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Diffstat (limited to 'source/know/concept/self-steepening')
| -rw-r--r-- | source/know/concept/self-steepening/index.md | 8 |
1 files changed, 5 insertions, 3 deletions
diff --git a/source/know/concept/self-steepening/index.md b/source/know/concept/self-steepening/index.md index 409f6c9..015aa40 100644 --- a/source/know/concept/self-steepening/index.md +++ b/source/know/concept/self-steepening/index.md @@ -97,7 +97,9 @@ $$E \equiv \int_{-\infty}^\infty |A|^2 \dd{t}$$ anymore, which is often used to quantify simulation errors. Fortunately, another value can then be used instead: it can be shown that the "photon number" $$N$$ -is still conserved, defined as: +is still conserved, defined like so, +where $$\omega$$ is the absolute frequency +(as opposed to the relative frequency $$\Omega$$): $$\begin{aligned} \boxed{ @@ -193,9 +195,9 @@ pulls the pulse apart before a shock can occur. The early steepening is observable though. A simulation of self-steepening without dispersion is illustrated below -for the following initial power distribution, +for the following Gaussian power distribution, with $$T_0 = 25\:\mathrm{fs}$$, $$P_0 = 3\:\mathrm{kW}$$, -$$\beta_2 = 0$$, $$\gamma = 0.1/\mathrm{W}/\mathrm{m}$$, +$$\beta_2 = 0$$, $$\gamma_0 = 0.1/\mathrm{W}/\mathrm{m}$$, and a vacuum carrier wavelength $$\lambda_0 \approx 73\:\mathrm{nm}$$ (the latter determined by the simulation's resolution settings): |