Functions for Coated Spheres (Core-Shell Particles)¶

MieQCoreShell(mCore, mShell, wavelength, dCore, dShell[, nMedium=1.0, asDict=False, asCrossSection=False])¶

Compute Mie efficencies Q and asymmetry parameter g of a single, coated particle. Uses CoreShell_ab() to calculate a_n and b_n , and then calculates Q_i following closely from the original BHMIE.

The code will return a warning if a non-unity nMedium is specified, since it was added naively. The mathematics to compute the effective index is the same as in the homogeneous particle functions.

Parameters

mCore : complex: The complex refractive index of the core region, with the convention $m=n+ik$ .
mShell : complex: The complex refractive index of the shell region, with the convention $m=n+ik$ .
wavelength : float: The wavelength of incident light, in nanometers.
dCore : float: The diameter of the core, in nanometers.
dShell : float: The diameter of the shell, in nanomaters. This is equal to the total diameter of the particle.
nMedium : float, optional: The refractive index of the medium. This must be positive, nonzero, and real. Any imaginary part will be discarded.
asDict : bool, optional: If True, returns the results as a dict.
asCrossSection : bool, optional: If specified and set to True, returns the results as optical cross-sections with units of nm².

Returns

qext, qsca, qabs, g, qpr, qback, qratio : float: The Mie efficencies described above.
cext, csca, cabs, g, cpr, cback, cratio : float: If asCrossSection==True, MieQCoreShell() returns optical cross-sections.
q : dict: If asDict==True, MieQCoreShell() returns a dict of the above efficiencies with appropriate keys.
c : dict: If asDict==True and asCrossSection==True, returns a dict of the above cross-sections with appropriate keys.

Considerations

When using this function in a script, there are three simplifying clauses that can speed up computation when considering both coated and homogeneous particles. Upon determining the size parameters of the core and the shell:

if x_core == x_shell, then MieQCoreShell() returns Mie efficencies calculated by MieQ(mCore,wavelength,dShell).
If x_core == 0, then MieQCoreShell() returns efficencies calculated by MieQ(mShell,wavelength,dShell).
If m_core == m_shell, then MieQCoreShell() returns efficencies calculated by MieQ(mCore,wavelength,dShell).

CoreShellScatteringFunction(mCore, mShell, wavelength, dCore, dShell[, nMedium=1.0, minAngle=0, maxAngle=180, angularResolution=0.5, normed=False])¶

Computes the angle-dependent scattering intensity of a coated sphere.

Parameters

mCore : complex: The complex refractive index of the core region, with the convention $m=n+ik$ .
mShell : complex: The complex refractive index of the shell region, with the convention $m=n+ik$ .
wavelength : float: The wavelength of incident light, in nanometers.
dCore : float: The diameter of the core, in nanometers.
dShell : float: The diameter of the shell, in nanomaters. This is equal to the total diameter of the particle.
nMedium : float, optional: The refractive index of the medium. This must be positive, nonzero, and real. Any imaginary part will be discarded.
minAngle : int, optional: The minimum scattering angle returned by the calculations.
maxAngle : int, optional: The maximum scattering angle returned by the calculations.
angularResolution : float, optional: The angular resolution returned by the calculations.
normed : bool, optional: Set to True to return normalized results.

Returns

theta : numpy.ndarray: An array of the angles used in calculations. Values will be spaced according to angularResolution, and the size of the array will be (maxAngle-minAngle)/angularResolution.
SL : numpy.ndarray: An array of the scattered intensity of left-polarized (parallel) light. Same size as the theta array.
SR : numpy.ndarray: An array of the scattered intensity of right-polarized (perpendicular) light. Same size as the theta array.
SU : numpy.ndarray: An array of the scattered intensity of unpolarized light, which is the average of SL and SR. Same size as the theta array.

CoreShellS1S2(mCore, mShell, xCore, xShell, mu)¶

Computes S1 and S2 of a coated sphere as a function of mu, the cosine of the scattering angle.

Parameters

mCore : complex: The complex refractive index of the core region, with the convention $m=n+ik$ .
mShell : complex: The complex refractive index of the shell region, with the convention $m=n+ik$ .
wavelength : float: The wavelength of incident light, in nanometers.
dCore : float: The diameter of the core, in nanometers.
dShell : float: The diameter of the shell, in nanomaters. This is equal to the total diameter of the particle.
mu : float: The cosine of the scattering angle.

Returns

S1, S2 : complex: The S₁ and S₂ values.

CoreShellMatrixElements(mCore, mShell, xCore, xShell, mu)¶

Calculates the four nonzero scattering matrix elements S₁₁, S₁₂, S₃₃, and S₃₄ as functions of μ=cos(θ), where θ is the scattering angle:

$S_{11}=\frac{1}{2}\left(|S_2|^2+|S_1|^2\right)$

$S_{12}=\frac{1}{2}\left(|S_2|^2-|S_1|^2\right)$

$S_{33}=\frac{1}{2}(S_2^*S_1^*+S_2S_1^*)$

$S_{34}=\frac{i}{2}(S_1S_2^*-S_2S_1^*)$

Parameters

mCore : complex: The complex refractive index of the core region, with the convention $m=n+ik$ .
mShell : complex: The complex refractive index of the shell region, with the convention $m=n+ik$ .
wavelength : float: The wavelength of incident light, in nanometers.
dCore : float: The diameter of the core, in nanometers.
dShell : float: The diameter of the shell, in nanomaters. This is equal to the total diameter of the particle.
mu : float: The cosine of the scattering angle.

Returns

S11, S12, S33, S34 : float: The matrix elements described above.