Dielectric surface in the field of an oscillating dipole

[gaganaut]

We have the equations available for computing the reflected and transmitted electric fields in the case when a plane wave is incident on a dielectric surface.

Now what I wish to do is compute similar reflected and transmitted components of the electric field due to an oscillating electric dipole. The equation for this type of electric field is available and is not of a plane wave nature. Now if we have a dielectric surface in this field, how do we go about computing the reflected and transmitted components?

I have referred to quite a few Electromagnetics textbooks but none seems to have a ready to use solution for this. Please direct me to a source that talks about this, if there is one.

Appreciate all the help.

Thanks

 

[gabbagabbahey]

We have the equations available for computing the reflected and transmitted electric fields in the case when a plane wave is incident on a dielectric surface.

Now what I wish to do is compute similar reflected and transmitted components of the electric field due to an oscillating electric dipole. The equation for this type of electric field is available and is not of a plane wave nature. Now if we have a dielectric surface in this field, how do we go about computing the reflected and transmitted components?

I have referred to quite a few Electromagnetics textbooks but none seems to have a ready to use solution for this. Please direct me to a source that talks about this, if there is one.

Appreciate all the help.

Thanks

The easiest thing to do might be to use Fourier decomposition to represent the fields of the oscillating dipole as a superpostion of plane waves. After all, the whole point of studying plane waves is that any EM wave can be decomposed as a superpostion of them.

 

[gaganaut]

The easiest thing to do might be to use Fourier decomposition to represent the fields of the oscillating dipole as a superpostion of plane waves. After all, the whole point of studying plane waves is that any EM wave can be decomposed as a superpostion of them.

Thanks Gabbagabbahey. That sounds interesting and really promising, now that I think about it. I will look into it and post my experience with it here. Thanks for the clue though, this might be it.

 

[Born2bwire]

This kind of problem is dealt with in textbooks by Stratton, Kong, and Chew. I prefer Kong's textbook or Chew's because I find Stratton's use of Hertzian potentials to be more unwieldy than Kong's and Chew's use of point source potentials. I am sure that Kong's text also has this, but Chew's also contains a discussion about the Sommerfeld integral and Weyl Identity which relate a point source to it's Fourier transform in terms of cylindrical waves and plane waves or just plane waves.

 

[gaganaut]

This kind of problem is dealt with in textbooks by Stratton, Kong, and Chew. I prefer Kong's textbook or Chew's because I find Stratton's use of Hertzian potentials to be more unwieldy than Kong's and Chew's use of point source potentials. I am sure that Kong's text also has this, but Chew's also contains a discussion about the Sommerfeld integral and Weyl Identity which relate a point source to it's Fourier transform in terms of cylindrical waves and plane waves or just plane waves.

Thank you Born2bwire. This is very helpful. I will now try and see if my library holds these books. I really appreciate.