Photonic Crystals

Preface and Acknowledgements. 1: Photonic Crystals and Other Obscure Topics. 1.1. In the Beginning, There Was Maxwell. 1.2. Periodic Surprises. 1.3. Photonic Crystals. 1.4. Things to Come. 1.4.1. Intersecting Optical Pipes. 1.4.2. Photonic-Crystal Slabs. 1.4.3. A New Photonic Crystal. 1.4.4. So, You Want To Study Photonic Crystals? 2: Gaps & Maxwells Equations: A Whirlwind Tour. 2.1. Maxwells Equations. 2.2. Maxwell Meets Bloch & Floquet. 2.3. The Origin of the Photonic Band Gap. 2.4. Localized Defect States. 3: Elimination of Crosstalk in Perpendicular Waveguide Intersections. 3.1. Introduction. 3.2. Eliminating Crosstalk by Symmetry. 3.3. Intersecting Photonic-Crystal Waveguides. 3.4. Intersecting Conventional Waveguides. 3.5. Summary. 4: Guided Modes in Photonic-Crystal Slabs. 4.1. Introduction. 4.2. Computational Method. 4.3. Photonic-Crystal Slab Band Structures. 4.4. Effects of Slab Thickness. 4.5. Slabs with Solid Backgrounds (Sandwiches). 4.6. Slabs with Periodic Backgrounds. 4.7. Slabs with Symmetry-Breaking Backgrounds. 4.8. Summary. 5: Linear Waveguides in Photonic-Crystal Slabs. 5.1. Introduction. 5.2. Computational Method. 5.3. Reduced-Index Waveguides. 5.4. Increased-Index Waveguides. 5.5. Strip Waveguides in Photonic-Crystal Slabs. 5.6. Waveguides in Other Directions. 5.7. Estimating the Field Energy in the Dielectric. 5.8. Summary. 6: High-Q Cavities in Photonic-Crystal Slabs. 6.1. Introduction. 6.2. Computational Method. 6.3. Mode Delocalization. 6.4. Multipole Cancellation. 6.4.1. The Multipole Expansion for Radiation Fields. 6.4.2. A Multipole Cancellation in 2d. 6.4.3. A Multipole Cancellation in 3d. 6.5. Summary and Conclusions. 7: Layered Photonic Crystal with a Complete Three-dimensional Band Gap. 7.1. Introduction. 7.2. Other Photonic-Crystal Structures. 7.3. Characterizing the New Structure. 7.4. Possible Fabrication Methods. 7.5. Summary. 8: Block-iterative Frequency-Domain Methods for Maxwells Equations. 8.1. Introduction. 8.2. The Maxwell Eigen Problem. 8.2.1. The Choice of Basis. 8.2.2. Inversion Symmetry. 8.2.3. The Effective Dielectric Tensor. 8.2.4. Preconditioners. 8.3. Iterative Eigensolvers. 8.3.1. Conjugate-gradient Minimization of the Rayleigh Quotient. 8.3.2. The Davidson Method. 8.3.3. Interior Eigenvalues. 8.3.4. To Block or Not To Block? 8.3.5. Scaling. 8.4. Summary. 9: Concluding Remarks. 9.1. Looking Back. 9.2. Looking Forward. Index.