Tru Physics

Mie Scattering

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Tru Physics
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Introduction

Mie scattering is a solution of Maxwell’s equations for the scattering of an electromagnetic plane wave by a homogeneous sphere. The term “Mie scattering” suggests scattering by particles that are similar in size to, or larger than, the wavelength of light. It is named after Gustav Mie, who first solved the scattering problem for a sphere in 1908.

Basics of Mie Scattering

In contrast to Rayleigh scattering, which only applies to particles that are small in relation to the wavelength of light, Mie scattering does not make any such assumption. It is a general form of scattering that can apply to any size particle, so long as it is spherical and homogenous.

The general solution of the scattering amplitude for Mie Scattering is quite complex. The scattering cross-section C_{\text{sca}} can be written as:

C_{\text{sca}} = 2\pi \left(\dfrac{k}{a}\right)^2 \displaystyle\sum_{n=1}^{\infty} (2n+1)\left(\left|a_n\right|^2 + \left|b_n\right|^2\right)

where:

  • k is the wavenumber of the incoming light, k = 2\pi/\lambda,
  • a is the radius of the spherical particle,
  • a_n and b_n are the complex Mie coefficients that depend on the size parameter x = ka and the relative refractive index of the sphere and surrounding medium.

Mie Scattering and Absorption

Mie scattering also includes absorption by the sphere. The absorption cross-section C_{abs} is given by:

C_{abs} = 2\pi \left(\dfrac{k}{a}\right)^2 \displaystyle\sum_{n=1}^{\infty} (2n+1)(a_n' + b_n')

where:

  • a_n' and b_n' are the real parts of the Mie coefficients.

Significance of Mie Scattering

Mie scattering is crucial in a variety of scientific and engineering domains. It is fundamental in understanding the color of objects, the appearance of the sky, remote sensing, and aerosol studies in atmospheric science. It also has applications in nanotechnology and materials science.

The Mie Scattering Pattern

Unlike Rayleigh scattering, which is independent of scattering angle, Mie scattering is highly dependent on the angle of scattering. This can lead to various interesting effects like the bright colors seen in opalescent glass or the vivid colors of certain beetles.

Conclusion

Mie Scattering provides an exact solution to Maxwell’s equations for light scattering by spherical particles. Despite the mathematical complexity, it is an essential concept in understanding a wide range of phenomena in physics, atmospheric science, and material science. The ability to solve these equations accurately has opened the door for a wide variety of technological and scientific advances.

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