Topology-Constrained Saddle-Point Reconstruction of Strong-Field Photoelectron Momentum Spectra Using Physics-Informed Neural Networks
Abstract
In strong-field ionization, complex-time saddle points govern electron ionization instant and quantum-orbit interference patterns. Neverthless, not all solutions to the saddle-point equation carry physical contributions. And saddle coalescence can also invalidate the isolated-saddle approximation. Within the strong-field-approximation framework, we propose a topology-constrained approach to reconstruct photoelectron momentum spectra. A physics-informed neural network is employed to produce candidate roots, which are subsequently refined via a Newton-type iteration. Picard–Lefschetz upward flows are adopted to pick out physically connected saddles, while local coherent continuation for pole-saddle pairs handles saddle-coalescence regions. A topological selector is defined by the non-zero support of intersection numbers to filter unphysical solutions. We test our method on hydrogen atoms subjected to six-cycle elliptically polarized laser fields and compare reconstructed spectra against direct numerical strong-field-approximation results. For 300 nm and 500 nm driving fields, the normalized relative L2 errors on the linear probability scale reach 3.793% and 3.520%, respectively.The topological selection eliminates disconnected non-physical contributions, and local continuation recovers quantum cancellation effects near saddle coalescence. Our method improves the physical interpretability of saddle-based spectrum reconstruction under strong-field approximation and is promising…
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