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 state-of-the-art in formulating and implementing computational models of these interactions. Maxwell's equations are solved using the finite-difference time-domain (FDTD) technique, pioneered by the senior editor, whose prior Artech House books in this area are among the top ten most-cited 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 cutting-edge resource helps you understand the latest developments in computational modeling of nanoscale optical microscopy and microchip lithography. You also explore cutting-edge details in modeling nanoscale plasmonics, including nonlocal dielectric functions, molecular interactions, and multi-level semiconductor gain. Other critical topics include nanoscale biophotonics, especially for detecting early-stage cancers, and quantum vacuum, including the Casimir effect and blackbody radiation.
Table Of Contents
Parallel-Processing Three-Dimensional Staggered-Grid Local-Fourier-Basis PSTD Technique -Introduction. Motivation. Local Fourier Basis and Overlapping Domain Decomposition. Key Features of the SL-PSTD Technique. Time-Stepping Relations for Dielectric Systems. Elimination of Numerical Phase Velocity Error for a Monochromatic Excitation. Time-Stepping Relations within the Perfectly Matched Layer Absorbing Outer Boundary. Reduction of the Numerical Error in the Near-Field to Far-Field Transformation. Implementation on a Distributed-Memory Supercomputing Cluster. Validation of the SL-PSTD Technique. Summary. ; Unconditionally Stable Laguerre Polynomial-Based FDTD Method -Introduction. Formulation of the Conventional 3-D Laguerre-Based FDTD Method. Formulation of an Efficient 3-D Laguerre-Based FDTD Method. PML Absorbing Boundary Condition. Numerical Results. Summary and Conclusions. ; Exact Total-Field/Scattered-Field Plane-Wave 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 Plane-Wave Fields in a Homogeneous Background Medium. FDTD Realization of the Basic TF/SF Formulation. On Constructing an Exact FDTD TF/SF Plane-Wave Source. FDTD Discrete Plane-Wave Source for the Exact TF/SF Formulation. An Efficient Integer Mapping. Boundary Conditions and Vector Plane-Wave 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 Frequency-Angle 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. Time-Domain 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. Lorentz-Drude Model for Metals. Direct-Bandgap 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 (1-D Systems). Application to Gold Nanowires (2-D Systems). Application to Spherical Gold Nanoparticles (3-D Systems). Summary and Outlook. Appendices.; Classical Electrodynamics Coupled to Quantum Mechanics for Calculation of Molecular Optical Properties: An RT-TDDFT/FDTD Approach -Introduction. Real-Time Time-Dependent Density Function Theory. Basic FDTD Considerations. Hybrid Quantum Mechanics/Classical Electrodynamics. Optical Property Evaluation for a Particle-Coupled Dye Molecule for Randomly. Numerical Results 1: Scattering Response Function of a 20-nm-Diameter 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. Time-Varying 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 Negative-Refractive-Index Lens. Transient Response of a Loaded Transmission Line Exhibiting a Negative Group Velocity. Planar Anisotropic Metamaterial Grid. Periodic Geometries Realizing Metamaterial Structures. The Sine-Cosine Method. Dispersion Analysis of a Planar Negative-Refractive-Index Transmission Line. Coupling the Array-Scanning and Sine-Cosine Methods. Application of the Array-Scanning Method to a Point-Sourced Planar Positive-Refractive-Index Transmission Line. Application of the Array-Scanning Method to the Planar Microwave Perfect Lensù. Triangular-Mesh FDTD Technique for Modeling Optical Metamaterials with Plasmonic Elements. Analysis of a Sub-Wavelength Plasmonic Photonic Crystal Using the Triangular-Mesh FDTD Technique. Summary and Conclusions.; Computational Optical Imaging Using the Finite-Difference Time-Domain 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 Finite-Difference Time-Domain 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 Fourier-Basis PSTD Techniques for Maxwell 's Equations. PSTD and SL-PSTD Modeling Applications. Summary.; GVADE FDTD Modeling of Spatial Solitons -Introduction. Analytical and Computational Background. Maxwell-Ampere 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 2-D Equivalent to a 3-D 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 3-D FDTD-Casimir 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 Space-Time Modeling. Materials. Enabling Typical Computations. User Interface and Scripting. Abstraction Versus Performance. Summary and Conclusions. ;