This book teaches the finitedifference frequencydomain FDFD method from the simplest concepts to advanced threedimensional simulations. It uses plain language and highquality graphics to help the complete beginner grasp all the concepts quickly and visually. This single resource includes everything needed to simulate a wide variety of different electromagnetic and photonic devices. The book is filled with helpful guidance and computational wisdom that will help the reader easily simulate their own devices and more easily learn and implement other methods in computational electromagnetics. Special techniques in MATLAB are presented that will allow the reader to write their own FDFD programs. Key concepts in electromagnetics are reviewed so the reader can fully understand the calculations happening in FDFD. A powerful method for implementing the finitedifference method is taught that will enable the reader to solve entirely new differential equations and sets of differential equations in mere minutes. Separate chapters are included that describe how Maxwells equations are approximated using finitedifferences and how outgoing waves can be absorbed using a perfectly matched layer absorbing boundary. With this background a chapter describes how to calculate guided modes in waveguides and transmission lines. The effective index method is taught as way to model many threedimensional devices in just twodimensions. Another chapter describes how to calculate photonic band diagrams and isofrequency contours to quickly estimate the properties of periodic structures like photonic crystals. Next a chapter presents how to analyze diffraction gratings and calculate the power coupled into each diffraction order. This book shows that many devices can be simulated in the context of a diffraction grating including guidedmode resonance filters photonic crystals polarizers metamaterials frequency selective surfaces and metasurfaces. Plane wave sources Gaussian beam sources and guidedmod