一維光子晶體缺陷層的單向吸收分析

Analysis of Unidirectional Absorption in a Defective Superconducting Photonic Crystal

黃志喜(Huang Chih-hsi)

指導教授 ： 張宗文 ； 廖書賢

國立臺灣師範大學/科技與工程學院/光電工程研究所/博士(2020年)

https://doi.org/10.6345/NTNU202001117

摘要

理論上研究了在一維缺陷超導光子晶體材料裡高頻光波出現單向傳播性質。我們考慮用一種非對稱性的光子晶體其結構為(AB)ND(BA)M排列堆疊而成，其中A層材料為具有介電質的材料，B層材料為超導材料，D層為具有電介質材質的缺陷層，然而N、M為堆疊的數目。在本次研究中發現堆疊層數目不同時 (N ≠ M)該光子晶體結構會造成高頻光波出現單向性傳播性，單向傳播共振吸收頻率位置會隨著堆疊層數目(N和M)之間差距越大而增加。其中我們還研究了入射光波偏振角與單向傳播之間的關係，從此次的研究結果發現，當在改變入射光波的偏振方向的狀況下，單向傳播的吸收率幾乎與偏振方向是沒有直接關係地，因此我們提出的這個光子晶體結構技術可以用於設計出與入射光偏振無關的光學元件。
接下來我們還有從理論計算方式下，研究了一維具有缺陷且不對稱堆疊光子晶體結構上光波傳遞的性質，這次的光子晶體結構為 air /(AB)MG(BA)N/air，air/(AQ)MG(QA)N /air和air/(BQ)MG(QB)N/air，其光子晶體堆疊結構中的A層材料是用具有損耗的負介電係數材料，B層則是用了具有損耗地mu-negative material材料，而G層和Q層是用不同折射率的介電材料，另外該光子晶體的堆疊層數目M和N是不同的(M≠N)。此次的研究中我們注意到了在某些條件下其入射光譜會被吸收，導致傳遞光波的光子晶體有單向傳播特性。還有在這個負折射係數材料中，依造我們的計算結果顯示了有兩種單向吸收峰值，一種是會因缺陷層(G)厚度的改變而導致其鋒值頻率位置也隨著變化，另一種吸收峰值就不會隨著缺陷層的厚度改變而波峰頻率位置有所變化，這種的波峰頻率位置是固定在某些頻率位置上，另外這種固定波譜頻率位置的波峰數目會與正向或者反向傳播有所不同，當正向傳播時其波峰數目會是（M-1）個，然而如果是逆向傳播時波峰數目會是N-1個。特別的是當正向傳播與逆向傳播時固定波譜位置這個波峰數目相同為M − N − 1時，該光子晶體的單向傳播特性將消失。
另外一個研究是從理論上研究了改用材料含有n-InSb半導體層且用stage 3 triadic-Cantor-setphotonic crystal（S3 TCS PC）來討論其傳輸特性，依著半導體(n-InSb)介電常數具有可以將光波共振頻率傳輸響分成三個區域，其三個區域分別為兩個傳輸共振頻率遠高於半導體(n-InSb)介電常數的諧振頻率和另一個低於其材料共振諧振頻率的區域，其中半導體的介電常數幾乎是正常數。在光波進入stage 3 triadic-Cantor-setphotonic crystal（S3 TCS PC）結構中，其結構會將光波分成兩組不同共振頻率區域透射波譜，其為缺陷缺陷模式Np模式和非缺陷模式的Np-1模式，，其中一組波譜可以用堆疊層周期數變化而改變其缺陷模式(Np)的波峰數目，另外還可以改變入射光波的角度也會造成TE波和TM波光譜頻率位置的改變，此外還可以調整每一層的厚度來控制非缺陷層模式（Np–1）頻率響應的位置。但是要注意當入射波譜頻率落在5.1~6.2 THz大小區域時Np模式波峰強度對會損耗很大。

關鍵字

光子晶體 ； 超導體 ； 負折射材料 ； 半導體

並列摘要

Terahertz unidirectional resonant absorption in a finite one-dimensional defective superconducting photonic crystal is theoretically investigated. We consider an asymmetric photonic crystal (AB)ND(BA)M, where A is a dielectric, B is a superconductor, D is the dielectric defect, and N, M are the stack numbers, respectively. At N≠M, it is found that the resonant absorption for the structure exhibits the unidirectional property. The unidirectional resonant absorption points increase as the difference between N and M increases. We also investigate the unidirectional property as a function of angle of incidence. The results show that the unidirectional absorption is nearly independent of the polarization at a given angle of incidence. The proposed structure can be used to design a polarization-independent optical device which may be technically used in superconducting photonics.
We theoretically study wave properties for one-dimensional defective asymmetric photonic crystals, air /(AB)MG(BA)N/air，air/(AQ)MG(QA)N /air and air/(BQ)MG(QB)N/air, where A is a lossy epsilonnegative material, B is a lossy mu-negative material, G and Q are dielectrics with different refractive indexes, and M and N are stack numbers with M ≠ N. Special attention has been paid to their absorption spectra. It is found that at certain frequencies the absorption can exhibit unidirectional properties. Our calculated results show two kinds of unidirectional absorption peaks. One is a single absorption peak whose frequency depends on the thickness of defect layer G. For the other peaks, its frequency does not change when the defect layer’s thickness changes. In addition, in the second kind of peaks, the peak numbers for forward and backward propagation are different, that is, there are (M − 1) absorption peaks for forward propagation, while there are (N − 1) absorption peaks for backward propagation. When the two kinds of unidirectional absorption peaks are merged, some new peaks appear, and both forward and backward propagation will have (M + N − 1) absorption peaks.
Terahertz transmission properties of a stage 3 triadic-Cantor-setphotonic crystal (S3 TCS PC) containing a semiconductor of n-InSb are theoretically investigated. With the resonant frequency in the permittivity function of n-InSb, transmission responses can be classified as three regions. In the two regions with frequencies well above and below the resonant frequency, the permittivity functions are nearly a positive constant and n-InSb is dielectric-like. For these two regions, transmittance response of S3 TCS PC at a given number of periods Np reveals that,within a photonic band gap, there are two groups of defect modes with numbers of Np and Np-1, respectively. Defect modes are shown to be blue-shifted as the angle of incidence increases for both TE and TM waves. Additionally,adjusting the layer thickness enables us to control mode positions for the group of (Np–1)-mode, but the one with Np-mode is not able to be controlled. In a region of 5.1–6.2 THz, where the loss is large, there also are many transmission modes.

並列關鍵字

Photonic crystal ； Superconducting ； Negative material ； Semiconductor

參考文獻

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