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The waves that make this field distribution in the vaccuum are the evanescent waves which result from total internal reflection of the ordinary waves inside the dielectric glue.
Your code will never give result because there is “k” in the integrand that is not numeric. Hankel function in terms of planewaves Ask Question. I found this article, but it addresses a completely different problem, actually.
functional analysis – Hankel function in terms of planewaves – Mathematics Stack Exchange
I like the physically based reasoning here, but I am not convinced using a high dielectric constant medium on the left will produce a reasonable answer, since its escape cone is infinitely narrow, meaning that only the normally incident planewave from the left is transmitted through though you can argue there is infinite impedance mismatch, so it is completely reflected.
Sign up or isb in Sign up using Google. For the following integrand, we can not get the symbolic result. I can’t find an analogous expression for expression Neumann functions in terms of planewaves.
Then if you take the analytical continuation, that is, the same function greater than 1, you get the Fourier transform of the Neumann function; that is, the radial component of it.
Sign up using Facebook. Let us assume a 2D space, and at fixed temporal frequency, the equation reduces to the Helmholtz equation.
Victor Liu 3, 11 If cylindrical harmonics are a complete basis, is there a closed form expression relating them to planewaves? Post as a guest Name.
Hankel USB Device driver – DriverDouble
Sign up using Email and Password. By using the laws of refraction you get the right distribution of ordinary waves to give you the desired current distribution on the boundary. Post as a guest Name. Those are exactly what you need to build up the Neumann functions.
However, a Hankel function’s real part is a bessel function while its imaginary part is a 2nd kind Bessel function Neumann function with a singularity at the origin.
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Knowing the laws of refraction, I can calculate the currents and arrange by Fourier components so that there is a net resultant of just a single line of current on the boundary. The expansion you’re looking for is derived in this articlewhich I found immediately as one of the first hits of a Google search for “hankel plane waves”.
Please google before posting. Sign up using Facebook. Home Questions Tags Users Unanswered. Marty Green 1, 1 13 I once worked out a method to get the Neumann functions in terms of plane waves by physical reasoning. My question is this: For electromagnetic waves, there are currents flowing in the boundary of two mediums. I was sort of hoping someone had already done the hard work for me: Numerical integration of Hankel functions Ask Question.