treams.special.vcw_rA

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

Regular helical vector cylindrical wave

The vector spherical wave is defined by

\[\boldsymbol A_{k_z m \pm}^{(1)}(x_\rho, \varphi, z) = \frac{\boldsymbol N_{k_z m}^{(1)}(x_\rho, \varphi, z) \pm \boldsymbol M_{k_z m}^{(1)}(x_\rho, \varphi, z)}{\sqrt{2}}\]

with treams.special.vcw_rM() and treams.special.vcw_rN(). 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:

  • 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

  • pol (bool, array_like) – Polarization

Returns:

complex, 3-array