My research works can be summarized into two principal topics: the first is mathematical modeling and asymptotic analysis in optics which is a continuation of my Phd thesis at Ecole Polytechnique; the second is inverse problems and imaging that has been initiated during my post-doctoral position at Michigan State University. I have also considered many other mathematical problems that do not fall into these two topics, including elliptic regularity in high contrasted material, observability inequalities, etc.