Dependence of autofocusing ability of a ring Airyprime beams array on the number of beamlets.

A ring Airyprime beams (RAPB) array, which consists of N evenly displaced Airyprime beamlets in the initial plane, is first introduced, to the best of our knowledge, in this Letter. Here, we focus on the effect of the number of beamlets N on the autofocusing ability of the RAPB array. With the given beam parameters, an optimal number of beamlets, which is the minimum number of beamlets to realize the saturated autofocusing ability, is selected.

Investigation of the effect of chirped factors on the interference enhancement effect of an Airyprime beam propagating in free space.

The first-order and the second-order chirped factors are imposed on the Airyprime beam, and the analytical expression of the chirped Airyprime beam propagating in free space is derived. The phenomenon that the peak light intensity on observation plane other than initial plane is greater than that on initial plane is defined as the interference enhancement effect, which is caused by the coherent superposition of the chirped Airyprime and the chirped Airy-related modes. The effects of the first-order and the second-order chirped factors on the interference enhancement effect are theoretically investigated, respectively.

Key to an extension or shortening of focal length in the enhancement of autofocusing ability of a circular Airyprime beam caused by a linear chirp factor.

Researchers are puzzled whether the enhancement of the abruptly autofocusing ability caused by a linear chirp factor is accompanied by the shortening or the extension of the focal length. In this Letter, a circular Airyprime beam is chosen as the research object to reveal this mystery. Extension or shortening of the focal length in the enhancement of the abruptly autofocusing ability depends on the exponential decay factor a and the dimensionless radius of the primary ring.

Simultaneously enhancing autofocusing ability and extending focal length for a ring Airyprime beam array by a linear chirp.

It is of great significance to solve the problem that improving autofocusing ability is always at the cost of shortening focal length. By introducing a linear chirp into a ring Airyprime beam array, an optimization scheme to simultaneously achieve the enhancement of autofocusing ability and the extension of focal length is proposed. The autofocusing ability can be enhanced by up to 72.

Effect of chirped factors on the abrupt autofocusing ability of a chirped circular Airyprime beam.

Recently, a new type of abruptly autofocusing beam called circular Airyprime beam (CAPB) has been reported. Its abrupt autofocusing ability has been proven to be approximately seven times that of a circular Airy beam under the same conditions. Further improving the abrupt autofocusing ability of the CAPB without changing the beam parameters is a concern in optical research.

Interference enhancement effect in a single Airyprime beam propagating in free space.

An analytical expression of a single Airyprime beam propagating in free space is derived. Upon propagation in free space, a single Airyprime beam in arbitrary transverse direction is the coherent superposition of the Airyprime and the Airy-related modes, which results in the interference enhancement effect under the appropriate condition. The Airy-related mode is the conventional propagating Airy mode with an additional π/2 phase shift and a weight coefficient of half the normalized propagation distance.

Generation of finite energy Airyprime beams by Airy transformation.

In this paper, the lone generation of a new kind of beam named finite energy Airyprime (FEA) beam through the Airy transformation of the coherent superposition of four different elegant Hermite-Gaussian modes is reported for the first time. Analytical expressions of the centroid, the r.m.

Abruptly autofocusing of generalized circular Airy derivative beams.

In this paper, we introduce a novel kind of abrupt autofocusing beams namely the generalized circular Airy derivative beams (CADBs) as an extension of circular Airy beam (CAB). The propagation dynamics of the CADBs is examined theoretically. Our results show that the CADBs exhibit stronger autofocusing ability than the CAB under the same condition.