Analysis of planar waveguides with the method of lines and absorbing boundary conditions

Dreher, Achim; Pregla, R.

doi:10.1109/75.91091

Cited by 37 publications

(16 citation statements)

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“…In [23], expressions for second-and third-order rational series approximations are derived. Dreher [24] and Pregla [22] adapted the second-and third-order versions to the MoL in Cartesian coordinates. Here, we develop the third-order terms for polar coordinates.…”

Section: Absorbing Boundary Conditions For Polar Coordinatesmentioning

confidence: 99%

“…Calculation of the local complex dielectric constant is then linked to a beam propagation algorithm for the pump and signal waves [11]. In Section IV, absorbing boundary conditions [22]- [24] based on the third-order rational series approximation are developed for polar coordinates. Solutions for typical geometries involving curved and folded slab guides are then presented in Section V, and it is shown that excessive curvature and curvature changes both reduce the overall gain more than would be expected simply from consideration of radiation loss.…”

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Analysis of folded erbium-doped planar waveguide amplifiers by the method of lines

Huang

Syms

1999

J. Lightwave Technol.

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Section: Absorbing Boundary Conditions For Polar Coordinatesmentioning

confidence: 99%

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confidence: 99%

Analysis of folded erbium-doped planar waveguide amplifiers by the method of lines

Huang

Syms

1999

J. Lightwave Technol.

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“…In this letter, we show that the folded-spiral layout (which can be used in a nested array) may be further improved using continuously varying bends. To do so, we combine a number of well-known curvature variations in a novel way to describe the whole of a complex EDWA layout.Optical simulations are carried out using a numerical algorithm, which links a five-level rate equation model with beam propagation by the method of lines [5], [6]. Full details of the model, which does not suffer from paraxial approximations, are given in [7].…”

mentioning

confidence: 99%

“…Optical simulations are carried out using a numerical algorithm, which links a five-level rate equation model with beam propagation by the method of lines [5], [6]. Full details of the model, which does not suffer from paraxial approximations, are given in [7].…”

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Folded-Spiral EDWAs With Continuously Varying Curvature

Portch

Syms

Huang

2004

IEEE Photon. Technol. Lett.

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Abstract-The layout of folded spiral erbium-doped planar waveguide optical amplifiers (EDWAs) is considered. A quasi-continuous function to describe the curvature of a folded-spiral layout is presented, based upon the use of cosine and raised-cosine variations in bend curvature. This layout provides greater gain in a given area than the corresponding fixed-radii layout. Analysis is initially based on simple geometric principles and the reduction of bending losses for 180 waveguide bends. Fold-back bends and complete EDWA layouts are then considered. Simulations are carried out using an algorithm that combines five-level rate equations with propagation by the method of lines.Index Terms-Erbium-doped waveguide amplifier (EDWA), optical amplifier. WITH THE evolution of optical systems, the market now requires compact low-cost optical amplifiers that meet the performance demands of metro and core/access networks. Erbium-doped waveguide amplifiers (EDWAs) have many advantages over erbium-doped fiber amplifiers, including reliability and the potential for integration with other optical components [1], [2]. The main limitation of EDWAs is their relatively low gain, which is restricted by the cooperative up-conversion that accompanies heavy Er doping [1]. As a result, most EDWAs require a complex layout [3].EDWAs based on continuous and folded spiral layouts, as shown in Fig. 1, have already been considered and ranked according to their ability to maximize gain in a given chip area [4]. This investigation was restricted to layouts using straight sections and right-angle bends of constant radius, and the optimum layout was identified as a continuous spiral containing waveguide intersections. However, this layout is unsuitable for arrangement as an EDWA array, which would allow integration costs to be reduced. In this letter, we show that the folded-spiral layout (which can be used in a nested array) may be further improved using continuously varying bends. To do so, we combine a number of well-known curvature variations in a novel way to describe the whole of a complex EDWA layout.Optical simulations are carried out using a numerical algorithm, which links a five-level rate equation model with beam propagation by the method of lines [5], [6]. Full details of the model, which does not suffer from paraxial approximations, are given in [7]. Here, bends with constant curvature were modeled by solving a discretised form of the Helmholtz equation in cylindrical coordinates. In the present work, bends with varying curvature are modeled by cascading sections of constant curva- ture, matching the waveguide position and slope at the interfaces between sections. The number of sections required for convergence is small; typically up to nine sections were used for a 180 bend.Simulations were performed for example parameters, as follows. The waveguide itself is a step-index planar guide with a core width of 3.2 m and core and cladding indexes of and , respectively, so that the guide is single-moded at 980-nm wavelength. The Er concent...

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Modified method of lines for open microstrip structures with finite metallization thickness and conductivity

Feng

Zhou

Fang

1999

Microw. Opt. Technol. Lett.

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A modified method of lines (MMoL) is developed to analyze open microstrip structures with finite metallization thickness and conductivity. The integration along the normal of the interface between the conductor and dielectric is analytically integrated before the method of lines transform. The periodic boundary conditions (PBC) are employed to simulate the open structure. Due to the uniform discretization which leads to the analytical form of eigenvalues and the application of the fast Fourier transform (FFT) technique, our approach can reduce the computation time significantly. The comparison between our results and published theoretical or experimental ones shows the accuracy and efficiency of this method. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 21: 60–63, 1999.

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Analysis of planar waveguides with the method of lines and absorbing boundary conditions

Cited by 37 publications

References 4 publications

Analysis of folded erbium-doped planar waveguide amplifiers by the method of lines

Analysis of folded erbium-doped planar waveguide amplifiers by the method of lines

Folded-Spiral EDWAs With Continuously Varying Curvature

Modified method of lines for open microstrip structures with finite metallization thickness and conductivity

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