本論文目的在研究單模玻璃奈米線之色散與光纖等效面積，以及設計具有低色散與小光纖等效面積的單模光纖以適合利用光纖非線性效應之應用。在1200 nm截止波長的條件下，於1550 nm具有最小光纖等效面積的玻璃奈米線之半徑為 662.77 nm，其色散為 -177.67 ps/km/nm，光纖等效面積為 1.38 μm2。另外我們發展一維圓柱形的全向量有限差分法，推導橫向電場聯立常微分方程式及其相關的邊界條件，以數值解光纖模態。使用自行發展的程式，考慮各種不同的折射率分佈光纖，我們發現步階折射率分佈 (step-index profile)具有最低色散與最小光纖等效面積。考慮 1.5 % 的纖蕊與纖殼折射率差異比例，在1200 nm截止波長的條件下，於1550 nm具有最小光纖等效面積的纖蕊半徑為 2.32μm，其色散為 -8.74 ps/km/nm，等光纖等效面積為 16.87μm2。

This thesis studies the dispersions and effective fiber areas of single-mode silica nano-wires and designs the single-mode fiber with loss dispersion and small effective fiber area that is suitable for the applications utilizing fiber nonlinearities. For 1200-nm cutoff wavelength, at 1550 nm the effective fiber area of the silica nano-wire is the smallest when its radius is 662.7 nm, in which the effective fiber area is 1.38μm2 and its dispersion is -177.67 ps/km/nm. The full vectorial finite difference method in one-dimensional cylindrical coordinates is developed. The coupled equations of the transverse fields and the relating boundary conditions are derived for numerically solving the mode fields of the fibers. With the developed source codes, the mode fields of the fibers of various index profiles are solved. It is found that both the absolute value of the fiber dispersion and the effective fiber area are the smallest with the step-index profile among the considered index profiles. Considering 1.5% relative index difference between fiber core and cladding, for 1200-nm cutoff wavelength, at 1550 nm the effective fiber area of the step-index fiber is the smallest when its radius is 2.32μm, in which the effective fiber area is 16.87μm2 and its dispersion is -8.74 ps/km/nm.

總目錄

誌謝 Ⅰ
中文摘要 Ⅱ
英文摘要 Ⅲ
總目錄 Ⅳ
表目錄 Ⅵ
圖目錄 Ⅶ

第一章 簡介 1
1.1前言 1
1.2研究動機 2
第二章 理論與公式推導 3
2.1前言 3
2.2. 數值分析方法 4
2.3理論假設 6
2.4圓柱座標系統電磁場空間配置 8
第三章 數值分析 10
3.1前言 10
3.2單模光纖及單模的條件 10
3.3單模玻璃奈米線(Silica nano-wire) 數據探討 11
3.4 漸變式折射率分佈的單模光纖設計 15
3.5各種折射率分佈的單模光纖設計數據探討 16
第四章 結論 26
參考文獻 27

[1]. Yamane, M. & Asahara, Y. Glasses for Photonics (Cambridge Univ. Press, Cambridge, UK, 2000).

[2]. Murata, H. Handbook of Optical Fibers and Cables 2nd edn (Marcel Dekker, New York, 1996).

[3]. Mynbaev, D. K. & Scheiner, L. L. Fiber-Optic Communications Technology (Prentice Hall, New York,2001).

[4]. Marcuse, D.Mode conversion caused by surface imperfections of a dielectric slab waveguide. Bell Syst.Tech. J. 48, 3187–3215 (1969).

[5]. Marcuse, D. & Derosier, R. M. Mode conversion caused by diameter changes of a round dielectric waveguide. Bell Syst. Tech. J. 48, 3217–3232 (1969).

[6]. Ladouceur, F. Roughness, inhomogeneity, and integrated optics. J. Lightwave Technol. 15, 1020–1025 (1997).

[7]. Lee, K. K. et al. Effect of size and roughness on light transmission in a Si/SiO2 waveguide: experiments and model. Appl. Phys. Lett. 77, 1617–1619 (2000). Erratum. Appl. Phys. Lett. 77, 2258 (2000).

[8]. L. Tong, R.R. Gattass, J.B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell and E. Mazur, “Subwavelengthdiameter silica wires for low-loss optical wave guiding,” Nature 426 (12), 816–819 (2003).

[9]. G. Brambilla, V. Finazzi and D.J. Richardson, “Ultra-low-loss optical fiber nanotapers,” Opt. Express 12 (10) 2258-63 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-10-2258

[10]. S.G. Leon-Saval, T.A. Birks, W.J. Wadsworth, P. St.J. Russell and M.W. Mason, “Efficient single-mode supercontinuum generation in submicron-diameter silica-air fibre waveguides,” postdeadline paper CPDA6,CLEO 2004.

[11] .“Subwavelength-diameter silica wires for low-loss optical wave guiding” Nature, 426 (6968): 816-819 DEC 18 2003; L. Wu and Sailing He,

[12]. F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation
into photonic crystal fibers by the finite element method,” Opt. Fiber Technol. 6, 181-191 (2000).

[13].G. E. Town and J. T. Lizer, “Tapered holey fibers for spot size and numerical-aperture conversion,” Opt.Lett. 26, 1042-1044 (2001).

[14].M. Qiu, “Analysis of guided modes in photonic crystal fibers using the finite-difference time-domain method,” Microwave Opt. Technol. Lett. 30, 327-330 (2001).

[15].T. P.White, R. C. McPhedran, C. M. de Sterke, L. C. Botten, andM. J. Steel, “Confinement losses in microstructured optical fibers,” Opt. Lett. 26, 1660-1662 (2001)

[16].K. S. Chiang, “Review of numerical and approximate methods for the modal analysis of general optical
dielectric waveguides,” Opt. Quantum Electron. 26, s113-s134 (1994).

[17].C. Vassallo, “1993-1995 optical mode solvers,” Opt. Quantum Electron. 29, 95-114 (1997).


[18] Z. Zhu, T. G. Brown. “Full-vectorial finite-difference analysis of microstructured optical fibers [J]”. Opt. Express, 2002, 10(17):853～864.

[19]. L. Tong, R.R. Gattass, J.B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell and E. Mazur, “Subwavelengthdiameter
silica wires for low-loss optical wave guiding,” Nature 426 (12), 816–819 (2003).

[20] Y. Chen, R. Mittra, and P. Harms, ‘‘Finite-difference time-domain algorithm for solving Maxwell’s equations in rotationally symmetric geometries,’’ IEEE Trans. Microwave. Theory Tech. 44, 832–839 (1996).

[21] Shen, G., Y. Chen, et al. (1999). "A Nonuniform FDTD Technique for Efficient Analysis of Propagation Characteristics of Optical-Fiber Waveguides." IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES VOL. 47(NO. 3).

[22] E.-G.neumann .“Single-Mode Fibers”.