Week 1: Introduction: Motivation and a brief introduction to photonic crystals, Overview of current status of research in academia and industry in the field of photonic crystals, Quick overview of electromagnetic theory of light: macroscopic Maxwell’s equations
Week 2: Fundamentals of electromagnetism in dielectric media: Electromagnetic (EM) properties of material: Constitutive relationships and material parameters; Electromagnetism as an Eigenvalue problem: General properties of the Harmonic modes; EM energy and variational principle; Scaling properties of Maxwell’s equations
Week 3: Symmetries and Electromagnetic modes of a dielectric structure: Symmetries for classification of electromagnetic modes; Continuous vs discrete translational symmetry; Real and reciprocal Lattice; Rotational symmetry and Irreducible Brillouin zone; Photonic band structures
Week 4: One-dimensional Photonic Crystals: Multilayer film as 1D photonic crystal; physical origin of photonic band gaps; size of photonic band gap; evanescent modes in photonic band gaps; off-axis propagation; Localized modes as defects; Surface states; Omnidirectional Multilayer Mirrors
Week 5: Two-dimensional Photonic Crystals: Two-Dimensional Bloch States; A Square Lattice of Dielectric Columns; A Square Lattice of Dielectric Veins; A Complete Band Gap for All Polarizations; Out-of-Plane Propagation; Localization of Light by Point Defects; Point defects in a larger gap; Linear Defects and Waveguides; Surface States
Week 6: Three-dimensional Photonic Crystals: Three-Dimensional Lattices; Crystals with Complete Band Gaps: Spheres in a diamond lattice, Yablonovite, The woodpile crystal, Inverse opals, A stack of two-dimensional crystals; Localization at a Point Defect; Localization at a Linear Defect; Localization at the Surface
Week 7: Periodic Dielectric Waveguides: Overview; A Two-Dimensional Model; Periodic Dielectric Waveguides in Three Dimensions; Symmetry and Polarization; Point Defects in Periodic Dielectric Waveguides; Quality Factors of Lossy Cavities
Week 8: Photonic-Crystal Slabs: Rod and Hole Slabs; Polarization and Slab Thickness; Linear Defects in Slabs: Reduced-radius rods, Removed holes, Substrates, dispersion, and loss; Point Defects in Slabs; Mechanisms for High Q with Incomplete Gaps: Delocalization, Cancellation
Week 9: Photonic-Crystal Fibers I: Mechanisms of Confinement; Index-Guiding Photonic-Crystal Fibers: Endlessly single-mode fibers, the scalar limit and LP modes, Enhancement of nonlinear effects; Band-Gap Guidance in Holey Fibers: Origin of the band gap in holey fibers, Guided modes in a hollow core;
Week 10: Photonic-Crystal Fibers - II: Bragg Fibers: Analysis of cylindrical fibers, Band gaps of Bragg fibers, Guided modes of Bragg fibers; Losses in Hollow-Core Fibers: Cladding losses, Inter-modal coupling
Week 11: Designing Photonic Crystals for Applications - I: Overview; Designing a mirror; Designing a waveguide; Designing a cavity; A Narrow-Band Filter; Temporal Coupled-Mode Theory: The temporal coupled-mode equations, The filter transmission
Week 12: Designing Photonic Crystals for Applications - II: A Waveguide Bend; A Waveguide Splitter; A Three-Dimensional Filter with Losses; Resonant Absorption and Radiation; Nonlinear Filters and Bistability ;Channel drop filters; Reflection, Refraction and isofrequency diagrams; Unusual refraction and diffraction effects
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