ABOUT THE COURSE: The course provides a detailed introduction to the versatile photonic-crystal technology by covering its fundamentals and an overview of the latest advancements with examples. The properties of light propagation in simple to complex photonic crystals are discussed thoroughly with appropriate theoretical tools which would help undergraduate students and postgraduate/industrial researchers in developing intuitions about how photonic crystals need to be designed for a specific application. The course begins with fundamentals of electromagnetic theory of light in periodic dielectric media, and then discusses 1D, 2D, and 3D photonic crystals/slabs in details. Later on, the course will focus on designing photonic crystals for applications such as mirrors, waveguides, cavity, filters, splitters, sensors etc. needed for in modern high-speed communication systems. With simple pre-requisite of familiarity with macroscopic Maxwell’s equations and eigenmodes, this course will provide a comprehensive platform with needed numerical and physical tools for designing photonic crystal devices for different applications.INTENDED AUDIENCE: B.Tech (Final year), M.Tech, M.Sc, and PhD students & Members of R&D in Electrical Engineering, Physics, Nanotechnology and Material EngineeringPREREQUISITES: Basic electromagnetic theory in undergraduate curriculum.INDUSTRY SUPPORT: Intel, IBM, Lumerical, Thorlabs, Photon Design, Comsol. Tejas Networks, DRDO, ISRO, DAE labs, and any Opto-electronics based industries.
Photonic Crystals: Fundamentals & Applications
Indian Institute of Technology Guwahati and NPTEL via Swayam
Overview
Syllabus
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
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
Taught by
Prof. Debabrata Sikdar
