Allen Taflove

• B.S.E.E., M.S.E.E. Ph.D.
• Professor (Full) at Northwestern University

This extensively revised and expanded third edition of the Artech House bestseller, Computational Electrodynamics: The Finite-Difference Time-Domain Method, offers the most up-to-date and definitive resource on this critical method for solving Maxwell’s equations. Material new to the third edition includes: • Advanced techniques for PSTD; • Advance...

In January 2015, in a Special Issue marking the 150th anniversary of the publication of Maxwell's equations, Nature Photonics prominently featured an interview with Prof. Taflove dealing with FDTD's multi-decade development and its historical significance, calling him the “father of the finite-difference time-domain technique.”

The Finite Difference Time Domain (FDTD) scheme has served the computational electrodynamics community very well and part of its success stems from its ability to satisfy the constraints in Maxwell's equations. Even so, in the previous paper of this series we were able to present a second order accurate Godunov scheme for computational electrodynam...

While classic finite-difference time-domain (FDTD) solutions of Maxwell's equations have served the computational electrodynamics (CED) community very well, formulations based on Godunov methodology have begun to show advantages. We argue that the formulations presented so far are such that FDTD schemes and Godunov-based schemes each have their own...

Remarkable breakthroughs have established the functionality of graphene and carbon nanotube transistors as replacements to silicon in conventional computing structures, and numerous spintronic logic gates have been presented. However, an efficient cascaded logic structure that exploits electron spin has not yet been demonstrated. In this work, we i...

Supplementary Figures, Supplementary Tables and Supplementary Note

Optical microscopy is the staple technique in the examination of microscale material structure in basic science and applied research. Of particular importance to biology and medical research is the visualization and analysis of the weakly scattering biological cells and tissues. However, the resolution of optical microscopy is limited to ≥200 nm du...

Combining finite-difference time-domain (FDTD) methods and modeling of optical microscopy modalities, we previously developed an open-source software package called Angora, which is essentially a "microscope in a computer." However, the samples being simulated were limited to nondispersive media. Since media dispersions are common in biological sam...

The spectrum registered by a reflected-light bright-field spectroscopic microscope (SM) can quantify the microscopically indiscernible, deeply subdiffractional length scales within samples such as biological cells and tissues. Nevertheless, quantification of biological specimens via any optical measures most often reveals ambiguous information abou...

Based on the difference between mean background of an optical sample refractive index n_0 and an outside medium, n_out, different than n_0, we study the reflection statistics of a one-dimensional weakly disordered optical medium with refractive index n(x)=n_0+dn(x). Considering dn(x) as color noise with the exponential spatial correlation decay len...

We previously established that spectroscopic microscopy can quantify subdiffraction-scale refractive index (RI) fluctuations in a label-free dielectric medium with a smooth surface. However, to study more realistic samples, such as biological cells, the effect of rough surface should be considered. In this Letter, we first report an analytical theo...

Angora is a free, open-source software package implementing the Finite-Difference Time-Domain (FDTD) Method. This article explains how to access and use Angora, and introduces its features. Examples of its confi guration and use are given. These include treatment of planar stratifi ed and random materials, the creation of current sources and incide...

Despite major importance in physics, biology, and other sciences, the optical sensing of nanoscale structures in the far zone remains an open problem due to the fundamental diffraction limit of resolution. We establish that the expected value of spectral variance (Σ[over ˜]^{2}) of a far-field, diffraction-limited microscope image can quantify the...

Exploration of nanoscale tissue structures is crucial in understanding biological processes. Although novel optical microscopy methods have been developed to probe cellular features beyond the diffraction limit, nanometer-scale quantification remains still inaccessible for in situ tissue. Here we demonstrate that, without actually resolving specifi...

This paper introduces an iterative scheme to overcome the unresolved issues presented in S-FDTD (stochastic finite-difference time-domain) for obtaining ensemble average field values recently reported by Smith and Furse in an attempt to replace the brute force multiple-realization also known as Monte-Carlo approach with a single-realization scheme....

We demonstrate how a tightly-focused coherent TEM mn laser beam can be computed in the finite-difference time-domain (FDTD) method. The electromagnetic field around the focus is decomposed into a plane-wave spectrum, and approximated by a finite number of plane waves injected into the FDTD grid using the total-field/scattered-field (TF/SF) method....

Spatial solitons with beamwidths on the order of a wavelength are studied numerically in the context of their propagation paths being modified by planar nanoplasmonic structures.The prospect of such media in certain configurations used as soliton guiding devices is quantitatively assessed. A finite‐difference time‐domain model is used that incorpor...

Various staining techniques are commonly used in biomedical research to investigate cellular morphology. By inducing absorption of light, staining dyes change the intracellular refractive index due to the Kramers–Kronig relationship. We present a method for creating 2D maps of real and imaginary refractive indices of stained biological cells using...

We report a frequency-domain near-field-to-far-field transform (NFFFT) for the numerical modeling of radiation and scattering in planar multilayered spaces. Although the results are equivalent to those of Demarest (1996), the formulation is more compact, more stable, and applicable to observation angles in the lower half space. Furthermore, the r...

Quantification of intracellular nanoscale macromolecular density distribution is a fundamental aspect to understanding cellular processes. We report a near-field penetrating optical microscopy (NPOM) technique to directly probe the internal nanoscale macromolecular density of biological cells through quantification of intracellular refractive index...

In this Letter, we describe an easy to implement technique to measure the spatial backscattering impulse-response at length scales shorter than a transport mean free path with resolution of better than 10 μm using the enhanced backscattering phenomenon. This technique enables spectroscopic measurements throughout the visible range and sensitivity t...

We consider the interaction between two (1+1)D ultra-narrow optical spatial solitons in a nonlinear dispersive medium using the finite-difference time-domain (FDTD) method for the transverse magnetic (TM) polarization. The model uses the general vector auxiliary differential equation (GVADE) approach to include multiple electric-field components, a...

Rigorous numerical modeling of optical systems has attracted interest in diverse research areas ranging from biophotonics to photolithography. We report the full-vector electromagnetic numerical simulation of a broadband optical imaging system with partially coherent and unpolarized illumination. The scattering of light from the sample is calculate...

We report what we believe is the first experimental confirmation at visible light wavelengths of the backscattering enhancement phenomenon of the photonic nanojet. A specially designed sample stage consisting of a multilayered sandwich of glass, solid polydimethylsiloxane (PDMS), and liquid PDMS, permitted the precise positioning of a gold nanopart...

Most cancers are curable if they are diagnosed and treated at an early stage. Recent studies suggest that nanoarchitectural changes occur within cells during early carcinogenesis and that such changes precede microscopically evident tissue alterations. It follows that the ability to comprehensively interrogate cell nanoarchitecture (e.g., macromole...

We report a study of the nanoscale mass-density fluctuations of heterogeneous optical dielectric media, including nanomaterials and biological cells, by quantifying their nanoscale light-localization properties. Transmission electron microscope images of the media are used to construct corresponding effective disordered optical lattices. Light-loca...

We provide a methodology for accurately predicting elastic backscattering radial distributions from random media with two simple empirical models. We apply these models to predict the backscattering based on two classes of scattering phase functions: the Henyey-Greenstein phase function and a generalized two parameter phase function that is derived...

We correct a typo found in [Opt. Express 17, 3722-3731 (2009)]. The overall approach and results stay unchanged.

This paper reviews the substantial body of literature emerging since 2004 concerning photonic nanojets. The photonic nanojet is a narrow, high-intensity, non-evanescent light beam that can propagate over a distance longer than the wavelength λ after emerging from the shadow-side surface of an illuminated lossless dielectric microcylinder or microsp...

A rigorous error analysis is presented for the scattering coefficient of biological random continuous media in the Born (or single-scattering) approximation. The analysis is done in two dimensions (2-D) for simplicity of numerical computation. Scattering coefficients of various tissue-like random media are numerically calculated via statistical fin...

We discuss the usage of the photonic nanojet to detect deeply subwavelength pits in a metal substrate for the purpose of high-density optical data storage. Three-dimensional finite-difference time-domain (FDTD) computational solutions of Maxwell's equations are used to analyze and design the system. We find that nanojet-illuminated pits having late...

An optically illuminated micron-scale dielectric sphere can generate a photonic nanojet – a nonresonant propagating beam phenomenon of high amplitude, narrow waist, and substantial sensitivity to the presence of nanometer-scale particles and geometric features located within the beam. Via three-dimensional finite-difference time-domain computationa...

Recently, there has been a major thrust to understand biological processes at the nanoscale. Optical microscopy has been exceedingly useful in imaging cell microarchitecture. Characterization of cell organization at the nanoscale, however, has been stymied by the lack of practical means of cell analysis at these small scales. To address this need,...

A straightforward procedure is described for accurately creating an incident focused light pulse in the 3-D finite-difference time-domain (FDTD) electromagnetic simulation of the image space of an aplanatic converging lens. In this procedure, the focused light pulse is approximated by a finite sum of plane waves, and each plane wave is introduced i...

We show that our recently reported microwave photonic jet technique for detection of deeply subwavelength pits in a metal substrate can be extended to optical wavelengths for purposes of high-density data storage. Three-dimensional finite-difference time-domain computational solutions of Maxwell’s equations are used to optimize the photonic nanojet...

We report a means to detect deeply subwavelength pits in optical data-storage media by employing the recently observed giant backscattering perturbation phenomenon of the photonic jet. We conducted microwave experiments with dimensionally scaled-up pits and lands in a simulated optical data-storage device. These measurements were backed up by three...

In the above titled paper (ibid., vol. 52, no. 8, pp. 2040-2045, Aug 04), the authors adapted and used with permission a code developed by C.-W. Shu, Brown University, Providence, RI. During the adaptation, data errors were introduced into the code. After the errors were corrected, the authors were unable to reproduce the microwave nonlinearity at...

An accurate description of the electrode-electrolyte interfacial impedance is critical to the development of computational models of neural recording and stimulation that aim to improve understanding of neuro-electric interfaces and to expedite electrode design. This work examines the effect that the electrode-electrolyte interfacial impedance has...

A numerical model based on the finite-difference time-domain FDTD method is developed to simulate thermal noise in open cavities owing to output coupling. The absorbing boundary of the FDTD grid is treated as a blackbody, whose thermal radiation penetrates the cavity in the grid. The calculated amount of thermal noise in a one-dimensional dielectri...

We theoretically investigate light scattering from a bi-sphere system consisting of a gold nanosphere and a lossless dielectric microsphere illuminated at a resonant optical wavelength of the microsphere. Using generalized multisphere Mie theory, we find that a gold nanosphere 100 times smaller than the dielectric microsphere can be detected with a...

Using the finite-difference time-domain method, we model the propagation of spatial optical solitons having two orthogonal electric field vector components, and the scattering of such solitons by compact subwavelength air holes (i.e., abrupt dielectric discontinuities in the direct paths of the solitons). Our propagation and scattering studies assu...

Wave propagation at the bottom of the electromagnetic spectrum (below 300 kHz) in the Earth-ionosphere waveguide system has been an interesting and important area of investigation for the last four decades. Such wave propagation is characterized by complex phenomena involving nonhomogeneous and anisotropic media, and can result in resonances of the...

We report anomalous oscillatory features in the spectra of cross-polarized backscattered light from inhomogeneous dielectric microparticles. Numerical experiments based on the finite-difference-time-domain method demonstrate that cross-polarized backscattered spectra exhibit oscillation frequencies with two a priori surprising features. First, the...

This paper arises from an invited plenary talk by the author at the 2006 Applied Computational Electromagnetics Society Symposium in Miami, FL (The 71 original slides can be downloaded at http://www.ece.northwestern.edu/ecefaculty/ taflove/ACES_talk.pdf). This paper summarizes the author's perspectives on the history and future prospects of finite-...

The authors report experimental confirmation of backscattering enhancement induced by a photonic jet emerging from a dielectric sphere, a phenomenon recently predicted by theoretical solutions of Maxwell's equations. To permit relatively straightforward laboratory measurements at microwave frequencies rather than visible light, they appropriately s...

This letter proposes a novel extremely low frequency (ELF) radar for localized D-region (altitude < 95 km) ionospheric anomalies that have been generated by natural geophysical processes. The proposed system would use the former U.S. Navy Wisconsin Transmitting Facility as a distant well-characterized impulsive ELF source. Sample calculations that...

The auxiliary differential equation finite-difference time-domain method for modeling electromagnetic wave propagation in dispersive nonlinear materials is applied to problems where the electric field is not constrained to a single vector component. A full-vector Maxwell’s equations solution incorporating multiple-pole linear Lorentz, nonlinear Ker...

1] We report a full-vector, three-dimensional, numerical solution of Maxwell's equations for optical propagation within, and scattering by, a random medium of macroscopic dimensions. The total scattering cross section is determined using the pseudospectral time domain technique. Specific results reported in this paper indicate that multiply scatter...

This paper reports the first application of an optimized geodesic, three-dimensional (3-D) finite-difference time-domain (FDTD) grid to model impulsive, extremely low-frequency (ELF) electromagnetic wave propagation within the entire Earth-ionosphere cavity. This new model, which complements our previously reported efficient 3-D latitude-longitude...

This paper reports an experimental and computational study of substrate integrated waveguides (SIWs) optimized for use as ultrahigh-speed bandpass waveguiding digital interconnects. The novelty of this study resides in our successful design, fabrication, and testing of low-loss SIWs that achieve 100% relative bandwidths via optimal excitation of th...

Using the generalized multiparticle Mie theory, we investigate optical coupling and transport through chains of dielectric microspheres. We identify two distinct coupling mechanisms of optical transport in terms of the coupling efficiency between neighboring microspheres, namely, evanescent coupling and nanojet coupling. We demonstrate that perfect...

An erratum is presented to acknowledge a reference omitted from the original paper.

This letter proposes a novel extremely low frequency (ELF) radar for major oil deposits. Using our recently developed whole-Earth electromagnetic wave propagation model based upon the finite-difference time-domain method, we have determined that detection of the radial (vertical) component of the scattered H-field provides a sensitive means to dete...

The design of metal microelectrodes that produce minimal damage to tissue and can successfully record from and stimulate targeted neural structures necessitates a thorough understanding of the electrical phenomena generated in the tissue surrounding the electrodes. Computational modeling has been a primary strategy used to study these phenomena, an...

We report what we believe to be a novel backscattering phenomenon associated with localized optical intensity peaks (spanning as little as 43 nm ) arising at the shadow-side surfaces of plane-wave-illuminated dielectric microcylinders of noncircular cross sections. Namely, for nanometer-scale dielectric particles positioned within the localized int...

We report a physical explanation for the phenomenon wherein the backscattering of light by dielectric particles of sizes between 100 and 1 nm is enhanced by 7-11 orders of magnitude. The phenomenon involves complex composite interactions between a dielectric microsphere and a nanoparticle positioned in close proximity to the microsphere. We provide...

The pseudospectral time-domain (PSTD) algorithm is implemented to numerically solve Maxwell’s equations to obtain the optical properties of millimeter-scale random media consisting of hundreds of micron-scale dielectric scatterers. Our methodology accounts for near-field interactions and coherent interference effects that are not easily modeled usi...

We discuss an emerging application of finite-difference time-domain (FDTD) computational electrodynamics: modeling transient ultra-low frequency (ULF) and extremely low frequency (ELF) propagation within the global Earth-ionosphere cavity. This permits for the first time a direct, three-dimensional, time-domain calculation of round-the-world ULV/EL...

We have performed a computational and experimental study of a promising new wireless interconnect for high-speed digital circuits employing linear defects in electromagnetic bandgap structures at 50 GHz center frequency. Our recent results confirm the scalability of this technology. We found that employing low-loss dielectrics can maintain the appr...

An emerging research area in biophotonics with potentially near-term clinical applications in early stage cancer detection involves the investigation of possible correlations of the elastic light scattering properties of tissues with alterations in their cellular composition and nanostructure. Until recently, exploring these correlations has been i...

The control of multifunctional myoelectric prostheses is a substantive area of research with the potential to dramatically improve the independence of transradial amputees. We present preliminary data for the development of a new technique for obtaining multiple electromyographic (EMG) signals for controlling multifunctional myoelectric hand and wr...

1] We report what we believe to be the first three-dimensional computational solution of the full-vector Maxwell's equations for hypothesized pre-seismic electromagnetic phenomena propagated within the entire Earth-ionosphere cavity. Periodic boundary conditions are used in conjunction with a variable-cell finite-difference time-domain (FDTD) space...

We report what we believe to be the first simulation of enhanced backscattering (EBS) of light by numerically solving Maxwell’s equations without heuristic approximations. Our simulation employs the pseudospectral time-domain (PSTD) technique, which we have previously shown enables essentially exact numerical solutions of Maxwell’s equations for li...

We study local and nonlocal correlations of light transmitted through active random media. The conventional approach results in divergence of ensemble-averaged correlation functions due to the existence of lasing realizations. We introduce a conditional average for correlation functions by omitting the divergent realizations. Our numerical simulati...

We extend the generalized total-field/scattered-field formulation of the finite-difference time-domain method to permit efficient computational modeling of three-dimensional (3-D) diffraction by infinite conducting and dielectric wedges. This new method allows: 1) sourcing a numerical plane wave having an arbitrary incident angle traveling into, or...

We determine the relationship between the depolarization properties of inhomogeneous particles and the statistical parameters of their internal refractive-index distributions. Our analysis demonstrates that the linear depolarization ratio of backscattered light by an inhomogeneous particle is approximately proportional to both the squared standard...

We report pattern formations during the drying of a sheet of an aqueous suspension of nanospheres. The structures self-assembled by nanospheres span several centimeters and exhibit order at scales ranging from nanometers to centimeters, although the substrate has no predefined pattern. Within these structures, several regular patterns can be identi...

We propose a simple yet effective modification to significantly improve the accuracy of the finite-difference time-domain (FDTD) near-to-far-field (NTFF) transformation for calculating the backscattering of objects having strong forward-scattering lobes. In the modified approach, we merely omit integrating over the near-field plane located in the f...

We report the phenomenon of ultra-enhanced backscattering of visible light by nanoparticles facilitated by the 3-D photonic nanojet – a sub-diffraction light beam appearing at the shadow side of a plane-wave-illuminated dielectric microsphere. Our rigorous numerical simulations show that backscattering intensity of nanoparticles can be enhanced up...

The letter reports the initial application of a geodesic finite-difference time-domain (FDTD) grid to model impulsive extremely low frequency electromagnetic wave propagation about the Earth sphere. The two-dimensional transverse-magnetic grid is comprised entirely of hexagonal cells, except for a small fixed number of pentagonal cells needed for g...

This Addendum provides a revised set of figures containing converged numerical data for total scattering cross section (TSCS), replacing the figures in our recent publication [Opt. Lett. 29, 1393 (2004)]. Due to the use of an overly large time step, our original TSCS data exhibited a systematic, nonphysical diminution above 150 THz for all cases st...

We report the development and validation of the equiphase-sphere (EPS) approximation for calculating the total-scattering cross-section (TSCS) spectra of inhomogeneous microparticles having complex interior structures. We show that this closed-form, analytical approximation can accurately model the TSCS of randomly inhomogeneous spherical particles...

A computational hydrodynamics model consisting of a system of four coupled time-domain partial differential equations is applied to study the response of the cellular sodium ion channel to a microwave electric-field excitation. The model employs a dynamic conservation law formulation, which has not been previously applied to this problem. Results i...

We extend the previously proposed concept of equiphase sphere (EPS) to analyze light-scattering properties of arbitrarily shaped particles. Our analyses based on the Wentzel-Kramers-Brillouin technique and numerical studies based on the finite-difference time-domain method demonstrate that a wide range of irregularly shaped particles can be approxi...

We report a new finite-difference time-domain (FDTD) computational model of the lasing dynamics of a four-level two-electron atomic system. Transitions between the energy levels are governed by coupled rate equations and the Pauli Exclusion Principle. This approach is an advance relative to earlier FDTD models that did not include the pumping dynam...

It is well-known that the finite-difference time-domain (FDTD) method is subject to significant errors due to the staircasing of surfaces that are not precisely aligned with major grid planes. Dey and Mittra introduced a locally conformal method (D-FDTD) that has shown substantial gains in the accuracy of modeling arbitrary surfaces in the FDTD gri...

As clock rates continue to rise, problems with signal integrity, cross-coupling, and radiation may render impractical the baseband metallic interconnects presently used in computers. A potential means to address this problem is to use bandpass wireless interconnects operating at millimeter-wave center frequencies. We have conducted experimental and...

In an earlier work [Proc. SPIE 4484, 216 (2001)] we proposed a new AA1 modulation sequence for random-modulation continuous-wave lidar. It possesses significantly better signal properties than other pseudorandom codes (the M, A1, and A2 sequences). We derive and compare the signal-to-noise ratio (SNR) of the new AA1 sequence with those of previous...

We report what we believe to be the first rigorous numerical solution of the two-dimensional Maxwell equations for optical propagation within, and scattering by, a random medium of macroscopic dimensions. Our solution is based on the pseudospectral time-domain technique, which provides essentially exact results for electromagnetic field spatial mod...

Understanding light scattering by nonspherical particles is crucial in modeling the transport of light in realistic structures such as biological tissues. We report the application of novel analytical approaches based on modified Wentzel–Kramers–Brillouin and equiphase-sphere methods that facilitate accurate characterization of light scattering by...

We applied a finite-difference time domain algorithm to the study of field and intensity correlations in random media. Close to the onset of Anderson localization, we observe deviations of the correlation functions, in both shape and magnitude, from those predicted by the diffusion theory. Physical implications of the observed phenomena are discuss...

We study local and nonlocal correlations of light transmitted through active random media. The conventional approach results in divergence of ensemble averaged correlation functions due to existence of lasing realizations. We introduce conditional average for correlation functions by omitting the divergent realizations. Our numerical simulation rev...

We report what we believe to be the first evidence of localized nanoscale photonic jets generated at the shadow-side surfaces of micron-scale, circular dielectric cylinders illuminated by a plane wave. These photonic nanojets have waists smaller than the diffraction limit and propagate over several optical wavelengths without significant diffractio...

We applied finite difference time domain (FDTD) algorithm to the study of field and intensity correlations in random media. Close to the onset of Anderson localization, we observe deviations of the correlation functions, in both shape and magnitude, from those predicted by the diffusion theory. Physical implications of the observed phenomena are di...

This paper reports the application of an efficient finite-difference time-domain (FDTD) algorithm to model impulsive extremely low frequency (ELF) propagation within the entire Earth-ionosphere cavity. Periodic boundary conditions are used in conjunction with a three-dimensional latitude-longitude FDTD space lattice which wraps around the complete...

We introduce the concept of the equiphase sphere for light scattering by nonspherical dielectric particles. This concept facilitates the derivation of a simple analytical expression for the total scattering cross section of such particles. We tested this concept for spheroidal particles and obtained a bound on the minor-to-major axis ratio for the...

We present what we believe to be the first algorithms that use a simple scalar-potential formulation to model linear Debye and Lorentz dielectric dispersions at low frequencies in the context of finite-element time-domain (FETD) numerical solutions of electric potential. The new algorithms, which permit treatment of multiple-pole dielectric relaxat...

We report the initial three-dimensional finite-difference time-domain modeling of a vertically coupled photonic racetrack. The modeling reveals details of the full suite of space–time behavior of electromagnetic-wave phenomena involved in guiding, coupling, multimoding, dispersion, and radiation. This behavior is not easily obtainable by analytical...

Finite-difference time-domain numerical experiments and supporting analyses demonstrate that the spectral dependence of the total scattering cross sections of randomly inhomogeneous dielectric spheres of sizes in the resonant range closely resemble those of their homogeneous counterparts that have a volume-averaged refractive index. This result hol...

The lumped-circuit, hybrid, finite-difference/FFT (fast Fourier transform) model described herein simulates effects of multiple discontinuities in a coaxial cable at variable distances on a time domain reflectometry (TDR) signature. This model is verified by comparison with measured reflections from perfectly defined, multiple deformities. Accurate...