臺灣博碩士論文加值系統

本研究探討B型抗諧振反射式光波導結構之光子晶體波導元件。B型抗諧振反射式光波導結構可傳輸橫向電場偏極化(TE)及橫向磁場偏極化(TM)的基模光，且具有較大的導光區可有效和單模光纖耦合。而B型抗諧振反射式光子晶體光波導中，若使光操作在光子晶體之完全能隙中，可同時有效率的傳輸橫向電場偏極化(TE)及橫向磁場偏極化(TM)的基模光，其垂直方向利用抗諧振反射式光波導結構導波，而水平方向則是利用光子晶體能隙導波原理。我們使用套裝軟體FULLWAVE，以平面波展開法(PWM)分析光子晶體能帶；有限差分時域分析法(FDTD)來模擬光在二維光子晶體波導中波的傳輸，以此得到最佳的平面結構參數，再利用FDTD模擬B型抗諧振反射式光子晶體光波導中波的傳播行為，模擬結果顯示在三角形結構中傳輸橫向磁場偏極化(TM)及橫向橫向電場偏極化(TE)可分別達到92.1%(0.357-dB loss)及89.7%(0.472-dB loss)，而在四方形結構中則分別為88.1%(0.550-dB loss)及86.1%(0.649-dB loss)。

In this research, we investigate the ARROW-B photonic crystal waveguide. The ARROW-B structure can guide light in the fundamental modes of TE and TM polarization, and provides a large core size compatible to single-mode fibers. An ARROW-B photonic crystal line defect waveguide can guide TE and TM modes simultaneously with a photonic crystal structure in the horizontal direction and an ARROW-B structure in the vertical direction. We use the plane wave expansion method (PWM) with a commercial software “FULLWAVE” to analyze the band structure in a 2D photonic crystal and use the finite difference time domain (FDTD) method to simulate the transmission of wave in a 2D PC waveguide to determine the optimal parameter of the lateral structure. We also use FDTD to simulate wave transmission in an ARROW-B PC line defect waveguide. The results show that high transmission of approximately 92.1% (0.357-dB loss) and 89.7% (0.472-dB-loss) for TM and TE, respectively, can be achieved simultaneously in the triangular ARROW-B-based PC waveguide if operating in the complete band gap. And in the square ARROW-B-based PC waveguide, the transmission value are approximately 88.1% (0.550-dB loss) and 86.1% (0.649-dB loss) for TM and TE mode, respectively.

1 Introduction 1
2 Eigenmodes of Photonic Crystals 5
2.1 Wave Equations and Eigenvalue Problems . . . . . . . . . . . . . . . . . 5
2.2 Bloch’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Eigenvalue Problems in Two-Dimensional Photonic Crystals . . . . . . . 12
2.4 The FDTD Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 ARROW-B Waveguides 18
3.1 Characteristics of an ARROW-B . . . . . . . . . . . . . . . . . . . . . . 20
3.2 Design of ARROW-B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4 ARROW-B-based Photonic Crystal Waveguide 25
4.1 2D Triangular PC Line Defect Waveguide . . . . . . . . . . . . . . . . . 26
4.2 ARROW-B-Based Triangular PC waveguide . . . . . . . . . . . . . . . . 30
4.3 2D Square PC Line Defect Waveguide . . . . . . . . . . . . . . . . . . . . 32
4.4 ARROW-B-Based Square PC Line Defect Waveguide . . . . . . . . . . . 42
5 Conclusion 52

[1] Robert D. Meade, Karl D. Brommer, Andrew M. Rappe, and J. D. joannopoulos,
“Existence of a photonic band gap in two dimensions,” Appl: Phys: Lett:; vol. 61,
no. 4, pp. 495-497, 1992.
[2] Pierre R. Villeneuve and Michel Piche, “Photonic band gap in two-dimensional
square and hexagonal lattices,” Physical Review B; vol. 46, no. 8, pp. 4969-4972,
1992.
[3] Edmond Chow, S.G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt,
G. A. Vawter, W. Zubrzycki, H. Hou & A. Alleman, “Three-dimensional control
of light in a two-dimensional photonic crystal slab,” Nature; vol. 407, pp. 984-986,
2000.
[4] Steven G. Johnson, Shauhui Fan, Pierre R. Villeneuve, and J. D. Joannopoulos
“Guided modes in photonic crystal slabs,” Physical Review B; vol. 60, no. 8, pp.
5751-5758, 1999.
[5] M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfei¤er, “Antiresonant re‡ecting
optical waveguides in SiO2-Si multilayer structures,” Appl: Phys: Lett:;vol. 49, no.
1, pp. 13-15, 1986.
[6] T. Baba, and Y. Kokubun, “New polarization-insensitive antiresonant re‡ecting
optical waveguide (ARROW-B),” IEEE Photon: Technol: Lett:; vol. 1, no. 8, pp.
234-234, 1989.
[7] T. Baba, and Y. Kokubun, “Scattering loss of antiresonant re‡ecting optical
wavegudes,” J: of Lightwave T echnol:; vol. 9, no. 5, pp. 590-597, 1991.
[8] W. P. Huang, A. Nathan, R.M. Shubair, and Y.L. Chow, “The modal characteristics
of ARROW structures,” J: of Lightwave Technol:; vol. 10, no. 8, pp. 1015-1022,
1992.
[9] S. L. Lee, Y. Chung, L. A. Coldren, and N. Dagli, “ On leaky mode approxima-tions
for modal expansion in multilayer open waveguides,” IEEE J: of Quantum
Electron:; vol. 31, no. 10, pp. 1790-1802, 1995.
[10] Steven G. Johnson, Shauhui Fan, Pierre R. Villeneuve, and J. D. Joannopou-los“
Guided modes in photonic crystal slabs,” Physical Review B; vol. 60, no. 8,
pp. 5751-5758, 1999.
[11] Kazuaki Sakoda, Optical Properties of Photonic Crystals, pp. 13-16, 2001.
[12] Kazuaki Sakoda, Optical Properties of Photonic Crystals, pp. 18-19, 2001.
[13] Kazuaki Sakoda, Optical Properties of Photonic Crystals, pp. 19-21, 2001.
[14] K. S. Yee, “Numerical solution of initial boundary value problems involving
Maxwell’s equations in isotropic media,” IEEE Trans: Antennas Propagat., AP-14,
302, 1966.
[15] T. Baba, and Y. Kokubum, “Dispersion and radiation loss characteristics of antires-onant
re‡ecting optical waveguides-numerical results and analytical expressions,”
IEEE J:of Quantum Electron:; vol. 28, no. 7, pp. 1689-1700, 1992.
[16] Dennis W. Prather, Janusz Murakowski, Shouyan Shi, Sriram Venkataraman,
Ahmed Sharkawy, Caihua Chen, and David Pustai, “High-e¢ ciency coupling struc-ture
for a single-line-defect photonuc crystal waveguide,” Optics Letters; Vol. 27,
No. 18, pp. 1601-1623, 2002.