二维材料与薄膜表面等离子体激元优化研究

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"这篇研究论文探讨了在导电二维材料和薄膜上优化表面等离子体（Surface Plasmon, SP）的激发和传播。" 在现代光学和纳米技术中，表面等离子体激元（Surface Plasmon Polaritons, SPPs）起着至关重要的作用，它们能够将光限制在亚波长尺度，从而实现高密度光子信息处理和增强的光物质相互作用。这篇由Feng Liang、Alexander B. Yakovlev（IEEE高级会员）和George W. Hanson（IEEE院士）共同撰写的论文，发表于2015年4月的IEEE Transactions on Antennas and Propagation期刊上，深入研究了二维材料（如石墨烯）和薄导电膜的表面导电性对SP激发和传播的影响。作者们提出，存在一种理想的表面导电状态，可以最大化特定位置的SP场强。这种理想状态是通过平衡传播损耗和与局部光子态密度相关的近场激发幅度来实现的。论文中考虑了无色散和德鲁德色散模型，并分析了能带间跃迁对SP的影响。他们还提供了简单的公式，用于确定在给定距离处获得最大SP场强的方法，并以石墨烯和薄金属膜为例进行了示例分析。文章首先介绍了引言部分，指出由于SP能将光束限制到远小于光波长的尺度，因此在光子学领域具有极大的潜力。论文接着详细讨论了二维材料（例如石墨烯）和薄金属膜的物理特性，这些材料因其独特的电子结构，特别适合SP的激发。在理论分析中，作者探讨了传播损失与SP激发之间的竞争关系。对于无色散材料，SP的传播不受频率影响，而在德鲁德模型中，SP的传播损耗与频率有关，这反映了材料的动态电导率。此外，能带间跃迁会引入额外的损耗，但也能增加SP的产生可能性。通过数值模拟和解析计算，论文展示了如何利用这些理论工具优化SP源的特性，以在目标位置达到最大的场强。对于石墨烯，由于其独特的零带隙特性，SP的激发和传播表现出独特的性质。而薄金属膜则受到更复杂的光学现象影响，如金属的吸收和反射。总结来说，这篇论文不仅提供了理解和优化SP在导电二维材料和薄膜上行为的理论框架，也为设计新型光学器件和传感器提供了实用的指导。通过精确控制SP的激发和传播，有可能实现高效光子集成、增强的光电探测以及新型光学通信技术。

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 63, NO. 4, APRIL 2015 1765

Optimum Surface Plasmon Excitation and

Propagation on Conductive Two-Dimensional

Materials and Thin Films

Feng Liang, Alexander B. Yakovlev, Senior Member, IEEE, and George W. Hanson, Fellow, IEEE

Abstract—The surface conductivity of two-dimensional (2-D)

materials and thin conductive ﬁlms is considered for surface plas-

mon (SP) excitation and propagation. It is shown that an ideal

surface conductivity exists to maximize the SP ﬁeld at a given

position, based on a tradeoff relating to propagation loss and

near-ﬁeld excitation amplitude associated with the local density of

photonic states. Dispersionless and Drude dispersion models are

considered, as well as the effect of interband transitions. Simple

formulas are presented to obtain a maximal SP ﬁeld at a given dis-

tance from a canonical source. Examples are shown for graphene

and thin metal ﬁlms, and a discussion of the competition between

propagation loss and SP excitation is provided.

Index Terms—Graphene, surface plasmon (SP), thin ﬁlms.

I. INTRODUCTION

ECAUSE of their ability to conﬁne light in subwave-

length spaces, surface plasmons (SPs) are of considerable

importance in a variety of areas, including optical sensors, opti-

cal antennas, solar cells, near-ﬁeld communications, and data

storage [1]. SPs can be conﬁned to a planar-like surface and

propagate along the surface, and are sometimes called surface

plasmon polaritons (SPPs), or they can be nonpropagating and

conﬁned to the surface of metallic particles or curved metal

objects, in which case they are called l ocalized surface plas-

mons (LSPs) [2] or particle plasmons. The main attributes of

both SPPs and LSPs are high electric ﬁeld amplitudes and sub-

wavelength energy conﬁnement. Although SPPs and LSPs have

many overlapping applications, uses of SPPs often involve their

propagation aspects for communications or sensing [3]–[6], and

many LSP applications center on their small size and station-

ary nature, such as creating localized hot-spots for biological/

medical imaging and cancer treatment [7], [8]. Planar structures

Manuscript received September 12, 2014; revised December 14, 2014;

accepted January 18, 2015. Date of publication January 22, 2015; date of

current version April 03, 2015. This work was supported in part by the

National Natural Science Foundation of China under Grant 61204041 and Grant

61331007, in part by the China Postdoctoral Science Foundation funded project

under Grant 2014M552335, in part by the Fundamental Research Funds for the

Central Universities of China under Grant ZYGX2013J049, and in part by the

China Scholarship Council.

F. Liang is with the School of Physical Electronics, University of

Electronic Science and Technology of China, Chengdu 610054, China (e-mail:

fengliang@uestc.edu.cn).

A. B. Yakovlev is with the Department of Electrical Engineering, University

of Mississippi, Oxford, MI 38677 USA (e-mail: yakovlev@olemiss.edu).

G. W. Hanson is with the Department of Electrical Engineering,

University of Wisconsin–Milwaukee, Milwaukee, WI 53211 USA (e-mail:

george@uwm.edu).

Color versions of one or more of the ﬁgures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TAP.2015.2395440

having propagating SPs are larger than typical LSP structures,

but are generally easier to fabricate and one does not need to

precisely position nanoparticles as is often required for LSP

applications.

Surface plasmons on two-dimensional (2-D) planar materials

such as graphene and MoS

, and on very thin three-dimensional

(3-D) materials such as thin metal layers, doped semiconduc-

tor ﬁlms, and 2-D electron gasses are of considerable interest

[9]–[15]. In all cases, the surface can be modeled by a surface

conductivity σ (S), and which can be controlled by chemical

doping and, for some materials like graphene and even thin

metals, can be controlled by an external dc electric or magnetic

ﬁeld bias [16], [17]. Frequency dispersion typically dictates a

desirable frequency range for s trong SP propagation. Moreover,

although it is beyond the scope of the present work, one can

engineer artiﬁcial surfaces to achieve desirable characteristics

(often analyzed by 2-D homogenization) [18]–[20].

In general, σ is complex valued, with the real part being

associated with loss (absorption) and the imaginary part being

associated with reactive energy storage. For many materials

of interest, there is a Drude component and an interband

component; Im(σ) < 0 for the Drude component is inductive

due to the kinetic energy of charge carriers, whereas for the

interband component Im(σ) > 0 is related to capacitance asso-

ciated with band transitions. Loss is associated with Re(σ)

due to electronic collisions with phonons, impurities, lattice

imperfections, and band transitions.

Given that the value of σ can be controlled by a range of geo-

metrical and electrical parameters, an important question arises

as to the optimal surface characteristics for SP excitation and

propagation. Obviously, we generally want a low-loss structure,

and so we will assume that Im(σ)  Re(σ) to have low sur-

face plasmon absorption, and also that the permittivity of the

material surrounding the surface has low dielectric loss. In this

work, we consider the optimum value of the surface conductiv-

ity of a 2-D surface and thin ﬁlm for strong SP excitation and

propagation. We consider several different models of increas-

ing complexity, including dispersionless and Drude dispersion

models, as well as the effect of interband transitions, to achieve

desirable SP characteristics.

II. S

URFACE PLASMON AND TOTAL FIELDS ON A 2-D

URFACE

Consider an inﬁnite 2-D material sheet with surface conduc-

tivity σ = σ



− jσ



immersed in a multilayered environment

as depicted in Fig. 1. In each region, the permittivity may

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二维材料与薄膜表面等离子体激元优化研究

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