- #1

Haorong Wu

- 413

- 89

- Homework Statement
- Suppose a particle of Ag with diameter of 100nm is partially embeded in a glass substrate so that half of the particle is surrounded by glass, while the other half is surrounded by air. The refractive index of the glass substrate is 1.5. Use Mie scattering theory to analyze the scattering and absorption spectrums between 300nm and 1000nm.

- Relevant Equations
- none

It is an open question. The professor asked us to find a suitable method to solve it with the help of a computer.

When I learned the Mie scattering, the equations are given for particles in homogenous medium. But now half of the particle is surrounded by glass while the other half by air.

First, I want to treat the particle as two independent particles one of which is surrounded only by glass, while the other by air only. Then I can use Mie scattering theory to calculate independently for them and then sum the results. I believe this could be an approach but it may not give a satisfying result.

Second, I think maybe I only need consider the medium in the outgoing direction. I note that the coefficients for extinction, scattering, and absorption are related to ##a_n## and ##b_n##. And ##a_n## and ##b_n## are related to the scattered fields $$ \mathbf {E} _{s}=\sum _{n=1}^{\infty }E_{n}\left(ia_{n}\mathbf {N} _{e1n}^{(3)}(k,\mathbf {r} )-b_{n}\mathbf {M} _{o1n}^{(3)}(k,\mathbf {r} )\right).$$ Besides, the incident light will excite the atoms based on its frequency ##\omega## which is not related to the refractive index of the medium. Also the scattering directions are randomly distributed, so I can calculate the scattering coefficients for pure air and for pure glass, and then add them up and divide them by 2. The same method will be applied to the extinction coefficients.

Is there any more reasonable method?

When I learned the Mie scattering, the equations are given for particles in homogenous medium. But now half of the particle is surrounded by glass while the other half by air.

First, I want to treat the particle as two independent particles one of which is surrounded only by glass, while the other by air only. Then I can use Mie scattering theory to calculate independently for them and then sum the results. I believe this could be an approach but it may not give a satisfying result.

Second, I think maybe I only need consider the medium in the outgoing direction. I note that the coefficients for extinction, scattering, and absorption are related to ##a_n## and ##b_n##. And ##a_n## and ##b_n## are related to the scattered fields $$ \mathbf {E} _{s}=\sum _{n=1}^{\infty }E_{n}\left(ia_{n}\mathbf {N} _{e1n}^{(3)}(k,\mathbf {r} )-b_{n}\mathbf {M} _{o1n}^{(3)}(k,\mathbf {r} )\right).$$ Besides, the incident light will excite the atoms based on its frequency ##\omega## which is not related to the refractive index of the medium. Also the scattering directions are randomly distributed, so I can calculate the scattering coefficients for pure air and for pure glass, and then add them up and divide them by 2. The same method will be applied to the extinction coefficients.

Is there any more reasonable method?