airy beams have received considerable attention due to their unique features on propagation, including non-spreading, self-healing, self-accelerating, and parabolic trajectories. Here in this work we study the propagation of linearly polarized Airy beams with an added spherical phase in uniaxial crystal orthogonal to the optical axis. Based on the beam transmission theory in uniaxial crystals, the analytical expressions for the intensity distribution of the beams in different view planes are derived. Numerical calculations are performed and some novel propagation features are presented graphically. It is shown that the Airy beam with an added spherical phase remains linearly polarized but cannot keep other properties unchanged during propagation in uniaxial crystal. Such a beam maintains its intensity profile in the near-field, then with the propagation distance increasing, converts into the Gaussian-Airy beams with different orientations at two specified distances which are codetermined by the extraordinary and ordinary refractive index of the crystal(namely ne and no)and the radius of the spherical phase, and most impressively, forms a mirror-like reflection profile in the far field, i.e., the intensity pattern in the far field returns to the initial Airy beam profile while its orientation on the transversal plane is reversed along the bisector line of the second and fourth quadrant. Note that the intensity pattern successively experiences two mirror transformations along the x and y coordinate axis when passing through these two critical positions, which can give rise to the mirror reflection effect for the whole Airy beam. Moreover, we further demonstrate that the sequences of these two mirror transformations are in close relation with the relative size between ne and no. Therefore, the results obtained in this paper reveal new propagation features in anisotropic medium of Airy beams with added spherical phase and provide a novel route to controlling propagation properties like the pattern profile and orientation of the Airy beams through choosing appropriate anisotropic materials and the radius of the spherical phase factor. Considering that it is easy to obtain an Airy beam with an added spherical phase which can be realized with an Airy beam through an ideal lens, our investigation may lead to potential applications in many fields where the ability to change profile and orientation of the intensity pattern and the ability to determine the refractive index of anisotropic medium are both required.