Analytic expressions for scattered power (flux)

[johnaparker]

For a system of dipoles and nanoparticles, the expansion coefficients of the source and system can be calculated with this:

def get_p_src(cluster, origin=[0,0,0]):
    """get the p_src expansion coefficients; assumes all sources are dipoles

    Arguments:
        cluster      miepy.cluster or miepy.sphere_cluster
        origin       origin around which to obtain expansion
    """
    if isinstance(cluster.source, miepy.sources.combined_source):
        p_src = []
        positions = []
        for dipole in cluster.source.sources:
            p_src_d = np.zeros([2,3], dtype=complex)
            p_src_d[0] = (dipole.weight[-1], dipole.weight[0], dipole.weight[1])
            p_src.append(p_src_d)
            positions.append(dipole.position)
        p_src = np.asarray(p_src)
        positions = np.asarray(positions)
    else:
        dipole = cluster.source
        p_src = np.zeros([2,3], dtype=complex)
        p_src[0] = (dipole.weight[-1], dipole.weight[0], dipole.weight[1])
        positions = np.array([dipole.position])
        p_src = np.array([p_src])

    return miepy.cluster_coefficients(positions, p_src, 
            cluster.material_data.k_b, origin, lmax=cluster.lmax)

def get_p_scat(cluster, origin=[0,0,0]):
    """get the p_scat expansion coefficients of the nanoparticles

    Arguments:
        cluster      miepy.cluster or miepy.sphere_cluster
        origin       origin around which to obtain expansion
    """
    return miepy.cluster_coefficients(cluster.position, cluster.p_scat,
            cluster.material_data.k_b, origin=origin, lmax=cluster.lmax)

Then the flux of the source (P0) and system (P) is:

Z0 = miepy.constants.Z0
k = 2*np.pi/wavelength
p_src = get_p_src(cluster)
p_scat = get_p_scat(cluster)
P0 = 0.5/Z0*np.pi/k**2*np.sum(np.abs(p_src)**2) # power source
P = 0.5/Z0*np.pi/k**2*np.sum(np.abs(p_scat + p_src)**2) # power system
enhance = P/P0

These functions should be added to MiePy in some way to make this type of calculation straightforward.