Transformation of a Hermite-Gaussian beam by an Airy transform optical system

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.

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. Due to the peak light intensity in the initial plane being set to be 1, the strength of interference enhancement effect is characterized by the maximum light intensity. The maximum light intensity of a single Airyprime beam propagating in free space is independent of the scaling factor and is only decided by the exponential decay factor. When the exponential decay factor is above the saturated value, the interference enhancement effect disappears. When the exponential decay factor decreases from the saturated value, the maximum light intensity of a single propagating Airyprime beam increases, and the position of maximum light intensity is getting farther away. With the increase of the scaling factor, the position of maximum light intensity of a single propagating Airyprime beam is extended. The intensity distribution and the transverse Poynting vector of a single propagating Airyprime beam are demonstrated in different observation planes of free space. The flow direction of transverse energy flux effectively supports the interference enhancement effect of a single propagating Airyprime beam. The Airyprime beam is experimentally generated, and the interference enhancement effect is experimentally confirmed. The interference enhancement effect is conducive to the practical application of a single Airyprime beam.

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.s beam width, the divergence angle, and the beam propagation factor of the FEA beam are derived in the output plane of Airy transformation, respectively. The effects of the Airy control parameters on the intensity distribution, the centroid, the r.m.s beam width, and the beam propagation factor are examined in detail through numerical examples. Unlike the Airy beam, the FEA beam upon free space propagation will be associated with an additional Airy mode, and the beam pattern of the FEA beams propagating in free space will evolve into a solid beam spot with two tails along two transverse directions, as well as the the intensity of main lobe of the FEA beam decays much slowly during free space propagation. Further, an experiment setup is established to generate the FEA beam via Airy transformation of four mixed elegant Hermite-Gaussian modes. The propagation characteristics such as the intensity distribution, the r.m.s beam width and the beam propagation factor are measured. The experimental results agree well with the theoretical predictions. Our study affords an effective and novel approach to generate the FEA beam, and is beneficial to expand the potential application of the FEA beam.

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. The physical mechanism of the abruptly autofocusing of the CADBs is interpreted by mimicking the Fresnel zone plate lens. Here, the abruptly autofocusing ability is described by a ratio K = Ifm/I_0m where Ifm and I_0m correspond to the maximum intensities in the focal and the source planes, respectively. As an example, the K-value of the circular Airyprime beam (CAPB, the first-order Airy derivative beam) is about 7 times of that of the CAB. In addition, the CAPB have narrower FWHM (full width at half maxima) in the focus position than the CAB, and the focal spot size of the CAPB is smaller than that of the CAB. Furthermore, we establish an optical system involving a phase-only spatial light modulator to generate the CAPB and measure its autofocusing characteristics experimentally. The measured K-value is about 9.4 percentage error between theory and experiment owing to the imperfection generation of the CAPB. The proposed generalized CADBs will find applications in biomedical treatment, optical manipulation and so on.