treams.special.vsw_M¶
- treams.special.vsw_M(l, m, x, theta, phi) = <ufunc 'vsw_M'>¶
Singular vector spherical wave M
The vector spherical wave is defined by \(\boldsymbol M_{lm}^{(3)} (x, \theta, \varphi) = h_l^{(1)} (x) \boldsymbol X_{lm}(\theta, \varphi)\) using
treams.special.spherical_hankel1()andtreams.special.vsh_X().This function is describing a transverse solution to the vectorial Helmholtz wave equation, that is also tangential on a spherical surface. This is often used to describe a transverse electric (in spherical coordinates) (TE) wave. Additionally, the term magnetic (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