Plane Wave Expansion: Solving Issues with Bohren and Huffman

In summary, the speaker has been working on a plane wave expansion in spherical harmonics as demonstrated in Bohren and Huffman. They have finished their code in Matlab and are now trying to expand and compare values with the exact solution. However, they are running into trouble when defining some components as zero, as one of the terms in the equations is divisible by a sin(m*phi) value which causes the result to become nonsensical. They are seeking help from anyone familiar with this field or has examples of such an expansion in a MATLAB framework.
  • #1
falcao
9
0
I've been working on a plane wave expansion in spherical harmonics.. as demonstrated in Bohren and Huffman (if anyone's familiar with it_)... I have more or less finished my code in Matlab and I'm putting in values to expand and compare with the exact solution...


in short, I'm having trouble when defining some of my components as zero... getting results going crazy all over the place.! now I appreciate this would seem like a problem with the code but looking at the equations in Bohren and Huffman(4.19) (and in my code) there seems to be a different problem!..

one of the terms is divisible by a sin(m*phi) value and of course this value is going to go to zero with my phi and then the term goes to infinity! so my result ends up being nonsensical..>

if anyone is familiar with the field t'would be nice to hear!:redface:
 
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  • #2
or even if anyone has any examples of such an expansion within a MATLAB framework>?!
 
  • #3
honestly... any help would be massively appreciated!

please!:cry::confused::cry:
 

FAQ: Plane Wave Expansion: Solving Issues with Bohren and Huffman

What is the Plane Wave Expansion method?

The Plane Wave Expansion (PWE) method is a numerical technique used to solve scattering and diffraction problems in classical electromagnetics. It involves expanding the incident and scattered fields in terms of plane waves and solving for the expansion coefficients using boundary conditions.

What issues does the PWE method solve in relation to Bohren and Huffman theory?

The PWE method addresses several issues with the traditional Mie theory developed by Bohren and Huffman. These include limitations on particle size, shape, and material properties, as well as numerical convergence issues for highly absorbing or large particles.

How does the PWE method improve upon the Mie theory?

The PWE method allows for more flexibility in the size, shape, and material properties of particles, as well as the ability to handle highly absorbing or large particles. It also provides more accurate results for particles with complex geometries or inhomogeneous material properties.

What are the limitations of the PWE method?

The PWE method is limited in its ability to handle particles with sharp edges or corners, as well as particles with extremely large size parameters. It also requires a large computational effort, especially for particles with high refractive index contrast.

What are the practical applications of the PWE method?

The PWE method has numerous practical applications, including modeling light scattering by atmospheric particles, biological cells, and nanoparticles. It is also used in the design of optical devices, such as photonic crystals and metamaterials.

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