Limits of the uni-directional pulse propagation approximation

Abstract

I apply the method of characteristics to both bi-directional and uni-directional pulse propagation in dispersionless media containing nonlinearity of arbitrary order. The differing analytic predictions for the shocking distance quantify the effects of the uni-directional approximation used in many pulse propagation models. Results from numerical simulations support the theoretical predictions, and reveal the nature of the coupling between forward and backward waves.

6 pages, 6 figures; this version contains an additional appendix not present in the published version

References in corpus (6)

• Few cycle pulse propagation
• Theory of directional pulse propagation
• Forward-backward equations for nonlinear propagation in axially-invariant optical systems
• Optical carrier wave shocking: detection and dispersion
• Pulse propagation methods in nonlinear optics
• Theory of directional pulse propagation: detailed calculations

Cited by in corpus (11)

• Nonlinear propagation of light in structured media: generalized unidirectional pulse propagation equations
• Four Poynting Theorems
• A uni-directional optical pulse propagation equation for materials with both electric and magnetic responses
• Carrier-wave steepened pulses and gradient-gated high-order harmonic generation using linear ramp waveforms
• The refractive index and wave vector in passive or active media
• Carrier field shock formation of long wavelength femtosecond pulses in dispersive media
• Dispersion in time and space: what propagating optical pulses in time (& not space) forces us to confront
• Super-resonant radiation stimulated by high-harmonics
• Acoustic waves: should they be propagated forward in time, or forward in space?
• A quantitative measure of carrier shocking
• Ultrashort opposite directed pulses dynamics