treams.special.vsw_A¶
- treams.special.vsw_A(l, m, x, theta, phi, p) = <ufunc 'vsw_A'>¶
Singular helical vector spherical wave
The vector spherical wave is defined by
\[\boldsymbol A_{lm\pm}^{(3)}(x, \theta, \varphi) = \frac{\boldsymbol N_{lm}^{(3)}(x, \theta, \varphi) \pm \boldsymbol M_{lm}^{(3)}(x, \theta, \varphi)}{\sqrt{2}}\]with
treams.special.vsw_M()andtreams.special.vsw_N(). 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