Nonstationary polarization optical forces, considering the influence of dispersion and diffraction

In the present work, the dynamic properties of an attractive longitudinal optical force and the applied potential, due to diffraction and dispersion of ultrashort laser pulses, propagating in air at distances of several diffraction and dispersion lengths, are presented. The results are based on an analytical solution of the linear 3D+1 paraxial amplitude equation and its application to the evolution in time of the longitudinal optical force. The current research provides valuable guidance for the development and creation of neutral particle laser accelerators with potential applications in the field of laser driven nuclear fusion.

💡 Research Summary

The paper investigates the dynamic behavior of an attractive longitudinal optical force and its associated potential that arise when an ultrashort laser pulse propagates through air, taking into account both diffraction and dispersion over distances of several diffraction and dispersion lengths. Starting from the linear 3 D + 1 paraxial amplitude equation
(i2k_{0}v_{g}\partial_{t}A = \Delta_{\perp}A - \beta\partial_{\xi}^{2}A)
with (\xi = z - v_{g}t) and (\beta = z_{\text{dis}}/z_{\text{dif}}), the authors assume an initial Gaussian pulse and solve the equation analytically via a three‑dimensional Fourier transform. The exact solution in real space is expressed as a Gaussian whose transverse and longitudinal widths evolve as
(1 - i v_{g}t/z_{\text{dif}}) and (1 + i v_{g}t/z_{\text{dis}}) respectively, reflecting the combined effects of diffraction and second‑order dispersion. From the intensity (|A|^{2}) the longitudinal polarization force density is derived as
(F_{\xi}=2n_{0}\chi^{(1)}v_{g}c,\partial_{\xi}|A|^{2}).
Because the derivative of the intensity with respect to (\xi) carries a negative sign, the force is negative: the front part of the pulse pulls neutral particles toward the pulse centre, while the trailing part also pushes them in the same direction, resulting in an overall attractive potential. The potential energy is obtained by integrating the force and reads
(U(x,y,\xi,t) = -2n_{0}\chi^{(1)}v_{g}c,A_{0}^{2}\frac{1}{