請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/29762完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 石明豐(Ming-Feng Shih) | |
| dc.contributor.author | Shao-Chuan Wang | en |
| dc.contributor.author | 王紹權 | zh_TW |
| dc.date.accessioned | 2021-06-13T01:17:50Z | - |
| dc.date.available | 2007-10-30 | |
| dc.date.copyright | 2007-07-20 | |
| dc.date.issued | 2007 | |
| dc.date.submitted | 2007-07-17 | |
| dc.identifier.citation | [1] Morandotti, R., Eisenberg, H. S., Silberberg, Y., Sorel, M., and Aitchison, J. S. Self-focusing and defocusing in waveguide arrays. Phys. Rev. Lett. 86(15), 3296-3299, Apr (2001).
[2] Pertsch, T., Zentgraf, T., Peschel, U., BrÄauer, A., and Lederer, F. Anomalous refraction and di®raction in discrete optical systems. Phys. Rev. Lett. 88(9), 093901, Feb (2002). [3] Malomed, B. A. and Kevrekidis, P. G. Discrete vortex solitons. Phys. Rev. E 64(2), 026601, Jul (2001). [4] Efremidis, N. K., Sears, S., Christodoulides, D. N., Fleischer, J. W., and Segev, M. Discrete solitons in photorefractive optically induced photonic lattices. Phys. Rev. E 66(4), 046602, Oct (2002). [5] Fleischer, J. W., Carmon, T., Segev, M., Efremidis, N. K., and Christodoulides, D. N. Observation of discrete solitons in optically induced real time waveguide arrays. Phys. Rev. Lett. 90(2), 023902, Jan (2003). [6] Fleischer, J. W., Segev, M., Efremidis, N. K., and Christodoulides, D. N. Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices. Nature 422(13), 147-150 (2003). [7] Kivshar, Y. S. Self-localization in arrays of defocusing waveguides. Opt. Lett. 18(14), 1147-1149 (1993). [8] Sukhorukov, A. A. and Kivshar, Y. S. Spatial optical solitons in nonlinear photonic crystals. Phys. Rev. E 65(3), 036609, Feb (2002). [9] Christodoulides, D. N. and Joseph, R. I. Discrete self-focusing in nonlinear arrays of coupled waveguides. Opt. Lett. 13(9), 794 (1988). [10] Mandelik, D., Eisenberg, H. S., Silberberg, Y., Morandotti, R., and Aitchison, J. S. Band-gap structure of waveguide arrays and excitation of Floquet-bloch solitons. Phys. Rev. Lett. 90(5), 053902 (2003). [11] Cohen, O., Schwartz, T., Fleischer, J. W., Segev, M., and Christodoulides, D. N. Multiband vector lattice solitons. Phys. Rev. Lett. 91(11), 113901,Sep (2003). [12] Eisenberg, H. S., Silberberg, Y., Morandotti, R., and Aitchison, J. S. Diffraction management. Phys. Rev. Lett. 85(9), 1863-1866, Aug (2000). [13] Kivshar, Y. S. and Agrawal, G. Optical Solitons: From Fibers to Photonic Crystals. Academic Press, (2003). [14] Eisenberg, H. S., Silberberg, Y., Morandotti, R., Boyd, A. R., and Aitchison, J. S. Discrete spatial optical solitons in waveguide arrays. Phys. Rev. Lett. 81(16), 3383-3386, Oct (1998). [15] Fleischer, J. W., Carmon, T., Segev, M., Efremidis, N. K., and Christodoulides, D. N. Observation of discrete solitons in optically induced real time waveguide arrays. Phys. Rev. Lett. 90(2), 023902, Jan (2003). [16] Mitchell, M., Chen, Z., Shih, M.-f., and Segev, M. Self-trapping of partially spatially incoherent light. Phys. Rev. Lett. 77(3), 490-493, Jul (1996). [17] Christodoulides, D. N., Coskun, T. H., Mitchell, M., and Segev, M. Theory of incoherent self-focusing in biased photorefractive media. Phys. Rev. Lett. 78(4), 646-649, Jan (1997). [18] Stegeman, G. I. and Segev, M. Optical Spatial Solitons and Their Interactions: Universality and Diversity. Science 286(5444), 1518-1523 (1999). [19] George Stageman, Demetrios Christodoulides, P. P. M. S. K. S. Solitonic Gateless Computing. (2006). [20] Gordon, J. P. Interaction forces among solitons in optical Fibers. Opt. Lett. 8(11), 596 (1983). [21] Anderson, D. and Lisak, M. Bandwidth limits due to incoherent soliton interaction in optical-‾ber communication systems. Phys. Rev. A 32(4), 2270-2274, Oct (1985). [22] Meier, J., Stegeman, G. I., Silberberg, Y., Morandotti, R., and Aitchison, J. S. Nonlinear optical beam interactions in waveguide arrays. Phys. Rev. Lett. 93(9), 093903 (2004). [23] Aceves, A. B., De Angelis, C., Peschel, T., Muschall, R., Lederer, F., Trillo, S., and Wabnitz, S. Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays. Phys. Rev. E 53(1), 1172-1189, Jan (1996). [24] Meier, J., Stegeman, G. I., Silberberg, Y., Morandotti, R., and Aitchison, J. S. Nonlinear beam interactions in 1d discrete kerr systems. Opt. Express 13, 1797-1807 (2004). [25] Pelinovsky, D. E., Sukhorukov, A. A., and Kivshar, Y. S. Bifurcations and stability of gap solitons in periodic potentials. Phys. Rev. E 70(3), 036618 (2004). [26] Ku, T.-S., Shih, M.-F., Sukhorukov, A. A., and Kivshar, Y. S. Coherence controlled soliton interactions. Physical Review Letters 94(6), 063904 (2005). [27] Pezer, R., Hrvoje Buljan, Guy Bartal, O. C., and Segev, M. Gap random-phase lattice solitons. Opt. Express 13, 5013-5023 (2005). [28] Evans, M. R., Foster, D. P., Godrµeche, C., and Mukamel, D. Spontaneous symmetry breaking in a one dimensional driven di®usive system. Phys. Rev. Lett. 74(2), 208-211, Jan (1995). [29] Yannouleas, C. and Landman, U. Spontaneous symmetry breaking in single and molecular quantum dots. Phys. Rev. Lett. 82(26), 5325-5328, Jun (1999). [30] Soljacic, M., Segev, M., Coskun, T., Christodoulides, D. N., and Vishwanath, A. Modulation instability of incoherent beams in noninstantaneous nonlinear media. Phys. Rev. Lett. 84(3), 467-470, Jan (2000). [31] Detlef Kip, Marin Soljacic, M. S. E. E. D. N. C. Modulation instability and pattern formation in spatially incoherent light beams. Science 290(5491), 495-498, Oct (2000). [32] Torres, J. P., Anastassiou, C., Segev, M., Solja·cic, M., and Christodoulides, D. N. Transverse instability of incoherent solitons in kerr media. Phys. Rev. E 65(1), 015601, Dec (2001). [33] Jeng, C.-C., Shih, M.-F., Motzek, K., and Kivshar, Y. Partially incoherent optical vortices in self-focusing nonlinear media. Phys. Rev. Lett. 92(4), 043904 (2004). [34] Burckhardt, C. B. Di®raction of a plane wave at a sinusoidally stratified dielectric grating. J. Opt. Soc. Am. 56(11), 1502-1509 (1966). [35] Grosso, G. and Parravicini, G. P. Solid State Physics, chapter I. Academic Press, 1st edition, April (2000). [36] Agrawal, G. Nonlinear Fiber Optics, chapter 2. Academic Press, 3rd edition, January (2001). | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/29762 | - |
| dc.description.abstract | 具有週期性結構的系統在自然界可說是隨處可見。帶有週期性結構的系統與連續性系統在許多物理行為表現上有著根本上的不同。在所有週期性結構中，由於光的可調變性(adaptability)以及可控制性(controllability)，讓波導陣列正好為研究週期系統開啟了一條康莊大道。在波導陣列中，當光束之擴散效應與非線性效應達到平衡時，光束將形成自定域態(self-localized modes)或稱做離散光孤子(discrete solitons)。在此論文中，將一一介紹光束在波導陣列中的行為，包括非尋常繞射(anomalous diffraction)以及無繞射傳播(diffraction-free propagation)等。
本論文主要針對「離散孤子之交互作用」以及「對稱孤子之對稱性破壞」進行研究。由於在非線性光學領域中，孤子之交互作用一直是國際上研究的焦點，因此，我們利用數值運算，針對離散孤子之交互作用作了一系列的探討。研究中發現，當離散光孤子的同調性降低時，將弱化其交互作用。此結果與先前研究在均勻介質中，利用光孤同調性控制其交互作用有相似的結果。最後，本論文亦針對對稱孤子之對稱性破壞進行研究。研究發現，當孤子之同調性下降時，將可抑制孤子之對稱性破壞。 | zh_TW |
| dc.description.abstract | Periodic systems are ubiquitous in nature and are known to exhibit behaviors that differ fundamentally from those of homogenous systems. Among all periodic systems, optical waveguide array opens a wide door for investigating the dynamics in nonlinear periodic systems for its adaptability and controllability of light. Self-localized modes in periodically modulated structures, or discrete solitons, form when the broadening effects (discrete diffraction) and the nonlinear effects are balanced. Many properties about the wave propagation in the (nonlinear) periodic systems are
demonstrated in this thesis, such as anomalous diffraction, diffraction-free propagation, and staggered and unstaggered modes. This thesis mainly focus on two topics: discrete soliton interactions and symmetry breaking of even discrete solitons. Since one of the most intriguing phenomena in the nonlinear optics is the soliton interaction, we perform numerical simulations of the discrete soliton interactions, and study the threefold interplay between statistical properties (coherence), the periodic refractive index, and the nonlinear effects. We show that when the two beams are made partially incoherent, the interaction force will become much weaker, and this result is similar to the previous study, done by T.S. Ku, that focuses on the coherence-controlled soliton interactions in the homogenous nonlinear media. In the final section, we discuss the symmetry breaking instability of discrete solitons with even parity and show how incoherence can suppress the instability. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T01:17:50Z (GMT). No. of bitstreams: 1 ntu-96-R94222005-1.pdf: 3304642 bytes, checksum: bb42790c2e32947686b0cdcccdf752ad (MD5) Previous issue date: 2007 | en |
| dc.description.tableofcontents | Acknowledgement i
Abstract-Chinese iii Abstract v 1 Coherent Spatial Discrete Optical Solitons 1 1.1 Floquet-Bloch Theory 2 1.2 Discrete Soliton Formation 6 1.2.1 Di®raction Theory 6 1.2.2 Soliton Formation 11 1.2.3 The Staggered and Unstaggered Modes 12 2 Partially Incoherent Discrete Solitons 15 2.1 Coherent Density Theory 17 2.2 Partially Incoherent Discrete Soliton Formation 21 3 Discrete Solitons Interactions 25 3.1 Nonlinear beam interactions in 1-D waveguide array 26 3.1.1 Unstaggered modes 26 3.1.2 Staggered modes 31 3.2 Coherence controlled interactions of discrete solitons 33 4 Symmetry Breaking of Discrete Solitons with Even Parity 39 4.1 Symmetry Breaking in Waveguide Array 41 4.2 Suppressing Symmetry Breaking by Spatial Incoherence 44 5 Summary 47 A Derivation of Floquet-Bloch Theory 49 A.1 The Paraxial Equation with Periodic Potential 49 A.2 Optical Bandgap 51 A.3 Bloch Waves 53 B Numerical Methods 57 B.1 Split-Step Fast Fourier Transform 57 B.2 Algorithm for Partially Incoherent Beam Propagation 59 C Kernel Codes 61 | |
| dc.language.iso | en | |
| dc.subject | 散孤子交互作用 | zh_TW |
| dc.subject | 非線性離 | zh_TW |
| dc.subject | 散光孤子 | zh_TW |
| dc.subject | 抑制對稱性破壞 | zh_TW |
| dc.subject | 部分非同調光孤子 | zh_TW |
| dc.subject | 佛洛 | zh_TW |
| dc.subject | 逵特-布洛 | zh_TW |
| dc.subject | 赫波 | zh_TW |
| dc.subject | Floquet-Bloch waves | en |
| dc.subject | Partially incoherent solitons | en |
| dc.subject | Suppressed symmetry breaking | en |
| dc.subject | Discrete soliton interactions | en |
| dc.subject | Nonlinear discrete solitons | en |
| dc.title | 在波導陣列中的離散光孤子 相干性控制交互作用以及抑制對稱性破壞 | zh_TW |
| dc.title | Discrete Optical Soliton in a Waveguide Array
- Controlled Soliton Interactions and Suppressed Symmetry Breaking by Incoherence | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 95-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 蔡定平(Din-Ping Tsai),曹培熙(Pei-Shi Tsao) | |
| dc.subject.keyword | 非線性離,散光孤子,離,散孤子交互作用,抑制對稱性破壞,部分非同調光孤子,佛洛,逵特-布洛,赫波, | zh_TW |
| dc.subject.keyword | Nonlinear discrete solitons,Discrete soliton interactions,Suppressed symmetry breaking,Partially incoherent solitons,Floquet-Bloch waves, | en |
| dc.relation.page | 75 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2007-07-19 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-96-1.pdf 未授權公開取用 | 3.23 MB | Adobe PDF |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。