Finite difference methods for stationary and time-dependent X-ray propagation.

Area of Science:

• Physics
• Optics
• Computational Science

Background:

• Accurate simulation of ultra-short pulse propagation is crucial for understanding light-matter interactions.
• Existing methods may not fully capture dispersion effects in novel optical elements like X-ray waveguides.

Purpose of the Study:

• To generalize finite-difference (FD) simulations for time-dependent field propagation.
• To investigate ultra-short X-ray pulse propagation and dispersion in X-ray waveguides.

Main Methods:

• Derivation of a generalized stationary paraxial wave equation.
• Efficient FD implementation for stationary and time-dependent field propagation using spectral decomposition.
• Validation against analytical solutions for tractable propagation problems.

Main Results:

• Demonstrated the non-dispersive nature of X-ray waveguides for sub-femtosecond pulses.
• Identified pronounced dispersion effects only when resonant absorption near X-ray edges is considered.
• Validated the numerical framework through comparison with analytical theory.

Conclusions:

• The generalized FD simulation framework accurately models ultra-short X-ray pulse propagation.
• X-ray waveguides are effective non-dispersive optical elements for a wide range of pulse widths.
• Resonant absorption is the primary source of dispersion in X-ray waveguides for ultrashort pulses.