Advances in FDTD Computational Electrodynamics Photonics and Nanotechnology -- Contents -- Preface -- Chapter 1 Parallel-Processing Three-Dimensional Staggered-Grid Local-Fourier-Basis PSTD Technique -- 1.1 INTRODUCTION -- 1.2 MOTIVATION -- 1.3 LOCAL FOURIER BASIS AND OVERLAPPING DOMAIN DECOMPOSITION -- 1.4 KEY FEATURES OF THE SL-PSTD TECHNIQUE -- 1.4.1 FFT on a Local Fourier Basis -- 1.4.2 Absence of the Gibbs Phenomenon Artifact -- 1.5 TIME-STEPPING RELATIONS FOR DIELECTRIC SYSTEMS -- 1.6 ELIMINATION OF NUMERICAL PHASE VELOCITY ERROR FOR A MONOCHROMATIC EXCITATION -- 1.7 TIME-STEPPING RELATIONS WITHIN THE PERFECTLY MATCHED LAYER ABSORBING OUTER BOUNDARY -- 1.8 REDUCTION OF THE NUMERICAL ERROR IN THE NEAR-FIELD TO FAR-FIELD TRANSFORMATION -- 1.9 IMPLEMENTATION ON A DISTRIBUTED-MEMORY SUPERCOMPUTING CLUSTER -- 1.10 VALIDATION OF THE SL-PSTD TECHNIQUE -- 1.10.1 Far-Field Scattering by a Plane-Wave-Illuminated Dielectric Sphere -- 1.10.2 Far-Field Radiation from an Electric Dipole Embedded within a Double-Layered Concentric Dielectric Sphere -- 1.11 SUMMARY -- REFERENCES -- Chapter 2 Unconditionally Stable Laguerre Polynomial-Based FDTD Method -- 2.1 INTRODUCTION -- 2.2 FORMULATION OF THE CONVENTIONAL 3-D LAGUERRE-BASED FDTD METHOD -- 2.3 FORMULATION OF AN EFFICIENT 3-D LAGUERRE-BASED FDTD METHOD -- 2.4 PML ABSORBING BOUNDARY CONDITION -- 2.5 NUMERICAL RESULTS -- 2.5.1 Parallel-Plate Capacitor: Uniform 3-D Grid -- 2.5.2 Shielded Microstrip Line: Graded Grid in One Direction -- 2.5.3 PML Absorbing Boundary Condition Performance -- 2.6 SUMMARY AND CONCLUSIONS -- REFERENCES -- Chapter 3 Exact Total-Field/Scattered-Field Plane-WaveSource Condition -- 3.1 INTRODUCTION -- 3.2 DEVELOPMENT OF THE EXACT TF/SF FORMULATION FOR FDTD -- 3.3 BASIC TF/SF FORMULATION -- 3.4 ELECTRIC AND MAGNETIC CURRENT SOURCES AT THE TF/SF INTERFACE.

3.5 INCIDENT PLANE-WAVE FIELDS IN A HOMOGENEOUS BACKGROUND MEDIUM -- 3.6 FDTD REALIZATION OF THE BASIC TF/SF FORMULATION -- 3.7 ON CONSTRUCTING AN EXACT FDTD TF/SF PLANE-WAVE SOURCE -- 3.8 FDTD DISCRETE PLANE-WAVE SOURCE FOR THE EXACT TF/SF FORMULATION -- 3.9 AN EFFICIENT INTEGER MAPPING -- 3.10 BOUNDARY CONDITIONS AND VECTOR PLANE-WAVE POLARIZATION -- 3.11 REQUIRED CURRENT DENSITIES Jinc AND Minc -- 3.12 SUMMARY OF METHOD -- 3.13 MODELING EXAMPLES -- 3.14 DISCUSSION -- REFERENCES -- Chapter 4 Electromagnetic Wave Source Conditions -- 4.1 OVERVIEW -- 4.2 INCIDENT FIELDS AND EQUIVALENT CURRENTS -- 4.2.1 The Principle of Equivalence -- 4.2.2 Discretization and Dispersion of Equivalent Currents -- 4.3 SEPARATING INCIDENT AND SCATTERED FIELDS -- 4.4 CURRENTS AND FIELDS: THE LOCAL DENSITY OF STATES -- 4.4.1 The Maxwell Eigenproblem and the Density of States -- 4.4.2 Radiated Power and the Harmonic Modes -- 4.4.3 Radiated Power and the LDOS -- 4.4.4 Computation of LDOS in FDTD -- 4.4.5 Van Hove Singularities in the LDOS -- 4.4.6 Resonant Cavities and Purcell Enhancement -- 4.5 EFFICIENT FREQUENCY-ANGLE COVERAGE -- 4.6 SOURCES IN SUPERCELLS -- 4.7 MOVING SOURCES -- 4.8 THERMAL SOURCES -- 4.9 SUMMARY -- REFERENCES -- Chapter 5 Rigorous PML Validation and a Corrected Unsplit PML for Anisotropic Dispersive Media -- 5.1 INTRODUCTION -- 5.2 BACKGROUND -- 5.3 COMPLEX COORDINATE STRETCHING BASIS OF PML -- 5.4 ADIABATIC ABSORBERS AND PML REFLECTIONS -- 5.5 DISTINGUISHING CORRECT FROM INCORRECT PML PROPOSALS -- 5.6 VALIDATION OF ANISOTROPIC PML PROPOSALS -- 5.7 TIME-DOMAIN PML FORMULATION FOR TERMINATING ANISOTROPIC DISPERSIVE MEDIA -- 5.8 PML FAILURE FOR OBLIQUE WAVEGUIDES -- 5.9 SUMMARY AND CONCLUSION -- ACKNOWLEDGMENTS -- APPENDIX 5A: TUTORIAL ON THE COMPLEX COORDINATE-STRETCHING BASIS OF PML -- 5A.1 Wave Equations -- 5A.2 Complex Coordinate Stretching.

5A.3 PML Examples -- 5A.4 PML in Inhomogeneous Media -- 5A.5 PML for Evanescent Waves -- APPENDIX 5B: REQUIRED AUXILIARY VARIABLES -- APPENDIX 5C: PML IN PHOTONIC CRYSTALS -- 5C.1 Conductivity Profile of the pPML -- 5C.2 Coupled-Mode Theory -- 5C.3 Convergence Analysis -- 5C.4 Adiabatic Theorems in Discrete Systems -- 5C.5 Toward Better Absorbers -- REFERENCES -- SELECTED BIBLIOGRAPHY -- Chapter 6 Accurate FDTD Simulation of Discontinuous Materials by Subpixel Smoothing -- 6.1 INTRODUCTION -- 6.2 DIELECTRIC INTERFACE GEOMETRY -- 6.3 PERMITTIVITY SMOOTHING RELATION, ISOTROPIC INTERFACE CASE -- 6.4 FIELD COMPONENT INTERPOLATION FOR NUMERICAL STABILITY -- 6.5 CONVERGENCE STUDY, ISOTROPIC INTERFACE CASE -- 6.6 PERMITTIVITY SMOOTHING RELATION, ANISOTROPIC INTERFACE CASE -- 6.7 CONVERGENCE STUDY, ANISOTROPIC INTERFACE CASE -- 6.8 CONCLUSIONS -- ACKNOWLEDGMENT -- APPENDIX 6A: OVERVIEW OF THE PERTURBATION TECHNIQUE USED TO DERIVE SUBPIXEL SMOOTHING -- REFERENCES -- Chapter 7 Stochastic FDTD for Analysis of Statistical Variation in Electromagnetic Fields -- 7.1 INTRODUCTION -- 7.2 DELTA METHOD: MEAN OF A GENERIC MULTIVARIABLE FUNCTION -- 7.3 DELTA METHOD: VARIANCE OF A GENERIC MULTIVARIABLE FUNCTION -- 7.4 FIELD EQUATIONS -- 7.5 FIELD EQUATIONS: MEAN APPROXIMATION -- 7.6 FIELD EQUATIONS: VARIANCE APPROXIMATION -- 7.6.1 Variance of the H-Fields -- 7.6.2 Variance of the E-Fields -- 7.7 SEQUENCE OF THE FIELD AND σ UPDATES -- 7.8 LAYERED BIOLOGICAL TISSUE EXAMPLE -- 7.9 SUMMARY AND CONCLUSIONS -- ACKNOWLEDGMENT -- REFERENCES -- Chapter 8 FDTD Modeling of Active Plasmonics -- 8.1 INTRODUCTION -- 8.2 OVERVIEW OF THE COMPUTATIONAL MODEL -- 8.3 LORENTZ-DRUDE MODEL FOR METALS -- 8.4 DIRECT-BANDGAP SEMICONDUCTOR MODEL -- 8.5 NUMERICAL RESULTS -- 8.5.1 Amplification of a 175-fs Optical Pulse in a Pumped Parallel-Plate Waveguide.

8.5.2 Resonance Shift and Radiation from a Passive Disk-Shaped GaAs Microcavity with Embedded Gold Nanocylinders -- 8.6 SUMMARY -- APPENDIX 8A: CRITICAL POINTS MODEL FOR METAL OPTICAL PROPERTIES -- APPENDIX 8B: OPTIMIZED STAIRCASING FOR CURVED PLASMONIC SURFACES -- REFERENCES -- SELECTED BIBLIOGRAPHY -- Chapter 9 FDTD Computation of the Nonlocal Optical Properties of Arbitrarily Shaped Nanostructures -- 9.1 INTRODUCTION -- 9.2 THEORETICAL APPROACH -- 9.3 GOLD DIELECTRIC FUNCTION -- 9.4 COMPUTATIONAL CONSIDERATIONS -- 9.5 NUMERICAL VALIDATION -- 9.6 APPLICATION TO GOLD NANOFILMS (1-D SYSTEMS) -- 9.7 APPLICATION TO GOLD NANOWIRES (2-D SYSTEMS) -- 9.8 APPLICATION TO SPHERICAL GOLD NANOPARTICLES (3-D SYSTEMS) -- 9.9 SUMMARY AND OUTLOOK -- ACKNOWLEDGMENTS -- APPENDIX 9A: NONLOCAL FDTD ALGORITHM -- REFERENCES -- Chapter 10 Classical Electrodynamics Coupled to Quantum Mechanics for Calculation of Molecular Optical Properties: An RT-TDDFT/FDTD Approach -- 10.1 INTRODUCTION -- 10.2 REAL-TIME TIME-DEPENDENT DENSITY FUNCTION THEORY -- 10.3 BASIC FDTD CONSIDERATIONS -- 10.4 HYBRID QUANTUM MECHANICS/CLASSICAL ELECTRODYNAMICS -- 10.5 OPTICAL PROPERTY EVALUATION FOR A PARTICLE-COUPLED DYE MOLECULE FOR RANDOMLY DISTRIBUTED INCIDENT POLARIZATION -- 10.6 NUMERICAL RESULTS 1: SCATTERING RESPONSE FUNCTION OF A 20-nm-DIAMETER SILVER NANOSPHERE -- 10.7 NUMERICAL RESULTS 2: OPTICAL ABSORPTION SPECTRA OF THE N3 DYE MOLECULE -- 10.7.1 Isolated N3 Dye Molecule -- 10.7.2 N3 Dye Molecule Bound to an Adjacent 20-nm Silver Nanosphere -- 10.8 NUMERICAL RESULTS 3: RAMAN SPECTRA OF THE PYRIDINE MOLECULE -- 10.8.1 Isolated Pyridine Molecule -- 10.8.2 Pyridine Molecule Adjacent to a 20-nm Silver Nanosphere -- 10.9 SUMMARY AND DISCUSSION -- ACKNOWLEDGMENT -- REFERENCES -- Chapter 11Transformation Electromagnetics InspiredAdvances in FDTD Methods -- 11.1 INTRODUCTION.

11.2 INVARIANCE PRINCIPLE IN THE CONTEXT OF FDTD TECHNIQUES -- 11.3 RELATIVITY PRINCIPLE IN THE CONTEXT OF FDTD TECHNIQUES -- 11.4 COMPUTATIONAL COORDINATE SYSTEM AND ITS COVARIANT AND CONTRAVARIANT VECTOR BASES -- 11.4.1 Covariant and Contravariant Basis Vectors -- 11.4.2 Covariant and Contravariant Components of the Metric Tensor -- 11.4.3 Covariant and Contravariant Representation of a Vector -- 11.4.4 Converting Vectors to the Cartesian Basis and Vice Versa -- 11.4.5 Second-Rank Tensors in the Covariant and Contravariant Bases -- 11.5 EXPRESSING MAXWELL'S EQUATIONS USING THE BASIS VECTORS OF THE COMPUTATIONAL COORDINATE SYSTEM -- 11.6 ENFORCING BOUNDARY CONDITIONS BY USING COORDINATE SURFACES IN THE COMPUTATIONAL COORDINATE SYSTEM -- 11.7 CONNECTION WITH THE DESIGN OF ARTIFICIAL MATERIALS -- 11.7.1 Constitutive Tensors of a Simple Material -- 11.7.2 Constitutive Tensors of an Artificial Material -- 11.8 TIME-VARYING DISCRETIZATIONS -- 11.9 CONCLUSION -- REFERENCES -- SELECTED BIBLIOGRAPHY -- Chapter 12 FDTD Modeling of Nondiagonal Anisotropic Metamaterial Cloaks -- 12.1 INTRODUCTION -- 12.2 STABLE FDTD MODELING OF METAMATERIALS HAVING NONDIAGONAL PERMITTIVITY TENSORS -- 12.3 FDTD FORMULATION OF THE ELLIPTIC CYLINDRICAL CLOAK -- 12.3.1 Diagonalization -- 12.3.2 Mapping Eigenvalues to a Dispersion Model -- 12.3.3 FDTD Discretization -- 12.4 MODELING RESULTS FOR AN ELLIPTIC CYLINDRICAL CLOAK -- 12.5 SUMMARY AND CONCLUSIONS -- REFERENCES -- Chapter 13 FDTD Modeling of Metamaterial Structures -- 13.1 INTRODUCTION -- 13.2 TRANSIENT RESPONSE OF A PLANAR NEGATIVE-REFRACTIVE-INDEX LENS -- 13.2.1 Auxiliary Differential Equation Formulation -- 13.2.2 Illustrative Problem -- 13.3 TRANSIENT RESPONSE OF A LOADED TRANSMISSION LINE EXHIBITING A NEGATIVE GROUP VELOCITY -- 13.3.1 Formulation -- 13.3.2 Numerical Simulation Parameters and Results.

13.4 PLANAR ANISOTROPIC METAMATERIAL GRID.