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

Realization of a circularly transformed Airyprime beam with powerful autofocusing ability

The reported autofocusing ability of a ring Airyprime beam array reaches up to 8632.40, while the strongest autofocusing ability of a circular Airyprime beam (CAPB) is only 1822.49. How can the autofocusing ability of a single beam reach the autofocusing ability of a beam array? To achieve this goal, a circularly transformed Airyprime beam (CTAPB) is introduced by following two steps. First, a circular equation transformation on the two transverse coordinates in the electric field expression of a propagating Airyprime beam is performed. Then, the electric field expression of a propagating Airyprime beam is integrated over the angle. The intensity profile of a CTAPB on the initial plane changes significantly with varying the primary ring radius r0. With increasing r0, therefore, the autofocusing ability of a CTAPB undergoes a process of first increasing and then decreasing, while the focal length always increases. A CTAPB exhibits more powerful autofocusing ability than a CAPB. The maximum autofocusing ability of a CTAPB can reach up to 8634.76, which is 4.74 times that of a CAPB, while the corresponding focal length is 95.11% of a CAPB. A CTAPB on the initial plane can be approximately characterized by a ring Airyprime beam array with sufficient number of Airyprime beams. Due to the better symmetry, a CTAPB has a slightly stronger autofocusing ability than a ring Airyprime beam array and almost the same focal length as a ring Airyprime beam array. The CTAPB is also experimentally generated, and the experimental results indicate that the CTAPB has powerful autofocusing ability. As a replacement of a CAPB and a ring Airyprime beam array, this introduced CTAPB can be applied to the scenes which involve abruptly autofocusing effect.

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. When a is small enough, there exists a critical value for the dimensionless radius. If the dimensionless radius is greater than the critical value, the focal length is shortened in the enhancement of the abruptly autofocusing ability. If the dimensionless radius is less than the critical value, the focal length is extended in the enhancement of the abruptly autofocusing ability. As a increases, the critical value for the dimensionless radius decreases until it reaches zero. The physical mechanism of extension or shortening of the focal length in the enhancement of the abruptly autofocusing ability is elucidated.

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. The first-order chirped factor only affects the transverse coordinates where the maximum light intensity appears. The strength of interference enhancement effect of the chirped Airyprime beam with any negative second-order chirped factor must be stronger than that of the conventional Airyprime beam. However, the improvement of the strength of interference enhancement effect caused by the negative second-order chirped factor is realized at the expense of shortening the position where the maximum light intensity appears and the range of interference enhancement effect. The chirped Airyprime beam is also experimentally generated, and the effects of the first-order and the second-order chirped factors on the interference enhancement effect are experimentally confirmed. This study provides a scheme to improve the strength of interference enhancement effect by controlling the second-order chirped factor. Compared with traditional intensity enhancement methods such as using lens focusing, our scheme is flexible and easy to implement. This research is beneficial to the practical applications such as spatial optical communication and laser processing.

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 72.28%, and the corresponding focal length is extended by 34.81%. The focal length can be extended by 110.28% at most, and the corresponding autofocusing ability is improved by 48.59%. To verify the feasibility of this scheme, we have carried out an experiment for the generation of a ring Airyprime beam array with a linear chirp, and the experimental results for autofocusing ability and focal length are in good agreement with theoretical results. Our findings have potential applications in many aspects, such as free space optical communication.

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. The focal spot size of the RAPB array remains unchanged before the number of beamlets reaches the optimal number of beamlets. More importantly, the saturated autofocusing ability of the RAPB array is stronger than that of the corresponding circular Airyprime beam. The physical mechanism of the saturated autofocusing ability of the RAPB array is interpreted by simulating the Fresnel zone plate lens. The influence of the number of beamlets on the autofocusing ability of the ring Airy beams (RAB) array under the same beam parameters with the RAPB array is also presented for comparison. Our findings are beneficial for the design and application of the ring beams array.