Perturbation Approach to the Diffraction of Electromagnetic Waves by Arbitrarily Shaped Dielectric Obstacles

A perturbation method is developed to consider the problem of the diffraction of electromagnetic waves by an arbitrarily shaped dielectric obstacle whose boundary may be expressed in the general form, in spherical coordinates, $r_p=r_0[1+\delta f_1(\theta , \phi )+{\delta }^2{f}_2(\theta , \phi )+\cdots ]$ where $r_0$ is the radius of an unperturbed sphere and $f_n(\theta , \phi )$ are arbitrary, single-valued and analytic functions. $\delta$ is chosen such that $\Sigma \stackrel{\infty }{n=1\mathrm{}}\left|{\delta }^n{f}_n\right(\theta , \phi \left)\right|<1, 0\le \theta \le \pi , 0\le \phi \le 2\pi .$ Detailed analysis is carried out to the first order in $\delta$. Procedures to obtain higher order terms are also indicated. The perturbation solutions are valid for the near zone region of the obstacle as well as for the far zone region and they are applicable for all frequencies. Possible applications of this perturbation technique to elementary-particle scattering problems and other electromagnetic scattering problems are noted.