Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers

Saitoh, Kunimasa; Koshiba, Masanori

doi:10.1109/jqe.2002.1017609

Cited by 520 publications

(215 citation statements)

References 26 publications

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“…where (13) in which or and In these equations, is the angular frequency, the permittivity of the free space, the speed of light in a vacuum, the electric conductivity, the maximum conductivity, the distance from the interface between the computational and the PML regions, the thickness of the PML, the order of the polynomial, and the theoretical reflection coefficient.…”

Section: Absorbing Boundary Conditionmentioning

confidence: 99%

“…Therefore, when an ABC is imposed on the computational window edge, only the amplitude of the field should be reduced without affecting the phase. Based on this consideration, we adopt only the real part of (13), while eliminating the imaginary part (similar but not exactly the same treatment can be found in [13]). This ABC is no longer the PML-ABC, since the impedance matching condition is not satisfied, and the traveling wave cannot be absorbed ( in (13), which is analytically expressed by a complicated form [15], [16] for the conventional PML, is empirically determined in Section III-B).…”

Section: Absorbing Boundary Conditionmentioning

confidence: 99%

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Eigenmode analysis of a light-guiding metal line loaded on a dielectric substrate using the imaginary-distance beam-propagation method

Shibayama

Yamazaki

Yamauchi

et al. 2005

J. Lightwave Technol.

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Abstract-Fundamental characteristics of a light-guiding metal line are revealed and discussed through the eigenmode analysis using the three-dimensional (3-D) imaginary-distance beam-propagation method (ID-BPM) based on the alternating-direction implicit scheme. For the present ID-BPM, the multiplication factor of the eigenmode is derived and the paper described how the present method works in the ID procedure. An efficient absorbing boundary condition is described, which is suitable for the eigenmode analysis using the ID-BPM. After confirming the effectiveness of the present method, the characteristics of the light-guiding line composed of a metal (Au) with a finite width and thickness on a substrate (SiO 2 ) are investigated. Numerical results for a metal thickness of 0.2 m show that the effective index and the propagation loss decrease as the metal width is reduced. It is shown that not only the higher order modes but also the first mode has a cutoff metal width. Near the cutoff width, the propagation loss of the first mode ( 10 dB/mm at a wavelength of 1.55 m) is less than those of the higher order modes. Finally, in order to reduce the propagation loss, a dielectric core was added under the metal line.Index Terms-Beam-propagation method (BPM), eigenmode analysis, imaginary-distance (ID) procedure, light-guiding metal line, surface plasmon-polaritons.

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Section: Absorbing Boundary Conditionmentioning

confidence: 99%

Section: Absorbing Boundary Conditionmentioning

confidence: 99%

Eigenmode analysis of a light-guiding metal line loaded on a dielectric substrate using the imaginary-distance beam-propagation method

Shibayama

Yamazaki

Yamauchi

et al. 2005

J. Lightwave Technol.

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“…Several numerical methods have been utilized to study the modal dispersion of solid-core photonic-crystal fibers (PCFs) and photonic-bandgap fibers. These include the plane-wave expansion (PWE) [5]- [7], the finite-element method (FEM) [4], [8]- [10], the beam-propagation method (BPM) [11], the finite-difference time-domain method (FDTD) [12], the multipole method [13]- [15], and the finite-difference frequency-domain method (FDFD) [16]- [18]. Although the majority of these methods have been demonstrated for PCFs only, they are applicable for realistic PBFs as well.…”

mentioning

confidence: 99%

“…Most of these methods involve discretizing space on a numerical grid and describing the permittivity profile of the fiber transverse cross section on this grid [4]- [18]. This grid can be square [5], [12], [16]- [18], or hexagonal [7], or it can consist of curvilinear hybrid edge/nodal elements [10], [11] or triangular elements [4], [8], [9]. In order to most accurately describe the modal properties of a photonic-bandgap fiber, the grid should have the same symmetry as the fiber.…”

mentioning

confidence: 99%

Birefringence Analysis of Photonic-Bandgap Fibers Using the Hexagonal Yee's Cell

Aghaie

Fan

Digonnet

2010

IEEE J. Quantum Electron.

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Abstract-A full-vectorial finite-difference scheme utilizing the hexagonal Yee's cell is used in this paper to analyze the modes of photonic-bandgap fibers with C 6 symmetry. Because it respects the fiber's native symmetry, this method is free from any numerical birefringence. We also incorporate in it techniques for reducing the memory requirement (up to 3 to 4 times) and computational time, in particular by exploiting some of the symmetry properties of these fibers. Using sub-pixel averaging, we demonstrate quadratic convergence for the fundamental mode's effective index dependence on spatial resolution. We show that this method can be used to calculate the beat length of PBFs in which a birefringence is introduced by applying a small unidirectional stretch to the fiber cross section along one of its axes. Abrupt variations of the modeled fiber geometries with spatial resolution lead to oscillatory beat length convergence behavior. We can obtain a better estimate for beat length by averaging these oscillations. We apply a strong perturbation analysis to the fiber's unperturbed mode, calculated by our finite-difference method, to perform this averaging in a rigorous way. By fitting a polynomial to the predicted beat lengths as a function of grid spacing, we obtain an accurate estimate of the beat length at zero grid spacing. Reasonable convergence for the beat length is observed using a single processor with 8 GB of memory.

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“…Each core is surrounded by small airholes, which are created in order to have a complete power transfer among the cores. To optimize the performance of the proposed device, we use a full-vectorial finite-element method (FEM) [15] and the beam propagation method (BPM) [16]. Through numerical simulations, it has been revealed that the complete power transfer takes place in a 5.8-mm-long multicore PCF having and , where , and are the hole diameter of the cladding, small airholes, and pitch constant of the PCF, as shown in Fig.…”

mentioning

confidence: 99%

Coupling Characteristics of Multicore Photonic Crystal Fiber-Based 1$\,\times\,$4 Power Splitters

Varshney

Saitoh

Sinha

et al. 2009

J. Lightwave Technol.

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Abstract-A new design of multicore photonic crystal fibers (PCFs) is proposed and investigated through full-vectorial finite-element method and finite-element beam propagation method. The fiber design comprises four identical cores surrounding a central core. The optical power launched into the central core is equally divided into other neighboring four cores with a 25% of coupling ratio. The coupled-mode analysis is also carried out to understand the supermode patterns and the coupling characteristics. Through numerical simulations, it is demonstrated that the optical power can be divided equally in a 5.8-mm-long multicore PCF. The power coupling characteristics obtained through coupled-mode analysis are in very good agreement with those calculated from beam propagation method solver.Index Terms-Fiber couplers, finite-element methods (FEMs), microstructured fibers, optical fiber devices, photonic crystal fiber, power splitter.

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Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers

Cited by 520 publications

References 26 publications

Eigenmode analysis of a light-guiding metal line loaded on a dielectric substrate using the imaginary-distance beam-propagation method

Eigenmode analysis of a light-guiding metal line loaded on a dielectric substrate using the imaginary-distance beam-propagation method

Birefringence Analysis of Photonic-Bandgap Fibers Using the Hexagonal Yee's Cell

Coupling Characteristics of Multicore Photonic Crystal Fiber-Based 1$\,\times\,$4 Power Splitters

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