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Fix LG spectrum amplitude:
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Replace theta with its sine. This is the correctly transformed version from a
Gaussian distribution in 2D k-space and corresponds to the already fixed implementation in meep.
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DanielKotik committed Nov 28, 2019
1 parent 12047fd commit aeca3d5
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2 changes: 1 addition & 1 deletion beam_profiles.ipynb
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Expand Up @@ -147,7 +147,7 @@
"The spectrum amplitude for Laguerre-Gaussian beams taken from eq. (2.22) in [[Bliokh2013](#Bliokh2013)] is given by\n",
"\n",
"\\begin{equation*}\n",
"f_\\text{LG}(\\theta,\\phi) = \\theta^{|m|} \\exp\\biggl[-\\Bigl(\\frac{kw_0}{2}\\theta\\Bigr)^2 \\biggr] \\exp(\\mathrm{i} m \\phi)\n",
"f_\\text{LG}(\\theta,\\phi) = \\theta^{|m|} \\exp\\biggl[-\\Bigl(\\frac{kw_0}{2}\\sin\\theta\\Bigr)^2 \\biggr] \\exp(\\mathrm{i} m \\phi)\n",
"\\end{equation*}\n",
"\n",
"with azimuthal angle $\\phi$, polar angle $\\theta$ and vortex charge $m$."
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