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A theoretical demonstration is given of coherent thermal emission via the visible region by exciting magnetic polaritons in isolated metal-dielectric-metal multilayer nanoshells and the collective behavior in a trimer comprising multilayer nanoshells. The dipolar metallic core induces magnetic polaritons in the dielectric shell creating a large enhancement of the emissivity, whose mechanism is different from that of film-coupled metamaterials. The coupling effect of the magnetic polaritons and the electric/magnetic modes of symmetric nanoparticle trimers is discussed to understand the collective behavior in self-assembled nanoparticle clusters with potential solar energy utilizations. The concept of hybridization is employed to understand the collective magnetic polaritons of a multilayer nanoshell trimer. The fundamental understanding gained herein opens up new ways to explore, control, and tailor spectral absorptance, thus facilitating rational design of novel self-assembled nanoclusters for energy harvesting.
© 2015 Optical Society of America
1. Introduction
Harvesting sunlight has engendered extraordinary interest in a world with an ever-increasing energy demand. In addition to the sunlight harvesting technologies currently under development [1], recently it has been observed that light-absorbing nanoparticles are capable of generating steam with remarkably high efficiencies [2] owing to the excitations of surface plasmon polaritons (SPPs) [3]. Like the excitations of SPPs, the excitations of magnetic polaritons [4] also have been demonstrated as the main mechanisms responsible for spectral selectivity in thermal absorption metamaterials [5]. Magnetic polaritons (MPs) refer to the resonance with a magnetic response [6] coupled to a nonmagnetic medium [4], which can generate coherent thermal emissivity [4,7,8] for energy utilizations. Magnetic polaritons in a nonmagnetic medium begin to tail off at relatively low frequencies and become possible in the visible spectrum owing to advances in the field of metamaterials [9]; such as split-ring resonators [10], film-coupled metamaterials [4], paired nanorods and nanostrips [11], metafluids [5,9] and nanoclusters [12–15]. Because film-coupled metamaterials and gratings have been intensively discussed, we indicate that MPs can be excited in an isolated multilayer nanoshell. Most studies on multilayer nanoshells have focused on the excitations of SPP and the interaction between different plasmon modes [3,16–19], but few have investigated the behavior of MPs in a single multilayer nanoshell.
In recent years, self-assembled nanoparticle clusters have been a hot topic of research in particle science and technology [20–25]. The interaction of SPPs supported by metallic nanostructures of more elementary shapes can be well described by the hybridization mode [3], similar to the hybridization of the atomic orbitals. In a nanoparticle cluster, the plasmons are distributed over the entire structure owing to interparticle interactions. To describe the plasmons in the nanoparticle clusters, linear combinations of the individual plasmons have been introduced analogous to the linear combinations of atomic orbitals, known as the 'group theoretical approach' [26]. The plasmons produced by nanoparticle aggregates possessing symmetry are described in terms of linear combinations of the plasmon modes corresponding to irreducible representations of a point group. In that approach there exists interactions between multipole modes but no mixing, and is an approach that was commonly used in the studies of plasmons in nanoparticle clusters [27–30]. Previous studies of nanoparticle clusters have mainly focused on the excitations of SPPs [28,31–34], of Fano-like plasmon resonances [29,30,35–37] and of left-handed materials and cloaking [10,12,24], but those studies were rarely conducted using visible light absorption of nanoparticle clusters with potential solar energy value.
This paper is organized as follows: first, we numerically study the behavior and effects of MPs in a single multilayer nanoshell using the finite difference time domain (FDTD) method. We indicate that an isolated Al@Al2O3@Al multilayer nanoshell can support MPs, which has potential applications in solar-based direct steam generation processes. Second, we employ a multilayer nanoshell trimer, which is an equilateral triangle-shaped aggregate of multilayer nanoshells, to investigate the coupling effects of multilayer nanoshells and the collective behavior of the cluster. Finally, the thermal absorption via magnetic responses are exposed and studied by adding metallic nanoparticles. The Al@Al2O3@Al multilayer nanoshell enhances the thermal absorption in the nanoparticle trimer and the collective behavior of the MPs is different from that of SPPs.
2. Numerical method
All of the calculations performed were covered with an aqueous embedding medium (n = 1.33) and the excitation sources were plane waves. Figure 1(a) shows the Al@Al2O3@Al multilayer nanoshell under investigation, and we note that aluminum was chosen as the metallic material because of its relative abundance. The radii of the core, the middle alumina layer, and the outer shell were r1, r2 and r3, respectively. We considered trimers composed of multilayer nanoshells (r3 = 80nm) with a 6 nm interparticle spacing and with orthogonal or tangential excitations. Because a concrete picture of the SPP has been presented in previous works, in this paper the SPP was employed to indicate the accuracy of the simulation work. The SPP can be excited by a transverse electric wave in the surface between magnetic layers 2 and 3 when:
where kinc is the normal component of the wavevector of the media, μ is the relative permeability [4], and the subscripts 2 and 3 indicate the magnetic layer. The electromagnetic wave with a wavevector k parallel to the Y-axis was incident onto the structure at an in-plane polarization angle θ, which is defined as the angle between the Z-axis and the magnetic field (H) vector. The trimer discussed in this paper belongs to the D3h point group, which supports nine dipolar displacement modes matching the nine degenerate dipolar degrees of freedom of the structure. The dipolar displacement of trimer can be described in the orthonormal basis set of nine modes such that:where is a 9-dimensional vector that describe the dipolar displacement of 3 nanoparticles, is symmetry adapted coordinates(SAC) predicted by group theory with the same dimension as , is the complex factor for . Note that not all modes have negligible weight in the overall dipolar displacement vector. As has been discussed in Ref [29], only two SACs must be considered in the resonance conditions studied, known as magnetic and electric dipole resonance (Fig. 1(d)). Two SACs are employed to qualitatively discuss the resonance conditions of trimer. As the magnetic field of the incident light is aligned with the magnetic dipole of the structure, the magnetic and electric dipole resonances are both excited with tangential excitation(Fig. 1(b)), in contrast, for orthogonal excitation(Fig. 1(c)), only the electric dipole resonance is excited. One finds that in tangential case, and , while in orthogonal incidence . Numerical simulations using FDTD method are performed using a mesh with a maximum element length of 3nm. Optical constants of both Al and Al2O3 were obtained from Palik’s data [37]. In this paper, the porosity () is defined as the area ratio of 14 evenly distributed hemispherical holes and outer shell, such that:where r4 is the radius of hemispherical holes in the surface, as shown in Fig. 1(e). The near-field spectrums are obtained by monitors defined as single FDTD cells at the certain positions discussed. In this paper, normalized field strength used in the near-field spectrums are defined as time average field strength with expressions as or .
Fig. 1 Schematic structure of nanoparticle (a) Midsectional view of Al@Al2O3@Al multilayer nanoshell. (b) Incident field for tangential excitation. (c) Incident field for orthogonal excitation. (d) Electric and magnetic dipole resonance. (e) Porosity model of multilayer nanoshell. Observation planes for the electromagnetic field distribution inside the (f) single nanoparticle (g) and tirmer.
3 Results and discussion
3.1 Absorption of isolated nanoparticles
The spectral absorption of the isolated Al@Al2O3@Al multilayer nanoshell (MN1) with r1/r2/r3 = 40/69/80 nm is presented in Fig. 2(a), and for comparison the spectral absorption for an Al nanoparticle with a diameter of 160 nm (AlN) is also plotted, which in general increases with wavelength. With the addition of a dielectric layer, two strong absorption peaks arising from MPs occur at wavelengths of 430 and 651 nm, respectively labeled as MPE1 and MPH1.The overall absorptance is raised from 0.27 to 0.46 at MPE1 and from 0.43 to 0.65at MPH1. To better understand the excitation of MP and SPP in nanoparticles, we investigate Al@SiO2@Al multilayer nanoshell (MN2) r1/r2/r3 = 40/69/80nm and Au@SiO2 nanoshell (AuN) with r1/r2/r3 = 0/60/85nm (exactly the nanoshell in Ref [2]. which exhibited remarkably high efficiencies in steam generating). It can be observed that both of the absorption peaks, MPH2 (λ MP = 537nm) and MPE2 (λ EP = 387nm, not plotted) appear for MN2. The higher absorption of AuN below λ = 600nm is associated with the bandgap transition of Au [8], beyond that wavelength region, the absorption decrease with wavelength. While the addition of dielectric shell in the metallic Al nanoparticle enhance the absorption of MN1 aboveλ = 600nm, indicate the mixture of MN1 and AuN might become a potential full-wave optical emission nanofluid. By comparing spectral absorption of MN1 and AuN, we can indicate the potential value of Al@Al2O3@Al multilayer nanoshell in solar energy utilization, because the two nanoparticles appear to be equally matched in absorption ability whereas MN1 is made of an abundant material.
Fig. 2 (a)Spectral absorption properties for Al@Al2O3@Al multilayer nanoshell (MN1), Al@SiO2@Al multilayer nanoshell (MN2), Al nanoparticle (AlN) and Au@SiO2 nanoshell (AuN). (b) Spectral absorption of MN1 with perturbed parameters.
According to the Mie theory, the resonant absorption associated with SPP excited at the surface of a metallic nanoparticle is nearly independent of the nanoparticle diameter [44], so the absorption peak (labeled as SPP with resonance wavelength λ SPP = 633nm) caused by the excitation of SPP in the interface between Au and SiO2 (with relative error e = 2.0% compared with Ref [3]. and e = 1.6% compared with Ref [22].) indicates the accuracy of numerical method. Recent advancements in the chemical synthesis of metal nanostructures have provided several methods, such as the direct-packed sol-gel method [2] and the Stober method [3], to prepare the proposed metal-dielectric-metal layered structure. In reality, however, it is very difficult with any process to maintain precision in the nanostructures. The spectral absorption of MN1 with a perturbed r1 and r2 are plotted in Fig. 2(b) to study the effects of fabrication tolerance, wherein only one parameter is changed to be different from the MN1 in Fig. 2(a). For the effect of radius of metallic core, the absorption peak move to longer wavelength as r1 or r2 increases. Note that even with enormous perturbations on Al shell (), the multilayer shell could maintain the trench on absorption enhancement. These findings imply in real fabrication the specific optical property could be approached.
3.2 Excitations of MPH and MPE in MN1 and effect of area porosity
The distribution of the electromagnetic fields at different mid-sections inside MN1 is illustrated in Fig. 3 for absorption peaks associated with MPs arising from the magnetic field (MPH) or from the electric field (MPE), where the arrows in the figure symbolize the electric field vectors and the contour represents the near-field distributions of the magnetic or electric field strength. At the MPH (Fig. 3(a)), the magnetic field is enhanced in the dielectric shell along the H-direction for the following reason: The dipole moment of the metallic core opposes the incident electric field according to Gauss’s law, and the dipolar metallic core induces an anti-parallel electric current loop in the dielectric shell along the H-direction. The dielectric shell functions as a capacitor while the metallic shell and core function as inductors to form a resonant LC (inductor/capacitor) circuit that produces anti-parallel currents (shown in Fig. 3(e)), and thereby produces a diamagnetic response [4]. Drifting of current or movement of charges causes inductances at the metallic core and at the outer metallic shell. Since displacement current is formed in the dielectric shell, capacitor can be added. Thus magnetic resonance occurs at the total impedance of the circuit is zero with wavelength expressed as:
Fig. 3 Electromagnetic field distributions for multilayer structures. (a)Electromagnetic field distributions at MPH in the midsection of MN1. (b)&(c) Electromagnetic field distributions at MPE in the midsection of MN1. (d)A zoom in view of Fig. 3(c). (e)The equivalent LC resonant circulating current.
However, accurate analytical expressions for each inductance and capacitance in the LC model for a mutilayer nanoshell is not as simple to obtain as those for gratings because the nonuniform charge distribution on the surface makes it challenging to predict the resonance condition. Even if the resonance wavelength of MPE and MPH share the same LC model, the distribution of the charge wave at a specific wavelength could change the expressions of the inductance and capacitance so that two different MP modes are observed. The coupling of the metallic core and the diamagnetic response causes an MP in the interface between the metallic core and the dielectric shell with the magnetic field greatly enhanced, which is similar to the behavior of the magnetic resonance previously observed in film-coupled grating structures [4,39,40,42,43]. At the MPE resonance (Fig. 3(b)), the magnetic field is enhanced in the dielectric shell along the E-direction, in contrast to the MPH. Another mid-section view (k-E plane) of the MPE resonance (Fig. 3(c)) and a zoomed-in view (Fig. 3(d)) are also employed. For the excitation of the MPE, arrows symbolize the opposing electric field vectors in the metallic core and the dielectric shell, while the contour shows the alternating strength for the magnetic and electric field. An anti-parallel electric current loop in the dielectric shell is also observed, similar to the MPH. In this case, the dipolar metallic core with dipole moments opposed to the incident E vector suppress the electric field in the dielectric shell along the E-direction, and an MP is correspondingly excited because of the law of energy conservation. Next, the dipolar metallic core excites MP with relatively weak strength compared with the incident electromagnetic field, creating an enhanced magnetic field localized in the interface between the metallic core and the dielectric shell. For the MPH, oscillations of the dipole moment generate an anti-parallel electric field, and the MP is excited as a diamagnetic response to the incident wave. For the MPE, however, the MP is excited by the destructive interference between the metallic core and the incident E field, so the differences in the electromagnetic field and the resonance wavelength are observed.
By changing the radius of the hemispherical holes (r4) in the surface, various values of the porosity as defined in Eq. (3) are studied. Table 1 summarizes the value of r4 and porosity β.
Table 1. Relation between porosity and the hole size
Contour plots of spectral absorptance as a function of porosity are calculated for MPE1 and MPH1 as shown in Figs. 4(a) and 4(b) respectively. In Fig. 4(a), a strip like resonance band is observed for MPE1, that the main reason is the hemispherical holes cause red shift in resonance condition. The wedge like resonance band observed in Fig. 4(b) indicating that the hemispherical holes cause red shift as well as band broaden for MPH1. Resonance conditions are plotted as a function of porosity in Figs. 4(c) and 4(d) respectively. Clearly, both the MPE1 and MPH1 resonance wavelengths increase in a near-linear fashion with the porosity. The effect of porosity upon the resonance condition can be qualitatively understood with the aid of the LC model, where the hemispherical holes in the outer surface increase the inductance at the outer metallic shell Lshell, but affect Lcore and Cshell only slightly. Therefore, the surface porosity affects the resonance between the dioplar core and the incident field and leads to the redshift of MPE1 and MPH1.
Fig. 4 Contour plots of spectral absorptance of MN1 as a function of porosity for (a) MPE1 and (b)MPH1. Resonance condition as a function of porosity for (c) MPE1 and (d)MPH1.
3.3 Magnetic polartions in multilayer nanoshell trimer with tangential excitation
To better illustrate the excitation of the magnetic dipole resonance in an Al@Al2O3@Al multilayer nanoshell trimer (MNT, aggregate of MN1 with 6 nm interparticle spacing), the spectral absorptance of an Al trimer (AlT, aggregate of Al nanoparticles with a diameter of 160 nm) and of the MNT are shown in Fig. 5(a). Following the discussion of the excitation of magnetic dipole resonance in a metallic trimer reported by previous researchers [22,27,29], in this paper we label the resonance as MPT1 (λMP = 480 nm). In addition, the absorptance peaks observed for MNT are labeled as MPT2 (λMP = 520 nm) and MPH1 (λMP = 651 nm).
Fig. 5 Spectral properties of trimer (a)Spectral absorptance of Al@Al2O3@Al multilayer nanoshell trimer(MNT) and Al trimer(AlT). (b) Schematic diagram of the spatial positions discussed in the paper. (c) Spectral absorptance of AlT with and without nanoparticles added, Px indicate the position where the nanoparticles added and Nx indicate the type of nanoparticles added. The spectral absorptance of P4 with N1 is not plotted as it has no difference comparing to P2 with N1, because position P2 and P4 are symmetrical in the structure. (d) Near-field spectral at position of P3 and P4. Near-field distributions of electric (e) and magnetic (f) fields in the midsection of Al trimer at wavelength of 480nm,the bright part indicate enhancement of electromagnetic field while the dark part indicate the suppression comparing to the incident light. (g) Schematic drawing of LC loop for Al trimer and short circuit caused by small nanoparticle addition.
To discover the mechanism of the thermal absorption caused by the magnetic response in the trimer, small Al particles are added at various spatial positions within the AlT. Four particular spatial locations within the trimer are employed, as shown in Fig. 5(b), and are P1 (center of the triangle), P2, P3 and P4 (junctions between the particles). Two types of Al particles are used in simulation, namely N1 (30 nm diameter) and N2 (40 nm diameter), and because both types of particles have an extremely small volume compared with the Al nanoparticle in the trimer (0.6% for N1 and 1.6% for N2), we focus only on the change of the electromagnetic field in the area where we add Al nanoparticles and the small changes of spectral absorptance caused by these small Al nanoparticles. The spectral absorptance distributions for the Al trimer with N1 or N2 additions are plotted in Fig. 5(c), where it can be seen that small Al nanoparticles located in the center of the triangle affect the resonance condition little while those located in the junctions show strong influences.
The near-field spectra for tangential incidence are plotted in Fig. 5(d), where it can be seen that the enhancements at point P3 and P4 are well correlated with the spectral absorptance peak of AlT. The excitation of the electromagnetic resonance causes the enhancement of electric field in the junctions between two metallic nanoparticles previously discussed in Ref [29], and the contour plots representing the near-field distributions of the electric (Fig. 5(e)) and magnetic (Fig. 5(f)) fields are similar to the near-field distributions of the Ag trimer with magnetic dipole resonance excitation shown in Ref [27]. The resonance within the Al trimer can be described as a closed loop of nanoinductors and nanocapacitors [22] (as shown in Fig. 5(g)), in which the metallic nanoparticles play the role of inductors and the junctions between nanoparticles play the role of capacitors. The addition of small nanoparticle in the gap changes the expression of L and C in LC circuit. But it's extremely challenging to quantitatively obtain the change of nonuniformity charge distribution in the surface and expressions of L &C, thus a simple model as short circuit of a single capacitance is employed to describe the change of capacitance & inductance in the LC circuit and absorption spectrum.
The small Al nanoparticles in the junctions cause a short circuit of the nanocapacitors so that the resonance condition and the spectral absorptance change greatly even though the nanoparticle is very small, but the nanoparticle in the center of triangle changes the resonance condition only slightly even as the diameter of nanoparticle increases becuase it has little influence upon nanoinductors and nanocapacitors comprising an LC loop. The time-varying incident light excites a rapid charge-discharge process in the equivalent capacitor, and so the short circuit causes enhancement of the dissipation and the redshift of the resonance condition. The remarkably high efficiencies reported in Ref [2]. can be explained by the excitation of an SPP that can generate high temperatures in the surface of the nanoparticles without heating the bulk fluid, and the resulting enhanced electric field in the junction known as a hot spot [32,44] shows great potential value in solar steam generation applications because the rapid charge-discharge process and the hot spot in the junction indicates tremendous heat generation, which can even enhance the efficiency.
Contour plots of the spectral absorptance (Fig. 6(a)) and the resonance condition (Fig. 6(b)) as a function of r2 is produced to investigate the MPTs. The dielectric shell causes a red shift and absorption enhancement owing to the excitation of the MP in the trimer. The distributions of the electromagnetic field at the excitation of MPT2 are plotted in Fig. 7(a), where it can be seen that the electric field is greatly enhanced in the junctions, and the ordered electric vectors in the plot indicate the dipolarization of the metallic core. A midsectional view of the second nanoparticle shows an enhanced magnetic field associated with the MPE that is well correlated to the dipole moment in the magnetic dipole resonance mode, wherein the coupling of the dipolar metallic core and the incident field result in an enhancement of the magnetic field in a direction oblique to the incident E vector. Besides MPE and MPH as discussed above, the enhanced electric field with opposed directions in the junctions associated with the first nanoparticle induces an anti-parallel electric current loop in the dielectric shell and causes an MP.
Fig. 6 Effect of particle radius on spectral absorptance (a) MPT as a function of r2 (b) Resonance condition.
Fig. 7 Near-field distributions with and without pores of electric (a) and magnetic (b, c) fields in the midsection of MNT at wavelength of 520nm, the bright part indicate enhancement of electromagnetic field while the dark part indicate the suppression comparing to the incident light, the arrows symbolizing electric field vectors. (d) Midsectional view of the 2nd nanoparticle without pores at five specific wavelengths to investigate phase shift between electric and magnetic mode.
It is interesting to discuss the inter-particle coupling in the nanocluster, and therefore the midsectional views of the second nanoparticle at different wavelengths are employed to indicate the phase shift between the electric and magnetic dipole resonance in the trimer with Tangential Excitation. As shown in Fig. 7(d), a T-like enhanced magnetic field is observed at wavelengths 430 and 480 nm, indicating the excitation of both electric and magnetic modes, as the dipolar metallic core enhances the magnetic field in the dielectric shell for MPE. At the wavelength of 200 nm, the electric vectors are disorganized and no obvious magnetic field enhancement is observed, but the electric vectors become ordered in the metallic core at a 430 nm wavelength, where both the electric vectors and the magnetic enhancement indicates a comparable electric and magnetic mode influence. At 480 nm, the crescent-like arrangement of the electric vectors indicate the shift between two modes, while the electric vectors are directed in a single orientation at 520 nm (MPT2), indicating the domination of magnetic mode that persists at a wavelength value of 660 nm. There is mutual exclusion between these two modes, and the magnetic mode needs to become the dominant one to make the trimer an electromagnetic wave container. Because the electromagnetic wave is caught in the structure, the dielectric shell can even enhance the thermal emission.
Futhermore, the field distributions of trimer with porosity are provided. The influence of pores on the overall field and polartions in the dielectric shell is insignificant, that is beacuse the pores in the outer surface increase the equivalent inductance of metallic shell but don't change the resonance mode of single nanoparticle, which has been discussed in 3.2. However, the hot-spot at position P3 disappears as the pores are placed face to face over the gap. The hot-spot is generated by the rapid charge-discharge process in the equivalent capacitor between nanoparticles, thus the break of capacitor lead to the disappearance of hot-spot.
Because the trimer plays the role of an electromagnetic wave container and the dielectric shell plays the role of a thermal emission promoter, MPs in a single nanoparticle cause weakening of the electromagnetic field outside. Therefore, the addition of a dielectric shell may weaken hot spots that generate at certain wavelengths while it may intensify coherent absorption in the wide band.
Midsectional views of the first nanoparticle at MPH1 are plotted in Fig. 8(a), wherein the first nanoparticle shares great similarities with the isolated case (not shown). In the case of tangential excitation, the dipole moment is parallel to the incident electric field in the first nanoparticle, thus there are no differences between this and the isolated case. The dipole moment of the second nanoparticle is oblique to the incident electric field, so the electromagnetic field distributions exhibit the coupling effect of both MPE and MPH (Fig. 8(b)). The near-field spectra of position P3 for MNT at two wave bands are plotted in Figs. 8(c) and 8(d), wherein spectral valleys correlated with MPE1 and MPH1 are observed. Contour plots of the spectral absorptance for MNT as a function of θ is plotted in Fig. 8(e), where it can clearly be seen that the resonance condition of magnetic dipole resonance exhibits great polarization sensitivity. When a time-varying electromagnetic field is incident on the trimer, an induced magnetic field is excited with its magnetic moment directed opposite to the incident magnetic field. To achieve greater diamagnetism, the trimer should appropriately guide the induced conduction current loop. The nanoparticles and the junctions between them require that the incident electric field parallel to the plane of the equilateral triangle produces a resonant circulating current, so the absorption peak correlated to the magnetic resonance vanishes as the incident electric field become perpendicular to this equilateral triangle plane.
Fig. 8 Near-field distributions of electromagnetic field at wavelength of 651nm (a) Midsectional views of the 1st nanoparticle at MPH1. (b)Midsectional views of the 2nd nanoparticle at MPH1. (c)&(d) Near-field spectral at position of P3 for MNT. (e) Contour plots of spectral absorptance of MNT as a function of polarization angle θ.
The near-field spectra of position P3 for MNT indicate the excitation of the magnetic resonance in a single nanoparticle, and so the electromagnetic field distributions are plotted to investigate the collective behavior in MNT in Fig. 9. Excitation of MPE1 requires a dipolar metallic core, but during tangential excitation only the magnetic mode produces an equivalent dipole in the first nanoparticle. Because the magnetic mode has not become the dominant mode at 430 nm, the metallic core cannot excite MPE, though the comparable electric and magnetic modes excite a T-like enhanced magnetic field oblique to the incident field at 430 nm. The right part of the second nanoparticle faces the third nanoparticle where the outside electromagnetic field is weaker, so the magnetic field enhancement exhibits a left-right asymmetry. Because the trimer needs magnetic dipole resonance excitation to become an electromagnetic wave container, the excitation of MPE1 in a single nanoparticle cannot promote absorption greatly with no spectral peak at 430 nm.
Fig. 9 Near-field distributions of electromagnetic field at 430nm wavelength, the bright part indicate enhancement of magnetic field while the dark part indicate the suppression comparing to the incident light, the arrows symbolizing electric field vectors for (a) isolated Al@Al2O3@Al multilayer nanoshell, (b) 1st nanoparticle, (c) 2nd nanoparticle.
3.4 Magnetic polartions in multilayer nanoshell trimer with orthogonal excitation
The spectral absorptance of MNT and AlT with orthogonal excitation are plotted in Fig. 10(a), where the absorptance peaks are labeled EPT1 (λEP = 411 nm), EPT2 (λEP = 469 nm) and MPH1 (λMP = 651 nm). To understand the mechanism of thermal emission in AlT with orthogonal excitation, we add small metallic nanoparticles to the AlT in the same fashion as the tangential excitation case. Unlike the tangential excitation case, no obvious change in the resonance condition is observed either in the junction between the nanoparticles or at the center of the triangle when small Al nanoparticles are added. With tangential excitation, nanoparticles and the junctions between them respectively play the roles of inductors and capacitors, forming an equivalent LC loop to guide the induced conduction current loop. In orthogonal excitation, however, excitation of the electric dipole resonance cannot guide the induced conduction current loop, so the small Al nanoparticles in the junctions have little influence upon the resonance condition. The near-field spectra for specific positions are plotted in Fig. 9(b), where enhancements correlated with spectral absorptance peak EPT1 is observed in the same fashion as the Ag trimer discussed in Ref [29], indicating the excitation of electric dipole resonance. Furthermore, the spectral absorptance exhibits polarization insensitivity in the same fashion as the Ag disc trimer discussed in Ref [28], so we only discuss the θ = 0 case in the orthogonal excitation.
Fig. 10 (a) Spectral absorptance of Al@Al2O3@Al multilayer nanoshell trimer (MNT) and Al trimer (AlT). (b) Near-field spectral at position of P3 and P4.
Near-field electromagnetic distributions of MNT at the MPH1 resonance is investigated, where it is observed that the electromagnetic field distribution of the first nanoparticle shares a great similarity to the isolated MN1 except the center of the bright part at the MPH1 resonance deviates slightly at the center (as shown in Fig. 11(b)). In electric dipole resonance, the first nanoparticle is not dipolar so the resonance condition is quite similar to the isolated case, but the addition of two dipolar nanoparticles possessing a mutual tilt of electric moments could enhance the anti-parallel current loop near the center so that a slight deviation would be observed. For the second nanoparticle, as shown in Fig. 11(a), an ordered arrangement of the electric vectors indicate the polarization of the metallic core with an equivalent dipole moment directed to the center of the triangle in the E-H plane. Because the dipole moment is oblique to the incident electromagnetic vector, the induced anti-parallel electric current loop and the enhanced magnetic field is correspondingly oblique to the incident E-H vector. As shown in Fig. 12, near-field spectral valleys correlated to MPH1 are observed that indicate excitation of MPH1 in the single nanoparticle, and the enhanced thermal emission and electromagnetic field outside the nanoparticle is weakened correspondingly.
Fig. 11 Near-field distributions of electromagnetic field at 651nm wavelength. (a) Midsectional views of the 1st nanoparticle at MPH1. (b)Midsectional views of the 2nd nanoparticle at MPH1.
Hybridization [3], wherein the similarity between the electron wave and the electromagnetic wave is used, describes the surface plasmon polarization of the trimer and other arbitrarily-shaped complex nanostructures and has been intensively discussed in previous works. Although there are fundamental differences between surface plasmon polarization and magnetic polarization, we claim that the basic concept of ‘hybridization’ is also suitable for magnetic polarization in a multilayer nanoshell trimer. Analogous to SPP, the interaction between single nanoparticles results in the splitting of the magnetic polarization into two new modes: the shortwave ‘bonding’ mode and longwave ‘antibonding’ mode. Figure 13(a) depicts the spectral absorptance of MNT with orthogonal excitation, wherein the absorption peaks are labeled EPT2 (λEP = 469 nm) and EPT3 (λEP = 393 nm), while the more basic resonance modes MPE1 (λMP = 430 nm) for the isolated multilayer nanoshell and EPT1 (λEP = 411 nm) for the metallic trimer are also plotted for comparison. Clearly, the interaction between MPE1 and EPT1 results in a red shift of the EPT2 mode and a blue shift of the EPT3 mode. We report the existence of a shift between basic modes and the interaction between them, resulting in a hybrid electromagnetic distribution.
Fig. 13 (a) Spectral absorption properties for Al@Al2O3@Al multilayer nanoshell trimer (MNT). (b) An energy-level diagram describing the magnetic polariton hybridization resulting from the interaction between the single multilayer nanoshell and metallic trimer. The two resonance modes are EPT3(bonding) mode and EPT2 (antibonding) with magnetic field contour and electric vectors also plotted. (c) Resonance condition as a function of r1 for EPT2, EPT3 and MPE1, fixed wavelength electric dipole resonance EPT1 is plotted for comparison.
Mid-sectional views of MNT for the EPT2 and EPT3 mode are plotted for comparison in Fig. 13(b). Both the EPT2 and EPT3 modes exhibit the hybridization of MPE1 and EPT1, and the enhanced magnetic field is observed to be oblique to the incident electric field with opposing electric vectors. The enhanced magnetic field in EPT3 is more broad and bright while the electric vectors in EPT2 are more disordered. To excite an enhanced magnetic field that is broad and bright requires an intensively polarized metallic core with a forced electric dipole and, in the orthogonal excitation, only electric dipole resonance can generate such a phenomenon. Therefore, we claim that the EPT1 mode dominates the resonance condition of EPT3. For EPT2 resonance, the poorly polarized metallic core cannot excite the bright and broad magnetic field like EPT1 can, and therefore the excitation of MPE1 in the single nanoparticle plays the main role of thermal emission enhancement. To verify our hypothesis, we plot the resonance conditions of the multilayer nanoshell trimer as a function of r1 in Fig. 13(c), where the r1 = 40 nm case is the MNT case we discussed earlier in the paper. An increase in the metallic core diameter leads to the red shift of the MPE1 mode for the isolated multilayer nanoshell, and the EPT2 mode for the trimer exhibits red shifts correspondingly at longer wavelengths indicating the dominance of the MPE1 mode in EPT2 resonance. Because the electric resonance mode is independent of the metallic core, there is only a slight oscillation observed in the resonance condition of EPT3, further confirming the shift between the two basic modes and the dominance of the EPT1 mode.
4. Conclusions
This work demonstrates that a dipolar metallic core can excite magnetic polaritons in the dielectric shell of a multilayer nanoshell via the visible region. Two modes of magnetic polaritons are identified, and the electromagnetic field distribution in the dielectric shell results in thermal emission enhancement compared with that of a metallic nanoparticle. The electromagnetic field distribution and near-field spectra are used to identify the polarization of the trimer and the shift between the electric and magnetic dipole resonances. The trimer exposed to tangential excitation can support an equivalent LC current loop, and the junction between the nanoparticles can enhance a hot spot with potential solar vapor-generating applications and can greatly influence the resonance condition. The trimer exposed to a tangential incidence requires a dominant magnetic dipole resonance mode to become an electromagnetic wave container, and the dielectric shell can even enhance thermal emission in the structure. We introduce the hybridization concept, which is used to describe the surface plasmon polariton in complex nanostructures, to understand the spectral splitting caused by the interaction between the multilayer structure and the nanoparticle cluster and verify our conclusion. The influence of the porosity and the polarization condition for the trimer are discussed to facilitate spectral absorptance tailoring of the nanoparticles/clusters. This study will facilitate the development of self-assembled nanoclusters in solar energy applications and enhance the magnetic response in the optical region.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Nos. 51276049, 51421063), the FoK Ying-Tong Education Foudation of China (No. 141055) and the program for New Century Excellent Talents in University (No. NCET-13-0173). A very special acknowledgment is made to the editors and referees whose constructive criticism has improved this paper.
References and links
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