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More convention table entries 

Former-commit-id: b821b2664292d006056b8fc98167a89e820327b6
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Marek Nečada 2019-07-08 17:54:36 +03:00
parent d2e9b4450f
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8
notes/conventions.md
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@ -4,7 +4,7 @@ VSWF conventions
| Source | VSWF definition | VSWF norm | CS Phase | Field expansion | Radiated power | Notes | | Source | VSWF definition | VSWF norm | CS Phase | Field expansion | Radiated power | Notes |
|--- |--- |--- |--- |--- |--- |--- | |--- |--- |--- |--- |--- |--- |--- |
| Kristensson I \cite kristensson_spherical_2014 | \f[ \wfkcreg, \wfkcout= \dots \f] | | | \f[ | Kristensson I \cite kristensson_spherical_2014 | \f[ \wfkcreg, \wfkcout= \dots \f] | | Yes, in the spherical harmonics definition, cf. sect. D.2. | \f[
\vect E = k \sqrt{\eta_0\eta} \sum_n \left( \wckcreg_n \wfkcreg_n + \wckcout_n \wfkcout_n \right), \vect E = k \sqrt{\eta_0\eta} \sum_n \left( \wckcreg_n \wfkcreg_n + \wckcout_n \wfkcout_n \right),
\\ \\
\vect H = \frac{k \sqrt{\eta_0\eta}}{i\eta_0\eta} \sum_n \left( \wckcreg_n \wfkcreg_n + \wckcout_n \wfkcout_n \right), \vect H = \frac{k \sqrt{\eta_0\eta}}{i\eta_0\eta} \sum_n \left( \wckcreg_n \wfkcreg_n + \wckcout_n \wfkcout_n \right),
@ -18,7 +18,11 @@ VSWF conventions
\f] | \f[ \f] | \f[
P = \frac{1}{2k^2\eta_0\eta} \sum_n \left( \abs{\wckrout_n}^2 +\Re \left(\wckrout_n\wckrreg_n^{*}\right)\right) 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$. | \f] | The \f$ \wckrreg, \wckrout \f$ coefficients have dimension \f$ \mathrm{V/m} \f$. |
| Reid \cite reid_electromagnetism_2016 | | | | | | | | Reid \cite reid_electromagnetism_2016 | | | | \f[
\vect E = \sum_\alpha \pr{ \wcrreg_\alpha \wfrreg_\alpha + \wcrout_\alpha wfrout_\alpha }, \\
\vect H = \frac{1}{Z_0Z^r} \sum_\alpha \pr{ \wcrreg_\alpha \sigma_\alpha\wfrreg_\overline{\alpha} +
\wcrout_\alpha \sigma_\alpha\wfrout_\overline{\alpha}},
\f] where \f$ \sigma_{lmM} = +1, \sigma_{lmN}=-1, \overline{lmM}=lmM, \overline{lmN}=lmM, \f$ cf. eq. (6). The notation is not extremely consistent throughout Reid's memo. | | |
| Taylor \cite taylor_optical_2011 | \f[ | 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} \\ \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)}, \\ +\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)}, \\

8
notes/mathjax_newcommands.js
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@ -28,7 +28,13 @@ MathJax.Hub.Config({
wcmtreg: "{q}", // regular magnetic wave coeff wcmtreg: "{q}", // regular magnetic wave coeff
wcetreg: "{p}", // regular electric wave coeff wcetreg: "{p}", // regular electric wave coeff
wcmtout: "{b}", // outgoing magnetic wave coeff wcmtout: "{b}", // outgoing magnetic wave coeff
wcetout: "{a}" // outgoing electric wave coeff wcetout: "{a}", // outgoing electric wave coeff
// Reid's VSWFs
wfrreg: "\\mathbf{\\mathcal{W}}^{\\mathrm{reg}}", // regular wave
wfrout: "\\mathbf{\\mathcal{W}}^{\\mathrm{out}}", // outgoing wave
wcrreg: "C^\\mathrm{inc}", // regular wave coeff
wcrout: "C^\\mathrm{scat}", // outgoing wave coeff
} }
} }
}); });