發(fā)布時(shí)間：2018-04-11 18:12

  本文選題：PT對(duì)稱復(fù)數(shù)勢(shì) + 渦旋光孤子�。� 參考：《華南理工大學(xué)》2016年博士論文

【摘要】：由于光束自然衍射效應(yīng)、介質(zhì)非線性效應(yīng)和復(fù)數(shù)勢(shì)增益/損耗效應(yīng)之間的相互平衡,光束可以在非線性介質(zhì)中保持形狀不變地進(jìn)行傳輸,進(jìn)而形成空間光孤子。由于空間光孤子所具有的這種獨(dú)特屬性,其在實(shí)現(xiàn)全光通信和全光器件方面具有巨大的應(yīng)用價(jià)值,尤其是攜帶角動(dòng)量的渦旋光孤子在光學(xué)微操縱、粒子捕獲、信息傳輸領(lǐng)域有著重要應(yīng)用。另一方面,空間光孤子的研究可以為相鄰學(xué)科的發(fā)展提供理論指導(dǎo),具有重要的學(xué)術(shù)價(jià)值。本文從描述光束傳輸特性的非線性薛定諤方程出發(fā),采用數(shù)值模擬、數(shù)值計(jì)算及數(shù)值分析的方法,研究了PT對(duì)稱復(fù)數(shù)勢(shì)光學(xué)格子中空間光孤子的傳輸特性。具體研究成果如下:1.研究了PT對(duì)稱正方形光學(xué)格子中的渦旋光孤子和同相位四極孤子的存在性、穩(wěn)定性以及傳輸特性。渦旋光孤子和同相位四極孤子存在于PT對(duì)稱復(fù)數(shù)勢(shì)布洛赫能帶第一帶隙且可以在一定的參數(shù)范圍內(nèi)穩(wěn)定。由不攜帶角動(dòng)量環(huán)形光束形成的同相位四極孤子比渦旋光孤子更穩(wěn)定。PT對(duì)稱復(fù)數(shù)勢(shì)勢(shì)深的減小或增益/損耗系數(shù)的增大都會(huì)導(dǎo)致渦旋光孤子穩(wěn)定范圍的縮小。當(dāng)渦旋光孤子不穩(wěn)定時(shí),其功率在傳輸過(guò)程中隨傳輸距離發(fā)生振蕩,而在實(shí)數(shù)勢(shì)光學(xué)格子中渦旋光孤子功率在傳輸過(guò)程中始終保持不變。PT對(duì)稱復(fù)數(shù)勢(shì)增益/損耗系數(shù)對(duì)渦旋光孤子形成有著重要影響,當(dāng)其取值接近臨界閾值時(shí),渦旋光孤子發(fā)生相變。2自聚焦飽和非線性介質(zhì)PT對(duì)稱光學(xué)格子中飽和系數(shù)以及PT對(duì)稱復(fù)數(shù)勢(shì)對(duì)渦旋光孤子都有著重要影響。只有當(dāng)非線性飽和系數(shù)大于某個(gè)臨界閾值時(shí)渦旋光孤子才可以穩(wěn)定存在。隨著飽和系數(shù)的增大,渦旋光孤子的存在范圍逐漸縮小,但其穩(wěn)定范圍先擴(kuò)大后縮小。當(dāng)飽和系數(shù)足夠大時(shí),模型中的非線性項(xiàng)可以近似為線性項(xiàng),此時(shí)渦旋光孤子不存在。保持飽和系數(shù)不變,隨著PT對(duì)稱復(fù)數(shù)勢(shì)增益/損耗系數(shù)的增大,渦旋光孤子的存在范圍和穩(wěn)定區(qū)間都會(huì)縮小。當(dāng)PT對(duì)稱復(fù)數(shù)勢(shì)增益/損耗系數(shù)等于其臨界閾值時(shí),渦旋光孤子仍然可以存在,但是它在傳輸過(guò)程中發(fā)散很快。在同一飽和系數(shù)下,異相位四極孤子比渦旋孤子穩(wěn)定范圍更大,而同相位四極孤子穩(wěn)定范圍最小。3.具有單點(diǎn)缺陷的PT對(duì)稱三角格子可以支持缺陷基本孤子和缺陷渦旋孤子的穩(wěn)定傳輸。三角格子缺陷深度對(duì)缺陷基本孤子的存在性有著重要影響;當(dāng)負(fù)缺陷深度絕對(duì)值足夠大時(shí),負(fù)缺陷基本孤子不存在。無(wú)缺陷和正缺陷以及負(fù)缺陷基本孤子的穩(wěn)定性符合anti-Vakhitov-Kolokolov準(zhǔn)則。然而負(fù)缺陷渦旋孤子在整個(gè)存在范圍內(nèi)不穩(wěn)定,而正缺陷和無(wú)缺陷渦旋孤子可以在一定的范圍內(nèi)穩(wěn)定存在,正缺陷在一定程度上可以抑制缺陷渦旋孤子的不穩(wěn)定性。最后,以正缺陷基本孤子為例,發(fā)現(xiàn)增大PT對(duì)稱復(fù)數(shù)勢(shì)增益/損耗系數(shù)不僅會(huì)使缺陷孤子的存在范圍縮小,而且會(huì)使缺陷孤子變得更不穩(wěn)定。4.兩維混合線性非線性PT對(duì)稱復(fù)數(shù)勢(shì)可以支持空間光孤子的穩(wěn)定傳輸。非線性調(diào)制深度對(duì)孤子的形成和存在有著重要影響。在非線性調(diào)制深度的一個(gè)確定范圍內(nèi),孤子隨傳播常數(shù)的變化會(huì)發(fā)生形變。孤子形變和PT對(duì)稱非線性調(diào)制深度和非線性虛部相對(duì)強(qiáng)度之間有著重要關(guān)系。不同的非線性調(diào)制深度會(huì)致使系統(tǒng)呈現(xiàn)自聚焦和自散焦兩種非線性效應(yīng)。在兩種非線性效應(yīng)下,空間光孤子的穩(wěn)定范圍在非線性調(diào)制虛部相對(duì)強(qiáng)度不變的情況下隨著非線性調(diào)制深度的增大先擴(kuò)大后縮小;而當(dāng)PT對(duì)稱非線線性調(diào)制深度不變時(shí),其穩(wěn)定范圍隨著虛部相對(duì)強(qiáng)度的增大逐漸縮小。非線性PT對(duì)稱光學(xué)格子周期的改變也會(huì)對(duì)空間光孤子的傳輸特性產(chǎn)生重大影響。當(dāng)光束的入射角較小時(shí),孤子在傳輸過(guò)程中保持形狀不變,但是孤子的質(zhì)心隨傳輸距離發(fā)生周期性振蕩,其振蕩幅度隨入射角的增大而變大。但是,當(dāng)光束入射角足夠大時(shí),孤子在傳輸過(guò)程中形狀發(fā)生改變,并且孤子質(zhì)心隨傳輸距離發(fā)生無(wú)規(guī)則振蕩。5.自散焦Kerr非線性介質(zhì)虛部為準(zhǔn)一維的兩維PT對(duì)稱復(fù)數(shù)勢(shì)光學(xué)格子中非PT對(duì)稱多峰孤子。發(fā)現(xiàn)具有峰數(shù)為偶數(shù)和奇數(shù)的多峰孤子均存在于第一帶隙,并且可以同相位非PT對(duì)稱多峰孤子在第一帶隙的某些范圍內(nèi)穩(wěn)定。但是對(duì)一些同相位非PT對(duì)稱的多峰孤子它們的穩(wěn)定區(qū)間是分段的,這和實(shí)數(shù)勢(shì)中的情況有很大不同。隨著復(fù)數(shù)勢(shì)的增益/損耗系數(shù)的增大,同相位非PT對(duì)稱多峰孤子的存在范圍和穩(wěn)定范圍都逐漸縮小。詳細(xì)分析了孤子的非對(duì)稱性。異相位非PT對(duì)稱多峰孤子在其存在范圍內(nèi)不穩(wěn)定。復(fù)數(shù)勢(shì)中具有PT對(duì)稱性對(duì)稱性的單峰、雙峰、菱形四峰和五峰孤子均存在于第一帶隙。單峰、雙峰和菱形五峰孤子可以在很大的范圍內(nèi)穩(wěn)定傳輸,而菱形四峰孤子不能穩(wěn)定存在。
[Abstract]:Because of the natural balance beam diffraction effect, nonlinear dielectric effect and complex potential gain / loss effect, can keep the shape of beam in nonlinear media constantly for transmission, and the formation of spatial optical solitons. Because of the spatial optical soliton has unique properties, it has great application value in optical communication and optical implementation the device, especially the vortex solitons carry angular momentum capture in optical micromanipulation, particle field, information transmission has important applications. On the other hand, providing theoretical guidance for the research of optical spatial solitons can be adjacent to the subject of development, which has important academic value. This paper from the nonlinear Schrodinger equation describing propagation properties starting with numerical simulation, numerical calculation and numerical analysis method, studied the transmission characteristics of PT space of complex symmetric solitons in optical lattice potential. Research results are as follows: 1. the existence of PT symmetric square optical lattice of optical vortex solitons and soliton phase with quadrupole, stability and transmission characteristics. Vortex solitons and the same phase soliton exists in PT complex symmetric quadrupole potential Bloch can take the first gap and can be stable in a certain range of the parameters is not. With stable.PT complex symmetric potential depth or the decrease of gain / loss coefficient increases will lead to stable vortex solitons in the narrowing of the scope more than optical vortex solitons with soliton phase quadrupole angular momentum annular beam is formed. When the vortex soliton is stable, its power in the process of transmission with transmission distance oscillation, and in the real potential of optical vortex solitons in optical lattice in the power transmission process remains the same.PT complex symmetric potential gain / loss coefficient of optical vortex soliton formation has important effect, when the The value is close to the critical threshold, vortex soliton phase.2 self focusing nonlinear medium saturation saturation coefficient PT symmetric optical lattice and PT complex symmetric potential on the optical vortex solitons have a significant impact. Only when the nonlinear coefficient is larger than a critical threshold value of optical vortex solitons can exist stably. With the increase of the coefficient of saturation the existence range, vortex solitons are gradually reduced, but the stable range of expanding shrink. When the saturation coefficient is large enough, the nonlinear model can be approximated as linear, the vortex solitons do not exist. Keep the saturation coefficient unchanged, with the increase of PT complex symmetric potential gain / loss coefficient, vortex solitons the existence of range and stable range will be reduced. When the PT of complex symmetric potential gain / loss coefficient is equal to the critical threshold, vortex solitons can still exist, but it is in the process of transmission The divergent soon. At the same saturation coefficient under different phase is greater than the quadrupole soliton stable vortex solitons, stable transmission and PT symmetric triangular lattice with single point defects in phase with the stable range of the minimum.3. quadrupole soliton can support the defects of basic soliton and vortex solitons. The triangular lattice defect defect depth of defects of basic soliton there have an important impact; when the absolute value of the negative defect depth is large enough, the negative defect fundamental soliton does not exist. No defects and defects and defects of basic stability of negative soliton accords with anti-Vakhitov-Kolokolov rule. However, the negative defect in the whole vortex solitons exist unstable range, and is defective and defect free vortex solitons can exist stably in a certain range, it can inhibit the defect defects of vortex solitons in a certain degree of instability. Finally, the positive defect soliton as an example, the increase of PT complex symmetric potential gain / loss coefficient will not only cause the defect of soliton existence range is narrow, and the defects become more unstable and stable soliton transmission.4. two dimensional mixed linear nonlinear PT complex symmetric potential can support spatial solitons. The nonlinear modulation depth of the soliton formation and plays an important role in a. A determined range of nonlinear modulation depth, with the changes of soliton propagation constant deformation will occur. There is important relationship between soliton deformation and PT symmetric nonlinear modulation depth and nonlinear imaginary relative intensity. Different nonlinear modulation depth will cause the system presents a self focusing and self defocusing nonlinear effect. Two in two kinds of nonlinear under the effect of the stable range of spatial solitons in the imaginary part of the relative intensity of nonlinear modulation unchanged with the increase of nonlinear modulation depth expanding shrink; and when PT Non symmetric linear modulation depth is constant, the stability range with the increase of the imaginary part of the relative strength gradually reduced. Nonlinear PT symmetric optical lattice periodic change will have a significant impact on the transmission characteristics of optical spatial solitons. When the beam incident angle is small, the soliton shape remains unchanged in the transmission process, but the centroid of the soliton with the propagation distance periodic oscillation, the oscillation amplitude with the increase of the incident angle becomes larger. However, when the incident angle is large enough, the soliton shape change during transmission, transmission distance and centroid with the soliton has no regular oscillations in self defocusing nonlinear media.5. Kerr virtual PT for non symmetrical multi peakons two dimensional PT complex symmetric quasi one-dimensional optical lattice potential. It was found that the multi peak soliton with peak number is even or odd exist in the first gap, and the same phase non symmetrical multi peak solitary PT In certain range of the first band gap in the stable. But for some stable interval phase with non PT symmetric multi peak soliton are segmented, and the real potential situation is very different. With the increase of the complex potential gain / loss coefficient, there is the same phase non symmetrical multi peak soliton PT and the range of stability is gradually narrowing. A detailed analysis of the non symmetry of the soliton phase. PT non symmetric multi peak soliton in the unstable range. With PT symmetry symmetry is unimodal, the complex potential in Shuangfeng, diamond four and five peaks were solitons exist in the first gap. A single peak, and Shuangfeng Five Diamond Peak soliton can be stable transmission in a large range, and there are four Diamond Peak solitons can not be stable.

【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O437

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