Quartic perfectly matched layers for dielectric waveguides and gratings

Chen, J. C.; Li, K.

doi:10.1002/mop.4650100605

Cited by 37 publications

(22 citation statements)

References 14 publications

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“…In a specific implementation, PML absorbers are often specified by an absorption profile, which is in general understood as a set of graded piecewise-constant PMLs stacked over a finite thickness. Examples are quadratic, 1 quartic, 8 or somehow optimized 9 absorption profiles. Through gradual variation, the objective is to minimize discretization errors and material-contrast reflections over a broad range of incidence.…”

Section: Introductionmentioning

confidence: 99%

Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization

2005

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A modified formulation of Maxwell's equations is presented that includes a complex and nonlinear coordinate transform along one or two Cartesian coordinates. The added degrees of freedom in the modified Maxwell's equations allow one to map an infinite space to a finite space and to specify graded perfectly matched absorbing boundaries that allow the outgoing wave condition to be satisfied. The approach is validated by numerical results obtained by using Fourier-modal methods and shows enhanced convergence rate and accuracy.

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Section: Introductionmentioning

confidence: 99%

Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization

2005

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“…Relative to the coordinate of (300, 0), those single defect are defined as center, upward, rightward, downward and leftward defect, respectively. The wavelength-add-drop properties of the waveguide are investigated using a vector finite-difference time-domain program with quartic perfectly matched layer boundaries (Chen and Li 1995). In our simulation, a dipole located at the entrance of the waveguide creates a pulse with a Gaussian envelope.…”

Section: Simulation and Discussionmentioning

confidence: 99%

Wavelength-drop properties of L-type defects in photonic bandgap structure for the terahertz regime

et al. 2009

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Using the finite difference time domain method, the electromagnetic field distribution of terahertz waves are simulated in photonic band gap structures with different single-defect, line-shaped defects and L-type defects composed of three single-defects. Introducing the photonic band gap structure with difference coordinates single-defects, the resonance frequency and amplitude of the single-defect along the vertical direction of lineshaped defects waveguide have more sensitive than the parallel direction. Introducing the photonic band gap structure with line-shaped defects composed of three defects, the resonant in the endpoint of line-shaped defects have high amplitude and in the middle of lineshaped defects have two resonant frequencies. Introducing the photonic band gap structure with L-type defects composed of three defects, three high-Q resonant frequencies appeared simultaneously in the some monitor coordinates.

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“…18,19 However, for continuous wave propagation problems generally square profile has been used. We have investigated various power-law profiles for the wave propagation problems.…”

Section: The Perfectly Matched Layer (Pml) Boundary Conditionmentioning

confidence: 99%

Parameters affecting the performance of a perfectly matched layer for beam propagation methods

Sharma

Agrawal

2004

SPIE Proceedings

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In numerical wave propagation methods, the perfectly matched layer (PML) boundary condition is employed to prevent spurious reflections. However, PML takes additional resources in number of computation points and time. In this study, the PML performance is examined with change in the distribution of sampling points and PML absorption profile with a view to optimizing its efficiency. We have used the collocation method in our examples. We have found that equally spaced field sampling points give better absorption of beams under both optimal as well as non-optimal conditions for lower PML widths. While at higher PML widths, unequally spaced basis points may be more advantageous. The behavior of different absorption profiles varies with point spacing. For numerical tests, Gaussian beam propagation in a homogeneous medium is considered. Comparing different profiles, we find that a new profile p sin with 4 = p and quartic profiles are the best in equally spaced points, while 2 sin and square profiles are the best in unequally spaced points.

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Quartic perfectly matched layers for dielectric waveguides and gratings

Cited by 37 publications

References 14 publications

Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization

Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization

Wavelength-drop properties of L-type defects in photonic bandgap structure for the terahertz regime

Parameters affecting the performance of a perfectly matched layer for beam propagation methods

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