3 Beam propagation method

Beam propagation method (BPM) is a semi-analytical technique that solves the paraxial approximation of the wave equation in either the time or the frequency domain using a stepwise propagation along a predefined direction. BPM can model the evolution of laser beams in optical systems, such as waveguides, lenses, gratings, and fibers, and can account for linear, nonlinear, and dispersive effects. BPM has some benefits over FDTD and FEM, such as the reduced dimensionality, the simplicity of implementation, and the low computational cost. However, BPM also has some limitations, such as the validity of the paraxial assumption, the restriction to a single propagation direction, and the inability to handle reflections and scattering.

4 Particle-in-cell method

Particle-in-cell (PIC) method is a hybrid technique that combines the FDTD method for the electromagnetic fields with the kinetic description of the charged particles. PIC can model the dynamics of laser-plasma interactions, such as ionization, acceleration, heating, and radiation. PIC can capture the nonlinear and relativistic effects that occur in high-intensity laser-matter interactions, and can simulate both collective and individual particle behaviors. PIC has some advantages over other methods, such as the flexibility of the particle representation, the scalability of the parallelization, and the compatibility with FDTD. However, PIC also has some drawbacks, such as the need for high resolution and stability conditions, the occurrence of numerical noise and instabilities, and the complexity of the implementation and analysis.

5 Quantum mechanical methods

Quantum mechanical methods are based on the solution of the Schrödinger equation or its variants for the electronic states of the atoms and molecules involved in the laser-matter interaction. Quantum mechanical methods can model the processes of absorption, emission, scattering, and ionization at the atomic and molecular level, and can provide detailed information on the energy levels, transition probabilities, and spectra. Quantum mechanical methods have some strengths over other methods, such as the accuracy of the physical description, the applicability to different regimes of laser intensity and wavelength, and the availability of software packages and databases. However, quantum mechanical methods also have some challenges, such as the high computational cost and memory demand, the difficulty of coupling with the electromagnetic fields and the macroscopic matter, and the uncertainty of the approximations and parameters.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?