coefficients

miepython.core.coefficients(m, x, n_pole=0, internal=False)[source]

Computes the Mie coefficients for a sphere.

This function calculates the Mie coefficients for electromagnetic scattering by a sphere. It supports both single values and arrays for the refractive index and size parameter. For arrays, the lengths of m and x must match. If the length of m or x is zero, the function assumes scalar values.

If n_pole > 0, the function returns only the 1 to nth multipole coefficients for each input.

Parameters:

  • m (complex or array-like) – The complex refractive index of the sphere. If an array, must match the length of x.

  • x (float or array-like) – The size parameter of the sphere. If an array, must match the length of m.

  • n_pole (int, optional) – The specific multipole order to compute. Defaults to 0, which calculates all terms and returns the full arrays of coefficients.

  • internal (bool, optional) – If True then returns Mie coefficients needed to calculate fields inside the sphere.

Returns:

ndarray –

[a, b], or [a, b, c, d] when internal is True. For

scalar m and x each entry is a 1-D array of coefficients, so the result has shape (2, n_terms) or (4, n_terms). For array input each entry gains a leading axis over the spheres, giving (2, n_spheres, n_pole) or (4, n_spheres, n_pole).

Notes

  • If the imaginary part of the refractive index is positive, it is automatically corrected to its conjugate value to ensure a valid input.

  • Every returned coefficient is a real term; the arrays carry no padding.

Examples

Compute coefficients for a single sphere:

>>> import miepython as mie
>>> a, b = mie.coefficients(1.5 - 0.1j, 0.1)
>>> len(a), len(b)
(3, 3)
>>> print(f"{a[0]:.6e}")
3.333700e-05-1.973631e-04j
>>> print(f"{b[0]:.6e}")
6.672963e-08-2.754694e-07j

Keep only the dipole term for each of several spheres:

>>> a, b = mie.coefficients([1.5 - 0.1j, 1.4 - 0.05j], [2.0, 1.8], n_pole=1)
>>> a.shape
(2, 1)
>>> print(f"{a[0, 0]:.6f}")
0.447946-0.386652j