treams.special.vcw_M

treams.special.vcw_M(kz, m, xrho, phi, z) = <ufunc 'vcw_M'>

Singular vector cylindrical wave M

The vector cylindrical wave is defined by

\[\boldsymbol M_{k_z m}^{(3)}(x_\rho, \varphi, z) = \left(\frac{\mathrm i m}{x_\rho} H_m^{(1)}(x_\rho)\boldsymbol{\hat{\rho}} - {H_m^{(1)}}'(x_\rho) \boldsymbol{\hat{\varphi}}\right) \mathrm e^{\mathrm i (k_z z + m \varphi)}\]

using treams.special.hankel1().

This function is describing a transverse solution to the vectorial Helmholtz wave equation, that is also tangential on a cylindrical surface. This is often used to describe a transverse electric (in cylindrical coordinates) (TE) wave.

Parameters:

• kz (float, array_like) – Z component of the wave

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

• xrho (float or complex, array_like) – Radial in units of the wave number \(k_\rho \rho\)

• phi (float, array_like) – Azimuthal angle

• z (float, array_like) – Z coordinate

Returns:

complex, 3-array