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authorPrefetch2024-10-15 18:08:29 +0200
committerPrefetch2024-10-15 18:08:29 +0200
commit8b8caf2467a738c0b0ccac32163d426ffab2cbd8 (patch)
tree07493748e5d4fa5539b6154c060891d3f32ff86a /source/know/concept/self-steepening
parent270adb174e9f536f408296ab0141478666dd1690 (diff)
Improve knowledge base
Diffstat (limited to 'source/know/concept/self-steepening')
-rw-r--r--source/know/concept/self-steepening/index.md8
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):