Analyze the electromagnetic scattering of a plane wave by a perfectly conducting sphere of finite radius. Determine the scattering cross-section as a function of the incident wavelength, sphere radius, and angle of incidence. Investigate the phenomenon of Mie scattering and its dependence on various parameters.
Guide On Rating System
Vote
The electromagnetic scattering of a plane wave by a perfectly conducting sphere of finite radius can be described using Mie theory. Mie theory is a mathematical approach that allows us to analyze the scattering of electromagnetic waves by spherical objects. It provides a complete solution for the scattering problem by considering multiple scattering orders.
The scattering cross-section for a sphere is given by the sum of the scattering cross-sections for each scattering order. In general, the scattering cross-section can be expressed as:
σ = σsca + σabs
Where σsca is the scattering cross-section and σabs is the absorption cross-section. The scattering cross-section represents the energy scattered by the sphere, while the absorption cross-section represents the energy absorbed by the sphere.
Mie theory allows us to calculate the scattering cross-section as a function of the incident wavelength, sphere radius, and angle of incidence. The scattering cross-section can be expressed in terms of dimensionless quantities called Mie coefficients. These coefficients depend on the ratio of the incident wavelength to the sphere radius (x), the refractive index of the sphere (m), and the order of scattering (n).
The Mie coefficients can be computed numerically using the Mie scattering theory equations. These equations involve a series expansion that converges rapidly for large values of x. The Mie coefficients determine the amplitude and phase of the scattering of the incident wave by the sphere.
In the case of Mie scattering, the scattering cross-section can exhibit various dependence on different parameters. For example, as the incident wavelength increases, the scattering cross-section tends to decrease. This is known as Rayleigh scattering. At certain wavelengths, known as resonant wavelengths, the scattering cross-section can increase due to resonance effects. These resonances occur when the incident wavelength matches the size of the sphere, resulting in enhanced scattering.
The scattering cross-section also depends on the sphere radius. As the sphere radius increases, the scattering cross-section tends to increase, with larger spheres scattering more light. However, for very large spheres, the scattering cross-section reaches a maximum and then decreases.
The angle of incidence also affects the scattering cross-section. Different angles of incidence can result in different scattering patterns. For example, at forward scattering angles, the scattering cross-section tends to be higher than at other angles.
Overall, Mie scattering is a complex phenomenon that depends on various parameters such as the incident wavelength, sphere radius, and angle of incidence. Detailed numerical calculations using Mie scattering theory can provide a quantitative analysis of the scattering cross-section for specific scenarios.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99