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137
A 3D Perfectly Matched Medium from Modified Maxwell's Equations with Stretched Coordinates
 Microwave Opt. Tech. Lett
, 1994
"... A modified set of Maxwell's equations is presented that includes complex coordinate stretching along the three cartesian coordinates. The added degrees of freedom in the modified Maxwell's equations allow the specification of absorbing boundaries with zero reflection at all angles of incid ..."
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Cited by 256 (18 self)
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A modified set of Maxwell's equations is presented that includes complex coordinate stretching along the three cartesian coordinates. The added degrees of freedom in the modified Maxwell's equations allow the specification of absorbing boundaries with zero reflection at all angles of incidence and all frequencies. The modified equations are also related to the perfectly matched layer that was presented recently for 2D wave propagation. Absorbing material boundary conditions are of particular interest for finite difference time domain (FDTD) computations on a singleinstruction multipledata (SIMD) massively parallel supercomputer. A 3D FDTD algorithm has been developed on a Connection Machine CM5 based on the modified Maxwell's equations and simulation results are presented to validate the approach. 1. Introduction The finite difference time domain method [1, 2] is widely regarded as one of the most popular computational electromagnetics algorithms. Although FDTD is conceptually v...
On Nonreflecting Boundary Conditions
 J. COMPUT. PHYS
, 1995
"... Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated ..."
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Cited by 219 (4 self)
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Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated condition. Second, the exact DtN boundary condition is derived for elliptic and spheroidal coordinates. Third, approximate local boundary conditions are derived for these coordinates. Fourth, the truncated DtN condition in elliptic and spheroidal coordinates is modified to remove difficulties. Fifth, a sequence of new and more accurate local boundary conditions is derived for polar coordinates in two dimensions. Numerical results are presented to demonstrate the usefulness of these improvements.
Numerical Solution Of Problems On Unbounded Domains. A Review
 A review, Appl. Numer. Math
, 1998
"... While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears most significant in many ..."
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Cited by 126 (19 self)
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While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems represent a wide class of important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms and interpretation of the results. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computa...
Adaptive Multilevel Methods for Edge Element Discretizations of Maxwell's Equations
, 1997
"... . The focus of this paper is on the efficient solution of boundary value problems involving the doublecurl operator. Those arise in the computation of electromagnetic fields in various settings, for instance when solving the electric or magnetic wave equation with implicit timestepping, when tackl ..."
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Cited by 32 (12 self)
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. The focus of this paper is on the efficient solution of boundary value problems involving the doublecurl operator. Those arise in the computation of electromagnetic fields in various settings, for instance when solving the electric or magnetic wave equation with implicit timestepping, when tackling timeharmonic problems or in the context of eddycurrent computations. Their discretization is based on on N'ed'elec's H(curl;\Omega\Gamma7131/59948 edge elements on unstructured grids. In order to capture local effects and to guarantee a prescribed accuracy of the approximate solution adaptive refinement of the grid controlled by a posteriori error estimators is employed. The hierarchy of meshes created through adaptive refinement forms the foundation for the fast iterative solution of the resulting linear systems by a multigrid method. The guiding principle underlying the design of both the error estimators and the multigrid method is the separate treatment of the kernel of the cu...
Design and fabrication of silicon photonic crystal optical waveguides
 Journal of Lightwave Technology
, 2000
"... Abstract—We have designed and fabricated waveguides that incorporate twodimensional (2D) photonic crystal geometry for lateral confinement of light, and total internal reflection for vertical confinement. Both square and triangular photonic crystal lattices were analyzed. A threedimensional (3D) ..."
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Cited by 32 (2 self)
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Abstract—We have designed and fabricated waveguides that incorporate twodimensional (2D) photonic crystal geometry for lateral confinement of light, and total internal reflection for vertical confinement. Both square and triangular photonic crystal lattices were analyzed. A threedimensional (3D) finitedifference timedomain (FDTD) analysis was used to find design parameters of the photonic crystal and to calculate dispersion relations for the guided modes in the waveguide structure. We have developed a new fabrication technique to define these waveguides into silicononinsulator material. The waveguides are suspended in air in order to improve confinement in the vertical direction and symmetry properties of the structure. Highresolution fabrication allowed us to include different types of bends and optical cavities within the waveguides. Index Terms—Finitedifference timedomain (FDTD) methods, nanooptics, optical device fabrication, photonic bandgap (PBG) materials, photonic crystals (PCS), photonic crystal waveguides. I.
Threedimensional computation of light scattering from cells
 IEEE J. Sel. Top. Quantum Electron
, 1996
"... Abstract — Using the finitedifference timedomain method, threedimensional scattering patterns are computed for cells containing multiple organelles. The scattering cross section and average cosine of the scattering angle are computed for cells as a function of volume fraction of melanin granules ..."
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Abstract — Using the finitedifference timedomain method, threedimensional scattering patterns are computed for cells containing multiple organelles. The scattering cross section and average cosine of the scattering angle are computed for cells as a function of volume fraction of melanin granules and mitochondria. Results show that small organelles play a significant role in light scattering from cells, and the volume fraction of organelles affects both the total amount of scattered light and the angular distribution of scattered light. I.
Ultrasmall and ultralow threshold GaInAsPInP microdisk injection lasers: Design, fabrication, lasing characteristics and spontaneous emission factor
 in Quantum Electronics 5
, 1999
"... Abstract—We have calculated lasing characteristics of current injection microdisk lasers of several microns in diameter, taking account of the scattering loss at center posts and the carrier diffusion effect. We found that the optimum width of the disk wing exposed to the air is 0.6–0.7 m and the mi ..."
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Cited by 25 (1 self)
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Abstract—We have calculated lasing characteristics of current injection microdisk lasers of several microns in diameter, taking account of the scattering loss at center posts and the carrier diffusion effect. We found that the optimum width of the disk wing exposed to the air is 0.6–0.7 m and the minimum threshold current is nearly 10 A for the disk diameter of 2 m. The internal differential quantum efficiency can be 95 % if the transparent carrier density is reduced to 7.5 1017 cm3 and the diffusion constant is increased to 8 cm2/s. In the experiment, we have obtained the room temperature continuouswave operation of a GaInAsP–InP device of 3 m in diameter, for the first time, with a record low threshold of 150 A. This achievement was mainly owing to the reduction of the scattering loss at the disk edge, and hence the reduction of the threshold current density. The spontaneous emission factor was estimated to be 6 103. This value was much reduced by the large detuning of the lasing wavelength against the spontaneous emission peak. A larger value over 0.1, which is expected for such a small device, will be obtained by the wavelength tuning and the narrowing of the spontaneous emission spectrum. Index Terms — FDTD, GaInAsP–InP, microcavity, microdisk, semiconductor laser, spontaneous emission control, whispering gallery mode. I.
Finitedifference timedomain simulation of ground penetrating radar on dispersive, inhomogeneous, and conductive soils
 IEEE Trans. Geosci. Remote Sensing
, 1998
"... Abstract — A threedimensional (3D) timedomain numerical scheme for simulation of ground penetrating radar (GPR) on dispersive and inhomogeneous soils with conductive loss is described. The finitedifference timedomain (FDTD) method is used to discretize the partial differential equations for tim ..."
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Cited by 24 (4 self)
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Abstract — A threedimensional (3D) timedomain numerical scheme for simulation of ground penetrating radar (GPR) on dispersive and inhomogeneous soils with conductive loss is described. The finitedifference timedomain (FDTD) method is used to discretize the partial differential equations for time stepping of the electromagnetic fields. The soil dispersion is modeled by multiterm Lorentz and/or Debye models and incorporated into the FDTD scheme by using the piecewiselinear recursive convolution (PLRC) technique. The dispersive soil parameters are obtained by fitting the model to reported experimental data. The perfectly matched layer (PML) is extended to match dispersive media and used as an absorbing boundary condition to simulate an open space. Examples are given to verify the numerical solution and demonstrate its applications. The 3D PMLPLRCFDTD formulation facilitates the parallelization of the code. A version of the code is written for a 32processor system, and an almost linear speedup is observed. Index Terms—Absorbing boundary conditions, dispersive media, electromagnetic underground propagation, finitedifference timedomain (FDTD) methods. I.
Discrete Transparent Boundary Conditions for the Numerical Solution of Fresnel's Equation
 Computers Math. Applic
, 1993
"... The paper presents a construction scheme of deriving transparent , i. e. reflectionfree, boundary conditions for the numerical solution of Fresnel's equation (being formally equivalent to Schrodinger's equation). These boundary conditions appear to be of a nonlocal Cauchy type. As it turn ..."
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Cited by 22 (3 self)
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The paper presents a construction scheme of deriving transparent , i. e. reflectionfree, boundary conditions for the numerical solution of Fresnel's equation (being formally equivalent to Schrodinger's equation). These boundary conditions appear to be of a nonlocal Cauchy type. As it turns out, each kind of linear implicit discretization induces its own discrete transparent boundary conditions. Key words. Fresnel equation, boundary condition, adaptive Rothe method Contents
A.Scherer, “Finitedifference timedomain calculation of the spontaneous emission coupling factor in optical microcavities
 IEEE J. Quan. Electronics
, 1999
"... Abstract — We present a general method for the factor calculation in optical microcavities. The analysis is based on the classical model for atomic transitions in a semiconductor active medium. The finitedifference timedomain method is used to evolve the electromagnetic fields of the system and ca ..."
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Cited by 21 (3 self)
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Abstract — We present a general method for the factor calculation in optical microcavities. The analysis is based on the classical model for atomic transitions in a semiconductor active medium. The finitedifference timedomain method is used to evolve the electromagnetic fields of the system and calculate the total radiated energy, as well as the energy radiated into the mode of interest. We analyze the microdisk laser and compare our result with the previous theoretical and experimental analyses. We also calculate the factor of the microcavity based on a twodimensional (2D) photonic crystal in an optically thin dielectric slab. From the calculations, we are able to estimate the coupling to radiation modes in both the microdisk and the 2D photonic crystal cavity, thereby showing the effectiveness of the photonic crystal in suppressing inplane radiation modes. Index Terms — factor, finitedifference timedomain methods, microcavity, microdisk, photonic crystals, spontaneous emission. I.