光子晶體濾波器諧振腔之研究

Research of Photonic Crystal Filters and Cavities

吳志榮(ChihJung Wu)

指導教授 ： 劉宗平

元智大學/電機通訊學院/電機工程學系/博士(2012年)

摘要

光子晶體領域是近年來發展非常迅速的研究領域，其作為控制光傳播的重要材料，己經得到了廣泛、深入的研究；此外，光子晶體具有的“光子禁帶”和“光子局域”特性又決定了它具有廣闊的應用前景。如何在實踐中充分利用光子晶體特殊的能帶結構、帶隙特徵及傳輸特性，依然是一個很有價值的課題。基於其廣泛的應用潛力，本論文主要對光子晶體濾波器諧振腔和含負折射率一維光子晶體的特性進行了相關的研究，系統性地分析了影響光子晶體濾波的主要因素及提高濾波效率的方法，並設計了高效的光子晶體多通道濾波器。
首先介紹了二維光子晶體全光學半加器的設計與研究。由於組成CPU基本單元的全加器一般是由半加器組成，因此進一步研究由全光學半加器(AOHA)實現的全光學CPU具有重要的意義。基於二維光子晶體“及”閘和“或”閘的分析，我們建立了基於交叉波導和缺陷腔結構的全光學半加器的模型，並且分析了光子晶體單元形狀、晶格結構、組成晶體的介質柱介電常數及介質佔空比對光子晶體帶隙大小的影響。經過分析發現介質柱介電常數越大，晶體的帶隙也越大；介質柱佔空比越大，晶體的帶隙也越大。此外，研究了諧振腔缺陷介質柱半徑大小與耦合波長之間的關係，模擬結果顯示當缺陷介質柱半徑小於晶體介質柱半徑時，波長隨著缺陷介質柱半徑的增加而增加；當缺陷介質柱半徑大於晶體介質柱半徑時，波長變小且耦合效率比較低。故缺陷介質柱半徑應當選擇小於光子晶體介質柱半徑。對缺陷波導進行了分析計算。首先分析了波導的反射特性，結果表明波導缺陷介質柱的介電常數設為晶體介質柱介電常數的整數倍時反射率最大；然後分析了提高波導和諧振腔間耦合效率的方法，通過分析發現，改變波導邊緣介質柱半徑對耦合效率有著很大的影響，還發現改變波導與相應諧振腔之間介質柱半徑大小及波導寬度對波導與諧振腔的效率也有很大的影響。利用時域有限差分法（FDTD），數學模擬實驗成功證實了半加器模型具有的全光學半加器的功能。此半加器結構由開到關的邏輯電平相對比率至少為16dB，在忽略Kerr效應的物質波回應時間時運行速度能達到0.91Tbits/s，這種半加器結構在設計全光學信號處理單元和光學計算系統時具有廣泛的用途。
接著對光子晶體太赫茲波導及太赫茲雙折射波導進行了研究。在理論上對相關波導元件進行了深入研究，並在實驗中對光子晶體太赫茲波導聯合腔體進行了設計與研究。為進行光子晶體諧振腔的設計與應用，首先建立了一維光子晶體諧振腔的物理模型，分析了諧振腔各參數之間的關係及相互影響。經過對光子晶體諧振腔進行了系統的研究，分析了諧振腔各參數之間的關係，並研究了高靈敏度太赫茲（THz）信號檢測聯合腔的結構及性質，經過試驗以及計算，結論是缺陷層厚度、諧振波長、品質因數三者之間的關係表明，對每一級次，隨著缺陷層厚度的增加，品質因數先增加後減小，中間存在一個極大值，其變化趨勢決定於週期性結構的禁帶情況；由光子晶體點缺陷腔(PDC)和光子晶體波導諧振器(WGR)耦合而成的聯合腔，在共振條件下，聯合腔中PDC場強比單獨的PDC場強很多，並且品質因數也得到大大地增加。此外，還可以通過在WGR中加入一個電介質板來實現聯合腔的同步諧振；如果在雙諧振中通過在PDC中加入絕緣棒，會使結構中的最大品質因數提高了34.7%，點諧振腔中的最大局部場強增加了314%。
為了方便理解光子晶體偏振器，本論文首先利用不同偏振模式在光子晶體中具有不同帶隙的特點，研究單個一維光子晶體的偏振特性，並設計出由單個一維光子晶體構成偏振器。本論文主要利用轉移矩陣法計算了一維光子晶體中TE和TM兩種偏振模式的特性，討論了一維光子晶體中兩種偏振模式隨介質填充比的變化而反映出的特性；由加入各向異性電介質材料的兩個一維光子晶體中組成的偏振器，證明了其具有頻域濾波和空間域濾波的功能。如果不在光子晶體中加入各向異性電介質是不能獲得對於0°入射波偏振器的。
最後研究了由特殊材料所組成的一維光子晶體濾波器特性，並且討論了含雙負缺陷的一維光子晶體腔結構。計算結果表明，如果改變缺陷的折射率，缺陷模之間的作用將發生改變，使得光子帶隙中的雜質帶也隨之改變。若缺陷的折射率取適當的值，就可以在禁帶中同時得到幾個尖銳的透射峰和較寬的通帶。本部分主要對含有特殊材料的光子晶體進行了系統性的研究，分析材料特性及結構參數對濾波特性的影響：基於零平均折射率帶隙的光子量子井，發現由於零平均折射率帶隙，光子量子井不依賴於入射角和偏振，對光子晶體的厚度也不敏感。由此，本論文提出了一種新的具有高斯分佈折射率的光學濾波器。這種濾波器能平滑的去掉透射光譜中尖的諧振峰值並能擴大通帶的延伸。對於TE模式，對於不同的入射角通帶的中心頻率可以很大的改變但通帶的寬度並不變；對於TM模式，當增大入射角時通帶中心的頻率會改變，並且其延伸度也會被大大擴大。研究結果表明具有高斯分佈厚度和高斯分佈折射率的光子層狀結構的光子晶體有相同的特性，其中的一些結論將會對光子晶體濾波器的設計提供有用的資訊。

關鍵字

光子晶體 ； 濾波器 ； 諧振腔

並列摘要

Photonic crystals is a new class developing very rapidly in recent years, it has been attracted much attention and deep study. Due to its "photonic band gap" and "photon localization" feature , photonic crystals have broad application prospects. But it is still a valuable subject that how to make full use of the special band structure, band gap and transmission characteristics in practice. Based on the wide application potential, the author mainly relate the research to the photonic crystal filter resonator and one-dimensional photonic crystals with negative refractive index , making a systematic analysis of the main factors influencing on the photonic crystals filter and the method of improving the filter efficiency, finally the writer designs an efficient multi-channel photonic crystals filter.

Firstly, the author introduces us the all-optical half adder based on cross structures in two-dimensional photonic crystals. As is known, full adders are the basic parts of CPU and they are built with the half adder. it is critical to investigate all-optical half adders (AOHA) for the realization of all-optical CPU. In this paper, we analysis “AND gate” and “XOR gate” of two-dimensional photonic crystals, then establish the models of the basic all-optical half adder based on the defect cavity and cross waveguide. After making research on the shape of the photonic crystal unit, the crystal structure and permittivity dielectric cylinder , we found that the greater the dielectric constant of dielectric, the greater the band gap crystals; the greater media column larger duty cycle，the greater the band gap crystals. Then we study the relationship between the radius of the resonance cavity defects and coupled wavelength, the simulation results show that when radius of the defects media rod is shorter than that of the crystal, the wavelength increases with the defective media rod radius increases; when the radius of defect media rod is longer than that of the crystal, the wavelength becomes shorter and the coupled efficiency is relatively low. Therefore, radius of defects media rod should be chosen smaller than that of the photonic crystal. After calculating defect waveguide, we analyze the reflective properties of the waveguide, and the results show that the dielectric constant is set to multiple times of the crystal dielectric constant, the reflective index gets the maximum; then we analyze the way to improve the waveguide and resonator coupling efficiency. Through the analysis, it is found that changing the radius of waveguide edge rod has a great impact on the coupled efficiency. It is also proved that changing the radius of medium rod between waveguide and its corresponding resonance cavity and width of waveguide influence a lot on the efficiency of the resonator and waveguide. Through the FDTD method, numerical simulations demonstrated successfully that the structure presented does function as an all-optical half adder. The ON to OFF logic-level contrast ratio for this half adder could reach at least 16dB, and when omitting the material-wave response time of Kerr effect, the optimal operating speed is found to be as high as 0.91Tbits/s. This structure is useful in designing all-optical signal processing circuits and optical computer systems.

Then we made research on the THz waveguide of photonic crystals and THz doubled reflective waveguide. In theory, deep study on relevant waveguide devices has been carried out. During the experiments, researches and designs on photonic crystal THz waveguide combined cavity are made. For guiding photonic crystals resonator’s design and application, firstly we create a physical model of one-dimensional photonic crystals resonant cavity, and analyze the relations and influences of the various parameters in the resonator. After a systematic study on photonic crystals cavity , relations between the various parameters, and the structure and nature of THz signal detection of the combined cavity with high sensitivity, through testing and calculations, we conclude that the relationship between defect layer thickness, resonance wavelength, the quality factor show that for every level, with the defect layer thickness increases, the quality factor increases and then decreases, and there is a maximum value, the changing trend depends on the periodic structure of the band; We have investigated a combined coupled cavity, composed of a PDC and a WGR. The field intensity in the PDC in the combined cavity under simultaneous resonance is much higher than that in a simple separate PDC. The quality factor is also promoted through the cavity combination and mutual coupling. To meet the requirement of simultaneous resonance, a dielectric slab for phase shifting is necessary to add in the WGR. If adding a dielectric pole in the PDC in double resonance, the maximum quality factor of the new structure is promoted by 34.7%, and the maximum localized field intensity in the point defect cavity is promoted by 314% over that in the earlier structure.

For the better understanding of photonic crystal polarizer, first we make use of the features that different polarization modes in photonic crystals have different band gap, thus we can have a study on polarization characteristic of the single one-dimensional photonic crystals, and design a polarizer made by one-dimensional photonic crystals. We mainly use the transfer matrix method to test characteristics of two polarization modes TE and TM in the one-dimensional photonic crystals. Then we discuss the characteristics of two kinds modes which vary with dielectric ratio; In conclusion, we have proposed and demonstrated a polarizer with integrated functions of both NBP frequency domain filtering and NTA space-domain filtering, by combining two one-dimensional with PCs anisotropic materials. Without introducing anisotropic materials into the PCs, one can not obtain a polarizer for normal (0°) incident waves.

Lastly, we study the characteristics of the one-dimensional photonic crystals composed by the special materials. We discuss the structure of the doubled defect one-dimensional photonic crystals. And the calculation show that if we change the refractive index of the defect, the interaction effect of defect modes will change, thus making the impurity band of the photonic gap band change. If taking the appropriate value of the refractive index, we can get several sharp peaks and wide pass band in the band gap.In this part, the author make a systematic analysis about the special materials of photonic crystals and its structure parameters’ impact on filtering properties; Based on the zero-n gap of the photonic QWs, the photonic QW is very weak dependent on the incident angle and polarization, and also insensitive to thickness disorder of the barrier PCs. These features are benefit to improve the performance of the multiple channeled filter. In summary, we propose the construction of new optical filters with Gaussian-distributed refractive index. This kind of filter can smooth the sharp resonant peaks in the transmission spectrum and enlarge the extension of the pass-bands. For different incident angles, the central frequency of the pass-band can be significantly changed but the pass-band width for the TE mode remains unchanged. However, for the TM mode, while increasing the incident angle, not only the central frequency of the pass-bands is shifted but also their extensions are evidently enlarged. We also observe that in the PCs with the Gaussian-distributed thickness of the optical barriers, they have quite similar characteristics to those of the PCs with the Gaussian modulation of the refractive index of the optical barriers. The main findings in this work may provide useful information for the design of the favorable PC filters.

並列關鍵字

Photonic Crystal ； Filter ； Cavities

參考文獻

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