treams.special.vcw_N

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

Singular vector cylindrical wave N

The vector cylindrical wave is defined by

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

using treams.special.hankel1().

This function is describing a transverse solution to the vectorial Helmholtz wave equation. This is often used to describe a transverse magnetic (in cylindrical coordinates) (TM) 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

• k (float or complex) – Wave number

Returns:

complex, 3-array