Review pubs.acs.org/CR
Active Plasmonics: Principles, Structures, and Applications Nina Jiang,†,‡ Xiaolu Zhuo,† and Jianfang Wang*,†,§ †
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong SAR 852, China College of Chemical Engineering, Huaqiao University, Xiamen 361021, China § Shenzhen Research Institute, The Chinese University of Hong Kong, Shenzhen 518057, China ‡
ABSTRACT: Active plasmonics is a burgeoning and challenging subfield of plasmonics. It exploits the active control of surface plasmon resonance. In this review, a first-ever indepth description of the theoretical relationship between surface plasmon resonance and its affecting factors, which forms the basis for active plasmon control, will be presented. Three categories of active plasmonic structures, consisting of plasmonic structures in tunable dielectric surroundings, plasmonic structures with tunable gap distances, and self-tunable plasmonic structures, will be proposed in terms of the modulation mechanism. The recent advances and current challenges for these three categories of active plasmonic structures will be discussed in detail. The flourishing development of active plasmonic structures opens access to new application fields. A significant part of this review will be devoted to the applications of active plasmonic structures in plasmonic sensing, tunable surface-enhanced Raman scattering, active plasmonic components, and electrochromic smart windows. This review will be concluded with a section on the future challenges and prospects for active plasmonics.
CONTENTS 1. Introduction 2. Principles of Active Plasmon Control 2.1. Control of Incident Light 2.2. Variation of the Dielectric Function of the Surrounding Medium 2.3. Change of the Charge Density and Dielectric Function of Plasmonic Materials 2.4. Control of the Interparticle Gap Distance 2.5. Control of the Symmetry of Plasmonic Nanostructures 2.6. Evaluation of the Performance of Active Plasmon Control 2.6.1. Spectral Response 2.6.2. Switching Time 2.6.3. Cycling Ability and Long-Term Stability 3. Active Plasmonic Structures 3.1. Plasmonic Structures in Tunable Dielectric Surroundings 3.1.1. Optically Active Materials 3.1.2. Thermocontrolled Materials 3.1.3. Electrically Controlled Materials 3.1.4. Electrochemically Controlled Materials 3.1.5. Magnetically Controlled Materials 3.1.6. Chemically Controlled Materials 3.2. Plasmonic Structures with Tunable Gap Distances 3.2.1. Dispersion in Solutions 3.2.2. Dispersion in or on Solid Matrices 3.3. Self-Tunable Plasmonic Structures 3.3.1. Metals
© 2017 American Chemical Society
3.3.2. Inorganic Semiconductors 3.3.3. Graphene 3.3.4. Polycyclic Aromatic Hydrocarbons 3.4. Comparison 4. Applications of Active Plasmonic Structures 4.1. Plasmonic Sensing 4.2. Tunable Surface-Enhanced Raman Scattering 4.3. Active Plasmonic Components 4.4. Electrochromic Smart Windows 5. Summary and Perspectives Author Information Corresponding Author ORCID Notes Biographies Acknowledgments References
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1. INTRODUCTION Plasmonics is a promising field of science and technology. It aims to exploit the interaction between light and matter through surface plasmon resonance (SPR) for a variety of properties and functions.1,2 SPR refers to the electromagnetic wave-induced collective oscillation of charge carriers at the interface between materials with positive and negative
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Special Issue: Plasmonics in Chemistry Received: May 7, 2017 Published: September 29, 2017 3054
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The exciting findings and advances in this direction mark the emergence of a new subfield under plasmonics, that is, active plasmonics. The concept of “active plasmonics” was originally coined for the active modulation of SPP in 2004,29 but now it is widely used to describe this new subfield of plasmonics. At the core of active plasmonics are active plasmonic structures that support reversibly tunable SPR. There have been many excellent reviews on the synthetic control of plasmonic metal nanostructures with single or multiple components for desired SPR frequencies.12,13,27,30,31 However, the modulation of SPR realized through synthetic control is static and passive. Transformation from plasmonic metal nanoparticles to active plasmonic structures needs the use of other active components and external stimuli that can trigger the reversible changes of SPR. To date, several review papers have been related or devoted to active plasmonic structures. They have focused on those consisting of plasmonic metals and particular types of active surrounding media, such as liquid crystals and dye molecules.32−36 In recent years, the family of plasmonic materials has been extended from traditional noble metals to semiconductors and graphene.37−40 A plethora of materials has been identified as ideal surrounding media for manipulating SPR in plasmonic structures. The search for new types of active plasmonic structures has been made at an extremely fast pace. In addition, the applications of active plasmonic structures in enabling the control of coupled and uncoupled LSPR have been explored substantially. However, this significant progress in active plasmonics has not been well summarized and discussed. In addition, a comprehensive theoretical analysis of the active control over SPR was not performed in the previous review papers. As a consequence, in this review article, we will endeavor to fully cover these aspects and to review a wide collection of the relevant literature. The aim of this review is to give a clear picture of what the fundamentals in active plasmon control are, how active plasmonic structures are made, how the modulation performances are characterized and optimized, and what the enabled applications are. Specifically, we will start with the basic principles underlying the active control of SPR, including SPP and uncoupled and coupled LSPR modes (section 2). We will present a thorough summary of the theoretical foundations and key evaluation parameters for active control. From this starting point, the rational design and construction of active plasmonic structures, whose plasmonic properties can be dynamically tuned under external stimuli, becomes possible. We will then expatiate on the state of the art in active plasmonic structures (section 3). Active plasmonic structures will be divided into three categories according to the involved modulation mechanisms: plasmonic structures embedded in tunable dielectric surroundings, plasmonic structures with tunable gap distances, and self-tunable plasmonic structures. The modulation performances of these active plasmonic structures will also be evaluated and compared, which can help in summarizing the strategies for further improving active plasmonic modulation. To this end, we will discuss the progress toward the applications of active plasmonic structures in plasmonic sensing, tunable surface-enhanced Raman scattering, and active optical signal control (section 4). Finally, we will assess the extent to which the challenges have been met and provide our own opinions on the future challenges and prospects in the field of active plasmonics. In this review, we will mainly highlight the most relevant research progress in active plasmonics since 2004, although some works before 2004
permittivities, typically a dielectric and a metal. Such electron oscillations can propagate along a planar interface (surface plasmon polariton, SPP) or be confined on a subwavelength structure (localized surface plasmon resonance, LSPR). Once excited, both forms of SPR can confine the incident electromagnetic field at a deep subwavelength scale, leading to a remarkable enhancement of the local field and allowing for the manipulation of light below the diffraction limit. The attractive capability of SPR empowers plasmonic materials with high potential of applications in a wide range of disciplines, including photonics,3,4 chemistry,5,6 energy,7 and life sciences.8−10 As a result, over the past two decades, scientific interest in plasmonic materials and their supported SPR has intensified. Important progress in lithographic techniques and classical wet-chemistry methods offers opportunities for synthetically controlling the sizes, shapes, dimensions, and surface topologies of plasmonic materials, often with nanometer precision.11−13 Based on the synthetic efforts, careful characterizations of the optical properties allow researchers to disclose the dependence of the SPR of plasmonic materials on their compositions, geometrical parameters, spatial arrangements, and surrounding dielectric environments.13,14 Understanding of this dependence relationship provides a clear guideline for further controlling SPR properties to reveal new aspects of their underlying science and to satisfy the demands of different technological applications. For example, recent advances in building complex plasmonic nanostructures have elucidated how the SPR in each nanostructure component couples to generate new plasmon modes, intriguing spectral responses and large electric field enhancements.14−18 Coupled plasmonic systems with large electric field enhancements have been applied in the amplification of fluorescence,14,19 infrared absorption,14 and Raman scattering signals.14,20,21 However, realizing the electromagnetic field amplification alone is not enough. Of further concern to researchers is how to reversibly and quantitatively control optical signals.22 Development of an actively tunable SPR that enables an on-demand enhancement of optical signals is therefore put on the agenda. In fact, developments in other important applications of plasmonic materials, such as subwavelength photonic devices and plasmonic sensing, also emphasize the need for having SPR controllable in a reversible manner. Early theoretical and experimental attempts to achieve the reversible control of SPR were associated with the development of light modulators in the 1980s.23−25 The operation principles of light modulators were to perturb the attenuated total reflection by mechanically controlling the excitation of the SPP signal or by electrically altering the refractive index of the medium around the metal grating supporting the SPP. Owing to the momentum mismatch between free-space light and SPP, the generation of SPP in these modulators had to rely on the prism-coupling configuration. Such a “bulky” optical configuration is not ideal for high-density integration and fast modulation. Fortunately, the progress of nanoscience and nanotechnology in the beginning of the 21st century provided new textured plasmonic surfaces for the free-space excitation of SPP and plasmonic nanostructures for supporting LSPR.26,27 Incorporation of these plasmonic structures permits the downscaling of photonic components.28 The past decade has therefore witnessed tremendous interest in actively controlling SPP and uncoupled or coupled LSPR through the use of plasmonic structures. The active-control functionality has immensely broadened the applicability of plasmonic structures. 3055
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will also be mentioned for the introduction of the fundamentals in active plasmonics and for coherency and completeness.
2. PRINCIPLES OF ACTIVE PLASMON CONTROL We provide in this section a brief theoretical framework to reveal the basis of active plasmon control. The essential theoretical concepts and principles of active plasmonics are selected from several representative review articles and books that have been devoted to the theoretical treatment of SPR.19,41−44 Our aim here is to provide an in-depth description of the theoretical relationship between SPR and the affecting factors, which will keep readers aware of the big picture behind the various active plasmonic structures that will be described in section 3. The SPR discussed here will include SPP and uncoupled and coupled LSPR. Although these forms of SPR can also be supported by many nonmetallic materials, such as graphene and highly doped semiconductors, the classic theories of SPR are based on metals. Consequently, in this section, the analysis of active plasmon control will be mainly devoted to the SPR in metals. Metals that are at nanoscale and contain a single type of metal are generally called “metal nanoparticles”. They can be either synthesized by chemical methods or fabricated by physical approaches. We also frequently use the term “metal nanocrystals” for the metal nanoparticles that are synthesized by wet-chemistry methods and have well-defined crystalline structures (single-crystalline or multiply twinned). In addition, we also often use the term “metal nanostructures” for those made of multiple components, such as bimetallic and hybrid structures. At the end of this section, evaluating the performances of active plasmon control will be described.
Figure 1. Excitation of SPP. (a) Dispersion relations of SPP, LSPR, free-space light, and light coupled into a prism, respectively. ω, c, k, and n represent the angular frequency of light, the velocity of light in vacuum, the propagation constant of light, and the refractive index of the prism, respectively. (b) Kretschmann configuration for SPP excitation. θSPP refers to the incidence angle at which the SPP at the interface can be excited. (c) Otto configuration for SPP excitation. The schematics in (b,c) were reprinted with permission from ref 45. Copyright 2004 Elsevier B. V. (d) Phase-matching of light to SPP using a grating. k denotes the wavevector of the incident light. Reprinted with permission from ref 44. Copyright 2007 SpringerVerlag.
2.1. Control of Incident Light
Inasmuch as SPR is a unique light−matter interaction, control of the incident light is a direct route toward the switching of SPR. The oscillating electric field from the incident light can couple with the SPR or, more exactly, SPP at a metal−dielectric interface when its momentum matches that of the plasmon. However, the propagation constant of free-space light is smaller than that of the SPP (Figure 1a). To realize the excitation of the SPP, a momentum transfer must be established. Some special techniques, such as the use of coupling devices (couplers) and metal surfaces with periodic corrugations for creating attenuated total reflection or diffraction, increase the propagation constant of the incident light so that it can match that of the SPP.26 If the changes in the propagation constant of the incident light made by these techniques are reversible, the excitation of the SPP can be actively switched. Let us take prism coupling and grating coupling, two frequently used techniques, as examples to elucidate the principle underlying active control over the excitation of SPP. The use of a prism allows for the coupling of SPP with the evanescent electromagnetic field that is produced by attenuated total internal reflection. This coupling mechanism can be applied in two different configurations, the Kretschmann and Otto configurations (Figure 1b,c).45 In the Kretschmann configuration, a high-refractive-index prism is interfaced with a metal−dielectric waveguide consisting of a metal film with a sufficiently small thickness (generally less than 100 nm for light in the visible and near-infrared (NIR) regions) and a dielectric with a refractive index nd (nd < np, np is the refractive index of the prism).46 A light wave passing through the prism can be reflected back and propagate in the metal in the form of an evanescent electromagnetic wave, when the incidence angle of
the light wave is above the critical angle for total internal reflection. The evanescent wave penetrates through the thin metal film and can be coupled with the SPP at the metal− dielectric interface (outer boundary of the metal film) by controlling the angle of incidence on the base of the prism according to the expression below 2π n p sin θ = β EW = Re{β SPP} (1) λ where λ is the wavelength of the incident light, θ is the incidence angle, np is the refractive index of the prism, Re{ } denotes the real part of a complex number, and βEW and βSPP represent the propagation constants of the evanescent wave and SPP at the metal−dielectric interface, respectively. Under the coupling condition, the SPP is excited by the incident light, which is detected as a dip at a particular wavelength in the spectrum of the reflected light from the prism. For light incident with a specific wavelength, the coupling condition is satisfied at a single incidence angle. As a consequence, in the Kretschmann configuration, actively controlling the incidence angle enables the modulation of the excitation of the SPP and induces the variation of the intensity of the reflected light. The Kretschmann configuration is not applicable to the excitation of SPP when direct contact between the prism and the metal surface is undesirable or the metal film is not thin enough for the penetration of the evanescent electromagnetic wave. To solve this problem, a dielectric layer with a refractive index (nd) smaller than that of the prism (np) is deposited between the prism and the metal film, which is named the Otto configuration (Figure 1c). Provided that nd is smaller than np, 3056
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light incident at a specific incidence angle, θ > sin−1(nd/np), can be totally reflected at the interface between the prism and the dielectric layer, generating an evanescent wave decaying exponentially with distance in the dielectric layer.47 If the thickness of the dielectric layer is adjusted properly, typically a few hundred nanometers in the optical regime, the evanescent wave can reach the dielectric−metal interface with sufficient strength for the excitation of the SPP. Hence, in the Otto configuration, the controllable factors on the excitation of the SPP include the incidence angle θ, the wavelength of the incident light λ, and the thickness of the dielectric layer d. The variation of d can change the resonance strength of the SPP, which can be detected by the amplitude variation of the light reflected from the base of the prism.23,48 Grating coupling, another common technique for the optical excitation of SPP, is based on the diffraction of light on a grating patterned on the metal surface (Figure 1d).44 The diffracted light can couple to the SPP if the momentum of the diffracted light parallel to the grating surface is equal to the propagation constant of the SPP49 2π 2π nd sin θ ± m = Re{β SPP} λ a0
1a) allows for its excitation by incident light over a wide range of angles.54 Nevertheless, the excitation of LSPR, including uncoupled and coupled forms, still relies highly on the wavelength and polarization state of the incident light. LSPR is excited under the condition that the wavelength of the incident light coincides with the LSPR wavelength. The polarization dependence is correlated with the shape and geometry of the plasmonic nanostructure under consideration. For example, Au nanorods possess the transverse and longitudinal dipolar plasmon resonance modes, which can be excited by light polarized along the width and length of the nanorods, respectively.13,55 Reversibly changing the polarization direction of the excitation light allows for the LSPR modes to be selectively excited. 2.2. Variation of the Dielectric Function of the Surrounding Medium
Varying the dielectric function of the surrounding medium is an effective way to achieve the active control of SPR. LSPR and SPP are sensitive to the variation of the dielectric function of the surrounding medium. To gain insight into the sensitivity of SPP to the surrounding medium, let us first look at the dispersion relation of SPP at a semi-infinite dielectric−metal interface, that is, how the propagating constant of the SPP mode, βSPP, varies with frequency
(2)
where a0 is the grating period and m = 1, 2, 3, ... For a given grating pattern on the metal surface, a0 and m are fixed. Therefore, the excitation of the SPP is actively controlled upon the reversible change of the incidence angle θ or the wavelength of the incident light λ in the grating coupling. Metallic hole arrays are considered an extreme form of grating. The incident light couples to the SPP on the incoming side of the metallic hole array through the grating coupling. The evanescent field associated with the SPP can span the metal film and be scattered by the periodic structure on the exiting side, thereby enabling the SPP to be scattered into the transmitted light.50 Switching the SPP in such a structure can be realized and studied by measuring the light transmission through the metal film. In the coupling schemes described above, the polarization state of the incident light also determines the excitation of the SPP. According to Maxwell’s equations and the boundary conditions, the propagation of SPP along the interface between a metal and a dielectric is possible only for transverse magnetic (TM) polarization.44 For this reason, only the component of the incident light that is polarized perpendicular to onedimensional corrugations (in the case of gratings) or to the metal surface itself (in the case of the prism-based schemes) can be coupled into SPP. Light adjusted to be in the orthogonal polarization does not couple to SPP, leading to a decrease in the SPP signal and a loss of information on the incident polarization state.51 Accordingly, controlling the polarization state of the incident light is recognized as an effective way to vary the strength of SPP. One should be aware that the polarization dependence mentioned above is derived from the fundamental theory of the SPP wave at a planar interface between a metal and an isotropic, homogeneous dielectric material. However, for an interface structure composed of a complex and anisotropic dielectric material and a metal, the SPP can be excited by TM and transverse electric (TE) polarized light.52,53 Control over the polarization state empowers the SPP with tunable directionality. Compared with its propagating counterpart, i.e., SPP, LSPR is launched without a need for complex techniques. The flat dispersion of LSPR supported by metal nanoparticles (Figure
β SPP =
c ω
εdεm εd + εm
(3)
where εm and εd are the dielectric functions of the metal and the adjacent dielectric, respectively. If the dielectric is nonabsorbing, then the imaginary part of εd equals zero, and εd = nd2. A change in εd (or the refractive index nd) of the dielectric medium leads to a variation of βSPP, which alters the coupling condition (eqs 1 and 2) and therefore affects the optical excitation efficiency of SPP. This effect can be observed by the intensity variation of the reflected light from the interface or of the transmitted light through the metal film. For example, in the Kretschmann configuration, the quantitative relationship between the reflectivity R and the propagation constant βSPP can be derived using Fresnel’s equations. Assuming that the dielectric function of the metal εm satisfies |Re{εm}| ≫ 1 and |Im{εm}| ≪ |Re{εm}|, the reflectivity R can be approximated by a Lorentzian-type relation56 R=1−
[β − (β SPP
4Im{β SPP}Im{Δβ} + Δβ)]2 + (Im{β SPP} + Im{Δβ })2 (4)
The term β is the propagation constant of the SPP in the prism−metal−air system. It is shifted by an amount Δβ from the dielectric−metal interface value βSPP. Δβ describes the effect of the prism and is determined by calculating the Fresnel reflection coefficients. It depends on the thickness of the metal layer.56 Im{} denotes the imaginary part of a complex number or function. Im{Δβ} and Im{βSPP} describe the radiation and absorption losses of the SPP, respectively. From eqs 3 and 4 above, we can see clearly that the variation of the dielectric function of the surrounding medium modifies the propagation constant of SPP, thereby affecting the intensity of the light reflected from the interface. To quantitatively evaluate the sensitivity of SPP to the surrounding medium, one can use a mathematical formalism arising from the refractive index response of the SPP on a planar noble metal surface57 3057
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λLSPR = λP 2εd + 1
(5)
where Δλ is the wavelength shift of the minimum in the reflected light intensity spectrum associated with the change in the refractive index of the layer adsorbed on the metal surface Δn, m is the refractive index sensitivity of the planar metal surface (δλ/δn), d is the thickness of the adsorbate layer, and L is the characteristic decay length of the local electromagnetic field on the metal surface. The refractive index sensitivity m is determined by the material composition and structural parameters of the metal surface. According to eq 5, for a given metal surface, the magnitude of the spectral response of the SPP depends on the refractive index of the adsorbate layer and the thickness of the adsorbate layer displaying the refractive index contrast. Given this relationship, we can design and construct high-performance active plasmonic structures through the incorporation of dielectric layers with optimized dimensions and dielectric properties. Next, let us see how the dielectric function of the surrounding medium affects LSPR. The dependence of LSPR on the dielectric function of the surrounding medium forms an essential basis for the active control of LSPR. We first consider the simplest model, the LSPR supported by a spherical metal nanoparticle, which can be described by the Mie theory. The classical Mie theory corresponds to the rigorous analytical solution to Maxwell’s equations for the optical properties of a spherical particle. It assumes that the particle and the surrounding medium are homogeneous.58 For a metal nanoparticle with a diameter of d far smaller than the wavelength of the incident light λ (i.e., d/λ < ∼0.1), the magnitude of the electric field appears static around the nanoparticle, and the metal nanoparticle is equivalent to an ideal dipole. In this limit, the Mie solution for the extinction cross-section σext(λ) of the metal nanoparticle, the sum of the absorption and scattering cross sections, reduces to σext(λ) =
18πVεd 3/2 ε2(λ) λ [ε1(λ) + 2εd]2 + [ε2(λ)]2
where λP is the wavelength corresponding to the plasma frequency of the bulk metal and εd = nd2. Consequently, we see that an increase of the dielectric constant or refractive index of the dielectric environment will result in a redshift of the LSPR peak of the spherical metal nanoparticle. By generalizing Mie’s solution to spheroidal particles of any aspect ratio in the small particle approximation, Gans provided the solution to the extinction of spheroidal particles, which is analogous to eq 6 above for a nanosphere.60 Rod-shaped nanoparticles are often approximated as prolate spheroidal ones so that the Gans theory can be applied. From the Gans theory, one can derive the longitudinal plasmon wavelength of a metal spheroid or nanorod as λLSPR = λP ε∞ +
(6)
ωP 2 ω2 + γ 2
(7)
where ωP and γ are the plasma frequency and damping frequency of the bulk metal, respectively. In the visible and NIR regions, γ ≪ ωP. When LSPR occurs, ε1 = −2εd. Accordingly, the LSPR frequency can be expressed by the following equation ωLSPR =
ωP 2εd + 1
⎛1 ⎞ ⎜ − 1⎟εd ⎝P ⎠
(10)
where ε∞ is the high-frequency dielectric constant of the metal and P is the depolarization factor along the long axis of the spheroid or nanorod. Clearly, for the metal nanorod, the LSPR peak is also red-shifted with the increase in the dielectric constant of the dielectric environment. The extinction of nanoparticles with shapes beyond spheres and spheroids cannot be found analytically as above and must be studied numerically. Many numerical and experimental results have shown that the LSPR spectral responses of arbitrarily shaped metal nanoparticles are affected by changes in the dielectric constant (or refractive index) of the surrounding medium. The redshifts of LSPR peaks in response to the increase of the dielectric constant (or refractive index) of the surrounding medium differ greatly owing to differences in size, shape, and composition of metal nanoparticles.59,61−63 In addition, plasmon coupling also affects the response of plasmonic metal structures to refractive index changes.14,64,65 The different spectral responses of metal nanoparticles can be predicted according to eq 5. Although this equation is proposed for evaluating the refractive index sensitivity of SPP, numerical and experimental results have verified the validity of this equation for describing the sensing characteristics of LSPR supported by metal nanoparticles.66,67 The refractive index sensitivities of plasmonic metal nanoparticles and structures are often expressed as the plasmon peak shift in wavelength caused by the change in the surrounding dielectric medium in one refractive index unit (RIU). There are three general rules. First, for a given composition and shape, the more red-shifted (lower in energy) a plasmon resonance is, the higher its refractive index sensiticity is.59,62 Second, plasmonic metal nanoparticles with sharp tips, such as nanostars, nanotriangles, and nanobipyramids, possess higher refractive index sensitivities than spherical metal nanoparticles.59,61−63 For example, the refractive index sensitivities of Au nanospheres are ∼40−90 nm RIU−1.,59,63,64 while those of Au nanorods (longitudinal plasmon wavelength 650−850 nm) and Au nanobipyramids (longitudinal plasmon wavelength 650−1100 nm) are ∼200− 290 and ∼150−540 nm RIU−1, respectively.63 Among various plasmonic metal nanoparticles in different shapes, Au nanorices have been found to exhibit the highest index sensitivity of ∼800 nm RIU−1 so far.59 Third, the refractive index sensitivities of plasmonic metal structures can be further increased by taking advantage of coupled LSPRs and Fano resonance.14,59,64,65 The index sensitivities of plasmonic metal structures supporting
where V is the nanoparticle volume, λ is the wavelength of light, εd is the dielectric constant of the surrounding medium (εd is assumed to be a positive and wavelength-independent real number), and ε1 + iε2 is the complex dielectric function of the metal.58 As presented in eq 6, the extinction cross-section will be maximized if ε1 equals −2εd and ε2 is small. This actually indicates the occurrence of LSPR in the metal nanoparticle. To determine the functional relation between the LSPR peak wavelength and the dielectric function of the surrounding medium, one can use the Drude model for the frequencydependent expression of ε1 ε1 = 1 −
(9)
(8)
Through the conversion from frequency to wavelength by λ = 2πc/ω, the equation above becomes59 3058
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Fano resonance have been found to reach ∼1200 nm RIU−1.64,65 We can understand the sensitivity of the LSPR peak to the variation of the dielectric constant of the surrounding medium from another simple physics perspective, as illustrated with a metal nanorod in Figure 2. Upon excitation by an external
For example, emitters such as quantum dots (QDs) transfer their excitation energy through radiationless transitions to the SPR supported by metals or semiconductors. The presence of such media, which are called gain media, can counteract the inherent absorption losses in the metal. Under the quasi-static approximation, the effect of εi of a gain medium on the quality factor Q of the LSPR in a metal nanoparticle can be described by the following proportional relation:71 −1 ⎛ ε2 |εi| ⎞ Q∝⎜ − ⎟ εr ⎠ ⎝ |ε1|
The quality factor Q representing the strength of a plasmon resonance increases with εi. Based on this criterion, we can integrate plasmonic structures with gain media to achieve the strengthening of the plasmon resonance. Furthermore, the strong coupling between an absorptive medium and SPR can induce peak splitting as a result of the formation of hybridized resonance states.69 The formation of the hybridized states is analogous to the generation of molecular states from the hybridization of two atomic states at similar energies. Consequently, the choice of an absorptive surrounding medium will exert a substantial effect on the functionality of active plasmonic structures, which will be illustrated with examples below (section 3.1).
Figure 2. Schematic showing the variation of the polarization charges around a metal nanorod induced by two surrounding environments with different dielectric constants. The increase in the amount of the induced polarization charges is due to a larger dielectric constant of the medium.
electromagnetic field, the separated charges on the metal nanorod induce polarization charges in the adjacent dielectric environment. The amount of induced polarization charges in the dielectric environment increases with the dielectric constant of the surrounding medium. As a result, the screening of the Coulombic restoring force that acts on the conduction-band electrons in the metal nanorod is increased. The weakened restoring force causes a redshift of the LSPR peak. For the sake of simplicity, the aforementioned dielectric function of the surrounding medium is assumed to be a real dielectric constant. However, it happens in some practical cases that the surrounding medium is absorptive so that it has a complex dielectric function (εd = εr + iεi) or a complex refractive index (ñ = n + ik). We should consider the case where the real and imaginary parts of the dielectric function change. For an absorptive surrounding medium having an electronic absorption energy far from the plasmon resonance energy, one finds that the increase in the real part of the dielectric function εr (or the refractive index n) induces a redshift of the LSPR peak, whereas the variation of the imaginary part of the dielectric function εi affects the attenuation of LSPR.68,69 To clarify this effect, we can use a simplified model, a semi-infinite degenerate electron gas bounded by a semi-infinite absorptive dielectric medium. The imaginary part of the resonance frequency ωi of the electron gas can be extracted. It gives the lifetime τ or the breadth of the resonance τ−1, according to the following equation:70 τ
−1
3/2
= 2ωi = ωrεi /(1 + εr)
(12)
2.3. Change of the Charge Density and Dielectric Function of Plasmonic Materials
The SPR in a plasmonic material depends on its size, shape, composition, and structure. However, these parameters are intrinsic to the plasmonic material. Once designed, they cannot be easily modified in a reversible manner. Only a few attempts have succeeded by reversibly changing the carrier density, chemical composition, or structure phase of plasmonic materials. The materials for realizing this type of active plasmon control belong to the category of self-tunable plasmonic structures. The specific works will be described below in section 3.3 in detail when self-tunable plasmonic structures are discussed. In essence, the composition or phase variation leads to changes in the dielectric function. To reveal the principle of such active plasmon control, we will fully elucidate the effect of the carrier density and dielectric function of plasmonic materials on SPR. The carrier density, N, dominates the bulk plasma wavelength, λP, according to the equation below54 λP =
2πc = ωP
4π 2c 2mε0 Ne 2
(13)
Combining this equation with the resonance condition for an anisotropic metal nanoparticle within the quasi-static approximation, we find that the change in the carrier density induces an SPR shift expressed by72
(11)
where ωr = ωP/(1 + εr)1/2 is obtained for the dielectric function having only the real part εr. Clearly, as εi is increased, the breadth of the resonance τ−1 increases and the lifetime τ decreases. This means that the increase of the imaginary part of the dielectric function of the surrounding medium aggravates the attenuation of SPR. Note that eq 11 is valid only for small values of εi. For large εi, the lifetime of SPR is so short that we are unable to observe in the spectrum a distinct breadth associated with the energy loss. As such, one cannot speak of the presence of SPR at the interface between a strongly absorptive medium and a plasmonic material. For an absorptive surrounding medium having its electronic absorption energy close to the plasmon resonance energy, its effect on SPR involves the so-called strong coupling regime.69
Δλ = −
⎛1 ⎞ ΔN λP ε∞ + ⎜ − 1⎟εd ⎝ ⎠ 2N P
(14)
where ΔN is the change in the carrier density of the metal nanoparticle, N is the carrier density in the original metal nanoparticle, ε∞ is the high-frequency contribution to the metal dielectric function, εd is the dielectric constant of a nonabsorptive surrounding medium, and P is the shape-dependent depolarization factor of the metal nanoparticle. Note that this equation clearly predicts that, for a fixed shape, one can tune the LSPR wavelength by changing the dielectric environment, 3059
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the carrier concentration, or the dielectric function of the metal. The magnitude of the carrier density characterizes the conductivity of a material. The conductivity and dielectric properties always go hand in hand. As a result, we can vary the dielectric function by changing the carrier density. The dielectric function of a metal is a key parameter in defining the propagation constant, βSPP, of the SPP mode. The real part of βSPP is related to the optical excitation condition of the SPP (see eqs 1 and 2), whereas the imaginary part of βSPP dominates the propagation length L = (2Im{βSPP})−1, which reflects the attenuation of the SPP.44 Accordingly, the dielectric function of the metal governs the optical excitation efficiency and propagation length of the SPP. For LSPR, its resonance peak position is to some extent determined by the real part of the dielectric function of the plasmonic material. In general, the real part of the dielectric function describes the material background screening of the surface charges induced by the plasmon resonance.73 A large real part of the dielectric function of the plasmonic material represents an efficient screening, yielding a redshift of the LSPR peak. To qualify this relationship, we note that the LSPR peak wavelengths (λLSPR) of metal nanospheres and nanorods increase with the wavelengths (λP) corresponding to their plasma frequencies when the dielectric constant of the surrounding medium remains identical, as shown by eqs 9 and 10. Considering eq 7 and applying λ = 2πc/ω, we find that the real part of the dielectric function of a metal (ε1) approximated by the Drude model is positively proportional to λP. Consequently, an increase in ε1 leads to a redshift of λLSPR. The size effect of metal nanoparticles is not involved in the description of the connection between the metal dielectric function and the LSPR peak wavelength. The dielectric function of the bulk metal expressed by the Drude model considers the contribution of free electrons but overlooks the contribution of boundary electrons. This overlooked contribution is due to the d−sp interband transitions and depends on the size of metal nanoparticles.74 For accuracy, the sizedependent term is required in the dielectric function, including the real and imaginary parts. The imaginary part of the dielectric function predominantly determines the broadening and absorptive dissipation of the surface plasmon due to the damping and dephasing of the electron oscillation. For a small nanoparticle, the imaginary part of the dielectric function directly determines the width (lifetime) of the plasmon resonance.73,75 For large nanoparticles, with diameters larger than ∼50 nm, retardation effects become important and radiation becomes the dominant contribution to the lifetime broadening of the plasmon resonance.41,76 The size of a metal nanoparticle affects not only its dielectric function but also the decay channels of the surface plasmon.77 However, a reversible control over the size of a metal nanoparticle has not been realized experimentally.
uncoupled one offers the possibilities for expanding the tunable spectral range and for switching local electric field enhancements and the wealthy plasmonic responses mentioned above. One of the underlying mechanisms for such active plasmon control is based on the sensitive dependence of LSPR on the dielectric function of the surrounding medium, which has been elucidated above (section 2.2). Regardless of whether LSPR is coupled, the LSPR wavelength and strength are sensitive to the variation of the dielectric function of the surrounding medium. In addition, another mechanism is based on the sensitive dependence of plasmon coupling on the interparticle gap distance. The gap-dependent behaviors of the dipolar coupling in plasmonic dimers, a basic coupled plasmonic system, can be theoretically interpreted in the context of the plasmon hybridization model.14 After plasmon coupling, the dipolar plasmon mode is split into two distinct plasmon modes: the bonding and antibonding hybridized plasmon modes.14 The bonding plasmon mode possesses two mutually aligned dipoles along the interparticle axis, which results in a large induced dipole and strong coupling to the far field. On the other hand, the dipoles in the antibonding plasmon mode are antialigned, leading to the occurrence of a zero net dipole moment. The antibonding mode consequently cannot be excited by far-field light. In other words, it becomes a “dark” plasmon mode. As a result, the optical properties of the plasmonic dimer are dominated by its lower-energy bonding mode. In the case of longitudinal (along the interparticle axis) excitation, the wavelength of the plasmon resonance mode corresponding to the lower-energy bonding mode is red-shifted as the gap distance is reduced. Quantitative studies on this gap-dependent behavior have indicated that the fractional plasmon shift (Δλ/ λ0) decays nearly exponentially with the interparticle gap distance in the unit of the particle size according to
2.4. Control of the Interparticle Gap Distance
Table 1. Characteristic Particle Sizes for Quantitatively Analyzing the Gap-Dependent Plasmon Coupling in Dimers of Metal Nanoparticles with Specific Shapes and Orientations
Δλ = Ae−d /(sτ) λ0
(15)
where d is the interparticle edge-to-edge distance, s is the particle size defined as the length of the particle along the interparticle axis (i.e., diameter for a nanodisk or nanosphere), τ describes the decay length of the electric field away from the particle surface, and A is the maximal fractional plasmon shift, representing the dipolar coupling strength.79 Such a nearexponential decay trend is universally independent of nanoparticle size, shape, metal type, or the surrounding dielectric medium, but the s, A, and τ parameters determining the absolute plasmon shift are related to the shape and orientation of the constituting nanoparticles.80 Size parameters for defining particle size s in eq 15 are listed in Table 1 for several types of metal nanoparticles of particular shapes and orientations.80 The exponential decay length τ and relative strength A expressing the dipole coupling can often be
LSPR in metal nanoparticles is especially sensitive to the presence of other nearby metal nanoparticles. When two metal nanoparticles are in close proximity, their LSPR modes will be coupled through a near-field interaction, enabling new plasmon resonance modes with large electromagnetic field enhancements. The interferences between different plasmon resonance modes in coupled plasmonic systems can further induce spectral splitting15,16 and plasmonic Fano resonance.16−18,78 As a result, the active control of a coupled SPR relative to an
nanosphere or nanodisk dimer
3060
orientation
edge to edge
size parameter
diameter
nanorod dimer end to end length
nanoprism dimer
nanocube dimer
tip to tip
side to side
bisector
edge length
DOI: 10.1021/acs.chemrev.7b00252 Chem. Rev. 2018, 118, 3054−3099
Chemical Reviews
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their relative orientation. In a coupled nanorod homodimer system with a small interparticle gap distance (
