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Former-commit-id: 1c6af1e8c28a8146eb11e535183dcff7508e37b2
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Marek Nečada 2019-07-08 16:37:07 +03:00
parent 784fa99f51
commit 259169a2ae
2 changed files with 11 additions and 1 deletions
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9
notes/conventions.md
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@ -19,5 +19,12 @@ VSWF conventions
P = \frac{1}{2k^2\eta_0\eta} \sum_n \left( \abs{\wckrout_n}^2 +\Re \left(\wckrout_n\wckrreg_n^{*}\right)\right)
\f] | The \f$ \wckrreg, \wckrout \f$ coefficients have dimension \f$ \mathrm{V/m} \f$. |
| Reid \cite reid_electromagnetism_2016 | | | | | | |
| Taylor \cite taylor_optical_2011 | | | | | | Different sign for regular/scattered waves! |
| Taylor \cite taylor_optical_2011 | \f[
\wfet_{mn}^{(j)} = \frac{n(n+1)}{kr}\sqrt{\frac{2n+1}{4\pi}\frac{\left(n-m\right)!}{\left(n+m\right)!}}P_{n}^{m}\left(\cos\theta\right)e^{im\phi}z_{n}^{j}\left(kr\right)\uvec{r} \\
+\left[\tilde{\tau}_{mn}\left(\cos\theta\right)\uvec{\theta}+i\tilde{\pi}_{mn}\left(\cos\theta\right)\uvec{\phi}\right]e^{im\phi}\frac{1}{kr}\frac{\ud\left(kr\,z_{n}^{j}\left(kr\right)\right)}{\ud(kr)}, \\
\wfmt_{mn}^{(j)} = \left[i\tilde{\pi}_{mn}\left(\cos\theta\right)\uvec{\theta}-\tilde{\tau}_{mn}\left(\cos\theta\right)\uvec{\phi}\right]e^{im\phi}z_{n}^{j}\left(kr\right)
\f] | | | \f[
\vect E = \sum_{mn} \pr{-i \pr{\wcetreg_{mn}\wfetreg_{mn} + \wcmtreg_{mn}\wfmtreg{mn}} +i \pr{\wcetout_{mn}\wfetout_{mn} + \wcmtout_{mn}\wfmtout_{mn}}}, \\
\vect H = n_{ext}\sum_{mn} \pr{- \pr{\wcmtreg_{mn}\wfetreg_{mn} + \wcetreg_{mn}\wfmtreg{mn}} + \pr{\wcmtout_{mn}\wfetout_{mn} + \wcetout_{mn}\wfmtout_{mn}}},
\f] | | Different sign for regular/scattered waves! Also WTF are the units of \f$ n_{ext} \f$? |

3
notes/mathjax_newcommands.js
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@ -5,6 +5,7 @@ MathJax.Hub.Config({
abs: ["{\\left|{#1}\\right|}",1],
ud: "{\\mathrm{d}}",
pr: ["{\\left({#1}\\right)}", 1], // parentheses to save typing
uvec: ["{\\mathbf{\\hat{#1}}}", 1],
// Kristensson's VSWFs, complex version (2014 notes)
wfkcreg: "{\\vect{v}}", // regular wave
wfkcout: "{\\vect{u}}", // outgoing wave
@ -18,6 +19,8 @@ MathJax.Hub.Config({
wckrout: "{f}", // outgoing wave coeff
// Taylor's VSWFs
wfmt: "{\\widetilde{\\vect{M}}}",
wfet: "{\\widetilde{\\vect{N}}}",
wfmtreg: "{\\widetilde{\\vect{M}}^{(1)}}", // regular magnetic wave
wfetreg: "{\\widetilde{\\vect{N}}^{(1)}}", // regular electric wave
wfmtout: "{\\widetilde{\\vect{M}}^{(3)}}", // outgoing magnetic wave