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The book provides a comprehensive treatment of band structure calculations for photonic crystals, including novel methods for photonic crystals made of dispersive materials. In the rapidly advancing field of photonics, photonic crystals stand out as a revolutionary technology due to their unique ability to manipulate electromagnetic waves through band gaps. The author delves into the heart of this technology, offering an essential resource for researchers, engineers, and students alike. This book begins with a thorough overview of photonic crystals, elucidating their structure, properties, and the fundamental principles underlying their operation. Readers are then introduced to a variety of methods for calculating band structures, each explained with clarity and precision. A significant portion of the book is dedicated to the finite element method (FEM), a powerful tool for modeling both non-dispersive and dispersive materials within photonic crystals. Detailed explanations, step-by-step instructions, and insightful numerical examples guide readers through the intricacies of FEM, ensuring a robust understanding of this critical technique. With its blend of theoretical insights and practical applications, this book is an indispensable guide for anyone looking to explore the fascinating world of photonic crystals and harness their potential in optical communications, filters, lasers, switches, and beyond.