treams.special.vsw_rA

treams.special.vsw_rA(l, m, x, theta, phi, p) = <ufunc 'vsw_rA'>

Regular helical vector spherical wave

The vector spherical wave is defined by

\[\boldsymbol A_{lm\pm}^{(1)}(x, \theta, \varphi) = \frac{\boldsymbol N_{lm}^{(1)}(x, \theta, \varphi) \pm \boldsymbol M_{lm}^{(1)}(x, \theta, \varphi)}{\sqrt{2}}\]

with treams.special.vsw_rM() and treams.special.vsw_rN(). The sign is determined by p, where 0 corresponds to negative and 1 to positive helicity.

This function is describing a transverse solution to the vectorial Helmholtz wave equation. Additionally, it has a well-defined helicity.

Parameters:

  • l (int, array_like) – Degree \(l \geq 0\)

  • m (int, array_like) – Order \(|m| \leq l\)

  • x (float or complex, array_like) – Distance in units of the wave number \(kr\)

  • theta (float or complex, array_like) – Polar angle

  • phi (float, array_like) – Azimuthal angle

  • p (bool, array_like) – Helicity

Returns:

complex, 3-array