From bcae81336764eb6c4cdf0f91e2fe632b625dd8b2 Mon Sep 17 00:00:00 2001 From: Prefetch Date: Sun, 23 Oct 2022 22:18:11 +0200 Subject: Optimize and improve naming of all images in knowledge base --- source/know/concept/step-index-fiber/index.md | 10 +++------- 1 file changed, 3 insertions(+), 7 deletions(-) (limited to 'source/know/concept/step-index-fiber/index.md') diff --git a/source/know/concept/step-index-fiber/index.md b/source/know/concept/step-index-fiber/index.md index dd83334..c0c95d1 100644 --- a/source/know/concept/step-index-fiber/index.md +++ b/source/know/concept/step-index-fiber/index.md @@ -240,14 +240,12 @@ $$\begin{aligned} \end{cases} \end{aligned}$$ - - - +{% include image.html file="bessel-full.png" width="100%" alt="First few solutions to Bessel's equation" %} Looking at these solutions with our constraints for $$R_o$$ in mind, we see that for $$\mu > 0$$ none of the solutions decay *monotonically* to zero, so we must have $$\mu \le 0$$ in the cladding. -Of the remaining candidates, $$\ln\!(r)$$, $$r^\ell$$ and $$I_\ell(\rho)$$ do not decay at all, +Of the remaining candidates, $$\ln(r)$$, $$r^\ell$$ and $$I_\ell(\rho)$$ do not decay at all, leading to the following $$R_o$$: $$\begin{aligned} @@ -394,9 +392,7 @@ An example graphical solution of the transcendental equation is illustrated below for a fiber with $$V = 5$$, where red and blue respectively denote the left and right-hand side: - - - +{% include image.html file="transcendental-full.png" width="100%" alt="Graphical solution of transcendental equation" %} This shows that each $$\mathrm{LP}_{\ell m}$$ has an associated cut-off $$V_{\ell m}$$, so that if $$V > V_{\ell m}$$ then $$\mathrm{LP}_{lm}$$ exists, -- cgit v1.2.3