以有限差分頻域法分析光子導線與多邊形光纖導管

本論文以全向量有限差分頻域法分析光波導，並引入完美匹配吸收層。本研究分析與討論包括光纖、光子導線、圓形與多邊形光纖導管。光子導線的計算結果顯示其傳播模態的洩漏及損耗特性，透過與其他數值方法的比較，也顯示此方法的高準確性。我們討論了完美匹配吸收層以及計算空間的參數對於有限差分頻域法精準度與收斂性的影響，較厚的完美匹配吸收層可以得到較高準確性，但在較薄的完美匹配吸收層中，較大的完美匹配吸收層反射係數的表現比較小的好。此外，若計算空間無法大到容納模態的場或是靠近邊界場值不夠小的話，計算準度就會降低。本研究亦分析多邊形光纖導管的模態特性，並改變半徑、介電質厚度、邊的個數等參數，探討其核心模態與高階介電質模態耦合所產生的法諾效應，結果顯示當邊的個數提高時，法諾效應發生的頻率往高頻移動，而且出現的密度變小；另外，法諾效應的頻率可以藉由改變管的半徑以及介電質厚度來控制。

關鍵字

有限差分頻域法；光波導；光子導線；多邊形光纖導管

並列摘要

In this thesis, the full-vectorial finite-difference frequency-domain (FDFD) method based on Yee's mesh with perfectly matched layer (PML) is utilized to analyze optical waveguides. Several optical waveguides such as photonic wires, circular tube fibers, and polygonal tube fibers are analyzed. The calculated results of the photonic wire show that the leaky and loss properties of the guided modes can be obtained with reasonably high accuracy as compared with reported results using different methods. Moreover, we discuss the effect of some parameters of PMLs and computational window on the accuracy and convergency of numerical results. Thicker PMLs could raise accuracy, but with thin PMLs the performance with larger reflection coefficient of PML is better than smaller one. Besides, if the computational window is not large enough such that the mode field is not enough small near the PMLs, numerical accuracy would be low. As for the polygonal tube fibers, their modal characteristics for various radii, dielectric thicknesses, and the side number of the polygon are investigated. Fano resonances caused by the coupling between the core mode and high order dielectric modes are analyzed and discussed. The results show that when the side number of the polygon increases, the Fano resonance frequencies become larger and their spectral densities decrease, and that the frequencies of Fano resonance can be manipulated by varying the tube radius or the dielectric thickness.

並列關鍵字

Finite-difference frequency-domain method ； optical waveguides ； photonic wires ； polygonal tube fibers

參考文獻

[1] Ahmed, G. P., and P. Daly, “Finite-element method for inhomogeneous waveguide,” Inst. Elec. Eng. Proc.-J, vol. 116, pp. 1661–1664, 1969.

[2] Ando, T., H. Nakayama, S. Numata, J. Yamauchi, and H. Nakano, “Eigenmode analysis of optical waveguides by a Yee-mesh-based imaginary-distance propagation method for an arbitrary dielectric interface,” J. Lightwave Technol., vol. 20, pp. 1627–1634, 2002.

[3] Andreani, L. C., and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B, vol. 73, p. 235114, 2006.

[4] Baken, N. H. G., M. B. J. Diemeer, J. M. V. Splunter, and H. Blok, “Computational modeling of diffused channel waveguides using a domain integral equation,” J. Lightwave Technol., vol. 8, pp. 576–586, 1990.

[5] B’erenger, J.-P., “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys., vol. 114, pp. 185–200, 1994.

國際替代計量

以有限差分頻域法分析光子導線與多邊形光纖導管

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