FDFD: A 3D Finite-Difference Frequency-Domain Code for Electromagnetic Induction Tomography

Champagne, N.J.; Berryman, James G.; Buettner, H.M.

doi:10.1006/jcph.2001.6765

Cited by 55 publications

(46 citation statements)

References 32 publications

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“…To address this key challenge in the design and understanding of lasers, a highly efficient approach to finding the nonlinear steady-state properties of complex laser systems has recently been introduced, known by the acronym SALT (steady-state ab initio laser theory). 1 In this paper, we present a technique to directly solve the SALT formulation [6][7][8] of the steady-state MB equations (using finite-difference frequency-domain (FDFD) [9,10] or finite-element methods (FEM) [11]), and we demonstrate that, unlike previous approaches to the SALT equations [7,8], our technique scales to full three-dimensional (3D) low-symmetry geometries (such as photonic-crystal slabs [12]). …”

Section: Introductionmentioning

confidence: 99%

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Scalable numerical approach for the steady-stateab initiolaser theory

Esterhazy¹,

et al. 2014

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We present an efficient and flexible method for solving the non-linear lasing equations of the steady-state ab initio laser theory. Our strategy is to solve the underlying system of partial differential equations directly, without the need of setting up a parametrized basis of constant flux states. We validate this approach in one-dimensional as well as in cylindrical systems, and demonstrate its scalability to full-vector three-dimensional calculations in photonic-crystal slabs. Our method paves the way for efficient and accurate simulations of microlasers which were previously inaccessible.

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Section: Introductionmentioning

confidence: 99%

“…Furthermore, we show in Sec. III E that analytical outgoingradiation boundary conditions, which are difficult to generalize to three dimensions [20], can be substituted by the standard PML (perfectly matched layer) method [10,20,21] which is equally effective at modeling open systems. We also demonstrate multimode laser solutions (Secs.…”

Section: Introductionmentioning

confidence: 99%

Scalable numerical approach for the steady-stateab initiolaser theory

Esterhazy¹,

et al. 2014

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“…III B) for these standing-mode solutions will no longer be given by the simple expressions in Eqs. (34) and (35), and will have to be numerically computed (nevertheless, we have empirically found that these standing-mode solutions are still unstable).…”

Section: Effects Of Chiralitymentioning

confidence: 99%

“…In many cases, the C nv -symmetric geometry we are trying to solve has a degeneracy that is broken when the geometry is approximated by a discretized grid for numerical solution on a computer [14,35,36] since the grid may no longer have the original C nv symmetry. For linear equations, this unphysical splitting is not an issue because it is usually straightforward to tell whether a pair of modes is "really" degenerate by how it corresponds to the eigenfunctions of the "real" symmetry group, and since all linear superpositions solve the equation in the infinite-resolution limit, we can construct arbitrary superpositions as needed after solving for both of the modes.…”

Section: C Nv Symmetry Broken By Discretizationmentioning

confidence: 99%

Symmetry, stability, and computation of degenerate lasing modes

Liu

Zhen

et al. 2017

Phys. Rev. A

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We present a general method to obtain the stable lasing solutions for the steady-state ab initio lasing theory (SALT) for the case of a degenerate symmetric laser in two dimensions (2D). We find that under most regimes (with one pathological exception), the stable solutions are clockwise and counterclockwise circulating modes, generalizing previously known results of ring lasers to all 2D rotational symmetry groups. Our method uses a combination of semianalytical solutions close to lasing threshold and numerical solvers to track the lasing modes far above threshold. Near threshold, we find closed-form expressions for both circulating modes and other types of lasing solutions as well as for their linearized Maxwell-Bloch eigenvalues, providing a simple way to determine their stability without having to do a full nonlinear numerical calculation. Above threshold, we show that a key feature of the circulating mode is its "chiral" intensity pattern, which arises from spontaneous symmetry breaking of mirror symmetry, and whose symmetry group requires that the degeneracy persists even when nonlinear effects become important. Finally, we introduce a numerical technique to solve the degenerate SALT equations far above threshold even when spatial discretization artificially breaks the degeneracy.

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“…Generally speaking, it is known that in FDFD (and FDFD) methods the assignment of the material properties to the grid cells (e.g., µ i,j,k r,xx ) is a fundamental step which can be performed by various techniques [29,33,34]. In [26], the pointwise value of the constitutive parameters has been assigned to each node in the Yee grid (i.e., µ i,j,k r,xx = µ r,xx (i∆x, (j + 0.5)∆y, (k + 0.5)∆z), for example), and the discretization grid has been chosen in order to avoid that any node could lay on a discontinuity of the dielectric permittivity or of the magnetic permeability [26].…”

Section: Fdfd Discretization Of Sharp Interfacesmentioning

confidence: 99%

Improving the Reliability of Frequency Domain Simulators in the Presence of Homogeneous Metamaterials - A Preliminary Numerical Assessment

Oliveri¹

2012

PIER

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Abstract-The accuracy of the finite difference frequency domain (FDFD) method in the solution of canonical waveguide discontinuity problems involving complementary or nearly complementary metamaterials (MTM s) is analytically discussed. It is shown that the good accuracy of the method (in comparison with other frequency-domain techniques) is due to the intrinsic approximation which it introduces in the finite-difference discretization of sharp dielectric interfaces. By exploiting such a result, a perturbation algorithm is proposed for the reliable modeling of MTM s devices when other frequency domain numerical methods are at disposal. A preliminary numerical analysis is carried out to assess the reliability and accuracy of the proposed modeling approach when canonical scattering problems are at hand.

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FDFD: A 3D Finite-Difference Frequency-Domain Code for Electromagnetic Induction Tomography

Cited by 55 publications

References 32 publications

Scalable numerical approach for the steady-stateab initiolaser theory

Scalable numerical approach for the steady-stateab initiolaser theory

Symmetry, stability, and computation of degenerate lasing modes

Improving the Reliability of Frequency Domain Simulators in the Presence of Homogeneous Metamaterials - A Preliminary Numerical Assessment

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