Translated Titles

Properties of Resonance Mode in Heterostructures Waveguide Array



Key Words

光波導陣列 ; 離散薛丁格方程式 ; 週期性 ; optical waveguide arrays ; discrete Schrodinger equation ; periodic



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Chinese Abstract

本篇論文利用離散的薛丁格方程式為基礎並分析光波導內的光學特性、能量傳遞分析、電場分佈、結果討論和應用。在此光波導陣列的分析結構主要分為兩種形式:第一種為雙均質波導陣列的邊界與光學特性,第二種則是將週期性波導陣列等結構嵌入在均質結構的光波導陣列中並改變波導層數以及折射率。前者是討論波導層數與傳播常數差變化對於光傳輸的影響;後者為改變波導的排列為週期性或準週期性系統並對於探討能量傳遞所造成的影響,結果會進一步在本論文中討論,以上波導陣列結構可以依據不同的排列、材料、層數的多寡決定此系統結構對於光頻譜的過濾特性有不同的效果,可應用在光整流器、光開關元件。 關鍵詞:光波導陣列、離散薛丁格方程式、週期性

English Abstract

A discrete Schrödinger equation is used to analyze optical properties such as dispersion relation, electric field distribution and the light propagation behavior under the heterostructure waveguide arrays. In this thesis, two fundamental structures, embedded heterostructure and periodic waveguide array are investigated. The embedded heterostructure waveguide array is to embedd a heterostructure inside the homogeneous waveguide arrays system, and the periodic waveguide array is to embedd periodic or aperiodic structure in homogeneous arrays. Based on the theory of discrete Snell's law, embedded heterostructure waveguide array concern the effect of guide layer number and change of propagation constant. Analysis to the periodic waveguide array focuses on the influence of the energy transport. Based on difference of arrangement, medium and number of layer of the waveguide, the filter characteristics of the light spectrum in this system can be decided, which can be apply to optical-switching and light rectifiers device. Key words:optical waveguide arrays, discrete Schrödinger equation, periodic

Topic Category 基礎與應用科學 > 海洋科學
工學院 > 工程科學及海洋工程學研究所
工程學 > 工程學總論
  1. [1] B. A. Lengyel, Lasers: Generation of Light by Simulated Emission, John Wiley, New York (1962).
  2. [2] M. Kerker, The Scattering of Light, and Other Electromagnetic Radiation,Academic Press, New York (1909).
  3. [3] W. W. Chow, S. W. Koch, Semiconductor-Laser Fundamentals, Springer,New York. (1999).
  4. [4] E. Yablonovitch, ‘‘Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
  5. [5] S. John, ‘‘Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
  6. [6] L. Rayleigh, ‘‘On the remarkable phenomenon of crystalline reflexion described by Prof. Stokes, ” Phil. Mag. 26, 256-265. (1888).
  7. [7] Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, ‘‘A dielectric omnidirectional reflector,”Science 282,1679 (1998).
  8. [8] M. Ibanescu1, Y. Fink, S. Fan1, E. L. Thomas, and J. D. Joannopoulos , ‘‘An all-dielectric coaxial waveguide,” Science 289, 415-419 (2000).
  9. [9] J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, ‘‘Omnidirectional reflection from a one-dimensional photonic crystal,”Opt. Lett. 23, 1573-1575 (1998).
  10. [10] E. Yablonovitch, ‘‘Engineered omnidirectional external-reflectivity spectra from one-dimensional layered interference filters,”Opt. Lett. 23, 1648 (1998).
  11. [11] A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, ‘‘High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787 (1996).
  12. [12] K. M. Ho, C. T. Chan, and C. M. Soukoulis, ‘‘Existence of a photonic gap in periodic dielectric structures,”Phys. Rev. Lett. 65, 3152(1990).
  13. [13] A. L. Jones, ‘‘Coupling of optical fibers and scattering in fibers,” J. Opt. Soc. Am. 55, 261-269 (1965).
  14. [14] S. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, ‘‘Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46-47 (1973).
  15. [15] R. R. Syms, ‘‘Approximate solution of eigenmode problems for layered coupled waveguide arrays,” IEEE J. Quant. Electron. 23, 525-532 (1987).
  16. [16] D. Christodoulides and R. Joseph, ‘‘Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794-796 (1988).
  17. [17] R. Morandotti,U. Peschel,and J. S. Aitchison, ‘‘Experimental observation of linear and nonlinear optical bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999).
  18. [18] H. Eisenberg, Y. Silberberg, R. Morandotti, and J. Aitchison, ‘‘Diffraction management,” Phys. Rev. Lett. 85, 1863-1866 (2000).
  19. [19] T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, ‘‘Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
  20. [20] D. Mandelik, R. Morandotti, J. S. Aitchison,and Y. Silberberg, ‘‘Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
  21. [21] T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, ‘‘Beam steering in waveguide arrays,” Appl. Phys. Lett. 80, 3247 (2002).
  22. [22] A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, ‘‘Quasi-incoherent propagation in waveguide arrays,” Appl. Phys. Lett. 90, 241113 (2007).
  23. [23] A. Kanshu, C. E. Rüter, D. Kip, P. P. Beličev, I. Ilić, M. Stepić,and V. M. Shandarov, ‘‘Linear and nonlinear light propagation at the interface of two homogeneous waveguide arrays,” Opt. Express 19, 1158 (2011).
  24. [24] A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. A. Sukhorukov, ‘‘Realization of reflectionless potentials in photonic lattices,” Phys. Rev. Lett. 106, 193903 (2011).
  25. [25] S. Lepri and G. Casati, ‘‘Asymmetric wave propagation in nonlinear systems,” Phys. Rev. Lett. 106, 164101 (2011).
  26. [26] Z. Cao, X. Qi, G. Zhang, and J. Bai, ‘‘Asymmetric light propagation in transverse separation modulated photonic lattices,” Opt. Lett. 38, 3212-3215 (2013).
  27. [27] J. M. Zeuner, M. C. Rechtsman, R. Keil, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit1, ‘‘Negative coupling between defects in waveguide arrays,” Opt. Lett. 37, 533 (2012).
  28. [28] N. K. Efremidis, Peng Zhang, Zhigang Chen, Demetrios N. Christodoulides Christian E. Rぴuter, and Detlef Kip, ‘‘Wave propagation in waveguide arrays with alternating positive and negative couplings,” Phys. Rev. Lett. 81, 053817 (2010).
  29. [29] A. J. Mart´ınez and M. I. Molina , ‘‘Surface solitons in quasiperiodic nonlinear photonic lattices,” Phys. Rev. Lett. 85, 013807 (2012).
  30. [30] G. Wang ‘‘Fragmentation of Bloch oscillations in quasiperiodic waveguide arrays,” Opt. Lett. 16, 015502 (2014).
  31. [31] A.Yariv, Optical Electronics, Wiley, New York (1991).
  32. [32] A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, ‘‘Control of directional evanescent coupling in fs laser written waveguides,” Opt. Express 15, 1579-1587 (2007).
  33. [33] A. Szameit and S. Nolte, ‘‘Discrete optics in femtosecond-laser-written photonic structures,” J. Phys. B 43, 163001 (2010).
  34. [34] S. Longhi and K. Staliunas, ‘‘Self-collimation and self-imaging effects in modulated waveguide arrays,” Opt. Commun. 281, 4343-4347 (2008).
  35. [35] A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, and A. Tünnermann, ‘‘Light evolution in arbitrary two-dimensional waveguide arrays,” Phys. Rev. Lett. 75, 053814 (2007).
  36. [36] S. Minardi, F. Eilenberger, Y. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, and L. Torner, ‘‘Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105, 263901 (2010).
  37. [37] N. N. Rao, Elements of Engineering Electromagnetics, Prentice-Hall, New York (2004).
  38. [38] A. Hardy and W. Streifer, ‘‘Coupled mode theory of parallel waveguides,” J. Lightw. Technol. 3, 1135-1146 (1985).
  39. [39] W.-P. Huang, ‘‘Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A 11, 963-983 (1994).
  40. [40] A. Yariv and P. Yeh, Optical Waves in Crystals, Wiley, New York (1984).
  41. [41] S. Longhi, ‘‘Invisibility in non-Hermitian tight-binding lattices,” Phys. Rev. A 82, 032111 (2010).
  42. [42] D. N. Christodoulides, F. Lederer, and Y. Silberberg, ‘‘Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817-823 (2003).
  43. [43] S. Longhi, ‘‘Transmission and localization control by ac fields in tight-binding lattices with an impurity,” Phys. Rev. B 73, 193305 (2006).
  44. [44] P. Kevrekidis, K. Rasmussen, and A. Bishop, ‘‘The discrete nonlinear Schrödinger equation: a survey of recent results,” Int. J. Mod. Phys. B 15, 2833-2900 (2001).
  45. [45] F. Lederer and Y. Silberberg, ‘‘Discrete solitons,” Opt. Photonics News 49, (2002).
  46. [46] C. Kittel and P. McEuen, Introduction to Solid State Physics, Wiley, New York, (1986).
  47. [47] A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, and A. Tünnermann, ‘‘Fresnel's laws in discrete optical media,” New J. Phys. 10, 103020 (2008).
  48. [48] P. Yeh, Optical Waves in Layered Media, Wiley, New York (1988).