N_odd

miepython.vsh.N_odd(n, lambda0, d_sphere, m_index, r, theta, phi)[source]

Compute the nth odd electric vector spherical harmonic (m=1).

This function calculates the odd-parity electric vector spherical harmonic, denoted as N_{omn}(rho), for the given multipole order n. The proper Bessel function is chosen based on whether the calculation is performed inside or outside the sphere.

The wavenumber k=2𝜋m/λ₀ where m is the index of refraction of the sphere or medium at a distance r from the center of the sphere. λ₀ is the wavelength in a vacuum.

The units on d_sphere, r and are should be the same (e.g., microns) and those on k should be the reciprocal (e.g. 1/microns)

The conventions used follow the “Vector Spherical Harmonics” Wikipedia page and Ladutenko’s paper (DOI: https://doi.org/10.1016/j.cpc.2017.01.017).

Parameters:

  • n (int) – Harmonic (1 for dipole, 2 for quadrupole, etc.).

  • lambda0 (float) – Wavelength in a vacuum.

  • d_sphere (float) – Diameter of the sphere.

  • m_index (complex) – Refractive index at position r.

  • r (float) – Radial distance from center of sphere.

  • theta (float) – Polar angle in radians (angle from z-axis).

  • phi (float) – Azimuthal angle in radians. (angle from x-axis).

Returns:

tuple – A tuple (N_r, N_theta, N_phi) representing the radial, polar, and azimuthal components of the odd electric vector spherical harmonic.