Propagation Properties of Controllable Dark Hollow Laser Beams in Uniaxial Crystals Along the Optical Axis

摘要

Analytical expressions of the ordinary and the extraordinary optical fields of controllable dark hollow laser beams propagating in uniaxial crystals along the optical axis are derived, respectively. The amplitude distribution, the intensity distribution, the distribution of the linearly polarized, the effective beam size, and the kurtosis parameter of the ordinary optical field, the extraordinary optical field, and the controllable dark hollow laser beam are investigated in the different observation planes of the uniaxial crystal, respectively. The amplitude distributions of the x-component of the ordinary and the extraordinary optical fields are both composed of two lobes, while those of the corresponding y-component have four lobes. Upon propagation in the uniaxial crystals, the x-component of a controllable dark hollow laser beam loses its circular symmetry. The intensity distribution of the extraordinary optical field is somewhat similar to that of the ordinary optical field rotating 90 degrees. When the observation plane is far enough, the dark region of the controllable dark hollow laser beam will appear in the sides of the light spot. The distribution of the linearly polarized angle of the controllable dark hollow laser beam is completely different from those of the ordinary and the extraordinary optical fields. When the observation plane is close to the boundary plane, the effective beam size of the controllable dark hollow laser beam is the largest among those of the ordinary optical field, the extraordinary optical field, and the controllable dark hollow laser beam, while the kurtosis parameter of the controllable dark hollow laser beam is the smallest. When the observation plane is far away from the boundary plane, the effective beam size of the controllable dark hollow laser beam is nearly same as that of the ordinary optical field, and the kurtosis parameter of the controllable dark hollow laser beam is the largest.