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We develop the shape derivative analysis of solutions to the problem ofscattering of time-harmonic electromagnetic waves by a bounded penetrableobstacle. Since boundary integral equations are a classical tool to solveelectromagnetic scattering problems, we study the shape differentiabilityproperties of the standard electromagnetic boundary integral operators. Thelatter are typically bounded on the space of tangential vector fields of mixedregularity $TH\sp{-1/2}(\Div_{\Gamma},\Gamma)$. Using Helmholtz decomposition,we can base their analysis on the study of pseudo-differential integraloperators in standard Sobolev spaces, but we then have to study the G\^ateauxdifferentiability of surface differential operators. We prove that theelectromagnetic boundary integral operators are infinitely differentiablewithout loss of regularity. We also give a characterization of the first shapederivative of the solution of the dielectric scattering problem as a solutionof a new electromagnetic scattering problem.

Shape derivatives of boundary integral operators in electromagnetic  scattering. Part II : Application to scattering by a homogeneous dielectric  obstacle