一种集窄带通和窄透射角滤波功能于一体的光子晶体偏振器外文翻译资料

A photonic-crystal polarizer integrated with the functions of narrow bandpass and narrow transmission-angle filtering

Abstract

Through the transfer matrix method, we demonstrated a special polarizer integrated with the functions of narrow band pass (NBP) and narrow transmission-angle (NTA) filtering at normal incidence in a stack of two one-dimensional defective photonic crystals (PCs). One of the PCs is made of an isotropic dielectric media, while the other PC is made of anisotropic media. The key point in designing the stack is to set the central frequencies of the defect modes of the two sub-PCs to be the same for one polarization at normal incidence, but different for oblique incidence or for other polarizations, so that

the stack structure could have the functions of three elements: a polarizer, an NBP filter, and an NTA filter.

1.Introduction

In recent years, much attention has been paid to photonic crystals (PCs), a new kind of optical material for controlling the motion of electromagnetic waves. PCs are structures formed by arraying two dielectrics of different refractive index periodically in one dimension (1D), two dimensions (2D), or three dimensions (3D) [1–4]. They are characterized by photonic band gaps (PBGs) in which the propagation of electromagnetic waves is strongly forbidden. Polarizers [5, 6] are important elements in optoelectronic signal receiving or detecting systems. Often, we need to pick up a signal with a narrow wavelength-band to get rid of noise of unwanted frequencies and a signal from a special direction to prevent interferences of waves from different directions. Thus in signal receiving or detecting systems, one needs polarizers, frequency filters and directional couplers. Such three elements may occupy a large volume and need to be arranged in a proper way to work together. This may boost the cost of the whole system. So, a single element exhibiting the three functions is of great interest to engineers. In [7], utilizing all isotropic dielectric materials, a structure with the functions of NBP and NTA filtering, together with the additional function of a polarizer at oblique incidence has been proposed.However, integration of the three-element function for normal incidence has not been solved until now. Since optical wavelength filters, optical angle filters, and optical polarizers in most optical devices are designed and mounted to operate for normal incidence of waves, to minimize the size of optical systems and to decrease the inserting losses of optical elements, it is necessary to pay attention to this unsolved problem.For isotropic media and normal incidence of light, s- and p-polarizations are identical for a 1D photonic crystal. This means that light with any polarization can pass through it at normal incidence. In order to obtain the function of a polarizer for normal incidence, we introduce anisotropic dielectric materials into the PCs. Here we propose a structure integrating the functions of the three elements stated above. For easy fabrication and low cost, we utilize one-dimensional defective PCs [7–12] to design such a structure. In Sect. 2, we present a physical model of the specified polarizer. In Sect. 3, we give the 4times;4 matrix formulation for calculating transmissions and reflections of waves with both p- and s-polarization in a multi-layer media. In Sect. 4, we show the numerical results and discussions. Finally, in Sect. 5, we draw a summary

2 Physical model

A photonic hetero-structure based on the 1D defective PC has been proposed to a realize sharp angle and narrowband filter by Wang et al. [7]. The structure given by Wang et al. is a simple combination of two point-defect photonic crystals and can be represented as { f1[(AB)sC(BA)s]}{ f2[(BA)sD(AB)s]}, where A and B are layers of different dielectric materials, the subscript s is the repeating number, f1 and f2 are scaling factors that scale the size of all the elements in the square brackets, and C and D are defective layers. C is made of the same dielectric material as A, and D is made of the same material as B. For proper values of f1 and f2, the defect modes of the two PCs have the same wavelength for normal incidence of waves. Since the wavelengths of the two defect modes change at different speeds as the incident angle increases, waves at other incident angles will be stopped by one of the two PCs in the combined structure. Thus such a structure can only allow a wave with a narrow band pass at normal incidence to pass through. For normal incidence of waves, however, we cannot separate waves by polarization through such a structure. For anisotropic media, the transmissions of p- and spolarization waves are different even at normal incidence. So, the defect modes of the two PCs will be different in wavelength for normal incidence of waves when anisotropic media are introduced. For proper choice of the operating parameters, the wavelengths of the defect modes of the sub-PC f1[(AB)sC(BA)s] and the sub-PC f2[(BA)sD(AB)s] are the same for an s-polarization wave at normal incidence, but different for a p-polarization wave, then the p-polarization wave will be blocked, and thus the additional function of a polarizer will be achieved. In this paper, we choose a uniaxial crystal as the high index dielectric A (Tl3AsSe3, n1 = 3.227, n2 = 3.419) and a homogeneous material as the low-index dielectric B (Na3AlF6) for the PCs. The narrow bandpass is designed to be near 1.55 micro;m. For convenience, we set C = mA and D = nB. To obtain large forbidden gaps, the optical thickness of A and that of B are all set to be a quarter of the wavelength of the tunneling wave.

3.Matric formulation

An appropriate formulation for the analysis of the propagation of light or electromagnetic waves in anisotropic stratified media is the 4times;4 matrix method, which was intro

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一种集窄带通和窄透射角滤波功能于一体的光子晶体偏振器

作者：毛栋，欧阳振，王建昌

国籍：中国

出处： Appl. Phys. B 90, 127–131 (2008)

中文译文：

摘要：

利用传输矩阵法，在两个一维缺陷光子晶体(PCs)的叠加层中设计了一种集窄带通(NBP)和窄透射角滤波(NTA)功能于一体的特殊偏振器。其中一个PC由各向同性介质组成，另一个PC由各向异性介质组成。关键在设计栈是设置的缺陷模式的中心频率两个sub-PCs一样一个偏振垂直入射,但不同倾斜入射或者其他的偏振光,所以堆栈结构可以有三个元素的功能:一个偏振镜,一个平衡的过滤器,和一个NTA过滤器。

1、介绍

光子晶体作为一种新型的控制电磁波运动的光学材料，近年来受到了人们的广泛关注。PCs是由一维(1D)、二维(2D)或三维(3D)的两种不同折射率介质周期性排列而成的结构[1-4]。它们的特征是光子带隙(PBGs)，在光子带隙中电磁波的传播被强烈禁止。

偏振器[5,6]是光电信号接收或检测系统中的重要元件。通常情况下，我们需要用窄波段的信号来去除不需要的频率的噪声，以及用特定方向的信号来防止不同方向的波的干扰。因此，在信号接收或检测系统中，需要偏振器、频率滤波器和定向耦合器。这三种元素可能会占用很大的空间，需要合理安排才能共同发挥作用。这可能会增加整个系统的成本。因此，工程师们对展示这三种功能的单个元素非常感兴趣。在[7]中，利用所有各向同性介质材料，提出了一种具有NBP和NTA滤波功能的结构，并在斜入射时附加了偏振器的功能。

然而，对于正入射的三元函数的积分问题至今尚未得到解决。因为光学波长过滤器,光角过滤器,和光学偏振器在大多数光学设备的设计和安装操作正入射波,减少光学系统的大小和减少光元素的插入损失,有必要注意这尚未解决的问题。

对于各向同性介质和正入射光，一维光子晶体的s极化和p极化是相同的。这意味着任何偏振的光都可以在正常入射时通过它。为了得到正入射偏振器的函数，我们在偏振器中引入了各向异性的介质材料。

在此，我们提出了一种整合上述三个要素功能的结构。为了易于制造和低成本，我们利用一维缺陷PCs[7-12]来设计这样的结构。

在第2节中，我们提出了一个特定偏振器的物理模型。在第3节中，我们给出了计算多层介质中p极化和s极化波的传输和反射的4times;4矩阵公式。在第4节中，我们展示了数值结果和讨论。最后，在第5节中，我们做了一个总结。

2、物理模型

王等人提出了一种基于一维缺陷PC的光子异质结构，用于实现锐角窄带滤波器。王等人给出的结构是两个点缺陷光子晶体的简单组合，可以表示为

{f1[(AB)sC (BA)s]} {f2[(BA)sD (AB)s)},

其中A和B是不同的介电材料层，下标s是重复数f1 和f2 是缩放因子，缩放方括号中所有元素的大小，C和D是有缺陷的层。C和A是由相同的介电材料制成的，D和b是由相同的材料制成的1 和f2当波垂直入射时，两者的缺陷模具有相同的波长。由于两个缺陷模的波长随着入射角的增加而以不同的速度变化，其他入射角的波将被组合结构中的两个缺陷模中的一个阻止。这样的结构只能允许在正常入射时通过窄带的波。然而，对于正常入射的波，我们不能通过这样的结构通过极化来分离波。

对于各向异性介质，p极化波和s极化波在垂直入射时的传输是不同的。因此，当引入各向异性介质时，两种介质的缺陷模在波长上是不同的。为了选择合适的工作参数，对其缺陷模的波长进行了分析1[(AB)sC (BA)s]和子pc f2[(BA)sD (AB)s]对于s极化波法向入射时相同，但对于p极化波不同，p极化波会被阻挡，从而实现偏振器的附加功能。

本文选用单轴晶体作为高折射率介质a (Tl)3美国卫生工程师协会(AsSe)3n1 n = 3.227,2 = 3.419)和均质材料作为低折射率介质B (Na3阿尔夫6)就个人电脑而言。窄带通被设计成接近1.55micro;m。为方便起见，设C = mA, D = nB。为了获得较大的禁隙，A和B的光学厚度都设置为隧道波波长的四分之一。

3、矩阵公式

分析光或电磁波在各向异性层状介质中传播的合适公式是4times;4矩阵法，该方法分别由Teitler和Henvis[13]提出，由Berre- man[14]和Yeh[15]发展。本文根据晶体光学的第一个方程，对单轴层状介质导出了一个类似的矩阵公式：

由于任意极化的波可以分解为s极化分量和p极化分量，因此界面1处的总电场可以看作是s极化部分(i1, r1)和p极化部分(i2, r2)，其中i和r分别表示入射场和反射场。同理，“界面2”处的总电场可以看作是s极化部分t的叠加1 p极化部分是t2，其中t为传输字段。那么我们可以写出接口1和接口2的总字段为

4、数值模拟与讨论

方便起见，我们表示[(AB)]6(马)(BA)6]和[(BA)6(nB) (AB)6]随着个人电脑m 和电脑n,分别。在接下来的模拟中，我们将A和B的光学厚度设置为0.3875micro;m。

第一步，我们考虑了s极化波窄带和窄透射角滤波的实现。我们首先计算了光子晶体缺陷模的中心波长m 和电脑n 对于正入射时的s极化，用lambda;表示m 和lambda;n ,分别。缺陷模的中心波长随缺陷因子m和n的变化而变化m 和电脑n 。然后，根据标度律，我们可以得到两个新的结构:

其缺陷模式与中心波长为1.55micro;m的正入射波长相同。随着入射角的变化，两种结构的波长不同，只有带通和正入射的窄波才能通过组合结构{fm (电脑m ]} {fn(电脑n]}。

使带通∆lambda;m 和∆lambda;n 在两种结构尽可能窄的情况下，我们研究了缺陷因子m和n对缺陷模带宽的影响，如图2所示。从图2可以看出，最小带宽位于m = 2或n = 2处。值得注意的是，f_m = f_n 当m = n = 2时= 1。在下面，我们将调用

指出了∆lambda;最小值的存在性m 和∆lambda;n 在m = n = 2时，是Mie和Bragg同时共振散射的结果。在这种共振条件下，缺陷模在结构中存在很强的局部性，使缺陷模的带宽达到极小值。

第二步，我们演示了组合结构{PC1}{PC2}偏振器的功能。

我们首先计算出PC1和PC2的缺陷模波长在两种极化情况下随入射角的变化，如图3所示。图3a显示，只有在s偏振的正入射(theta; = 0◦)时，PC1和PC2的两个缺陷模波长才完全相同;而从图3b中可以看出，对于p偏振入射的任何角度，它们都是不同的。这意味着组合结构{PC1}{PC2}可能具有偏振器的附加功能。

图4显示了组合结构{PC1}{PC2}对入射角和入射波波长的透射情况。结果表明，只有在垂直入射时带宽和入射角较窄的s极化波才能通过该组合结构，即:它集成了NBP滤波器、NTA滤波器和偏光镜的功能。从图4c中可以看出，当变速器的通过角超过0.01时，最大通过角为1.8◦。组合结构的带通范围为1.54937micro;m ~ 1.55003micro;m。

这里我们只是设计了一个s偏振镜，因为我们可以通过类似的过程得到p偏振镜。然而，s偏振器可以作为p偏振器通过旋转结构90◦由z轴在图1。

我们指出，利用电磁波理论中的标度定律，可以设计出工作在其他波长的结构。

我们还指出，采用各向异性较高的单轴晶体可以获得较好的极化分离效果。此外，通过增加周期数，可以获得更窄的带通和更窄的通角。

5、总结

最后，我们提出并演示了一种具有NBP频域滤波和NTA空域滤波两种功能的极化器。没有引入各向异性材料到PCs，一个不能获得正常(0◦)入射波偏振器。

附：原文外文

A photonic-crystal polarizer integrated with the functions of narrow bandpass and narrow transmission-angle filtering

Abstract

Through the transfer matrix method, we demonstrated a special polarizer integrated with the functions of narrow band pass (NBP) and narrow transmission-angle (NTA) filtering at normal incidence in a stack of two one-dimensional defective photonic crystals (PCs). One of the PCs is made of an isotropic dielectric media, while the other PC is made of anisotropic media. The key point in designing the stack is to set the central frequencies of the defect modes of the two sub-PCs to be the same for one polarization at normal incidence, but different for oblique incidence or for other polarizations, so that

the stack structure could have the functions of three elements: a polarizer, an NBP filter, and an NTA filter.

1.Introduction

In recent years, much attention has been paid to photonic crystals (PCs), a new kind of optical material for controlling the motion of electromagnetic waves. PCs are structures formed by arraying two dielectrics of different refractive index periodically in one dimension (1D), two dimensions (2D), or three dimensions (3D) [1–4]. They are characterized by photonic band gaps (PBGs) in which the propagation of electromagnetic waves is strongly forbidden. Polarizers [5, 6] are important elements in optoelectronic signal receiving or detecting systems. Often, we need to pick up a signal with a narrow wavelength-band to get rid of noise of unwanted frequencies and a signal from a special direction to prevent interferences of waves from different directions. Thus in signal receiving or detecting systems, one needs polarizers, frequency filters and directional couplers. Such three elements may occupy a large volume and need to be arranged in a proper way to work together. This may boost the cost of the whole system. So, a single element exhibiting the three functions is of great interest to engineers. In [7], utilizing all isotropic dielectric materials, a structure with the functions of NBP and NTA filtering, together with the additional function of

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