Flexible autofocusing properties of ring Pearcey beams by means of a cross phase

Transmission mode transformation of rotating controllable beams induced by the cross phase

In this paper, complex-variable sine-Gaussian cross-phase (CVSGCP) beams are proposed, and the transmission dynamics properties of the CVSGCP beams in strongly nonlocal nonlinear media are investigated. CVSGCP beams can produce a variety of mode transformation characteristics during transmission. The roles of parameters in the sine and cross-phase terms of the initial light field expression in the evolution of light intensity modes, phase, and beam width are analyzed in detail, and it is proved that the effect of cross phase is to cause the beams to rotate. The control of different modes can be achieved by selecting suitable parameters, which have certain advantages in the practical application of CVSGCP beams. CVSGCP beams can be regarded as generalized high-order breathers because light intensity modes and beam width show periodic oscillation distribution during transmission. The typical evolution characteristics of the CVSGCP beams are verified by numerical simulation. Strongly nonlocal nonlinear optical media can be mathematically equivalent to a variety of optical systems, such as gradient index potential wells and resonant potential wells, so the conclusions in this paper can also be extended to these equivalent optical systems.

Propagation dynamics of self-accelerating second-order Hermite complex-variable-function Gaussian wave packets in a harmonic potential

This paper investigates the evolutionary dynamics of self-accelerating second-order Hermite complex-variable-function Gaussian (SSHCG) wave packets in a harmonic potential. The periodic variation of the wave packets is discussed via theoretical analysis and numerical simulation. The control variables method is applied to manipulate the distribution factor, cross-phase factor, potential depth, and chirp parameter, enabling the realization of unique propagation dynamics. In three-dimensional models, the SSHCG wave packets exhibit rotational states, featuring butterfly shape, three peaks shape, two polarity shape, elliptical shape, and ring-shaped double-vortex structures. Furthermore, the energy flow and the angular momentum of the wave packets are investigated. Additionally, the performance of the radiation force on a Rayleigh dielectric particle is studied. This investigation results in the emergence of distinct SSHCG wave packet propagation dynamics, and potential applications in optical communications and optical trapping are presented.

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.

Polarization state evolution of a twisted vector optical field in a strongly nonlocal nonlinear medium

The evolution of the state of polarization (SoP) in a twisted vector optical field (TVOF) with an astigmatic phase in a strongly nonlocal nonlinear medium (SNNM) is investigated. The effect of an astigmatic phase on the propagation dynamics of the twisted scalar optical field (TSOF) and TVOF during propagation in the SNNM leads to reciprocally periodical evolutions of stretch and shrink, accompanied by the reciprocal transformation of the beam shape between an initial circle shape and threadiness distribution. The TSOF and TVOF rotate along the propagation axis if the beams are anisotropic. In particular, the reciprocal conversions between the linear and circular polarizations occur in the TVOF during propagation, which are strongly related to the initial powers, twisting strength coefficients, and initial beam reshapes. The numerical results confirm the analytical predictions by the moment method for the dynamics of the TSOF and TVOF during propagation in a SNNM. The underlying physics for the polarization evolution of a TVOF in a SNNM are discussed in detail.

On z-coherence of Schell-model sources carrying a prescribed astigmatic phase

A simple expression for the correlations of beams radiated by Schell-model sources carrying a prescribed astigmatic phase (cross phase) in 3D space is derived. The z-coherence of such sources upon free-space propagation is investigated in detail. It is demonstrated that the z-coherence does not decrease to zero with an increasing separation of two axial points. Our results show that the initial cross phase, coherence, and correlation state of such sources affect the distribution of the z-coherence. Furthermore, the cross phase plays a role in maintaining z-coherence, which will be useful in applications where high z-coherence is required.

Structurally stable beams in the turbulent atmosphere: dark and antidark beams on incoherent background [Invited]

We demonstrate analytically and verify numerically that recently discovered, and experimentally realized, partially coherent dark and antidark beams are structurally stable on propagation in a statistically homogeneous, isotropic random medium, such as the turbulent atmosphere. The dark/antidark beams defy diffraction in free space, and they manifest themselves as dark/bright notches/bumps against an incoherent background. The structure of a bump/notch remains invariant on propagation of the beam through the random medium, while the peak amplitude of the bump/notch decays with the propagation distance in the medium at a rate dependent on the strength of the medium turbulence. We also evaluate numerically the scintillation index of such beams and show that it is significantly lower than that of generic, low-coherence Gaussian Schell-model beams. The combination of structural stability and low scintillations makes partially coherent dark/antidark beams very promising candidates for information transfer and optical communications through atmospheric turbulence.

Multi-focus autofocusing circular hyperbolic umbilic beams

We propose and demonstrate a type of multi-focus autofocusing beams, circular hyperbolic umbilic beams (CHUBs), based on the double-active variable caustics in catastrophe theory. The mathematical form is more general compared to circular Airy, Pearcey and swallowtail beams. The CHUBs can generate multi-focus at its optical axis, while the on-axis intensity fluctuates up to two orders of magnitude that of the maximum intensity in the initial plane. Using the concept of topographic prominence, we quantify the autofocusing ability. We construct the criteria for selecting the effective foci, and then explore the influence of related parameters. Our findings suggest that the CHUBs could be a suitable tool for multi-particle manipulation, optical tweezers, optical lattices and related applications.

Polarization and coherence properties in self-healing propagation of a partially coherent radially polarized twisted beam

With the help of generalized Huygens-Fresnel integral, an analytical expression for the self-healing of a partially coherent radially polarized twisted (PCRPT) beam is derived. The coherence and polarization properties of the PCRPT beam in self-healing propagation are studied in detail. It shows that the existence of the twist phase is a double-edged sword for the self-healing properties of the beam. With the increase of the twist factor, the self-healing ability of beam intensity distribution decreases. However, the anti-disturbance performance of beam polarization improves at the same time. Besides, the polarization and coherence distribution of the beam are proved that own a slight self-healing ability when the obstacle is small. Our results will be helpful to the fields of optical tweezers, microscopy, optical communication, and so on.

Generation and control of tornado waves by means of ring swallowtail vortex beams

Tornado waves (ToWs), which refer to a light that accelerates and twists over both the radial and the angular directions, have gained a great deal of interest since the concept was introduced by Brimis et al [Opt. Lett.45, 280 (2020)10.1364/OL.45.000280]. In this paper, we superimpose two pairs of ring swallowtail vortex beams (RSVBs) to generate ToWs and we call them tornado swallowtail waves (ToSWs). Each pair consists of RSVBs while carrying orbital angular momentum of opposite helicity and slightly different with the radius of the main ring of RSVBs. The waves spiral forward and reveal intensity maxima, exhibiting a tornado-like intensity profile during propagation. Meanwhile, the angular acceleration of the ToSWs is illustrated via tracing the angular position of the high-intensity main lobes. It is found that ToSWs present very high values of angular acceleration. Compared with typical tornado waves, ToSWs are more diverse and tunable, giving a new degree of freedom to tailor the propagation dynamics due to the flexibility of the swallowtail diffraction catastrophe. In addition, we confirm such waves experimentally and the results match well with the numerical ones. Also, we demonstrate the ability of optical manipulation of ToSWs for the first time in that they allow for particles not only to be trapped but also to be rotated. Finally, we analyze the poynting vectors and power exchange of ToSWs to demonstrate convincingly the physical mechanism.

Dual-focusing behavior of a one-dimensional quadratically chirped Pearcey-Gaussian beam

In this paper, we provide analytical solutions describing the dynamic behavior of the Pearcey-Gaussian beams propagating in free space. Based on the analytical solutions, explicit expressions governing the focusing distances of the Pearcey-Gaussian beams are found and verified by numerical simulations. For the linearly chirped Pearcey-Gaussian beam, it exhibits a uni-focusing behavior during propagation. Particularly, the focusing distance is independent on the linear chirp parameter and remains z_f = 2 unchanged. Of particular interest is that the quadratically chirped Pearcey-Gaussian beam focuses twice when the quadratic chirp parameter β < 0. The first and the second focusing distances are determined by z_f1 = 2/(1 - 4β) and z_f2 = -1/(2β), respectively. Furthermore, we numerically investigate the peak powers at the different focusing positions and find that as β increases, the peak powers at z_f1 and z_f2 linearly decrease. It is expected that the characteristics can be used for manipulating the focusing distances and the peak powers to generate an optical beam with high peak power by adjusting the chirp parameter β.