Propagation of Cosh-Airy and Cos-Airy Beams in Parabolic Potential

Autofocus properties of astigmatic chirped symmetric Pearcey Gaussian vortex beams in the fractional Schrödinger equation with parabolic potential

Described by the fractional Schrödinger equation (FSE) with the parabolic potential, the periodic evolution of the astigmatic chirped symmetric Pearcey Gaussian vortex beams (SPGVBs) is exhibited numerically and some interesting behaviors are found. The beams show stable oscillation and autofocus effect periodically during the propagation for a larger Lévy index (0 < α ≤ 2). With the augment of the α, the focal intensity is enhanced and the focal length becomes shorter when 0 < α ≤ 1. However, for a larger α, the autofocusing effect gets weaker, and the focal length monotonously reduces, when 1 < α ≤ 2. Moreover, the symmetry of the intensity distribution, the shape of the light spot and the focal length of the beams can be controlled by the second-order chirped factor, the potential depth, as well as the order of the topological charge. Finally, the Poynting vector and the angular momentum of the beams prove the autofocusing and diffraction behaviors. These unique properties open more opportunities of developing applications to optical switch and optical manipulation.

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.

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.

Accelerating trajectory manipulation of symmetric Pearcey Gaussian beam in a uniformly moving parabolic potential

We derive analytical solutions that describe the one-dimensional displaced and chirped symmetric Pearcey Gaussian beam in a uniformly moving parabolic potential. The multiple effective manipulations of the beam, which are originated from the diverse configurations of the dynamic parabolic potential, are demonstrated. On the whole, the accelerating trajectory can transform into a linear superposition form of the oblique straight line and the simple harmonic motion. Meanwhile, we discuss the further modulation of the accelerating trajectory characteristics such as slope, amplitude and phase shift. Additionally, the extension into a two-dimensional scenario is also proposed. Our results theoretically improve the practical value of the Pearcey beam, and lead to potential applications in trajectory manipulation and particle manipulation.

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

Analytical expression of the Airy transform of an arbitrary Hermite-Gaussian beam is derived. The optical field in the x-direction of the Airy transform of Hermite-Gaussian beams with transverse mode number m is the sum of the zero-order derivative to mth-order derivative of the Airy function with different weight coefficients. The analytical expressions of the centre of gravity and the beam spot size of an arbitrary Hermite-Gaussian beam passing through an Airy transform optical system are also presented, which are very concise. Because the Airy transform of a Hermite-Gaussian beam has the same evolution law in the two transverse directions, only the effects of the control parameter α and the transverse mode number m on the normalized intensity distribution, the centre of gravity, and the beam spot size in the x-direction are theoretically investigated, respectively. The Airy transform of Hermite-Gaussian beams is also realized in the experiment. The influence of the control parameters on the normalized intensity distribution, the centre of gravity, and the beam spot size is experimentally investigated, respectively. The experimental results are consistent with the theoretical simulation results. When Hermite-Gaussian beams pass through an Airy transform optical system, the number of lobes may change, and the importance of lobes with the same status in the input plane may become different. By using the Airy transform of Hermite-Gaussian beams, the practical applications of Hermite-Gaussian beams can be extended.

Airy transform of Laguerre-Gaussian beams

Airy transform of Laguerre-Gaussian (LG) beams is investigated. As typical examples, the analytic expressions for the Airy transform of LG₀₁, LG₀₂, LG₁₁, and LG₁₂ modes are derived, which are special optical beams including the Airy and Airyprime functions. Based on these analytical expressions, the Airy transform of LG₀₁, LG₀₂, LG₁₁, and LG₁₂ modes are numerically and experimentally investigated, respectively. The effects of the control parameters α and β on the normalized intensity distribution of a Laguerre-Gaussian beam passing through Airy transform optical systems are investigated, respectively. It is found that the signs of the control parameters only affect the location of the beam spot, while the sizes of the control parameters will affect the characteristics of the beam spot. When the absolute values of the control parameters α and β decrease, the number of the side lobes in the beam spot, the beam spot size, and the Airy feature decrease, while the Laguerre-Gaussian characteristic is strengthened. By altering the control parameters α and β, the performance of these special optical beams is diversified. The experimental results are consistent with the theoretical simulations. The Airy transform of other Laguerre-Gaussian beams can be investigated in the same way. The properties of the Airy transform of Laguerre-Gaussian beams are well demonstrated. This research provides another approach to obtain special optical beams and expands the application of Laguerre-Gaussian beams.