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Non-Linear Radiation Forces and Confinement of Neutral Particles into the Pulse Envelope

A pre-proof study of Optik explains analytical formulas of the non-linear radiation forces and potential densities resulting from a laser pulse traveling in a dielectric medium. The effective averaged longitudinal real force of the laser pulse can be determined by these analytical expressions.

Study: Radiation Forces and Confinement of Neutral Particles Into the Pulse Envelope. New Regime of Collision Ionization. Image Credit: Micha Weber/

The non-linear radiation force is inversely proportional to the time duration of the pulse and proportionate to the starting pulse energy. The forces strength increases in the femtosecond range, allowing neutral particles to be contained within the pulse envelope and translated with the group velocity in gases.

Transverse optical forces with continuous-wave laser beams manipulate non-contact micro-scale objects. Many unexpected physical effects connected to the influence of the Poynting vector on the longitudinal part of the optical force can be detected using pulse-mode lasers instead of continuous wave lasers.

Significance of Non-Linear Polarization

Laser pulses operating in the continuous wave (CW) regime can capture particles. The analytical equation of the non-linear radiation force acting on a single particle is proportional to the transverse gradient of the square of the electrical field and is determined using the dipole approximation.

Extra terms related to the Poynting vector and energy flow are needed when the CW regime is replaced by optical pulse propagation. Forces influence the polarization of atoms and molecules, and non-linear polarization plays a vital role in determining these forces.

Investigation of Analytical Equations of the Non-Linear Radiation Force

A laser pulse in a continuous dielectric medium applies imprecise radiation forces on neutral particles with linear and nonlinear polarization. Kovachev et al. obtained and analyzed the analytical equations of the longitudinal non-linear radiation force density.

Femtosecond optical pulses propagating in the diffraction-free regime with power values below the nonlinear wave-guiding regime can be used to confine neutral atoms or molecules in the air. These regimes have starting pulse energies ranging from 10 nJ to 1-2 mJ, with pulse durations of around 100 fs and widths of 1 to 10 mm. The impact energies range from 12 to 24 GeV and are sufficiently more significant than the energy required to ionize neutral atoms.

The researchers demonstrated the effects of nonlinear polarization on radiation force. The real force at the level of the pulse width is inversely proportional to the pulse time duration and the resultant force density is directly proportional to the first derivative of the pulse time envelope. This explains why the force to vanish in the CW regime traps particles into the pulse envelope in the femtosecond zone. The high density of trapped particles in the pulse envelope increases the chances of collision with free air molecules and atoms.

Fundamental Experimental and Theoretical Studies on Non-Linear Radiation Forces

The fundamental experimental and theoretical studies on non-linear radiation forces focus on investigating the radiation forces produced by individual Rayleigh dielectric particle interactions with laser beams and pulses.

This research investigates the effects of the radiation force on an ensemble of neutral particles and a continuous medium (air). The method converts the individual force applied on an atom into a force per volume called density force.

The non-stationary and non-linear nature of the optical response of dielectric media of laser pulses makes it possible to get an analytical expression for the longitudinal density force and density potential of a Gaussian laser pulse traveling in a gaseous medium. Theoretical and experimental studies for the diffraction-free regime and nonlinear wave-guiding propagation of ultra-short femtosecond laser pulses assist the integration of these densities using the first order of dispersion approximation in optics. As a result, a useful longitudinal potential and force acting at the pulse width level in the media are obtained.

Research Findings

The length of the laser pulse affects the longitudinal radiation force. The force strength increases as the laser pulse duration decrease. One mJ of energy from a Gaussian laser pulse has a longitudinal potential in the air that is twelve orders of magnitude larger than the Boltzmann energy of free particles. The proven regulated conditions under which the neutral particles can be contained in the pulse envelope and flow at the same speed as the group velocity are significant findings of this research.

The chance of collision with free air molecules and atoms increases when the trapped particles in the pulse have a high density. The collisions can ionize the neutral atoms at energies between 12 and 24 GeV. As a result, under strong femtosecond pulse propagation in air, a novel sort of collision ionization can be observed.

This novel type of collision ionization differs from multi-photon and tunnel ionization. In collision ionization, all processes are considered when determining pulse width. Due to collisions between trapped and free particles, the new ionization regime produces a single conical emission of charged particles.


Kovachev, L. M. (2022). Radiation Forces and Confinement of Neutral Particles Into the Pulse Envelope. New Regime of Collision Ionization. Optik, 169943.

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Usman Ahmed

Written by

Usman Ahmed

Usman holds a master's degree in Material Science and Engineering from Xian Jiaotong University, China. He worked on various research projects involving Aerospace Materials, Nanocomposite coatings, Solar Cells, and Nano-technology during his studies. He has been working as a freelance Material Engineering consultant since graduating. He has also published high-quality research papers in international journals with a high impact factor. He enjoys reading books, watching movies, and playing football in his spare time.


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