Table 1 With \(\varphi ={\mathrm{atan}}\left(y,x\right)\), the first row shows the phase singularities attached to each polarization of a \(\left(m,\lambda \right)\) beam of well-defined \({\text{TAM}}=m\) and helicity \(\lambda =\pm 1\)
From: Light structuring via nonlinear total angular momentum addition with flat optics
\({{\bf{e}}}_{R}=\left(\hat{{\bf{x}}}+{\text{i}}\hat{{\bf{y}}}\right)/\sqrt{2}\) | \({{\bf{e}}}_{L}=\left(\hat{{\bf{x}}}-{\text{i}}\hat{{\bf{y}}}\right)/\sqrt{2}\) | \({{\bf{e}}}_{z}\) | |
|---|---|---|---|
\(\left(m,{\rm{\lambda }}\right)\) \({\theta }_{\max }\to 0,\left(m,1\right)\) \({\theta }_{\max }\to 0,\left(m,-1\right)\) | \({J}_{m-1}\exp \left({\text{i}}\left(m-1\right)\varphi \right)\) \(\to {J}_{m-1}\exp \left({\text{i}}\left(m-1\right)\varphi \right)\) \(\to 0\) | \({J}_{m+1}\exp \left({\text{i}}\left(m+1\right)\varphi \right)\) \(\to 0\) \(\to {J}_{m+1}\exp \left(\text{i}\left(m+1\right)\varphi \right)\) | \({J}_{m}\exp \left(\text{i}\mathrm{m\varphi }\right)\) \(\to 0\) \(\to 0\) |
