Photonic Crystals: The Road from Theory to Practice explores the theoretical road leading to the practical application of photonic band gaps. These new optimal devices are based on symmetry and resonance and the benefits and limitations of hybrid "two dimensional" slab systems in three dimensions. The book also explains that they also signify a return to the ideal of an omnidirectional band gap in a structure inspired by and emulating the simplicity of two dimensions. Finally, the book takes a look at computational methods to solve the mathematical problems that underlie all undertakings in this field. Photonic Crystals: The Road from Theory to Practice should rapidly bring the optical professional and engineer up to speed on this intersection of electromagnetism and solid-state physics. It will also provide an excellent addition to any graduate course in optics.
Preface and Acknowledgements. 1: Photonic Crystals and Other ObscureTopics.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 ofCrosstalk 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: LinearWaveguides 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 inPhotonic-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 CompleteThree-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-iterativeFrequency-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.