Sign up or log in Sign up using Google. 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. My question is this:. Sign up using Facebook. Sign up or log in Sign up using Google.
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Kamov Sergey 9. I arrange for sine waves to arrive on the boundary from the left so they create currents on the boundary.
Can you try along the same direction as your other question ? Sign up or log in Sign up using Google. Home Questions Tags Users Unanswered.
Drivers >>> Hankel USB Device driver
Hankel function in terms of planewaves Ask Question. Sign up using Email and Password. I found this article, but it addresses a completely different problem, actually. Please point out when you hnakel not doing so unnecessarily duplicates efforts.
Hankel USB Device driver – DriverDouble
In cylindrical coordinates, the most appropriate solutions are the two kinds of Hankel functions, representing outgoing and incoming wave solutions. Your code will never give result because there is “k” in the integrand that is not numeric. Although the presence of homoegeneous waves in the cited paper does not agree with Marty’s refraction argument. The Radon transform might be relevant read the first page. The resulting field in the vaccuum must be physically correct, and it is made up of the evanescent portion of the incident waves from the left hand side.
I once hankwl out a method to get the Neumann functions in terms of plane waves by physical reasoning.
Post as a guest Name. 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”. It is well know that planewaves are a complete basis for solutions to the wave equation. By using the laws of refraction you get the right distribution of ordinary waves to give you the desired current distribution on the boundary.
That’s the beauty of it! 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. For the following integrand, we can not get the symbolic result.
Numerical integration of Hankel functions – Mathematica Stack Exchange
Considering for a moment just the 0th order bessel function, you can map from hanmel circular distribution into a 1-dimensional Fourier transform giving just the radial component of the wave. 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.