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

Abstract

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.

Dynamic Optical Vortex Trajectory Guided by the Symmetric Pearcey Gaussian Vortex Beam in the Uniformly Moving Parabolic Potential

“…Making a comparison between the third term on the left side of Equation ( 4) and the third term on the left side of Equation (3) in ref. [23], the major difference is that Equation (4) contains d 2 m(Z)∕dZ 2 . We consider that d 2 m(Z)∕dZ 2 indicates the acceleration of the dynamic potential to affect the propagation trajectory in this transformed frame.…”

“…It is worth noting that Equation (4) shares the same mathematical form with Equation (3) in ref. [23] when d 2 m(Z)∕dZ 2 = 0, which means the acceleration of the dynamic potential is zero, that is, the form of the static parabolic potential. However, it is difficult to find the solution of Equation ( 4) directly.…”

“…The uniformly moving parabolic potential, one kind of the dynamic potential, implies the potential will change uniformly with the enhancement of the propagation distance and affect the evolution of the optical beam, acting as an "external force" to stretch or suppress the beam during propagation. [22,23] In contrast to the beam propagates in the static potential, [24,25] the force from the dynamic potential is more flexible, and more parameters can control the accelerating trajectory. That means the beam can follow a pre-designed trajectory by configuring the refractive index of the medium.…”

Controlling the Trajectory of Swallowtail Gaussian Beams in Dynamic Parabolic Potentials

“…In the paraxial approximation, the propagation of the beams in the dynamic parabolic potential is described by the (1+1)D dimensionless Schrödinger equation [ 23,24 ] $$$$\begin{equation} 2i \frac{\partial \varphi (x, z)}{\partial z}+\frac{\partial ^2 \varphi (x, z)}{\partial x^2}-\alpha ^2[x-f(z)]^2 \varphi (x, z)=0 \end{equation}$$$$where φ is the beam envelope, α is the parabolic potential depth, x and z are the normalized transverse coordinate and propagation distance respectively. Assuming a medium with a parabolic potential, the refractive index can be expressed as $$n^{2}(r)=n_{0}^{2}(1-\alpha ^{2} r^{2})$$, where $$\alpha =(n_{0}^{2}-n_{1}^{2})^{1 / 2} /(n_{0} r_{1})$$.…”

“…[15] The photonic potential refers to an external potential that can effectively modify the dynamic behavior of the beam, which is based on the refractive index distribution of the medium. Various potential models, such as linear, [16][17][18][19][20] parabolic, [20][21][22] and general dynamic potentials [23,24] have been proposed by researchers to manipulate the acceleration trajectory of the beam. Regarding the parabolic potential, researchers have examined the propagation dynamics of different types of beams, [25][26][27][28] revealing some unique and intriguing characteristics during the propagation process, such as periodic inversion and focusing, as well as self-induced Fourier transformation.…”