The function mie3d can be used to calculate the scattering, absorption, and extinction efficiencies of a spherical particle made of any (non-magnetic) material embedded in any ambient dielectric material. The efficiencies are simply the cross sections normalized to the geometric cross section of the particle (\(\pi r^2\)).
References:
[1] Bohren C.F. and D.R. Huffman, “Absorption and Scattering of Light by Small Particles”, John Wiley, New York, NY, 1983.
[2] Documentation of Mätzler C. “MATLAB Functions for Mie Scattering and Absorption, Version 2”, IAP Res. Rep. No. 2002-11, August, 2002.
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Syntax |
Description |
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Q = mie3d(m,x); |
The result Q is a struct which contains quantities Qext, Qabs and Qscat (Qext = Qabs+Qscat). These will have the same length as x. The arguments are: m: the ratio of the refractive index of the sphere to the refractive index of the ambient dielectric medium. This quantity may be complex-valued because the refractive index of the sphere may be complex. This quantity should either have a singleton value, or be the same length of x for dispersive media. x: the size parameter which is defined as 2*pi*r/lambda0*n1 where lambda0 is the free space wavelength, r is the sphere radius, and n1 is the real-valued refractive index of the ambient medium. |
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Q = mie3d(m,x,nmax); |
nmax : the maximum number of orders to calculate for the mie coefficients. The default value is 0, and in this case the nmax = ceil(x+4*x^(1/3))+2. There is typically no need to modify the default value. |
Example
In this example we will calculate and compare the extinction efficiencies for 1 micron spheres of n=1.5, dispersive glass and gold over the visible spectrum.
# input parameters
n1 = 1;
n2 = 1.5;
lambda0 = linspace(400e-9,700e-9,10000);
radius = 1000e-9;
# calculate m,x and call mie3d
m = n2/n1;
x = 2*pi*radius/lambda0*n1;
Q1 = mie3d(m,x);
# recalculate with dispersive glass
n2 = getindex("SiO2 (Glass) - Palik",c/lambda0);
m = n2/n1;
Q2 = mie3d(m,x);
# recalculate with Al
n2 = getindex("Au (Gold) - Palik",c/lambda0);
m = n2/n1;
Q3 = mie3d(m,x);
plot(lambda0*1e9,Q1.Qext,Q2.Qext,Q3.Qext,"wavelength (nm)","Q extinction");
legend("n = 1.5","Glass (Palik)","Gold (Palik)");
See Also