treams.special.vpw_A

treams.special.vpw_A(kx, ky, kz, x, y, z, p) = <ufunc 'vpw_A'>

Vector plane wave of well-defined helicity

The vector plane wave is defined by

\[\boldsymbol A_{\boldsymbol k \pm}(\boldsymbol r) = \frac{\boldsymbol N_{\boldsymbol k \pm}(\boldsymbol r) \pm \boldsymbol M_{\boldsymbol k}(\boldsymbol r)}{\sqrt{2}}\]

with treams.special.vpw_M() and treams.special.vpw_N(). 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:

  • kx (float or complex, array_like) – X component of the wave vector

  • ky (float or complex, array_like) – Y component of the wave vector

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

  • x (float, array_like) – Y coordinate

  • y (float, array_like) – X coordinate

  • z (float, array_like) – Z coordinate

  • p (bool, array_like) – Helicity

Returns:

complex, 3-array