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

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.

Highly efficient enhancement and extension of focusing ability for ring Pearcey beam by means of dual-region parabolic trajectory offset modulation

It is a highly significant area of research to investigate how to effectively enhance the focusing ability of abruptly auto-focusing beams (AAFBs) while extending the focal length. We introduce a dual-region parabolic trajectory offset modulation to auto-focusing ring Pearcey beams (RPBs), presenting a novel, to the best of our knowlege, approach to extend the focal length while greatly enhancing their auto-focusing capabilities. Unlike directly introducing a linear chirp, which inevitably shortens the focal length to enhance the auto-focusing ability and allows only single focusing in the RPBs, our scheme can achieve a multi-focusing effect. Furthermore, we have experimentally generated such a beam, verifying our theoretical predictions. Our findings offer promising possibilities for generating optical bottles, trapping multiple particles periodically, and enhancing free-space optical communication capabilities.

Focusing property of autofocusing Bessel beams

We introduce what we believe to be a new family of abruptly autofocusing waves named autofocusing Bessel beams (ABBs). Since the beams only strongly influence the area near the focus, it holds promise for medical laser treatment and optical tweezers. By the angular spectrum method, ABBs are proved to be a class solution for the Helmholtz equation. The focal length is well-defined and easily tuned in our mathematical description. Under the finite energy limitation, the abruptly autofocusing and vortex characteristics of Gaussian-modulated ABBs are studied. Interestingly, we found a kind of abruptly autofocusing waves focusing twice on the propagation axis, which is formed by an ABB passing through a focusing lens. Dual-focus ABBs make it possible for a single laser to manipulate two particles on the propagation axis simultaneously. In the experiment, the autofocusing of ABBs and the dual focus of ABBs passing through a focusing lens are observed. This article provides a theoretical model and experimental protocol for studying abruptly autofocusing waves.

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.