Understanding the construction of vector spherical wave functions

[dave86wave]

Understanding the construction of vector spherical wave functions!

Hi guys,

I'm looking at electromagnetic scattering just now, and in particular, how multipole fields are constructed and then how the wavefunctions are represented as the incident, internal and scattered fields. When you satisfy the vector Helmholtz equation, you get three independent vector solutions to it, typically described as L, M, and N. However, when you get to the final expressions for wavefunctions, they are described in terms of multipole fields M and N. What does happen to L and what does it represent? I'll appreciate any feedback on this strange question. Thanks.

 

[abi]

Hi guys,

I'm looking at electromagnetic scattering just now, and in particular, how multipole fields are constructed and then how the wavefunctions are represented as the incident, internal and scattered fields. When you satisfy the vector Helmholtz equation, you get three independent vector solutions to it, typically described as L, M, and N. However, when you get to the final expressions for wavefunctions, they are described in terms of multipole fields M and N. What does happen to L and what does it represent?

Peace!M and N are used for the representation of purely solenoidal functions or in other words when the given function is purely solenoidal , the expansion is made in terms of M and N alone.
And if the divergence of the function does not vanish terms in L must be included.

when we are dealing with EM field and we know that divergence of EM vanishes so we can't write EM field in term of L. And we also know that EM field is solenoidal, that why we represent in terms of M and N

The vector functions L, M, and N have certain notable properties that follow directly from their definitions.
Curl of L = 0
divegence of M =0
divegence of N =0 For the construction of these functions you can check Electromagnetic Theory By J.A. Stratton
Reference : Electromagnetic Theory By J.A. Stratton

I'll appreciate any feedback on this strange question. Thanks.

Its not strange for me at all. :DPeace!