在適當的條件下，正向入射激光束令GaAs量子阱微腔產生方向的不穩定性，並生成橫向光學圖案。方向不穩定性的形成是由於極化子，即光子及量子阱激子的強非線性耦合的本徵態，在微腔內散射的結果。電腦模擬顯示，通過一個非常弱的控制激光束，橫向光學圖案可以從一個方向切換到另一個。它可以作為一個全光學開關，而全光開關可有效地改善計算機的性能。 / 本論文先介紹GaAs量子阱微腔的理論及其數值模擬，以顯示GaAs量子阱微腔能夠產生光學圖案和全光學開關。然而，透過複雜的模擬數據去理解其規律及原理實在太困難。為此，我們發展一個低維的群種競爭模型，以理解這些現象。 / 為了分析群種競爭模型，我們應用了一些數學工具，如Gröbner bases 和廣義判式，以減少計算模型的相圖所需的電腦負荷。此外，我們也利用了突變理論來分類和解釋所有相圖中的相界。這個人口競爭模型使我們對不同物理系統中的圖案生成現象有一個全面的定性理解。 / 在本論文的最後一部分，我們研究量子阱雙微腔，即兩個耦合的微腔，而每個微腔中間也有一個量子阱。透過傳輸矩陣的方法，我們獲得了雙微腔的色散關係，並與實驗結果作比較。我們預期沿著這個研究方向在未來能夠加快實現全光開關。 / Under favorable conditions, laser beams incident normally to a GaAs quantumwell microcavity develop directional instabilities and generate transverse patterns in the far field. The directional instabilities are driven by scattering among polaritons inside the microcavity, where the polaritons are the eigenstates of strong linear coupling between the cavity photons and the excitons inside the quantum-well. It has been predicted that the transverse pattern can be switched from one to another by the use of a very weak control beam. It can serve as an all-optical switching, which can potentially be used to improve computers’ performance. / In this thesis, the theory of the GaAs quantum-well microcavity is first introduced and numerical results showing the formation of patterns and the all-optical switching scheme are presented. However, understanding the patterns and their dynamics through numerical simulations turns out to be very complicated. To this end, we derive a low-dimensional population-competition model for the interpretation of these behaviors. / To facilitate the analysis the population-competition model, we apply mathematical tools such as the Gröbner basis and the generalized discriminant to reduce the computational load in finding the ‘phase diagrams’ of the populationcompetition model. Besides, we also make use of the catastrophe theory to classify and explain all the phase boundaries in the phase diagrams. This population-competition model enables us to acquire an overall qualitative picture of pattern formation in various physical systems. / In the last part of this thesis, we use the transfer-matrix method to study the polariton spectrum of a quantum-well double-microcavity, which is two coupled optical cavities each containing a quantum well, and compare the spectrum with the experimental results. We expect our efforts along this direction could expedite realization of all-optical switching in the future. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Tse, Yuen Chi = 分析橫向光學圖案的低維群種競爭模型 / 謝沅志. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 112-119). / Abstracts also in Chinese. / Tse, Yuen Chi = Fen xi heng xiang guang xue tu an de di wei qun zhong jing zheng mo xing / Xie Yuanzhi. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Optical computation and all-optical switching --- p.3 / Chapter 1.2 --- Nonlinear optics and low-intensity ultra-fast all-optical switching of transverse optical pattern --- p.4 / Chapter 1.3 --- Pattern formation and amplitude equation formalism --- p.6 / Chapter 1.4 --- Semiconductor quantum-well double-microcavity and transfermatrix method --- p.9 / Chapter 2 --- Semiconductor quantum-well microcavity --- p.10 / Chapter 2.1 --- Physical configuration and theroy --- p.10 / Chapter 2.2 --- Simplified models --- p.19 / Chapter 2.3 --- Directional instability and the effect of anisotropy in model PCO-Q --- p.25 / Chapter 2.4 --- Effect of control beam and all-optical switching in PCO-Q --- p.30 / Chapter 2.5 --- Simulation results of model PCO-L, a model without quadratic dependence --- p.33 / Chapter 3 --- Population-competition model --- p.37 / Chapter 3.1 --- Derivation of PC model --- p.37 / Chapter 3.1.1 --- Approximation from the simulation results --- p.38 / Chapter 3.1.2 --- Adiabatic approximation for the field equations --- p.39 / Chapter 3.1.3 --- Revised dynamical equations --- p.40 / Chapter 3.1.4 --- Taylor expansion approximation about phase locking --- p.42 / Chapter 3.1.5 --- Comparison with the simulation results --- p.45 / Chapter 3.1.6 --- Modelling of the control beam --- p.47 / Chapter 3.1.7 --- Reduction in the number of parameters --- p.47 / Chapter 3.2 --- Physical meaning of the simplified PC model --- p.49 / Chapter 3.3 --- Comparison with amplitude equations formalism and others competition models --- p.49 / Chapter 4 --- Mathematical tools --- p.52 / Chapter 4.1 --- Steady states and linear stability analysis --- p.52 / Chapter 4.2 --- Gröbner basis --- p.54 / Chapter 4.3 --- Generalized discriminant --- p.55 / Chapter 4.4 --- Algorithm for conditions for qualitative changes --- p.56 / Chapter 4.5 --- Reduction in computational power --- p.57 / Chapter 4.6 --- Elementary catastrophe theory --- p.58 / Chapter 5 --- Population-competition model analysis --- p.66 / Chapter 5.1 --- Symmetric model L without source term --- p.67 / Chapter 5.2 --- Symmetric model Q without source term --- p.70 / Chapter 5.3 --- Asymmetric model L and Q without source term --- p.74 / Chapter 5.4 --- Symmetric models L and Q with control beam S₂ --- p.80 / Chapter 5.5 --- Asymmetric Model L and Q with control beam S₂ --- p.81 / Chapter 6 --- Semiconductor quantum-well double-microcavity --- p.91 / Chapter 6.1 --- Motivation --- p.91 / Chapter 6.2 --- Transfer-matrix method inside dielectrics --- p.94 / Chapter 6.3 --- Transfer-matrix method across QW --- p.97 / Chapter 6.4 --- Analysis of the QWDM through transfer-matrix method --- p.98 / Chapter 7 --- Conclusion and Outlook --- p.105 / Chapter 7.1 --- Conclusion --- p.105 / Chapter 7.2 --- Outlook --- p.107 / Chapter 7.2.1 --- Extension of the PC model --- p.107 / Chapter 7.2.2 --- Extension of the transfer-matrix method to nonlinear analysis --- p.109 / Bibliography --- p.112 / Chapter A --- Dispersion relations inside QWM --- p.120 / Chapter B --- Analysis on the steady states with and without off-axis instability --- p.122 / Chapter B.1 --- Steady states of E₀ and p₀ --- p.122 / Chapter B.2 --- Analysis on the steady states without off-axis instability --- p.123 / Chapter B.3 --- The effects of instability on E₀ and p₀ --- p.124 / Chapter C --- Analytical derivation of the phase diagram asymmetry versus quadratic terms (δβ1 vs γ) without control beam (S₂ = 0) --- p.127 / Chapter D --- Verification of the elliptic umbilic (D₋₄) singularity --- p.129
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328591 |
| Date | January 2013 |
| Contributors | Tse, Yuen Chi., Chinese University of Hong Kong Graduate School. Division of Physics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource (xvi, 130 leaves) : ill. (some col.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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