摘要
在制造光学超晶格的过程中 ,如果极化条件控制得不合适 ,常常会出现”缩并”现象 .定义广义Fibonacci光学超晶格为 :Sj=Smj- 1Skj- 2 ,其初始条件为 :S1=B ,S2 =An1Bn2 .定义缩并规则为AB→A ,B→B ,通过连续缩并 ,一个广义二组元Fibonacci超晶格可以扩展为一系列超晶格 .比如 ,若初始超晶格序列为ABBABBBABBABBBABBABBABBBABBABBBABBABBABBB ...那么 ,经过一次缩并 ,产生新的超晶格序列ABABBABABBABABABBABABBABABABB ...类似地 ,可以定义膨胀规则为AB←B ,B←B ,通过连续膨胀 ,一个广义二组元Fibonacci超晶格亦可扩展为一系列超晶格 .研究了这两个超晶格系列 ,发现它们的倒空间结构是几乎相同的 .因此 ,可以将这两个超晶格系列归为一类 ,称之为二组元超晶格族 .定义三组元超晶格为Sj=Smj- 1Sj- 3,其初始条件为S1=A ,S2 =AnC ,S3=AnCB ,在三组元超晶格中做相同的操作 ,同样发现了具有相同倒空间结构的超晶格系列 ,将之归为三组元超晶格族 .这个结果可以扩展到k组元的情形 .普通Fibonacci超晶格结构具有自相似性 ,研究了一个二组元金Fibonacci超晶格的倒空间里的峰值 ,发现在所谓的约化区间的方案中 ,它们可以归为一系列组中 .不同组中的峰值点彼此之间通过一个无理数关联 。
During the process of fabricating the needed optical superlattice,if the polarization condition is not set properly,the phenomenon of superlattice deflation will happen frequently.We investigated this phenomenon by defining a general Fibonacci superlattice as S j =S mj-1 S kj-2 ,with the initial conditions of S 1 =B,S 2 =A n 1 B n 2 .By introducing the definition of deflation rule as AB→A,B→B,a general two-component Fibonacci superlattice is expanded into a series of superlattices.For example,an original array is defined as ABBABBBABBABBBABBABBABBBABBABBB ABBABBABBB...and then we deflated this array and produced a new array by using the above deflation rule,and the result is ABABBABABBABABABBABABBABABABB...A similar operation can be done on the same superlattice under the definition of inflation rule as AB←A,B←B,which also produces a series of superlattices.We investigated the reciprocal space structures of the superlattices belonging to these two series,and found that they are nearly the same.So we included these superlattices into one family named the two-component superlattice family.We extended these operations to the three-component Fibonacci superlattice,which was defined as S j =S mj-1 S j-3 ,with the initial conditions of S 1 =A,S 2 =A n C,S 3 =A n CB,and also found that the reciprocal space structures of the produced superlattices are nearly the same,so we also included them into one family named the three-component superlattice family.Similar operations can be extended to the case of k- component Fibonacci superlattice. It is well known that Fibonacci superlattice structures have the property of self-similarity.We investigated the peaks in the reciprocal space of a two-component golden Fibonacci superlattice,and found that they can be classified into different groups according to the so-called reduced cell scheme.Every Peak in the different groups is related to each other by means of an irrational number,the characteristic number of the two-component golden Fibonacci superlattice.We also found that the abscissa of the peak could be given by solving the well-known Pell equation,KK ˇ =-P 2 +pq+q 2 =N,the solutions of which have the property of self-similarity.The relationship between the peak abscissa and the solutions of Pell equation reveals the reason why the Fibonacci superlattice structures have the property of self-similarity.
出处
《南京大学学报（自然科学版）》
CAS
CSCD
北大核心
2004年第4期409-417,共9页
Journal of Nanjing University（Natural Science）
