1. Introduction

Recent development in the fabrication, simulation and the optical characterization of metallic nanostructures has provided rich opportunities to study behaviors of collective oscillations of surface free electrons, known as surface plasmons, excited by incident electromagnetic waves [1]. In complex plasmonic nanostructures, many intriguing optical responses are results of hybridization among plasmons arising from individual components of the nanostructures [2,3]. This hybridization has been shown to give rise to a wide range of coherent phenomena, such as artificial magnetism [4–13], electromagnetically induced transparency (EIT) [14] and Fano Resonances (FRs) [15,16] which can find analogues in systems as diverse as atomic physics [3], coupled mechanical oscillators [17] and resonant electrical circuits [18]. Novel optical properties of these phenomena in plasmonic structures provide great prospects for various nanophotonics applications.

Metal-Dielectric-Metal (MDM) structures are widely used in obtaining artificial magnetism [4–13,19–21]. Well studied MDM structures are nanosandwiches [4,6,7,9,13], photonic cavities [10], metamaterial molecules [8,12] and fishnets [11,19–21]. In such structures, when anti-parallel moments in the top and bottom metallic layers oscillate out of phase, the electric fields are very strong with opposite directions at two sides of the dielectric layer. Therefore, a magnetic moment appears inside the dielectric layer and pushes magnetic resonance to emerge. This phenomenon leads to another type of plasmon oscillation, so called magnetic plasmons. On the other hand, 2D planar structures, such as ring-disk cavities, Dolmen structures, and nanoshells, being introduced to show coherent phenomena, such as EIT and FR [14,15,18], are based on the electric plasmons driven by an electric field. Such structures are usually used to generate dipole and high order electric modes, which can have constructive and destructive interferences.

Among planar plasmonic structures, plasmonic oligomers are of high interest [22–33]. Oligomers are aggregated nanoparticles with sufficiently small inter-particle gaps, which have been proved as excellent candidates to generate FR in visible and near infra-red (NIR) range. Such effect is due to the coupling among anti-parallel modes arisen from the neighboring metallic nanoparticles along the lateral direction at certain wavelength ranges. In fact, this classical FR in oligomers is a result of hybridization among electric plasmons. Such FRs in this paper are called as electric FRs. Recently, Halas and associates have shown that certain arrangement of planar oligomers can also be used to excite a magnetic resonance [34,35] in addition to the electric FR. Multi-heptamers investigated by Liu et al. [34,35] give rise to anti-parallel magnetic dipole moments [36], which are attributed to the circulating current in each individual heptamer.

In this paper, we introduce novel MDM oligomers which can excite both electric FR and magnetic resonances with high tunability of the magnetic resonance. Previously, it has been shown that constructional manipulation in regular MDM structures led to change in the position and intensity of both magnetic and electric surface plasmon resonances [4–13,19–21]. But in the MDM oligomers, one can tune the spectral position and intensity of magnetic resonance, while the electric resonance is kept constant. It is a major advantage of the MDM oligomers as compared to the previous studied artificial magnetic cells [4–13,19–21]. This ability of MDM oligomers provides rich opportunities to induce interference among electric and magnetic resonances once these two resonances overlap. It leads to the emergence of an additional FR as compared to classical electrical FR in regular oligomers. This new FR is based on the interference of magnetic-electric resonances and we call such FR as magneto-electric FR. Meanwhile, monitoring the absorption behavior in such structures proves a remarkable peak corresponding to the position of magneto-electric FR. It makes the MDM oligomers as functional artificial devices with capability to exhibit both electric and magneto-electric FRs at the same time, which may find potential applications in optical spectra modulation, non-linear optics, higher-order harmonics generations, slow-light and bio-chemical sensing [2,3,15,16,34–37].

2. Methodology

In the present work, the optical properties of the MDM oligomers were investigated through numerical simulations. Lumerical FDTD solutions were used for the 3D finite-difference time-domain (FDTD) simulations. Cross section spectra of various MDM oligomers on glass substrates were studied at wavelength ranging from 400 to 1300 nm. A total field scattered field (TFSF) plane wave was applied as the source. Two boxes of monitors, one in the total field region and the other in the scattered field region, were defined to calculate the absorption and scattering cross sections. The extinction cross section is defined as the sum of absorption and scattering cross sections. Therefore, the extinction cross section is equal to 1- transmission [22–35]. Meanwhile, in order to avoid coupling among optical diffraction arising from individual unit cells with periodic-type boundary [38], optical properties of the MDM oligomers in this research were investigated in isolated boundary. Perfect matched layers were used as an effective absorbing boundary condition. The dielectric functions of Au structures and glass substrate are referred to the experimental data of Johnson and Christy [39] and Palik book [40], respectively.

3. Results and discussion

Figure 1(a) illustrates artificial images of designed Au-SiO₂-Au oligomers, which consist of a central MDM element surrounded by several satellite MDM components. The thickness for the bottom and top Au layers are 20 nm, while SiO₂ layer is 10 nm and the radius for each single disk is 70 nm. The inter-particle distance between the central MDM element and each satellite component is 20 nm. Dimensions of disks and inter-particle gaps are chosen based on previous optimizations [25]. Figures 1(b) and 1(c) show simulated extinction cross section spectra of both planar single layer and MDM oligomers, respectively, corresponding to Fig. 1(a). As can be seen, all planar oligomers exhibit a single electric FR at around 800 nm. The physics behind this resonance is due to the interference of electric plasmon moments, which has been widely explained before [22–32]. However, once the configuration changes to the MDM oligomers, the signature of another resonance as a small peak appears in the NIR range. The emergence of significant magnetic field intensity in the middle dielectric layer shown in Fig. 1(d) reveals that this peak is due to appearance of magnetic flux in the dielectric layer. It is in direct agreement with physics of magnetic resonance generation in MDM structures [4–13].

 

Fig. 1 (a) 3D illustration of the MDM oligomers consisting of 20 nm Au layers at the bottom and top and 10 nm dielectric SiO₂ layer at the middle. The extinction cross section spectra of (b) planar single layer (single Au layer at 20 nm thickness) and (c) MDM oligomers corresponding to (a). (d) H intensity plots in dielectric middle layers at the positions indicated by arrows in (c), which correspond to the magnetic resonances.

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Figure 1(d) plots magnetic field intensity distribution in the middle dielectric layer at the position of magnetic resonance as indicated by arrows in Fig. 1(c). The existence of remarkable magnetic field in all elements can be clearly observed in these plots. Interestingly, some differences among the magnetic intensities in individual elements can be seen, which have direct agreement with direction of H-component of incident light. For further consideration, pentamers are chosen due to their unique format of anti-parallel dipole pattern in each layer. In planar pentamers, antiparallel dipole modes are arisen from three middle elements versus the elements at the top and bottom [22,25,27,28,32]. It is unlike other planar oligomers, in which the anti-parallel modes are mostly arisen from central element versus outer satellite elements [22–32]. In MDM pentamers, higher amount of H field intensity can be seen in the elements at the top and bottom. Previous detail research works on pentamers have revealed that at the right wing of electric FR at a longer wavelength, E-component of incident light mostly excites electric plasmons at three middle horizontal elements and the elements at the bottom and top are less excited [27]. But as can be seen at the position of magnetic resonance, three middle vertical disks have more contribution to push magnetic flux in dielectric layers. Keeping in mind that generally anti-parallel electric modes, which push magnetic flux in between, are introduced as a responsible factor for magnetic resonance generation. These electric modes are the result of plasmon excitation by E-component of incident light. But observations in Fig. 1(d) reveal the need to study the influence of both E- and H-components of incidence in the process of magnetic resonance generation.

In order to get physical insight into this magnetic resonance and the contribution of E- and H-components of incident light on electric and magnetic plasmons, we applied a simple but clear proof. With pentamers as an example, we changed the incident light angle to study the contribution of E- and H-components of incident light in exciting electric and magnetic resonances. Figure 2(a) illustrates the extinction cross section spectra of the MDM pentamers with the same dimensions as shown in Fig. 1 but different incident angles. To avoid the influence from the substrate [41,42], the glass substrate is removed temporarily in this simulation. Extinction spectra at different incident angles are shown in Fig. 2(a). As it has been shown previously [22,28] at normal incidence, E-components of light excite electric plasmons in each metallic layer of pentamers, which leads to the appearance of electric FR around 700 nm (see black curve). Meanwhile, the H field intensities plots at the magnetic resonance of 1130 nm in the middle dielectric layer as shown in Fig. 2(b), reveals that at normal incidence, H and Hy intensities of magnetic field are identical while Hz intensity is very small. It agrees well with H-component of incident light along y-axis at normal incidence.

 

Fig. 2 (a) Extinction cross section spectra of the MDM pentamer with of 20 nm Au layers at the bottom and top and 10 nm dielectric SiO₂ layer in the middle at incident light angle of 0, 30, 60 and 90 degrees. Magnetic field intensity accompanied with its x and y components corresponding to (b) 0 degree and (c) 90 degree of incidence.

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Furthermore, once incident light is angled as shown in the inset of Fig. 2(a), the direction of E-component of incidence remains constant. But H-component divides into two components of Hy and Hz. Therefore, the contribution of Hy is less than the previous case. It affects excited magnetic plasmons, as can be seen in red curve, where the magnetic resonance is less excited. This trend is confirmed with further increasing of light incident angle. At 60 degree, very weak Hy-component of incident light only exhibits a shoulder in the extinction spectra (see blue curve), while at 90 degree magnetic resonance is totally disappeared (see cyan curve). In cyan curve, we do not observe considerable magnetic resonance, while H intensities plots with high magnification in Fig. 2(c) shows that even this small amount of H intensity is the contribution of Hz-component of incident light, which does not lead to the excitation of magnetic plasmon and magnetic resonance. Interestingly, it shows the analogy between H-components of incident light and H field intensity in the dielectric layer. It reveals the role of H-component of incidence in magnetic field generation in the dielectric layer. In fact, absence of magnetic resonance observed in cyan curve transmits the requirement of proper direction and intensity of incident H-component in magnetic resonance generation in addition to E-component. It should be reminded that in all considered cases in Fig. 2, E-component possess the same direction and intensity. Therefore, as can be seen at 90 degree of incidence (cyan curve), signature of electric FR which is based on E-component of incidence is still observable, while the pathway of light propagation affects the shape and position of this electric FR. However, the E-component is no longer able to generate magnetic flux when incident Hy-component vanishes.

Extensionally, we found that the MDM oligomers possess an excellent capability to tune the spectral position of magnetic resonance by changing the thickness of consisting layers while the spectral position of electric FR is kept constant. It provides a rich opportunity to induce an overlap between magnetic and electric resonances. It is a rare potential which allows not only exciting both FR and artificial magnetic resonance together, but also induces hybridization of these resonances for novel optical properties. Geometrical manipulation of other proposed structures, which exhibit magnetic resonance, can also tune the position of magnetic resonance, but simultaneously it changes the position of electric resonance [4–9,13], which prevents spectral overlap of electric and magnetic resonances. Figure 3 reveals the capability of hybridization of magnetic and electric resonances among MDM pentamers. Detail studies on planar single layer pentamers can be found in [22,27,28], where, it has been shown that around the position of electric FR in the extinction spectra, a weak fluctuation can be seen in absorption curve [27]. This trend is similar to asymmetric quadrumers [33] in which the existence of these absorption fluctuations are regarded as an evidence of FR. It has been shown that such absorption increase comes to existence due to the nature of appeared subradiant dark mode which is weakly lifetime broadened with a small decay rate due to nonradiative loss [3,15,16,27,33]. For the case of planar pentamers, a weak fluctuation can only be observed around FR since signature of FR is mostly formed by subgroups, which are efficiently excited at their spectral peak positions [27].

 

Fig. 3 (a) Extinction and (b) absorption cross section spectra of the MDM pentamers consisting of 20, 30 and 40 nm thick Au layer, respectively. Each set shows spectra corresponding to 10 (red curve), 20 (blue curve) and 30 (cyan curve) nm thick middle SiO₂ layers.

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We found that the interference between magnetic and electric resonances leads to emergence of another FR with much more obvious signature in absorption spectra. Figure 3(a) shows three different sets of MDM pentamers at different thicknesses of Au and dielectric layers. In all sets, an increase in the dielectric thickness leads to significant blue shift in magnetic resonance. Due to the similarity of the MDM structures with LC resonator models, a recall of basic LC rules can be used to explain the mechanism of this shift simply. It is well known that the resonant frequency of a LC resonator can be calculated by $\omega =1/\sqrt{LC}$, where C is capacitance and L the inductance of magnetic coil. An increase in the gap among coils leads to reduction in C value [43], increasing $\omega$ value. With this analogy, one can summarize that when the gap among metallic layers of MDM structures increases, the wavelength of magnetic resonance decreases.

Importantly, all spectra corresponding to the MDM pentamers shown in Fig. 3(a) reveal that the change in the dielectric thickness does not affect the position of electric FRs. This characteristic is highly useful in designing the spectrum to shift the magnetic resonance and induce interference between magnetic and electric resonances. The plots corresponding to different sets of MDM pentamers show that when the thickness of dielectric layer is equal to 10 nm, the magnetic resonance is sufficiently far from the wing of electric FR. It rarely can lead to interference among magnetic and electric resonances. But the increase of dielectric thickness to 20 and 30 nm leads to a spectral blue shift in the magnetic resonance. When this magnetic resonance gets close enough to the wing of electric FR, a signature of second Fano shape in extinction spectra comes to existence. This asymmetric Fano shape is more obvious in the MDM oligomers at thicker Au layers. To confirm that this Fano line shape is due to the appearance of FR, absorption spectra of all studied MDM pentamers in Fig. 3(a) are calculated as shown in Fig. 3(b). Meanwhile, the positions of absorption peaks are indicated with color dash lines in Fig. 3(b). Accordingly, the same wavelength positions are marked with the same color dash lines in extinction spectra in Fig. 3(a) for a better comparison of spectral behavior between extinction and absorption. As can be seen, around the position of the electric FR located at the shorter wavelength, a fluctuation appears in the absorption spectra, which is in agreement with previous explanations of electric FR [27,33]. The signature of this absorption fluctuation remains constant at all MDM pentamer sets. It is another evidence to show that different thicknesses in this system do not influence electric FR.

On the other hand, the position and intensity of this absorption peak prove clearly that when the magnetic resonance gets closer to the wing of electric resonance, the interference between these two resonances gets stronger, which enhances dark mode. Therefore, more portion of incident light gets absorbed. It introduces a new family of FRs in plasmonic oligomers based on the interference between magnetic-electric resonances rather than electric-electric resonances. When the thickness of dielectric layer is equal to 10 nm (see red curves), the magnetic resonance and electric resonance are very far from each other. Both extinction and absorption spectra experience a weak spectral peak due to the nature of magnetic resonance [4,6,7,9,10,13]. This trend can be seen in all sets of studied MDM oligomers with different thicknesses of Au layers. But when the thickness of dielectric layer increases to 20 nm, the magnetic resonance becomes sufficiently close to the electric resonance, which results in interference between these resonances (see blue curves). In these MDM pentamers with 30 and 40 nm thick Au layers, more intense absorption peaks can be observed around the second dip positions of extinction spectra at 857 and 818 nm, respectively. It is a signature of dark mode which is due to the coupling between superradiant and subradiant modes with less radiative loss and a small decay rate. It is in direct agreement with physics behind FR [15,16,27,33]. This trend can be seen in MDM pentamers with 30 nm dielectric thicknesses (see green curves) as well. Small observed differences between positions of absorption peak and extinction dip are due to the oligomeric configuration in which the interference among modes starts a few tens of nanometres before extinction dip [27,32]. Meanwhile, as can be seen, since the thicknesses of all Au layers are more than skin depth of Au (12 ~15nm [44]), the thickness of Au layers does not play as a significant role as the thickness of dielectric layer.

As can be observed, proposed MDM oligomers exhibit second FR with more observable signature in the absorption responses rather than extinction responses. It can find high potential applications as FR slow light devices, which are mostly based on the absorption enhancement. Meanwhile, such oligomers still exhibit regular classic electric FR which can find potential applications as filters. One should be noted here that, further increase in the thickness of dielectric layers will push the magnetic resonance to the wavelength window in which electric FR appears. Therefore, the complex resulting spectra may avoid MDM oligomers to be unique devices with capability to exhibit both electric and magneto-electric FRs.

4. Conclusions

In summary, magnetic resonance in the MDM oligomers is investigated. It is shown that in addition to E-component of incident light which drives electric plasmons, H-component of incident light also has a remarkable contribution to the emergence of magnetic flux in middle dielectric layer of MDM structures. It is established by angling the incident light which affects H-component contribution in plasmons excitations while E-component contribution remains constant. It is found that at 90 degree incident light, pure E-component is not able to induce magnetic flux since H-component is no longer effective. Furthermore, it is shown that changing the thickness of metallic and dielectric layers provides an opportunity to shift the magnetic resonance, while the position of classical electric FR of oligomers remains constant. It is in contrary with regular MDM structures in which typically magnetic and electric resonances are separated. Therefore, interference between magnetic and electric resonances in the MDM oligomers can be induced artificially. It gives rise to another FR, which possesses novel magneto-electric characteristics. The evidence of this magneto-electric FR in absorption response is much more observable than classic electric FR in planar oligomers. It makes the MDM oligomers as unique plasmonic devices, which possess both electric and magneto-electric FRs at the same time.