Spherical Vector Wave Functions and Surface Green's Functions

In summary, spherical vector wave functions are used to describe electromagnetic wave propagation and surface Green's functions are used to calculate the interaction between two surfaces.
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brian_haggis8
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Homework Statement




I'm currently doing research to try and find a way of calculating simultaneously both the internal and external fields of elliptic shaped dielectric and metallic nanoparticles with a depression on one of its sides so as it would look like a bean. We use spherical vector wave functions to expand the propagating wave this much I know however I don't actually know how to explain what spherical vector wave functions are so any simplified explanation would be helpful. Also we are going to use a surface Green's function to give an exact relation between the internal and scattered fields and the incident fields however again I've covered calculating Green's functions in other classes but not sure what a Layman's explanation of them would be so any information you could help me with would be very much appreciated.
Thanks :)

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The Attempt at a Solution

 
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Spherical vector wave functions are functions which describe the propagation of electromagnetic waves (such as light or radio waves) through space in terms of spherical coordinates. They can be used to calculate the electric and magnetic fields of the wave as it propagates. The wave functions are related to the wave's angular frequency, its wavelength, and its direction of propagation. A surface Green's function is a mathematical representation of the interaction between two surfaces. It gives an exact relation between the internal and scattered fields and the incident fields. This means that when light strikes a surface, the surface Green's function can be used to calculate the intensity of the light that is reflected, refracted, or absorbed by the surface. It is also used to calculate the amount of energy that is transmitted through the surface.
 

1. What are Spherical Vector Wave Functions?

Spherical Vector Wave Functions are mathematical functions that describe the behavior of electromagnetic waves in spherical coordinates. They are used to model the propagation of electromagnetic radiation in three-dimensional space.

2. How are Spherical Vector Wave Functions related to Surface Green's Functions?

Surface Green's Functions are derived from Spherical Vector Wave Functions and are used to describe the electromagnetic field at a given point on a surface. They take into account the boundary conditions at the surface and allow for the calculation of the electric and magnetic field components.

3. What are some applications of Spherical Vector Wave Functions and Surface Green's Functions?

Spherical Vector Wave Functions and Surface Green's Functions are used in a variety of fields, including electromagnetics, acoustics, and quantum mechanics. They are particularly useful in studying the behavior of electromagnetic waves in spherical systems, such as antennas and spherical resonators.

4. How are Spherical Vector Wave Functions and Surface Green's Functions calculated?

Both Spherical Vector Wave Functions and Surface Green's Functions can be calculated using various mathematical techniques, such as series expansions, integral transforms, and numerical methods. The specific method used depends on the problem being solved and the desired level of accuracy.

5. Are there any limitations or assumptions when using Spherical Vector Wave Functions and Surface Green's Functions?

Like any mathematical model, there are limitations and assumptions when using Spherical Vector Wave Functions and Surface Green's Functions. They are most accurate when used in free space and may not accurately describe the behavior of electromagnetic waves in complex materials or structures. Additionally, they assume that the medium is linear and isotropic.

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