## Abstract

We experimentally demonstrated an approach based on dipole and dual-quadrupole coupling to construct a planar metamaterial supporting multi-spectral plasmon induced transparency. The structure consists of two short silver wires (dipole) and two long silver wires (dual-quadrupole). The in-plane coupling between the dipole and the dual-quadrupole leads to two transmission windows even in the absorbance linewidth of the dipole. This phenomenon is well described and understood by numerical analyses and a classical oscillator model.

© 2014 Optical Society of America

## 1. Introduction

Electromagnetically induced transparency (EIT) is a quantum interference effect that eliminates light absorption in an atomic media [1, 2]. This phenomenon allows for a spectrally narrow optical transmission window accompanied with extreme dispersion, which is highly desirable for sensing and slow light applications [3, 4]. Recent studies have revealed that EIT-like optical resonances can be obtained in plasmonic metamaterial systems at optical-radio frequencies [5–16]. In particular, since the concept of a plasmonic EIT analogue (plasmon induced transparency: PIT) has first theoretically been proposed [6], EIT-like resonances based on a dipole-quadrupole coupling [6, 9–11], that have sharp spectral features of the quadrupole resonance and therefore show extremely high sensitivity to structural or surrounding changes, are playing an increasingly prominent role in physics and applications. This single dipole-quadrupole coupling, however, induces a PIT effect at only single resonance. On the other hand, metamaterial systems supporting multiple coupled dipole-quadrupole can offer PIT responses at multi-spectral windows [17], which will open a new route toward metamaterial applications operating at multiple frequency domains. In general, the multi-spectral PIT resonances are observed in a complex layered (stacked) structure for multiple coupling [17, 18]. However, the small modulation depth in the resonances, as well as the fabrication of the complicated structures that is time-consuming and needs advanced techniques for surface planarization and layer positioning in multilayer stacking procedures, severely hinder the potential applications.

In this paper, we provide a first demonstration enabling construction of a planar metamaterial supporting multi-spectral PIT by utilizing terahertz metamaterials with in-plane dipole and dual-quadrupole coupling. The proposed structure consists of two short silver wires (dipole antennas) and two long silver wires (quadrupole antennas); the dipole and quadrupole antennas are oriented perpendicular to each other (Fig. 1). The two short silver wires, which are strongly coupled to incident light as dipole antennas (bright modes), support the spectrally broad-linewidth absorption due to radiative damping. The two long silver wires act as two non-radiative quadrupole antennas (dark modes) and their resonance frequency is adjusted within the absorbance linewidth of the dipole antennas. Due to close proximity, the two antennas are strongly coupled. This coupling generates single/multi-spectral PIT, depending on the resonance frequency of the quadrupole antennas. Single-spectral PIT can be induced for quadrupole antennas with the same wire length (same resonance frequency). This can be considered as a single dipole-quadrupole coupling [6, 10]. In contrast, multi-spectral PIT appears for quadrupole antennas with different wire lengths (different resonance frequency). The resonant frequency difference of quadrupole antennas leads to coupling between three kinds of oscillators, which results in splitting of the PIT resonance and therefore generates two transmission windows. This phenomenon is well described by a classical oscillator model. The resulting PIT effects provide a new possibility in planar metamaterials for applications toward sensing, nonlinear optics and optical information processing at multiple frequency domains.

## 2. Metamaterial overview

Figure 1(a) schematically shows the metamaterial structure design; the two long wires are arranged between the short wire pair with the gap of *g* = 1 *μ*m. The lateral displacement of the long wires with respect to the symmetry axis of the short wire pair is defined as *s*. The lengths of upper and lower quadrupole antennas are defined as *l*_{1} and *l*_{2}, respectively. To induce the strong resonance, the unit cells are arranged in a skewed lattice (the periods in the *x* and *y* directions are 19 *μ*m and 7 *μ*m, respectively, and the unit cells are shifted by half of the *x* period along the *y* axis.). This arrangement leads to the increase of the net area for the interaction between incident light and the dipole antennas, resulting in strong resonances in the spectrum (a rectangular grid also supports the PIT resonances (not shown), but it shows weak resonances in the spectrum).

The metamaterials were fabricated by mask-less UV lithography technique [19, 20], which allows for a short-time fabrication procedure (several minutes per one sample patterning). All samples are fabricated on a silicon substrate and have a total area of 20 mm × 15 mm, consisting of about 2300000 unit cells. Figure 1(b) shows a scanning electron microscopy (SEM) image of a typical structure (*s* = 1.5 *μ*m, *l*_{1} = 13 *μ*m and *l*_{2} = 14 *μ*m). An enlarged normal view is presented in the inset of Fig. 1(b). The optical properties of the metamaterials at normal incidence were measured with terahertz fourier transform infrared (FT-IR-6200, JASCO Corporation) with electric field polarization along the dipole antennas. The measurements were carried out on vacuum conditions (6.0 × 10^{2} Pa) to prevent atmospheric absorption.

## 3. Single-spectral plasmon induced transparency

As a proof of concept, we first present the single-spectral PIT in the metamaterials with the same wire length of two quadrupole antennas (*l*_{1} = *l*_{2} = 14 *μ*m). The experimental transmittance spectra in dependence on the lateral displacement *s* are presented in Fig. 2. In the case of *s* = 0 *μ*m, which means the quadrupole antenna located on the symmetry axis of the dipole antenna pair, there is only a single resonance observable in the transmittance spectrum. This resonance corresponds to the excitation of dipole antennas, giving rise to a broad resonance in the spectrum. In this case, the quadrupole antenna does not contribute as the charges of the dipole antennas do not induce the quadrupole modes. The coupling between the dipole and quadrupole antennas can be induced by shifting the lateral displacement to the end of the dipole antennas. As presented in *s* = 1.0 *μ*m, a tiny transmittance peak appears within the broad resonance profile. By enlarging *s*, corresponding to the increase of the coupling strength, the transmission window grows in strength and becomes more prominent (see *s* = 1.5 *μ*m). The above phenomena can be interpreted in terms of PIT. It can be explained by the destructive interference between the two excitation pathways of the dipole antennas: the direct excitation by the incident light field and the excitation by the coupling with the quadrupole antennas (excited beforehand by the dipole antennas) [6, 10]. The two pathways destructively interfere each other, therefore dramatically reducing extinction and enhancing transmittance. Furthermore, the linewidth of the transmission window becomes wider as the lateral displacement (the coupling strength) further increases (see *s* = 2.5 *μ*m). This phenomenon can be understood by considering the effect of normal mode splitting (hybridization), which is a spectral splitting owing to the strong coupling between two kinds of oscillators with same resonance frequency [21].

In order to further analyze the optical properties of the metamaterials, rigorous coupled wave analysis (RCWA) and finite-difference time-domain (FDTD) calculations were carried out. In this analysis, the close agreement between RCWA and FDTD calculations can be seen (not shown). The calculated spectra by RCWA are presented as red dashed curves in Fig. 2 and show good agreement with the experiment, supporting our measured spectral response.

## 4. Multi-spectral plasmon induced transparency

Once the resonance frequency of one of the quadrupole antennas is shifted, strong coupling between three different kinds of antennas causes splitting of the PIT resonances and leads to multi-spectral PIT behavior; it can be predicted from the classical oscillator model. We now discuss the optical properties of the asymmetric metamaterials (*l*_{1} ≠ *l*_{2}) for multi-spectral PIT behavior. The lateral displacement *s* and the one wire length *l*_{2} were fixed to 1.5 *μ*m and 14 *μ*m, respectively. The experimental transmittance and extinction spectra in dependence on the wire length *l*_{1} are presented in Fig. 3.

In the case of *l*_{1} = 14 *μ*m, that is the symmetric metamaterials (*l*_{1} = *l*_{2}), the single transmission window can clearly be observed. On the other hand, in the case of *l*_{1} = 13 *μ*m, the transmission window splits into two peaks and the multi-spectral PIT effect arises. This is due to the resonance shift of one of the quadrupole antennas, as the shorter wire length makes the resonance frequency higher. This phenomenon can also be derived by model calculations of a three-oscillator coupling system. We note that these multi-spectral resonances can be achieved only in a three or more oscillators system with bright and dark modes, highlighting our metamaterials ideal for the realization of multi-spectral PIT in a planer system. By further shortening *l*_{1}, however, the multi-spectral transmission window disappears and the single transmission window appears. This can be understood by the decrease of the coupling strength. The shorter quadrupole antenna leads the weak coupling between antennas due to the wide gap, so the upper quadrupole antenna does not contribute in this case. The calculated spectra are also plotted as red dashed curves in Fig. 3(a). The results show qualitative agreement with the experiment, it further supports the measured multi-spectral PIT behaviour.

In order to better understand the underlying physics, the electric field distributions (*E*_{z}) at the transmittance peaks as indicated by the green triangles (A–C) in Fig. 3(a) are shown in Fig. 3(c). At transmittance peak A for the single-spectral PIT, the two quadrupole antennas are characterized by symmetric charge oscillations along the center axis of the long wires; it corresponds to the excitation of two wire-quadrupoles [22]. The excited dual-quadrupole fields induces extremely weak field in the dipole antennas by the destructive interference (cancelling) of the dipole excitation [6], which means the nearly complete suppression of optical extinction at the resonance frequency. At peak B for the multi-spectral PIT, the dipole fields are canceled due to the strongly excited lower quadrupole fields. The opposite situation can be seen at peak C; the upper quadrupole fields cancel the dipole fields. These facts indicate that the two transmission windows are individually induced from the destructive interference owing to the excitation of the resonantly corresponding quadrupole antennas. In other words, the resonance shift of the upper quadrupole antenna directly induces splitting of the PIT resonance and it therefore generates the multiple PIT spectra.

## 5. Classical three-oscillator model analysis

To provide a quantitative description of multi-spectral PIT systems, we consider a three-oscillator PIT model. The dipole antennas in our metamaterial are represented by oscillator D, which is driven by an external electric field *E*. The quadrupole antennas are represented by oscillator Q_{1} and Q_{2}, which can be excited only through coupling with oscillator D. From the coupled differential equations, the energy dissipation of the considered system is obtained as follows:

*A*is given by

*ω*

_{d},

*ω*

_{q1}and

*ω*

_{q2}are the resonance frequency of oscillators D, Q

_{1}and Q

_{2}, respectively.

*γ*

_{d},

*γ*

_{q1}and

*γ*

_{q2}represent the damping factors in oscillators D, Q

_{1}and Q

_{2}, respectively.

*κ*

_{q1}and

*κ*

_{q2}are the coefficient of the coupling between oscillators Q

_{1}and D, and oscillators Q

_{2}and D, respectively. The equation 1 was derived with the approximation

*ω*∼

*ω*

_{d,q1,q2}≫

*κ*

_{q1,q2}.

Subsequently, experimentally observed extinction spectra in Fig. 3(b) were fitted with equation 1 as presented by red dashed lines in the same figure, which shows well fitted results. The discrepancies are likely due to the fabrication imperfection and the measurement tolerances. To explore the multi-spectral resonance mechanism, Fig. 4 shows the fitting values for *ω*_{d,q1,q2}, *γ*_{d,q1,q2} and *κ*_{q1,q2} as a function of the wire length *l*_{1} in frequency units. The resonance frequency *ω*_{q1} increases with the decrease of *l*_{1}, whereas *ω*_{d} and *ω*_{q2} are almost constant. This fact shows the resonance shift of the quadrupole antenna due to shortening of the antenna length, which directly causes the splitting of the PIT spectrum. The coupling coefficient *κ*_{q1} decreases to zero at *l*_{1} = 12 *μ*m, while *κ*_{q2} is almost constant. This supports the fact that the disappearance of the second window at *l*_{1} = 12 *μ*m is caused by no-coupling between the dipole antenna and the upper quadrupole antenna owing to their wide spatial gap. The quadrupole damping factors *γ*_{q1} and *γ*_{q2} are roughly constant at 0.3 THz. They are nearly four times smaller than the dipole damping factor *γ*_{d} (∼ 1.2 THz), which leads to the rise of the narrow and sharp transmission windows in the dipole absorbance linewidth [10].

These quantitative results strongly support our expectation on multi-spectral PIT mechanism; the dual-quadrupole modes excitation induces reduction of optical extinctions of the system at the multiple resonance frequencies and it therefore facilitates the multi-spectral PIT effects. It is noteworthy that the revealed mechanism clearly indicates that further transmission windows can be induced by introducing additional quadrupole wires into our system. This promising prospect greatly highlights our planar metamaterial concept for future PIT applications operating at multiple frequency domains, considering the fact that other planar or stacked PIT metamaterials [7, 15, 17, 18] fundamentally have a structural limit for the multiple coupling to induce three or more transmission windows. Furthermore, we note that, while we demonstrated the concept only in the terahertz frequency, the general structural design and mechanism can be readily extended to shorter wavelengths such as optical frequencies.

## 6. Conclusion

In conclusion, we have demonstrated multi-spectral PIT phenomenon using a novel planar metamaterial based on dipole and dual-quadrupole coupling. Single and multiple transmission peaks with narrow linewidths were observed in our experiment. The results are well described by numerical calculations and a three-oscillator model analysis. We believe that the planar design for multi-spectral PIT provides deep insight into low-loss metamaterials, and will open a new route for metamaterial applications such as sensing [11] and slow light [23] devices at multiple frequencies. Furthermore, our work offers great promise for designing and understanding complex plasmonic structures associated with multiple dipole-multipole interactions and bright-dark mode coupling.

## Acknowledgments

This work was supported by Grant-in-Aid for Scientific Research B ( 25286007) from the Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT). One of the authors (M. Miyata) is supported by Research Fellowships of Japan Society for the Promotion of Science (JSPS) for Young Scientists.

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