臺灣博碩士論文加值系統

本論文是於光子晶體中製造缺陷來做成波長分波的應用。光子晶體是一種微結構系統，因其介電常數呈週期性變化而具有光子能隙，波長落在此能隙中的光子無法通過系統，因而可藉由在光子晶體內植入缺陷，形成能循特定路徑引導光傳遞將的波導，亦可製造能將光侷限於非常小空間的微空腔。
首先，吾人利用在頻率域的平面波展開法來計算出色散關係並找出其光子晶體能隙；在時域中利用有限差分法並搭配完美匹配層的邊界條件來解決麥克斯威爾方程式亦是模擬電磁波的動態行為。利用改變光子晶體中缺陷的大小可明顯地從結構表面汲取出特定的波長；另外，利用改變缺陷腔的大小來引導特定的波長沿著波導作傳遞。最後，吾人利用此結構可以實現稠密/粗式波長分波多工器的功能，在超高速與超高容量的光通訊與資訊處理應用中，它將扮演極重要的關鍵元件；有鑒於奈米技術的提昇，在積體電路上實現光子晶體的元件將是一大突破。

In this thesis, it discussed the application of defects in the photonic crystals could be design to produce the multi-wavelength. Photonic crystals (PCs) are nanostructured materials in which a periodic variation of the dielectric constant of the material results in a photonic band gap. Photons with wavelengths or energies in this band gap cannot travel through the crystal. By introducing defects into PCs, it is possible to build waveguides that can channel light along certain paths. It is also possible to construct microcavities that can localize photons in extremely small volumes.
First, we compute the photonic crystals dispersion relations and find the bandgap out by the plane wave expansion method (PWE) in the frequency domain. Then, the finite difference time domain method (FDTD) with the perfectly matched layer boundary conditions is solved Maxwell’s equations, namely simulated the movement behavior of the Photonic crystals. By properly varying the size of the defect on the PCs, it could really drop the particular wavelength from the surface. In addition, by modulating the size of the cavity on the PCs, it introduced the particular wavelength into the waveguide. Finally, we proposed the two structures that could function as dense /coarse wavelength division multiplexers (DWDM / CWDM). It would be a potential key component in the applications of ultra-high-speed and ultra-high-capacity optical communication and optical data processing systems. Deciding that the nanofabrication improves gradually, it will demonstrate a practical breakthrough for the realization of devices based on the photonic crystal integrated circuits.

Chapter 1： Introduction
1.1 Overview
1.2 Research Motivations and Goals
1.3 Organizations of the Thesis
Chapter 2： Numerical Analysis Methods
2.1 Introduction
2.2 Plane Wave Expansion Method, PWE
2.2.1 Simulation by PWE- Perfect 2D Photonic Crystals
2.2.2 Simulation by PWE- Imperfect 2D Photonic Crystals
2.3 Finite Difference Time Domain Method, FDTD
2.3.1 Simulation by FDTD-Photonic Crystal Waveguides
Chapter 3： Multi-wavelength Drop Filters of Out-plane Type Based on 2D PCs
3.1 Introduction
3.2 Analysis
3.3 Numerical Results
3.4 Summary
Chapter 4： A New Design of Four In-plane Channel Add/Drop Filters Based on 2D PCs
4.1 Introduction
4.2 Analysis
4.3 Numerical Results
4.4 Summary
Chapter 5： Conclusions
5.1 Summary
5.2 Suggestions for Future Researches
References

[1]J. D. Joannopoulos, R. D. Meade, and J. N. Winn, 1995, Photonic Crystals: Molding the flow of light, Princeton University Press, New York.
[2]S. John, 1987, “Strong localization of phonics in certain disordered dielectric superlattice,” Phys. Rev. Lett., Vol.58, pp.2486-2489.
[3]E. Yablonovitch, 1987, “Inhibited spontaneous emission in solid-state physics electrons,” Phys. Rev. Lett., Vol.58, pp.2059-2062.
[4]H. Takahashi, S. Suzuki, and I. Nishi, 1994, “Wavelength multiplexer based on SiO2-Ta2O5 arrayed waveguide grating,” J. Lightwave Technol., Vol.12, pp.989-995.
[5]Dragone, 1989, “Efficient N X N star couplers using Fourier optics,” J. Lightwave Technol., Vol.7, pp.479-489.
[6]K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, 1978, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication.,” Appl. Phys. Lett., Vol.32, pp.647-649.
[7]H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, 1999, “Photonic crystals for micro lightwave circuits using wavelength dependent angular beam steering.” Appl. Phys. Lett., Vol.74, pp.1370-1372.
[8]M. Koshiba, 2001, “Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers.” J. Lightwave Technol., Vol.19, pp.1970-1975.
[9]A. Sharkawy, S. Shi, and D. W. Prather, 2001, “Multichannel wavelength division multiplexing with photonic crystals,” Appl. Opt., Vol.40, pp.2247-2252.
[10]H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamaura, T. Sato, and S. Kawakami, 1998, “Superprism phenomena in photonic crystals,” Phys. Rev. B, Vol.58, pp.R10096-R10099.
[11]H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamaura, T. Sato, and S. Kawakami, 1999, “Superprism phenomena in photonic crystals toward microscale lightwave circuits,” J. Lightwave Technol.,” Vol.17, pp.2032-2038.
[12]H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamaura, T. Sato, and S. Kawakami, 1999, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett., Vol.74, pp.1212-1214.
[13]B. Gralak, S. Enoch, and G. Tayeb, 2000, “Anomalous refractive properties of photonic crystals,” J. Opt. Soc. Am. A., Vol.17, pp.1012-1020.
[14]T. Baba, and M. Nakamura, 2002, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum Electron., Vol.38, pp.909-914.
[15]R. D. Meade, A. Devenyi, J. D. Joannopoulous, O. L. Alerthand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phy., Vol.75, pp.4753-4755.
[16]S. Fan, J. N. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, 1995, “Guided and defect modes in periodic dielectric waveguides,” J. Opt. Soc. Am. B, Vol.12, pp.1267-1272.
[17]A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, 1996, “High transmission through sharp bends in photonic crystal,” Phys. Rev. Lett., Vol.77, pp.3787-3790.
[18]S. Y. Lin, E. Chow, V. Hietch, P. R. Villeneuve, and J. D. Joannopoulos, 1998, “Experimental demonstration of guiding and bending of light in a photonic crystal,” Science, Vol.282, 274-278.
[19]A. Mekis, S. Fan, and J. D. Joannopoulos, 1998, “Bound states in photonic crystal waveguides and waveguide bends,” Phys. Rev. B, Vol.58, pp.4809-4817.
[20]S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, 2001, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B, Vol.18, pp.162-165.
[21]E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J.D. Joannopoulos, 2001, “Quantitative analysis of bending efficiency in photonic crystal waveguide bends at 1.55 um wavelengths,” Optics Letters, Vol.26, pp.286-288.
[22]J. N. Winn, R. D. Meade, and J. D. Joannopoulos, 1994, “Two-dimensional photonic band-gap materials,” J. of Modern Optics, Vol.41, pp.257-273.
[23]O. Painter, J. Vuckovic, and A. Scherer, 1999, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B, Vol.16, pp.275-285.
[24]J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, 2001, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E, Vol.65, pp.016608-1-11.
[25]S. Y. Lin, E. Chow, S. G. Johnson, and J.D. Joannopoulos, 2001, “Direct measurement of the quality factor in a two-dimensional photonic-crystal microcavity,” Optics Letters, Vol.26, pp.1903-1905.
[26]K. Srinivasan, P. E. Barclay, and O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, 2003, “Experimental demonstration of a high quality factor photonic crystal microcavity,” Appl. Phys. Lett., Vol.83, pp.1915-1917.
[27]Y. Akahane, T. Asano, B. S. Song, S. Noda, 2005, “Fine-tune high-Q photonic-crystal nanocavity,” Optics Express, Vol.13, pp.1202-1214.
[28]K. Srinivasan, O. Painter, 2003, “Fourier space of high-Q cavities in standard and compressed hexagonal lattice photonic crystal,” Optics Express, Vol.11, pp.579-593.
[29]Y. Akahane, T. Asano, B. S. Song, and S. Noda, 2003, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature, Vol.425, pp.944-947.
[30]Y. Akahane, T. Asano, B. S. Song, and S. Noda, 2003, “Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett., Vol.83, pp.1512-1514.
[31]K. Srinivasan, and O. Painter, 2002, “Momentum space design of high-Q photonic crystal optical cavities,” Optics Express, Vol.10, pp.670-684.
[32]P. Yao, X. Chen, B. Chen, Y. Lu, P. Wang, X. Jiao, H. Ming, and J. Xie, 2004, “Optical reflector and high Q filter based on two-dimensional photonic-crystal waveguide,” Opt. Comm., Vol.236, pp.101-107.
[33]E. Miyai and K. Sakoda, 2001, “Quality factor for localized defevt modes in a photonic crystal slab upon a low-index dielectric substrate,” Opt. Lett., Vol.26, pp.740-742.
[34]P. Lalanne, S. Mias, and J. P. Hugonin, 2004, “Two physical mechanisms for boosting the quality factor to cavity volume ratio of photonic crystal microcavities,” Optics Express, Vol.12, pp.458-467.
[35]S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, 1998, “Channel drop filters in photonic crystals,” Optics Express, Vol.3, pp.4-11.
[36]S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, 1998, “Channel drop tunneling through localized states,” Phys. Rev. Lett., Vol.80, pp.960-963.
[37]C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, 1999, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron, Vol.35, pp.1322-1331.
[38]S. Fan, P. R. Villeneuve, J. D. Joannopouls, M. J. Khan, C. Manolatou, and H. A. Haus, 1999, “Theoretical analysis of channel analysis of channel drop tunneling process,” Phys. Rev. B, Vol.59, pp.15882-15892.
[39]P.R. Villeneuve, S. Fan, and J. D. Joannopoulos, 1996, “Microcavities in photonic crystals: mode symmetry, tenability, and coupling efficiency,” Phys. Rev. Lett., Vol.54, pp.7837-7842.
[40]F. Jian, and H. S, Ling, 2000, “Analysis of high order channel dropping tunneling process in photonic crystals,” Chin Phys. Lett., Vol.17, 737.
[41]C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, 1999, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron, Vol.35, pp.1322-1331.
[42]S. Noda, A. Chutinan, and M. Imada, 2000, “Trapping and emission of photons by single defect in a photonic bandgap structure,” Nature, Vol.407, pp.608-610.
[43]A. Chutinan, M. Mochizuli, M. Imada, and S. Noda, 2001, “Surface-emitting channel drop filters using single defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett., Vol.79, pp.2690-2692.
[44]T. Asano, M. Mochizuki, S. Noda, M. Okano, M. Imdad, 2003, “A channel drop filter using a single defect in a 2-dimensional photonic crystal slab-defect engineering with respect to polarization mode and ratio of emissions from upper and lower sides,” J. Light. Technol., Vol.21, pp.1370-1376.
[45]Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, 2003, “Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab,” Appl. Phys. Lett., Vol.82, pp.1341-1343.
[46]B. S. Song, T. Asano, Y. Akahane, Y. Tanaka, and S. Noda, 2005, “Multichannel add/drop filter based on In-Plane hetero photonic crystals,” J. Light. Technol., Vol.23, pp.1449-1455.
[47]H. Takano, Y. Akahane, T. Asano, and S. Noda, 2004, “In-plane-type channel drop filter in a two-dimensional photonic crystal slab,” Appl. Phys. Lett., Vol.84, pp.2226-2228.
[48]H. Takano, B. S. Song, T. Asano, and S. Noda, 2005, “High efficient in-plane channel drop filter in a two-dimensional heterophotonic crystal,” Appl. Phys. Lett., Vol.86, pp.241101-1-3.
[49]B. S. Song, T. Asano, Y. Akahane, and S. Noda, 2005, “Role of interfaces in heterophotonic crystals for manipulation of photons,” Phys. Rev. B, Vol.71, pp.195101-1-5.
[50]Y. Akahane, T. Asano, H. Takano, B. S. Song, Y. Takama, and S. Noda, 2005, “Two-dimensional photonic-crystal-slab channel-drop filter with flat-top response,” Optics Express, Vol.13, pp.2512-2530.
[51]D. Ohnishi, K. Sakai, M. Imada, and S. Noda, 2003, “Continuous wave operation of surface emitting two-dimensional photonic crystal laser,” Electron. Lette., Vol.39, pp.612-614.
[52]H. Hirayama, T. Hamano, and Y. Aoyagi, 1996, “Novel surface emitting laser diode using photonic band-gap crystal cavity,” Appl. Phys. Lett., Vol.69, pp.791-793.
[53]D. Ohnishi, T. Okano, M. Imada, and S. Noda, 2004, “Room temperature continuous wave operation of a surface-emitting two-dimensional photonic crystal diode laser,” Optics Express, Vol.12, pp.1562-1568.
[54]M. Yokoyama, S. Noda, 2005, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Optics Express, Vol.13, pp.2869-2880.
[55]M. Fujita, T. Ueno, K. Ishihara, T. Asano, and S. Noda, 2004, “Reduction of operating voltage in organic light-emitting diode by corrugated photonic crystal structure,” Appl. Phys. Lett., Vol.85, pp.5769-5771.
[56]M. Boroditsky, T. F. Krauss, R. Coccioli, R. Bhat, and E. Yablonovitch, 1999, “Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals,” Appl. Phys. Lett., Vol.75, pp.1036-1038.
[57]T. F. Krauss, R. M. De, and L. Rue, 1999, “Photonic crystals in the optical regime past, present and future,” Progress in Quantum Electron, Vol.23, pp.51-96.
[58]M. Fujita, K. Ishihara, T. Ueno, T. Asano, S. Noda, H. Ohata, T. Tsuji, H. Nakada, and N. Shimoji, 2005, “Optical and electrical characteristics of organic light-emitting diodes with two-dimensional photonic crystals in organic/electrode layers,” Japan. J. Appl. Phys., Vol44, pp.3669-3677.
[59]M. Thorhauge, L. H. Frandsen, and P. I. Borel, 2003, “Efficient photonic crystal directional couplers,” Optics Express, Vol.28, pp.1525-1527.
[60]F. Cuesta, A. Griol, and J. Marti, 2003, “Experimental demonstration of photonic crystal directional coupler at microwave frequencies,” Electron. Lett., Vol.39, pp.455-456.
[61]M. Shirane, A. Gomyo, K. Miura, H. Yamada, 2003, “Optical directional coupler based on autocloned photonic crystals, Electcon. Lett., Vol.39, pp.53-54.
[62]J. Zimmermann, M. Kamp, A. Forchel, and R. Marz, 2003, “Photonic crystal waveguide directional coupler as wavelength selective optical filter,” Optics Communication, Vol.230, pp.387-392.
[63]J. C. Knight, T. A. Birks, P. St. J. Russel, and D. M. Atkin, 1996, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett., Vol.19, pp.1547-1549.
[64]T. A. Birks, J. C. Knight, and P. St. J. Russell, 1997, “Endlessly single-mode photonic crystal fiber,” Opt. Lett., Vol.22, pp.961-963.
[65]A. Ferrando, E. Silvestre, J. J. Miret, and P. Andres, and M. V. Andres, 1999, “Full-vector analysis of a realistic photonic crystal fiber,” Opt. Lett., Vol.24, pp.276-278.
[66]J. Broeng, S. E. Barkou, T. Sondergaard, and A. Bjarklev, 2000, “Analysis of air-guiding photonic bandgap fibers,” Opt. Lett., Vol.25, pp.96-98.
[67]K. M. Ho, C. T. Chan, and C. M. Soukouils, 1990, “Existence of a photonic gap in periodic dielectric structures,” Phy. Rev. Lett., Vol.65, pp.3152-3155.
[68]K. M. Leung, and Y. F. Liu, 1990, “Photon band structures: The plane-wave method,” Phys. Rev. B, Vol.41, pp.10188-10190.
[69]Z. Zhang and S. Satpathy, 1990, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett., Vol.65, pp.2650-2653.
[70]B. C. Gupta, C. H. Kuo, and Z. Ye, 2004, “Propagation inhibition and localization of electromagnetic waves in two-dimensional random dielectric systems,” Phys. Rev. E., Vol.69, pp.06615-1-6.
[71]P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, 1995, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun., Vol.85, pp.306-322.
[72]K. S. Kunz and R. J. Luebbers, 1993, The finite difference time domain method for electromagnetics, Boca Raton FL: CRC Press.
[73]G. S. Smith, M. P. Kesier, J. G. Maloney, and B. L. Shirely, 1996, “Antenna design with the use of photonic band-gap materials as all-dielectric planar reflectors,” Microwave and optical technology letters, Vol.11, pp.169-174.
[74]J. G. Maloney, M. P. Kesier, B. L. Shirely, and G. S. Smith, 1997, “A simpled description for waveguiding in photonic bandgap materials,” Microwave and optical Technology Letters, Vol.14, pp.261-266.
[75]C. Kittel, 1996, Introduction to Solid State Physics, Wiley.
[76]K. S. Yee, 1966, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas and Propagation, Vol.14, pp.802-807.
[77]J. P. Berenger, 1994, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys., Vol.114, pp.185-200.
[78]J. P . Berenger, 1996, “Perfect matched layer for the FDTD solution of wave-structure interaction problems,” IEEE. Trans. Antennas and Propagation, Vol.44, pp.110-117.
[79]A. Giorgio, R. Diana, and A. G. Perri, 2004 “A method to design DWDM filters on photonic crystals,” Electronics, Circuits and System, ICECS 2004. Proceedings of 2004 11th IEEE International Conference, pp.463-466.
[80]C. Climinelli, F. Peluso and M. N. Armenise, 2005 “2D guided-wave photonic band gap single and multiple cavity filters,” Fibres and Optical Passive Components, 2005. Proceedings of 2005 IEEE/LEOS Workshop, pp.404-409.
[81]John Huh, Jeong-Ki Hwang, Han-Youl Ryu, and Yong-Hee Lee, 2002, “Nondegenerate monopole mode of single defect two-dimensional triangular photonic band-gap cavity,” J. Appl. Phys., Vol.92, pp.654-659.
[82]E. M. Purcell, 1946, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev., Vol.69, pp.681.
[83]P. R. Vileneuve, S. Fan, S. G. Johnson, J. D. Joannopoulos, 1998, “Three-dimensional photon confinement in photonic crystals of low-dimensional periodicity,” Inst. Elect. Eng. Proc-Optoelectron., Vol.145, pp.384-390.
[84]A. Mekis, S. Fan, and J. D. Joannopoulos, 1998, “Bound states in photonic crystal waveguides and waveguide bends,” Phys Rev. B., Vol. 58, pp.4809-4817.
[85]M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, 2001, “Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals,” Phys. Rev. B., Vol.64, pp.155113-1-5.
[86]H. Y. Ryu, J. K. Hwang, Y. H. Lee, 2003, “The smallest possible whispering-gallery-like mode in the square lattice photonic crystal slab single-defect cavity,” IEEE J. Quantum Electron., Vol.39, pp.314-322.
[87]C. Kim, W. J. Kim, A. Stapleton, J. R. Cao, J. D. O’brien, P. D. Dapkus, 2002, “Quality factors in single-defect photonic crystals lasers with asymmetric cladding layers,” J. Opt. Soc. Am. B Vol.19, pp.1777-1781.
[88]L. Dobrzynski, B. Djafari-Rouhani, A. Akjouj, and J. O. Vasseur, and J. Zemmouri, 1999, “Resonant tunneling between two continua,” Phys. Rev. B, Vol.60, pp.10628-10631.
[89]Y. Xu, Y. Li, R. K. Lee, and A. Yariv, 2000, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E, Vol.62, pp.7389-7404.
[90]R. Adar, C. H. Henry, C. Dragine, R. C. Kistler, and M. A. Milbrodt, 1993, “Broad-band array multiplexers made with silica waveguides on silican,” J. Lightwave Technol., Vol.11, pp.212-219.
[91]H. A. Haus and Y. Lai, 1992, “Narrow-band optical channel-dropping filter,” J. Lightwave Technol., Vol.10, pp.57-62.
[92]B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, 1997, “Microring resonator channel dropping filters, J. Lightwave Technol., Vol.15, pp.998-1005.