Rigorous modal analysis of two‐dimensional photonic crystal waveguides

Yasumoto, Kiyotoshi; Jia, Hongting; Sun, Kunquan

doi:10.1029/2004rs003192

Cited by 22 publications

(29 citation statements)

References 9 publications

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“…We have performed the same computation with Ref. [6] and obtained accurate values as 2.34338750 × 10 6 m −1 for the even guided-mode and 2.05692809 × 10 6 m −1 for the odd one. We use these values as the reference ones.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The method presented in Ref. [6] is known to provide highly accurate results for the guided-modes of the PCW formed by circular cylinders though it is not available for analyzing the evanescent-modes. We have performed the same computation with Ref.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The Floquet-modes are the eigenmodes in periodic structures, and the Floquet theorem asserts that the fields in the structure can be expressed by superposition of the Floquet-modes [4]. Since each Floquet-mode has a pseudo-periodic property, several papers [5][6][7] introduce the generalized Fourier series expansion to express the fields and the dispersion equation is derived by the multilayer technique for periodic structures [8]. These approaches make us possible to obtain the guided Floquet-modes in very high accuracy, but they do not seem to be applicable to obtain the evanescent ones.…”

Section: Introductionmentioning

confidence: 99%

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Spectral-Domain Formulation of Pillar-Type Photonic Crystal Waveguide Devices of Infinite Extent

Nakatake¹,

Watanabe²

2013

PIER

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Abstract-This paper presents a novel formulation for the modeling of electromagnetic wave propagation in pillar-type photonic crystal waveguide devices. The structure under consideration is formed in an infinitely extended pillar-type photonic crystal and the wave propagation is controlled by removing some cylinders from the original periodic structure. The structure is considered as cascade connections of straight waveguides, and the input/output properties of the devices are obtained using an analysis method of multilayer structure. Each layer includes periodic circular cylinder array with defects, and the transfer-matrix is obtained by using a spectral-domain approach based on the recursive transition-matrix algorithm with the lattice sums technique and the pseudo-periodic Fourier transform.

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Section: Numerical Experimentsmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spectral-Domain Formulation of Pillar-Type Photonic Crystal Waveguide Devices of Infinite Extent

Nakatake¹,

Watanabe²

2013

PIER

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“…As discussed above, the upper and lower boundaries at y ϭ h and y ϭ 0, viewed from the 0 th region, are characterized by the reflection matrices R ഫ and R പ , if we assume that the x component of the propagation constant of a guided wave is equal to ␣, varying as e i␣x in the x direction. Since the matrices R ഫ and R പ are the function of ␣, the dispersion equation of the guided modes may be written as follows [16,18]:where Y 0 is a diagonal matrix whose diagonal elements are defined by e ikymh . Figure 5 shows the dispersion curve of a coupled cavity waveguide, where r ϭ 0.25h, r ϭ 10, and r ϭ rs ϭ rs ϭ 1.0.…”

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confidence: 99%

Rigorous analysis of photonic crystals with periodic defects

Jia

Yasumoto

2005

Microw. Opt. Technol. Lett.

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with a lumped amplifier and a high-output coupler. This implementation not only increases the pulse energy, but also improves the spectrum quality. High-quality rectangle-shaped spectra without the 1 st -order sidebands will be very attractive for numerous applications such as amplification, frequency doubling, and supercontinuum generation. ACKNOWLEDGMENTSThis work was supported by the National Science Foundation of China (90201011). The authors thank Dr. F.O. Ilday from Cornell University, for his help. During the past decade, photonic crystals have received growing attention because of their novel scientific and potential engineering applications [1][2][3], such as narrowband filters, high-quality resonant cavities, laser reflectors, antenna substrates, strongly guiding devices, and so on. These artificial materials, which are periodic arrangements of discrete dielectric or metallic objects, have the very interesting nature of stop-bands in which any electromagnetic-wave propagation is forbidden. This property is crucial in the development of photonic-crystal devices applying to microwave, millimeter-wave, and optical systems. If we introduce a defect on a perfect photonic crystal, it is possible to create localized electromagnetic modes. Therefore, electromagnetic waves in a certain frequency band can locally be trapped inside the defect area. This important property can be widely used in various applications. The frequency response in reflectance, the frequency range, and the mode propagation have been developed using the cylindricalharmonic expansion method [4], the T-matrix and lattice sums' method [5][6][7], the Fourier series method [8 -10], the scattering matrix and mode-matching method [11], the finite-element method [12], the differential method [13], and time-domain techniques [14]. Among those approaches, the T-matrix and lattice sums' method is a rigorous and effective technique with a very simple formulation. In order to extend the scope of applications and to improve the computing accuracy, an improved T-matrix and lattice sums' method [15] was recently proposed, which successfully solved various periodic problems with complex structures.In this paper, we describe a very simple and effective formulation to analyze 2D photonic crystals with periodic defects. This method is an extension of the improved T-matrix and lattice sums' method [15]. The proposed formula is in S-matrix form and is defined by space harmonics, so that it is very suitable for multilayered structures. The problem of coupled-cavity waveguides, which consist of chains of defects in a perfect photonic crystal, is a very important issue, because they allow more freedom to engineer the dispersive properties of propagating modes than channel waveguides do [2,3,16]. For these problems, the improved T-matrix and lattice sums' method [15] is a very effective technique, but we propose another very simple formula for this kind of special structure, because the proposed method has a much simpler formula, much faster convergence, and much ...

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“…However, since the computation errors are comparatively easy to accumulate in periodic structures, FDTD method seems to require special techniques in accurate calculations. The structure is fully periodic in the propagation direction, and several papers (Jia & Yasumoto, 2006;Tanaka et al, 1994;Yasumoto et al, 2004) introduce therefore the generalized Fourier series to expand the electromagnetic fields. Maxwell's equations and the constitutive relations yield a coupled ordinary differential-equation set in terms of the generalized Fourier coefficients.…”

Section: Introductionmentioning

confidence: 99%