本論文以易辛模型的模擬研究面射型半導體雷射之偏振切換的現象。針對面射型半導體雷射光的兩種特性(空間同調與偏振有序到有序的轉換)進行探討。首先，我們主要研究的雷射是一個高斯單橫模的面射型半導體雷射。從空間同調性的角度來看，我們將一個帶有高斯基模形狀之交互作用加入二維的易辛模型中。而它對於無序到有序的轉變呈現一個弱一階相變，其原因是高斯基模形狀之交互作用所造成的空間不勻稱性，故說明這樣形式的交互作用並不適用於敘述雷射的空間同調性。對於面射型半導體雷射之偏振切換的有序到有序轉變，有外加場的易辛模擬給予一個現象上的描述，並暗示面射型半導體雷射之偏振切換是一個一階相變。雖然面射型半導體雷射的共振腔有著良好的圓對稱，但比較兩系統後，結果指出面射型半導體雷射之偏振切換的系統中存在一個由電流引發的對稱破缺作用，同時也暗示對於快速偏振切換且帶有遲滯的系統中，交互作用的強度需要足夠讓整個系統處於一個自發性的有序態。而在易辛模型中這個參考的交互作用力強度約為1/2.3。本研究提供一個可能的解答，對於面射型半導體雷射之偏振切換的交互作用。我們更期待未來有更多快速偏振切換與緩慢偏振切換的實驗能驗證此項研究。

An Ising simulation is used to investigate the phase transition in the polarization switching (PS) of vertical-cavity surface-emitting lasers (VCESLs). This study focuses on two features of VCSELs’ light. One is the spatial coherence of beam, and the other is the order-to-order transition of VCSELs’ PS (VPS). The main laser represented in this thesis is a single-transverse-mode VCSEL with a Gaussian beam profile. From a point of view of an excellent spatial coherence due to stimulated emission, we added a Gaussian-function distribution in the interaction energy of a 2-D Ising model. The simulation result shows a weak first-order phase transition for disorder-to-order transition because of the inhomogeneous interaction in space, and suggests that it is an improper way to imitate the spatial coherence of laser. For the order-to-order transition in the VPS, the Ising simulation with an external field could give a phenomenological description to understand the interaction in VPS and suggest VPS is a first order phase transition (FOPT). Although the cavity of VCSEL has a great circular symmetry, the results also indicate an existence of a symmetry-breaking mechanism induced by injection current in VPS system and imply the interaction for an abrupt VPS with hysteresis should be strong enough to make the whole system be in a spontaneous order state. The reference value of the interaction strength is 1/2.3 for the Ising model. This study proposes a possible answer to VPS’s interaction. We hope more experiments for the abrupt and the gradual VPS could support it.

Approval i
Acknowledgement ii
Abstract (Chinese) iii
Abstract (English) iv
Contents v
Figure contents vi
Table contents viii
Chapter-1 Introduction 1
Chapter-2 Operating Principles of VCSELs and Ising model 4
2-1 Operating Principles of Laser 4
2-1.1 Two-level system and stimulated emission 4
2-1.2 Pump and population inversion 5
2-1.3 Gain medium and cavity 5
2-2 Polarization switching of vertical-cavity surface-emitting lasers 7
2-3 Ising model 9
2-3.1 Introductions 9
2-3.2 Second order phase transition and first order phase transition 9
2-3.3 Critical phenomenon 11
Chapter-3 Earlier studies of polarization switching and dynamic Ising model 14
3-1 Experiment of VPS as dynamical bifurcation 14
3-2 Dynamical bifurcation of VPS due to temperature delay 16
3-3 Critical phenomena in VPS 18
3-4 Dynamical Ising simulation 20
Chapter-4 Experiment setup and simulation method 23
4-1 Experiment setup 23
4-1.1 VECSL Arima ADL-85013VL 23
4-1.2 Laser driving system 24
4-1.3 Detection system Detection system 25
4-1.4 Temperature controlling system 26
4-2 Simulation method 27
Chapter-5 Experiment and simulation results 30
5-1 Gaussian-distribution interaction and weak first order phase transition 30
5-2 Hysteresis in VPS and IM in a time-dependant external field (TFIM) 33
5-3 Relaxation time and critical slowing down 34
5-3.1 Quasi-step current for VCSEL 34
5-3.2 Step temperature for CIM and GDIM 35
5-3.3 Step external field for Ising model at low T and high T 37
Chapter-6 Conclusion 39
References ix

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