treams.special.vsw_N¶
- treams.special.vsw_N(l, m, x, theta, phi) = <ufunc 'vsw_N'>¶
Singular vector spherical wave N
The vector spherical wave is defined by
\[\begin{split}\boldsymbol N_{lm}^{(3)}(x, \theta, \varphi) = \nabla \times \boldsymbol M_{lm}^{(3)}(x, \theta, \varphi) \\ = \left({h_l^{(1)}}'(x) + \frac{h_l^{(1)}(x)}{x}\right) \boldsymbol Y_{lm}(\theta, \varphi) + \sqrt{l (l + 1)} \frac{h_l^{(1)}(x)}{x} \boldsymbol Z_{lm}(\theta, \varphi)\end{split}\]with
treams.special.vsw_M(),treams.special.vsh_Y(),treams.special.vsh_Z(), andtreams.special.spherical_hankel1().This function is describing a transverse solution to the vectorial Helmholtz wave equation. This is often used to describe a transverse magnetic (in spherical coordinates) (TM) wave. Additionally, the term electric (refferring to the multipole) is used for this solution.
- 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
- Returns:
complex, 3-array