Module polarizability

The file mie_functions.py contain all the functions needed to calculate the (dipolar) polarizability of Mie spherical particles.

List of functions:

  • sph_jn, sph_yn, sph_djn, sph_dyn, (Spherical Bessel functions of integer order)

  • psi, diff_psi, xi, diff_xi (Auxiliary functions)

  • Mie_an, Mie_bn (Mie coefficients)

  • get_alpha (dipolar polarizability)

cemd_metasurf.polarizability.mie_functions.sph_jn(n, x)[source]

Spherical Bessel function of the first kind.

Parameters:

  • n (int) – Order

  • x (float) – Argument

Returns:

Spherical Bessel function of the first kind.

cemd_metasurf.polarizability.mie_functions.sph_yn(n, x)[source]

Spherical Bessel function of the second kind.

Parameters:

  • n (int) – Order

  • x (float) – Argument

Returns:

Spherical Bessel function of the second kind.

cemd_metasurf.polarizability.mie_functions.sph_djn(n, x)[source]

Derivative of the spherical Bessel function of the first kind.

Parameters:

  • n (int) – Order.

  • x (float) – Argument.

Returns:

Derivative of the spherical Bessel function of the first kind.

cemd_metasurf.polarizability.mie_functions.sph_dyn(n, x)[source]

Derivative of the spherical Bessel function of the second kind.

Parameters:

  • n (int) – Order.

  • x (float) – Argument.

Returns:

Derivative of the spherical Bessel function of the second kind.

cemd_metasurf.polarizability.mie_functions.psi(n, x)[source]

Auxiliary function for Mie coeficients.

Parameters:

  • n (int) – Order.

  • x (float) – Argument.

Returns:

Auxiliary function.

cemd_metasurf.polarizability.mie_functions.diff_psi(n, x)[source]

Auxiliary function for Mie coeficients.

Parameters:

  • n (int) – Order.

  • x (float) – Argument.

Returns:

Auxiliary function.

cemd_metasurf.polarizability.mie_functions.xi(n, x)[source]

Auxiliary function for Mie coeficients.

Parameters:

  • n (int) – Order.

  • x (float) – Argument.

Returns:

Auxiliary function.

cemd_metasurf.polarizability.mie_functions.diff_xi(n, x)[source]

Auxiliary function for Mie coeficients.

Parameters:

  • n (int) – Order.

  • x (float) – Argument.

Returns:

Auxiliary function.

cemd_metasurf.polarizability.mie_functions.mie_n(k0, r_p, m_p, m_bg, order)[source]

Calculation of Mie coeficients.

Parameters:

  • k0 (float) – Vacuum wavevector.

  • r_p (float) – Particle radius.

  • m_p (float) – Particle refractive index.

  • m_bg (float) – Background refractive index.

  • n (int) – Order.

Returns:

  • The first element is the electric Mie coefficient, an.

  • The second element is the magnetic Mie coefficient, bn.

cemd_metasurf.polarizability.mie_functions.get_alpha_mie(k0, r_p, m_p, m_bg)[source]

Calculation of the dipolar polarizability using the Mie coeficients.

Parameters:

  • k0 (float) – Vacuum wavevector.

  • r_p (float) – Particle radius.

  • m_p (float) – Particle refractive index.

  • m_bg (float) – Background refractive index.

Returns:

6x6 polarizability matrix alp.