Analysis of Perpendicular Crossing Dielectric Waveguides With Various Typical Index Contrasts and Intersection Profiles

Chang, Hung‐Wen; Wu, Yan-Huei

doi:10.2528/pier10081008

Cited by 8 publications

(10 citation statements)

References 41 publications

(47 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Ref. [1] we conducted detail numerical calculations of B with the exact dispersion relation (Equations (27)-(28)) and found that ε LFE- 9 1 for all θ ∈ [0, 2π] and all V ∈ [0, π]. But for LFE-5, the relative B-K differences are much larger, thus ε LFE- 5 1 is not always satisfied.…”

Section: Numerical Verification Of the First-order Error Analysismentioning

confidence: 99%

See 1 more Smart Citation

Theoretical Foundation for the Method of Connected Local Fields

Mu¹,

Chang²

2011

PIER

Self Cite

View full text Add to dashboard Cite

Abstract-The method of connected local fields (CLF), developed for computing numerical solutions of the two-dimensional (2-D) Helmholtz equation, is capable of advancing existing frequency-domain finitedifference (FD-FD) methods by reducing the spatial sampling density nearly to the theoretical limit of two points per wavelength. In this paper, we show that the core theory of CLF is the result of applying the uniqueness theorem to local EM waves. Furthermore, the mathematical process for computing the local field expansion (LFE) coefficients from eight adjacent points on a square is similar to that in the theory of discrete Fourier transform. We also present a theoretical analysis of both the local and global errors in the theory of connected local fields and provide closed-form expressions for these errors.

show abstract

Section: Numerical Verification Of the First-order Error Analysismentioning

confidence: 99%

“…From these FourierBessel coefficients we derived FD-like, compact nine-point stencils for the 2D Helmholtz equation. We show that CLF is capable of advancing existing FD-FD methods [5][6][7][8][9] by reducing the sampling density to just a little more than two points per wavelength, which is theoretical limit for spatial sampling.…”

Section: Introductionmentioning

confidence: 98%

Theoretical Foundation for the Method of Connected Local Fields

Mu¹,

Chang²

2011

PIER

Self Cite

View full text Add to dashboard Cite

show abstract

“…Dielectric-loaded horns utilize the dominant or hybrid modes in the uniform dielectric waveguides to constitute the aperture-field distribution attenuating radially with low cross-polarization [2,[7][8][9]. A dielectric-loaded diagonal horn can concentrate most of the electromagnetic energy in the dielectric remaining minor fraction near the metal wall, producing a Gaussian field distribution in the dielectric cross-section [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

DIAGONAL HORN GAUSSIAN EFFICIENCY ENHANCEMENT BY DIELECTRIC LOADING FOR SUBMILLIMETER WAVE APPLICATION AT 150 GHz

Xu¹

2011

PIER

View full text Add to dashboard Cite

Abstract-The dielectric pyramid loaded and the dielectric cone loaded diagonal horn working at 150 GHz are investigated by using Gaussian beam mode analysis. With extremely low cross-polarized and axially symmetrical field distribution in the horn aperture, the calculated fundamental Gaussian mode coupling achieves about 98%. The far field radiation patterns of the two antennas are analyzed using fundamental Gaussian mode aperture-field distribution model whose results agree with high-accuracy CST TM software computations, indicating that the dielectric loaded horns radiate fine Gaussian beams. The dielectric loaded geometry may be used to modify the diagonal horns with distorted beam.

show abstract

“…We shall prove in future paper that high-order compact stencils like Eqs. (7), (9), and (10) can be derived from LFE-9 formulation.…”

Section: The Full 2d Lfe-9 Formulationmentioning

confidence: 99%

“…In recent years hybrid FD-FD methods have been successfully applied to study many time-harmonic electromagnetic problems and even complex dielectric waveguide devices [1][2][3][4][5][6][7][8][9]. When combined with effective transparent boundary conditions such as the PML [10,11] and the recently developed LM-TBC method [12], the hybrid FD-FD method can be quite computationally efficient for certain passive optoelectronic devices.…”

Section: Introductionmentioning

confidence: 99%

Semi-Analytical Solutions of 2-D Homogeneous Helmholtz Equation by the Method of Connected Local Fields

Chang¹,

Mu²

2010

PIER

Self Cite

View full text Add to dashboard Cite

Abstract-The frequency-domain finite-difference (FD-FD) methods have been successfully used to obtain numerical solutions of the twodimensional (2-D) Helmholtz equation. The standard second-order accurate FD-FD scheme is known to produce unwanted numerical spatial and temporal dispersions when the sampling is inadequate. Recently compact higher-order accurate FD-FD methods have been proposed to reduce the spatial sampling density. We present a semianalytical solution of the 2-D homogeneous Helmholtz equation by connecting overlapping square patches of local fields where each patch is expanded in a set of Fourier-Bessel (FB) series. These local FB coefficients correspond to a total of eight points, four on the sides and four on the corners of the square patch. The local field expansion (LFE) analysis leads to an improved compact nine-point FD-FD stencil for the 2-D homogeneous Helmholtz equation. We show that LFE formulation possesses superior numerical properties of being less dispersive and nearly isotropic because this method of connecting local fields merely ties these overlapping EM field patches which already satisfy the Helmholtz equation.

show abstract

Analysis of Perpendicular Crossing Dielectric Waveguides With Various Typical Index Contrasts and Intersection Profiles

Cited by 8 publications

References 41 publications

Theoretical Foundation for the Method of Connected Local Fields

Theoretical Foundation for the Method of Connected Local Fields

DIAGONAL HORN GAUSSIAN EFFICIENCY ENHANCEMENT BY DIELECTRIC LOADING FOR SUBMILLIMETER WAVE APPLICATION AT 150 GHz

Semi-Analytical Solutions of 2-D Homogeneous Helmholtz Equation by the Method of Connected Local Fields

Contact Info

Product

Resources

About