This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. the book contains cutting-edge discourses on areas motivated by emerging technology in optics that provide significant challenges and opportunities for applied mathematicians, researchers, and engineers. Each of the three topics is presented through a series of survey papers to provide a broad overview focusing on the mathematical models. chapters are organized to present model problems, physical principles, mathematical and computational approaches, and engineering applications corresponding to each of the three areas. while some of the subject matter is classical, the topics presented are new and represent the latest developments in their respective fields. This book is intended to help researchers and especially graduate students gain broad exposure to model problems in the areas of optical science:diffractive optics, photonic band gap structures, and waveguides. it includes up-to-date results and references for more experienced researchers while providing introductory material for those less familiar with these areas