A quantitative measure of carrier shocking

I propose a definition for a "shocking coefficient" $S$ intended to make determinations of the degree of waveform shocking, and comparisons thereof, more quantitative. This means we can avoid having to make ad hoc judgements on the basis of the visual comparison of wave profiles.Comment: 5 pages, 6 figure

Dispersion in time and space: what propagating optical pulses in time (& not space) forces us to confront

I derive a temporally propagated uni-directional optical pulse equation valid in the few cycle limit. Temporal propagation is advantageous because it naturally preserves causality, unlike the competing spatially propagated models. The exact coupled bi-directional equations that this approach generates can be efficiently approximated down to a uni-directional form in cases where an optical pulse changes little over one optical cycle. They also permit a direct term-to-term comparison of the exact bi-directional theory with its corresponding approximate uni-directional theory. Notably, temporal propagation handles dispersion in a different way, and this difference serves to highlight existing approximations inherent in spatially propagated treatments of dispersion. Accordingly, I emphasise the need for future work in clarifying the limitations of the dispersion conversion required by these types of approaches; since the only alternative in the few cycle limit may be to resort to the much more computationally intensive full Maxwell equation solvers.Comment: v3: updates and clarifications. arXiv admin note: text overlap with arXiv:0810.568