Caustics and catastrophes in strong-field physics $-$ Picard-Lefschetz theory as a universal approach to saddle-point methods in attosecond science

Ultrashort laser pulses on the attosecond timescale are typically achieved via high-order harmonic generation (HHG), a nonlinear process in which atoms interact with intense light fields to emit a broad spectrum of harmonics. HHG is commonly described in terms of a `quantum orbits' model based on se