treams.special.tl_vcw

treams.special.tl_vcw(kz1, mu, kz2, m, k, xrho, phi, z) = <ufunc 'tl_vcw'>

Translation coefficient for vector cylindrical waves from scattered to incident modes

Definded by

\[\begin{split}\begin{cases} H_{m - \mu}^{(1)}(x_\rho) \mathrm e^{\mathrm i ((m - \mu) \varphi + k_{z,1}z)} & \text{if }k_{z,1} = k_{z,2} \\ 0 & \text{otherwise} \end{cases}\end{split}\]

where \(H_{m - \mu}^{(1)}\) are the Hankel functions.

These coefficients are used to translate from incident to incident modes and from scattered to scattered modes.

Parameters:

• kz1 (float, array_like) – Z component of the destination mode’s wave vector

• mu (integer, array_like) – Order of the destination mode

• kz2 (float, array_like) – Z component of the source mode’s wave vector

• m (integer, array_like) – Order of the source mode

• xrho (complex, array_like) – Translation in radial direction in units of the wave number

• phi (float, array_like) – Azimuthal angel

• z (float, array_like) – Translation in z direction

Returns:

complex