# Knowledge Base

 Navigation: Scripting Language > Functions mie3d

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).

 Note: This script command was introduced in the 2017a R5 release.

 Supported Product: FDTD, MODE, INTERCONNECT, DEVICE

### 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.

 Syntax Description 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. 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);

# calculate m,x and call mie3d

m = n2/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)");