Ultrafast pulse dynamics in a transport-compatible phase-space representation

Ultrafast laser pulses possess coupled spatial, temporal, spectral and directional structure that is conventionally described within electromagnetic-field formulations. Transport-oriented methods instead operate on rays, samples or distribution functions and require a positive representation that can be evolved according to optical transport and interaction rules within explicit geometries. Accordingly, we develop an energy-normalized, transport-compatible phase-space representation of an ultrafast laser pulse in terms of transverse position, local pulse time, propagation direction and optical frequency. The framework represents the phase-space distribution by energy-weighted samples, evolves them under optical transport rules and reconstructs selected envelope-level spatial, temporal and spectral observables from the resulting ensemble. The representation–transport–reconstruction procedure is first benchmarked for free-space propagation of a transform-limited Gaussian reference pulse. Analytical predictions and numerical reconstructions agree for the pulse spreading, directional evolution, radial spectral redistribution and geometrical path-delay broadening. ... mehrThe applicability of the framework to an explicit optical geometry is then demonstrated by numerically transporting the pulse through a dispersive lens. The resulting ensemble captures the principal near-focus spatiotemporal concentration, post-focal expansion and accompanying evolution of the pulse’s spatially resolved spectral structure. The framework also reproduces compensation of an initial linear chirp and temporal compression in an ideal four-grating compressor. These results show that a positive, energy-weighted transport ensemble can reproduce selected free-space, near-focus and pulse-compression dynamics of an ultrafast pulse while preserving access to its local energy, frequency, direction and arrival-time distributions. The formulation is intended to support the incorporation of envelope-level ultrafast pulse structure into ray-based, Monte Carlo and distribution-based transport frameworks.