In boundary value problems like scattering from wedges, the scalar wave function is written by Bessel function and the Hankel function is left out due to the irregularity in the origin while the electric field calculated from this scalar wave function is also singular at the origin.
Can any body please help me?
Hello,
As Dr. Farid has suggested that is the best way to solve your problem because there are other ways to use Hankel functions. as domain decomposition methods are used to solve a boundary value problem by splitting it into smaller boundary value problems on subdomains. Go through these books along with book suggested above decomposition methods Schwarz alternating method, Neumann–Dirichlet Neumann–Neumann Poincaré–Steklov operator. read some books like Electromagnetic wave theory is based on Maxwell's equations, and electromagnetic boundary-value problems must be solved to understand electromagnetic scattering, propagation, and radiation. Electromagnetic theory finds practical applications in wireless telecommunications and microwave engineering.That will be helpful for research.
Thanks
Thank you Farid and Smrity but I think You have misunderstand my question. I mean when solving boundary value problems like an optical fiber wave guide for example, the z component of the electric field in TM mode inside the core has the form:
Ez = A*Besselj(h*r)*exp(i*n*phi)*exp(-i*betta*z)
where the Hankel function is not used since it is not regular at the origin. But the Phi component of the electric field using Maxwell equations is:
Ephi = i/h^2*(-betta/r*d(Ez)/d(phi)+...)
where it can be seen that Ephi is singular at the origin (r=0). So I think our 1st justification to not using Hankel function is some how negated.
Thanks.
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