【摘要】：隨著納米加工和表征技術(shù)的快速發(fā)展,人們對(duì)人工超材料、超表面的研究達(dá)到了一個(gè)新的階段。這些周期性納米結(jié)構(gòu)具有豐富的電磁性質(zhì),并在光信號(hào)的相位調(diào)控、光子能量選擇性透過(guò),近場(chǎng)成像以及非線性光學(xué)響應(yīng)等領(lǐng)域展現(xiàn)出了極大的應(yīng)用前景。近年來(lái)的研究表明,利用多層膜可以實(shí)現(xiàn)超材料的構(gòu)建以獲得光學(xué)傳輸?shù)挠行д{(diào)控。之前的大量研究工作主要集中在將各向同性的薄膜材料作為基元進(jìn)行周期性地排列,設(shè)計(jì)出各向異性的超材料,從而獲得特定的光學(xué)響應(yīng)。值得注意的是,通常這樣一類深亞波長(zhǎng)尺度的多層膜結(jié)構(gòu)的有效介電常數(shù)具有獨(dú)特的雙曲色散特性,我們稱之為"雙曲材料"。最近,有人將"雙曲材料"作為基元來(lái)構(gòu)建新型多層膜超材料,但是對(duì)于這種超材料的有效介電參數(shù)的全局描述鮮見(jiàn)報(bào)道。本文以超材料介電常數(shù)的全局參數(shù)描述為科學(xué)問(wèn)題,在理論上利用多層膜體系含有位相信息的反射和透射系數(shù),發(fā)展了一般的數(shù)學(xué)方法,研究了由各向同性或者各向異性材料為基元構(gòu)成的光子超材料的有效介電常數(shù)(permittivity,εeff)、磁導(dǎo)率(permeability,μeff)以及以及波常數(shù)(包括有效波矢k和有效阻抗z),為特定功能的新型光子超材料的設(shè)計(jì)提供了可靠的理論方法。論文主要研究?jī)?nèi)容包括以下幾個(gè)方面:1、論文介紹了光子晶體以及各向異性光學(xué)材料,著重介紹了 "雙曲材料"的介電和介磁特性;提出了本文主要采用的物理思想和數(shù)學(xué)方法,特別是著重描述了我們具體研究所使用的四維傳輸矩陣法;2、介紹當(dāng)前被廣泛使用的基本的平均場(chǎng)近似理論(Effective Medium Theory,EMT),并在此基礎(chǔ)上,推導(dǎo)出以各向異性材料為基元構(gòu)成的多層膜超材料的有效介電張量以及磁張量,詳細(xì)討論了這種等效介質(zhì)理論在進(jìn)行多層膜體系描述時(shí)的適用范圍。3、利用我們所發(fā)展函數(shù)擬合方法和解析法這兩種數(shù)學(xué)方法,從含有位相信息的反射和透射系數(shù)中,得到描述多層膜超材料更加精確的全局性有效介質(zhì)參數(shù)和波參數(shù)。
[Abstract]:With the rapid development of nanoprocessing and characterization technology, the study of artificial supermaterial and supersurface has reached a new stage. These periodic nanostructures have abundant electromagnetic properties and show great application prospects in the fields of optical signal phase control photon energy selective transmission near-field imaging and nonlinear optical response. Recent studies have shown that the use of multilayer films can realize the construction of metamaterials to achieve effective control of optical transmission. Previous studies have focused on the periodic arrangement of isotropic thin film materials as elements and the design of anisotropic supermaterials to obtain specific optical responses. It is worth noting that the effective permittivity of this kind of deep subwavelength scale multilayer structure usually has unique hyperbolic dispersion characteristics, which we call "hyperbolic material". Recently, "hyperbolic material" has been used as the basic element to construct a new type of multilayer film supermaterial, but the global description of the effective dielectric parameters of this metamaterial is rarely reported. In this paper, the global parameter of permittivity of metamaterials is described as a scientific problem. In theory, a general mathematical method is developed by using the reflection and transmission coefficients of the multilayer system with phase information. The effective permittivity (permittivity, 蔚 eff), permeability (permeability, 渭 eff) and wave constants (including effective wave vector k and effective impedance z),) of photonic supermaterials consisting of isotropic or anisotropic materials are studied. It provides a reliable theoretical method for the design of new photonic supermaterials with specific functions. The main contents of this paper are as follows: 1. The photonic crystal and anisotropic optical materials are introduced, and the dielectric and magnetic properties of hyperbolic materials are emphasized. The physical thought and mathematical method used in this paper are put forward, especially the four-dimensional transmission matrix method used in our research is described emphatically. 2. The basic theory of mean field approximation (Effective Medium Theory,EMT), which is widely used at present, is introduced. On the basis of this, the effective dielectric properties of multilayer supermaterials composed of anisotropic materials and magnetic Zhang Liang are derived. The scope of application of this equivalent medium theory in the description of multilayer film system is discussed in detail. Using the two mathematical methods developed by us, the function fitting method and the analytical method, the reflection and transmission coefficients with phase information are analyzed. More accurate global effective medium parameters and wave parameters describing multilayer supermaterials are obtained.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TB383.2;TB34
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本文編號(hào)：2364798