Description
Advances in photonics and nanotechnology have the potential to revolutionize humanity's ability to communicate and compute. To pursue these advances, it is mandatory to understand and properly model interactions of light with materials such as silicon and gold at the nanoscale, i.e., the span of a few tens of atoms laid side by side. These interactions are governed by the fundamental Maxwell's equations of classical electrodynamics, supplemented by quantum electrodynamics. This book presents the current stateoftheart in formulating and implementing computational models of these interactions. Maxwell's equations are solved using the finitedifference timedomain (FDTD) technique, pioneered by the senior editor, whose prior Artech House books in this area are among the top ten mostcited in the history of engineering. You discover the most important advances in all areas of FDTD and PSTD computational modeling of electromagnetic wave interactions. This cuttingedge resource helps you understand the latest developments in computational modeling of nanoscale optical microscopy and microchip lithography. You also explore cuttingedge details in modeling nanoscale plasmonics, including nonlocal dielectric functions, molecular interactions, and multilevel semiconductor gain. Other critical topics include nanoscale biophotonics, especially for detecting earlystage cancers, and quantum vacuum, including the Casimir effect and blackbody radiation.
Table Of Contents
ParallelProcessing ThreeDimensional StaggeredGrid LocalFourierBasis PSTD Technique Introduction. Motivation. Local Fourier Basis and Overlapping Domain Decomposition. Key Features of the SLPSTD Technique. TimeStepping Relations for Dielectric Systems. Elimination of Numerical Phase Velocity Error for a Monochromatic Excitation. TimeStepping Relations within the Perfectly Matched Layer Absorbing Outer Boundary. Reduction of the Numerical Error in the NearField to FarField Transformation. Implementation on a DistributedMemory Supercomputing Cluster. Validation of the SLPSTD Technique. Summary. ; Unconditionally Stable Laguerre PolynomialBased FDTD Method Introduction. Formulation of the Conventional 3D LaguerreBased FDTD Method. Formulation of an Efficient 3D LaguerreBased FDTD Method. PML Absorbing Boundary Condition. Numerical Results. Summary and Conclusions. ; Exact TotalField/ScatteredField PlaneWave Source Condition Introduction. Development of the Exact TF/SF Formulation for FDTD. Basic TF/SF Formulation. Electric and Magnetic Current Sources at the TF/SF Interface. Incident PlaneWave Fields in a Homogeneous Background Medium. FDTD Realization of the Basic TF/SF Formulation. On Constructing an Exact FDTD TF/SF PlaneWave Source. FDTD Discrete PlaneWave Source for the Exact TF/SF Formulation. An Efficient Integer Mapping. Boundary Conditions and Vector PlaneWave Polarization. Required Current Densities Jinc and Minc. Summary of Method. Modeling Examples. Discussion.; Electromagnetic Wave Source Conditions  Overview. Incident Fields and Equivalent Currents. Separating Incident and Scattered Fields. Currents and Fields: The Local Density of States. Efficient FrequencyAngle Coverage. Sources in Supercells. Moving Sources. Thermal Sources. Summary. ; Rigorous PML Validation and a Corrected Unsplit PML for Anisotropic Dispersive Media Introduction. Background. Complex Coordinate Stretching Basis of PML. Adiabatic Absorbers and PML Reflections. Distinguishing Correct from Incorrect PML Proposals. Validation of Anisotropic PML Proposals. TimeDomain PML Formulation for Terminating Anisotropic Dispersive Media. PML Failure for Oblique Waveguides. Summary and Conclusions. Appendices. ; Accurate FDTD Simulation of Discontinuous Materials by Subpixel Smoothing Introduction. Dielectric Interface Geometry. Permittivity Smoothing Relation, Isotropic Interface Case. Field Component Interpolation for Numerical Stability. Convergence Study, Isotropic Interface Case. Permittivity Smoothing Relation, Anisotropic Interface Case. Convergence Study, Anisotropic Interface Case. Conclusions. Appendices. ; Stochastic FDTD for Analysis of Statistical Variation in Electromagnetic Fields Introduction. Delta Method: Mean of a Generic Multivariable Function. Delta Method: Variance of a Generic Multivariable Function. Field Equations. Field Equations: Mean Approximation. Field Equations: Variance Approximation. Sequence of the Field and œÉ Updates. Layered Biological Tissue Example. Summary and Conclusions. ; FDTD Modeling of Active Plasmonics Introduction. Overview of the Computational Model. LorentzDrude Model for Metals. DirectBandgap Semiconductor Model. Numerical Results. Summary. Appendices.; FDTD Computation of the Nonlocal Optical Properties of Arbitrarily Shaped Nanostructures Introduction. Theoretical Approach. Gold Dielectric Function. Computational Considerations. Numerical Validation. Application to Gold Nanofilms (1D Systems). Application to Gold Nanowires (2D Systems). Application to Spherical Gold Nanoparticles (3D Systems). Summary and Outlook. Appendices.; Classical Electrodynamics Coupled to Quantum Mechanics for Calculation of Molecular Optical Properties: An RTTDDFT/FDTD Approach Introduction. RealTime TimeDependent Density Function Theory. Basic FDTD Considerations. Hybrid Quantum Mechanics/Classical Electrodynamics. Optical Property Evaluation for a ParticleCoupled Dye Molecule for Randomly. Numerical Results 1: Scattering Response Function of a 20nmDiameter Silver Nanosphere. Numerical Results 2: Optical Absorption Spectra of the N3 Dye Molecule. Numerical Results 3: Raman Spectra of the Pyridine Molecule. Summary and Discussion. ; Transformation Electromagnetics Inspired Advances in FDTD Methods Introduction. Invariance Principle in the Context of FDTD Techniques. Relativity Principle in the Context of FDTD Techniques. Computational Coordinate System and Its Covariant and Contravariant Vector Bases. Expressing Maxwell 's Equations Using the Basis Vectors of the Computational Coordinate System. Enforcing Boundary Conditions by Using Coordinate Surfaces in the Computational Coordinate System. Connection with the Design of Artificial Materials. TimeVarying Discretizations. Conclusion. ; FDTD Modeling of Nondiagonal Anisotropic Metamaterial Cloaks Introduction. Stable FDTD Modeling of Metamaterials Having Nondiagonal Permittivity Tensors. FDTD Formulation of the Elliptic Cylindrical Cloak. Modeling Results for an Elliptic Cylindrical Cloak. Summary and Conclusions. ; FDTD Modeling of Metamaterial Structures Introduction. Transient Response of a Planar NegativeRefractiveIndex Lens. Transient Response of a Loaded Transmission Line Exhibiting a Negative Group Velocity. Planar Anisotropic Metamaterial Grid. Periodic Geometries Realizing Metamaterial Structures. The SineCosine Method. Dispersion Analysis of a Planar NegativeRefractiveIndex Transmission Line. Coupling the ArrayScanning and SineCosine Methods. Application of the ArrayScanning Method to a PointSourced Planar PositiveRefractiveIndex Transmission Line. Application of the ArrayScanning Method to the Planar Microwave Perfect Lensù. TriangularMesh FDTD Technique for Modeling Optical Metamaterials with Plasmonic Elements. Analysis of a SubWavelength Plasmonic Photonic Crystal Using the TriangularMesh FDTD Technique. Summary and Conclusions.; Computational Optical Imaging Using the FiniteDifference TimeDomain Method Introduction. Basic Principles of Optical Coherence. Overall Structure of the Optical Imaging System. Illumination Subsystem. Scattering Subsystem. Collection Subsystem. Refocusing Subsystem. Implementation Examples: Numerical Microscope Images. Summary. Appendices.; Computational Lithography Using the FiniteDifference TimeDomain Method Introduction. Projection Lithography. Computational Lithography. FDTD Modeling for Projection Lithography. Applications of FDTD. FDTD Modeling for Extreme Ultraviolet Lithography. Summary and Conclusions. Appendices.; FDTD and PSTD Applications in Biophotonics Introduction. FDTD Modeling Applications. Overview of FourierBasis PSTD Techniques for Maxwell 's Equations. PSTD and SLPSTD Modeling Applications. Summary.; GVADE FDTD Modeling of Spatial Solitons Introduction. Analytical and Computational Background. MaxwellAmpere Law Treatment of Nonlinear Optics. General Vector Auxiliary Differential Equation Method. Applications of GVADE FDTD to TM Spatial Soliton Propagation. Applications of GVADE FDTD to TM Spatial Soliton Scattering. Summary. ; FDTD Modeling of Blackbody Radiation and Electromagnetic Fluctuations in Dissipative Open Systems Introduction. Studying Fluctuation and Dissipation with FDTD. Introducing Blackbody Radiation into the FDTD Grid. Simulations in Vacuum. Simulations of an Open Cavity. Summary and Outlook.; Casimir Forces in Arbitrary Material Geometries Introduction. Theoretical Foundation. Reformulation in Terms of a Harmonic Expansion. Numerical Study 1: A 2D Equivalent to a 3D Configuration. Numerical Study 2: Dispersive Dielectric Materials. Numerical Study 3: Cylindrical Symmetry in Three Dimensions. Numerical Study 4: Periodic Boundary Conditions. Numerical Study 5: Fully 3D FDTDCasimir Computation. Generalization to Nonzero Temperatures. Summary and Conclusions. ; Meep: A Flexible Free FDTD Software Package Introduction. Grids and Boundary Conditions. Approaching the Goal of Continuous SpaceTime Modeling. Materials. Enabling Typical Computations. User Interface and Scripting. Abstraction Versus Performance. Summary and Conclusions. ;
Author

Steven G. Johnson
Steven G. Johnson is an associate professor of applied Mathematics at the Massachusetts Institute of Technology. He holds a B.S. degrees in physics, mathematics, and computer science and a Ph.D. in physics, all from the Massachusetts Institute of Technology.

Ardavan Oskooi
Ardavan Oskooi is a postdoctoral associate at Kyoto University. He holds a B.S. in engineering science from the University of Toronto, and an M.S. in computation and engineering and Sc.D. in materials science and engineering from the Massachusetts Institute of Technology.

Allen Taflove
Dr. Allen Taflove has pioneered the finitedifference timedomain method since 1972, and is a leading authority in the field of computational electrodynamics. He is a professor at Northwestern University, where he also received his B.S., M.S. and Ph.D. degrees. A Fellow of IEEE, Dr. Taflove is listed on ISIHighlyCited.com as one of the mostcited researchers in the world.