Analytical propagation expression of an Airy beam in uniaxial crystals orthogonal to the optical axis is derived. The ballistic dynamics of an Airy beam in uniaxial crystals is also investigated. The Airy beam propagating in uniaxial crystals orthogonal to the optical axis mainly depends on the ratio of the extraordinary refractive index to the ordinary refractive index. As an example, the propagation of an Airy beam in the positive uniaxial crystals orthogonal to the optical axis is demonstrated. The acceleration of an Airy beam in the transversal direction along the optical axis is more rapidly than that in the other transversal direction. With increasing the ratio of the extraordinary refractive index to the ordinary refractive index, the acceleration of the Airy beam in the transversal direction along the optical axis speeds up and the acceleration of the Airy beam in the other transversal direction slows down. The Airy beam propagating in uniaxial crystals orthogonal to the optical axis follows a ballistic trajectory. The effective beam size of the Airy beam in the transversal direction along the optical axis is always larger than that in the other transversal direction.

Based on the vector angular spectrum of the electromagnetic beam and the method of stationary phase, the analytical vectorial structure of the Laguerre–Gaussian beam has been presented in the far field. According to the analytical electromagnetic representations of the TE and TM terms, the energy flux distributions of the TE term, the TM term, and the whole beam are investigated in the far field, respectively. The formulas obtained are applicable not only to the paraxial case, but also to the nonparaxial case. The physical pictures of Laguerre–Gaussian beams are well illustrated from the vectorial structure, which may provide a new approach to manipulate laser beams.

Cavitation, characterized by formation of vapor bubbles in a low-pressure or high-temperature region of a liquid, is often destructive, but it can be harnessed for actuators and robots. We exploit cavitation to accumulate substantial energy in superheated liquids by suppressing its immediate release until reaching a stability limit. The energetic, unstable bubbles collapse violently, producing a burst of high power and force that initiates motion. Notably, a millimeter-scale device launched by cavitation can jump to a height of 1.5 meters—reaching a 12 meters per second (m/s) peak velocity, a 7.14 × 10 ⁴ m/s ² acceleration, and a 0.64% energy efficiency—and can also swim on water at 12 centimeters per second. Cavitation-based launching works with a broad range of device materials, liquid media, stimuli, and operational environments.

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 = I_fm/I_0m where I_fm 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.

Lorentz–Gauss beams are introduced to describe certain laser sources that produce highly divergent beams. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz–Gauss beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz–Gauss beam passing through an FRFT system has been derived. By using the derived expression, the properties of a Lorentz–Gauss beam in the FRFT plane are graphically illustrated with numerical examples.

The propagation of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere has been investigated. The analytical expressions for the average intensity and the degree of the polarization of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system are derived in turbulent atmosphere, respectively. The average intensity distribution and the degree of the polarization of a partially coherent hollow vortex Gaussian beam in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters, the topological charge, the transverse coherent lengths, and the structure constant of the atmospheric turbulence on the propagation of a partially coherent hollow vortex Gaussian beam in turbulent atmosphere are also examined in detail. This research is beneficial to the practical applications in free-space optical communications and the remote sensing of the dark hollow beams.