【摘要】：光學(xué)渦旋在現(xiàn)代光學(xué)物理中有著重要的作用.本文研究了來自于非線性幾何光學(xué)中的兩個模型,第一個模型是由兩束激光耦合得到的Schrodinger方程組,我們首先利用直接變分法和山路引理建立了該模型的一系列穩(wěn)態(tài)解的存在性定理;其次,利用約束變分法建立了該模型的徑向?qū)ΨQ正解的存在性定理,并給出了波傳播常數(shù)β的下界估計;最后,利用山路引理建立了鞍點(diǎn)解的存在性定理.第二個模型是兩束光耦合傳播的非線性Kerr模型,我們證明了該模型無非零穩(wěn)態(tài)解,并利用約束變分法建立了該模型渦旋解的存在性定理及參數(shù)λ的范圍.
[Abstract]:Optical vortex plays an important role in modern optical physics. In this paper, two models from nonlinear geometric optics are studied. The first model is the Schrodinger equations obtained by coupling two laser beams. In this paper, we first establish a series of existence theorems of the steady-state solutions of the model by using direct variational method and mountain pass Lemma, and then, by using the constrained variational method, we establish the existence theorems of the radial symmetric positive solutions of the model. The lower bound estimate of wave propagation constant 尾 is given. Finally, the existence theorem of saddle point solution is established by using mountain pass Lemma. The second model is a nonlinear Kerr model for the coupled propagation of two beams of light. We prove that the model has zero steady-state solution and establish the existence theorem of vortex solution and the range of parameter 位 by using the constrained variational method.
【學(xué)位授予單位】：河南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175;O435

【參考文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前1條

1 陳筱;非線性幾何光學(xué)中渦旋解的存在性[D];河南大學(xué);2014年

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本文編號：2170380