Plasmon induced transparency in cascaded π-shaped metamaterials

Arif E. Çetin; Alp Artar; Mustafa Turkmen; Ahmet Ali Yanik; Hatice Altug

doi:10.1364/OE.19.022607

1. Introduction

Electromagnetically induced transparency (EIT) is the elimination of absorption over a narrow spectral region in a broad absorption regime [1,2]. This phenomenon results in a highly enhanced nonlinear susceptibility in the spectral region of induced transparency accompanied with steep dispersion [1]. This strong dispersion plays the key role to reduce the group velocity or even completely stop the light [3–6]. The EIT medium is modeled as a 3-level atomic system composed of ground state |0>, with transition allowed |1>, and forbidden states |2>. A broad absorption regime occurs when there is no coupling between states |1> and |2>. However, when the coupling is induced; via the interference of the excitation pathways, |0> - |1> and |0> - |1> - |2> - |1>, a narrow transparency window occurs in the broad absorption regime [1]. EIT phenomenon is first demonstrated by Boller et al. [1]. In their experiment, they apply a temporally smooth coupling laser between the bound state of an atom and upper state of the transition which will be transparent. This transparency is due to the destructive interference between these two dressed states. However, realization of the EIT phenomenon is challenging due to the experimental drawbacks, i.e., laser stabilization and need for low temperature. To overcome these experimental limits, classical analogues of EIT can be used in wide variation of systems, such as, split ring resonators [7,8], RLC circuits [9] and metamaterials [10–13]. Plasmonic structures are also investigated for the EIT-like applications since they can operate in room temperature, have wide operational bandwidth and are easy to integrate into nano-scale circuits [14–17]. The plasmonic metamaterial analogue of EIT (or plasmon induced transparency) has been first introduced by Zhang et al. by using a π-shaped structure composed of a single metal strip (dipolar antenna) and two parallel metal strips (quadrupolar antenna) [14]. The dipolar antenna, (bright plasmonic mode) strongly couples to the external light source but suffer from losses due to the radiative damping. However the quadrupolar antenna (dark plasmonic mode) cannot directly couple to the external light and has a narrower spectral response in comparison to the dipolar antenna due to the suppression of radiation damping. When these antennas are placed closely to each other, the dark mode can be indirectly excited by the bright mode [14–22]. In atomic systems, the transparency is created by applying a temporally smooth coupling laser source between two states. In contrast, the plasmonic analog does not need any external coupling mechanism, since it is achieved by the near-field interactions between two oscillators [14,21].

In this paper, we demonstrate a composite metamaterial, possessing plasmonic EIT-like characteristics, for spatial control of near-field distribution. The system consists of two cascaded π-shaped structures where dipolar and quadrupolar antennas of individual π-structures are uniquely coupled. The single π-shaped structures are arranged asymmetrically with a distance, d, as shown in Fig. 1(a) . Here, d, determines the coupling between two structures. The individual π-structures in the cascaded design is found to exhibit the similar EIT-like behavior with a single π-structure. We show that the near-field interaction between cascaded π-structures can be used to control the EIT-like spectral behavior. By adjusting the constituent elements, we are able to control the intensity enhancement location in a great precision. Further investigating the coupling between two individual π-shaped structures in the cascaded system, we achieve a more compact design composed of two merged π-shaped structures that supports the similar EIT-like behavior. Interestingly, this design is observed to funnel the near-field enhancement in a smaller area which significantly reduces the optical mode volume. Providing fine tuning of near-field distribution and small mode volumes, our proposed structure may serve for wide range of applications including bio-sensing, optical modulators/filters and switching devices.

Fig. 1 (a) Geometry of the cascaded π-structure composed of asymmetrically positioned identical π-structures. (b) Scanning electron microscope (SEM) image of the fabricated structure with the corresponding parameters: W = 100 nm, L = 400 nm, s = 200 nm, d = 100 nm, h = 50nm and t = 30 nm.

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2. Cascaded π-shaped structure

Over large freedom of different arrangements, we start with a cascaded design composed of two identical π-structures positioned asymmetrically as it supports strong EIT-like behavior over the others. Figures 1(a-b) show the schematic view and scanning electron microscope (SEM) image of the cascaded structure. We investigate the structure through numerical simulations using 3-dimensional finite difference time domain (3D-FDTD) analysis [23]. In our simulations, we use the noble metal, gold, with a thickness, t = 30 nm [24]. The structure stands on a 5-nm thick titanium substrate supported by a silicon nitride (SiN_x) film. The width (W) and the length (L) of the metal strip are 100 and 400 nm, respectively. In the individual π-structures, the distance between two parallel metal strips (s) is 200 nm and the distance between the dipolar and quadrupolar antennas (h) is 50 nm. The period of the structure in both x-and y-direction is p_x = p_y = 1.8 µm. In the unit cell consisting of the cascaded structure, periodic boundary condition is used along the x- and y-axes and perfectly matched layer is used along ±z (the direction of the illumination source). The polarization of the illumination source is parallel to the dipolar antenna (x-polarized) as illustrated in Fig. 1(a).

Orientation of the π-structures in the cascaded system is of utmost importance and it provides an extra degree of freedom in the design space to tailor the inter-particle near-field interactions that governs the spectral features of the total system. Here, we consider two different cascaded designs, composed of symmetrically and asymmetrically located two π-structures as illustrated in the inset of Figs. 2(a) and 2(b), respectively. We compare their response with a single π-structure given in Fig. 2(c). As it is shown in the respective calculated reflection spectra, for the case of d = 100 nm, indicated by the red curves in Figs. 2(a)-(b), when the individual π-structures are strongly coupled, EIT-like dip of the asymmetric design (Fig. 2(b)) is much more prominent when compared to the symmetric design (Fig. 2(a)). In both cascaded designs, when the distance between the individual π-structures are increased to d = 700 nm, indicated by the black curves, the near-field interactions decrease and the spectral response of the cascaded system converges to a single π-structure response.

Fig. 2 Numerical reflection data for (a) the cascaded structure where the individual π-shaped structures are symmetrically placed and (b) the cascaded structure where the individual π-shaped structures are asymmetrically placed. The distance between constituent elements are 100 nm (red curve) and 700 nm (black curve). (c) Numerical reflection data for the single π-shaped structure. In figures, the charge and total magnetic field distributions are determined at the corresponding resonance dip (For cascaded structures, the distributions are determined for d = 100 nm case). The corresponding parameters are W = 100 nm, L = 400 nm, s = 200 nm, h = 50 nm and t = 30 nm. (d) Quadrupolar excitation ( $\vec{P}$ ) is compared for the cascaded and single π-shaped structures. (e) For a cascaded structure, numeration of the dipole and quadrupolar antennas and the corresponding rod elements of each antenna are shown. In addition, R_mn, the displacement vector is illustrated.

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In order to better identify how the magnitude of the EIT-like dip of the cascaded system depends on the effect of orientation of the individual π-structures, coupled dipole approximation (CDA) can be utilized. In the cascaded structure, both of the dipolar antennas drive each quadrupolar antenna. The polarizations of the quadrupolar antennas can therefore be denoted as:

{\vec{P}}_{Q 1} = α_{Q 1} ((κ_{11} + κ_{12}) {\vec{P}}_{D 1} + (κ_{21} + κ_{22}) {\vec{P}}_{D 2})

{\vec{P}}_{Q 2} = α_{Q 2} ((κ_{13} + κ_{14}) {\vec{P}}_{D 1} + (κ_{23} + κ_{24}) {\vec{P}}_{D 2})

Here, α denotes the polarizability of the quadrupolar antennas and κ is the respective near-field coupling parameters between the dipolar antennas and nanorod elements of each quadrupolar antennas. Within the quasistatic approximation, these coupling parameters can be written as the electro-static propagator term acting on the nanorod elements of the quadrupolar antennas as:

κ_{n m} = \frac{{\vec{p}}_{n} \cdot {\vec{p}}_{m}}{r_{n m}^{3}} - 3 \frac{({\vec{p}}_{n} \cdot {\vec{R}}_{n m}) ({\vec{p}}_{m} \cdot {\vec{R}}_{n m})}{r_{n m}^{5}}

Here,

\vec{p}

is the dipole moment of the respective nanorod in the system and

{\vec{R}}_{n m}

is the displacement vector (described in Fig. 2(e)) connecting the rod elements, enumerated as n (n = 1, 2 for dipoles) and m (m = 1, 2 first quadrupole and m = 3, 4 second quadrupole) and r is the magnitude of the displacement vector. Only the second term in Eq. (2) contributes to the coupling parameter since the dipole moments of the rod elements of the quadrupolar and dipolar antennas are orthogonal to each other (

{\vec{p}}_{n} ⊥ {\vec{p}}_{m}

). Derived from the charge distributions shown in Figs. 2(a), an inspection of Eq. (2) reveals that for the symmetric configuration, the coupling term pairs acting on a single quadrupolar antenna in Eq. (1), i.e. (κ₁₁, κ₂₁) and (κ₁₂, κ₂₂) (similarly, (κ₁₃, κ₂₃) and (κ₁₄, κ₂₄)) have different signs. Hence, there will be a partial cancellation of the near-field couplings which will reduce the overall excitation efficiency (thus the effective polarization) of the corresponding quadrupolar antenna. This will directly reduce the magnitude of the EIT-like feature, as confirmed by the numerical analysis in Fig. 2(a). In contrast, these coupling terms have the same sign for the asymmetric cascaded design, which will result in a better excitation efficiency of the quadrupolar antennas (Fig. 2(b)). As an illustration, we show the sign of the coupling terms for the first quadrupolar antenna on the charge distribution in Figs. 2(a)-(b). For the asymmetric design, the magnitude of both (κ₁₁ + κ₁₂) and (κ₂₁ + κ₂₂) terms in Eq. (1)(a) have the same signs. However, for the symmetric design, these terms have opposite signs in magnitude. Discussion of the analytical results is summarized in Fig. 2(d), where the excitation efficiency of the quadrupolar antennas for both designs (

{\vec{P}}_{Q 1, Q 2}

) is shown with respect to the distance between the individual π-structures in the cascaded system. Here, the minimum distance between two π-structures is set to d = 50 nm. As the distance between the structures is increased, the excitation efficiency of both designs converges to that of the single π-structure (

{\vec{P}}_{\sin g l e - π}

). The length of the nanorods that are used as the building blocks of the structure is 400 nm and it is small compared to the wavelength regime of interest (l ≈λ/5). Therefore, the quasistatic approximation is valid. The far-field response also exhibits the similar trend. As the distance between two π-structures increases, the spectral response of the cascaded system for both designs, (black curve in Figs. 2(a-b)) converges to the single-π structure response (Fig. 2(c)). Our numerical simulations (total magnetic field, |H|²) also show that the asymmetric cascaded π-shaped system shows strong EIT-like behavior. Here, most of the field is concentrated at the quadrupolar antennas where the field localization at the dipolar antennas is weak. However, the symmetric cascaded system shows weak EIT-like behavior. For this configuration, we observe considerable amount of field enhancement in the dipolar antennas. Our proposed configuration also allows large near-field intensity enhancements supported by the constituent rod elements. We calculate the field enhancement capabilities of the proposed structures through FDTD analysis. In simulations, the mesh sizes in x- and y-directions are chosen to be 5 nm. We observe that at the EIT-like dip, for both single and asymmetric cascaded π-structures, the enhanced near-fields are mainly concentrated at the corners of the quadrupolar antennas. The near-field intensity enhancement of each system is calculated by a field monitor located at 5 nm above the top surface (air/metal interface) of the metal rods. For the single π-shaped structure, a field enhancement of 550 is obtained at the EIT-like dip. For the asymmetric design, a similarly large near-field enhancement, as large as 350, is observed. The near-field enhancement supported by the plasmonic structures is crucial for nonlinear optics since the efficiency of nonlinear processes can be greatly enhanced [25,26]. Hence, the proposed geometry, by favoring large field enhancements supported by quadrupolar antennas could be useful for non-linear optics.

For the single π-structure, the EIT-like behavior varied by the coupling between dipolar and quadrupolar antennas. This coupling depends on the vertical and horizontal distance between these two individual elements. Therefore, we fabricate cascaded structures to experimentally investigate similar effects on the overall spectral behavior. Here, we change the horizontal relative distance between two dipolar antennas as shown in the inset of Fig. 3(a) . The fabrication of our planar metamaterial (or 2D metamaterials) can be simply achieved through lithography based nano-fabrication schemes. However, more complex designs, including chiral unit cells and stacked layers enabled by new fabrication techniques can result in metamaterials with exotic spectral responses [15,27]. We start the fabrication process with a SiN_x film. We first coat the film with a resist (polymethylmethacrylate, PMMA) and perform electron-beam lithography (EBL). The EBL performed patterns are then removed by a development (MIBK-IPA) solution. We then deposit 5 nm titanium (adhesion layer) and 30 nm gold with a directional electron-beam evaporator. Finally, we perform a lift-off process to remove the gold in the unexposed film surface. Optical characterization of the structures is done by a Fourier Transform Infrared (FTIR) microscope with a light source incident to the array polarized along the x-direction as illustrated in Fig. 1(a). Our experimental set-up consists of an IR microscope coupled to a Bruker^TM FTIR spectrometer with a KBr beam splitter. Reflected signal is collected using a Cassagrian reflection optics and coupled into a liquid N₂-cooled mercury cadmium telluride detector. Reflection data are then normalized using an optically thin gold standard.

Fig. 3 (a) Experimental reflection data for the double π-shaped structure with different Δd values. In figure inset, the shifting procedure for the upper dipolar antenna is illustrated. (b) SEM image of the double π-structures with shifting amounts of 200 and 500 nm. (c) Total magnetic field distribution, |H|², at the calculated EIT-like resonance dip for the double π-structures with different ‘Δd’ values (For Δd = 500 nm, the field distribution is calculated at the reflection peak). The corresponding parameters are: W = 100 nm, L = 400 nm, s = 200 nm, d = 100 nm, h = 50 nm and t = 30 nm.

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We analyze the coupling effect by shifting the top dipolar antenna towards left which is schematically illustrated in the inset of Fig. 3(a). The figure shows the experimental data for the reflection spectrum of the structure with different shifting amounts in horizontal direction, Δd. Figure 3(b) shows the SEM image of the two fabricated structures with, Δd = 200 and 500 nm. With increasing Δd, the left (right) peak in the reflection spectrum is red (blue) shifted while the magnitude of the reflection dip increases. When Δd = 500 nm, corresponds to the system where the two dipolar antennas are aligned vertically, we observe that the EIT-like dip totally disappears. In Fig. 3(c), for the structures with Δd = 0 to 400 nm, total magnetic field distribution at the EIT-like dip in the reflection spectrum. While for the structure with Δd = 500 nm, total magnetic field distribution at the reflection peak are shown as there is no corresponding dip due to disappearance of EIT-like behavior. For Δd = 0 to 300 nm, the location of the hot spots with high near field enhancement supported by the quadrupolar antennas of individual π-structures varies with different shifting amounts. For these cases, dipolar antennas supports weak near-field enhancement. Initially (Δd = 0), the field enhancement is localized at the individual elements of both quadrupolar antennas. At 100 nm shift, for the constituent elements of the cascaded π-structure, field enhancement is localized at right metal rod of the quadrupolar antennas. At Δd = 200 nm, field enhancement is mainly localized at the right metal rod of the first quadrupolar antenna (Q1, indicated in Fig. 2(e)). At Δd = 300 nm, field enhancement is localized at the right metal rod of the first quadrupolar antenna and weakly localized at the left metal rod of the second quadrupolar antenna (Q2). Further shifting of the top dipolar antenna, Δd = 400 nm, EIT-like behavior significantly diminishes as shown by the black solid curve in Fig. 3(a). The field distribution, calculated at the EIT-like dip, indicates that the filed enhancement starts to localize near the dipolar antennas. However, for this configuration we still observe field enhancement localization at the quadrupolar antennas, corresponds to the right (left) metal rod of the first (second) quadrupolar antenna. When the two dipolar antennas are aligned vertically, Δd = 500 nm, EIT-like behavior totally disappears. Here, only the dipolar antennas couple to the illumination source of the system and support high near-field enhancement. Such spectral behaviors depend on the structural symmetry-breaking which allows the excitation of quadrupolar antennas by the coupling with the dipolar antennas [21]. Here, ∆d determines the asymmetry of the structure along the x-axis. By varying ∆d, the corresponding reflection spectrum can be controlled. When ∆d = 500 nm (two dipolar antennas are vertically aligned), only the two dipolar antennas are excited. As they are coupled to the incident light, a broad reflection peak is observed. By introducing structural asymmetry, d = 400 nm, a tiny reflection dip is observed. When the asymmetry is further increased, i.e., ∆d = 300 nm to 0, the quadrupolar antennas are effectively coupled to the dipolar antennas. Consequently, the reflection dip gets narrower and sharper. These results show that, by arranging the dipolar antenna location, we can tune the overall EIT-like behavior of the cascaded structure and control the hot spot locations with a great precision.

3. More compact cascaded structure

In order to understand the dependence of the near-field enhancement location on the coupling between the two individual π-structures in the cascaded design, we investigate the system with different distances between two single π-elements, d as illustrated in Fig. 1(a). The numerical and the experimental results of the reflection spectrum for different d values are shown in Figs. 4(a) . We observe that the far-field behaviors of the double π-structures with different d values are almost the same. We further analyze the field distributions at the reflection dip indicated by the red arrow in the figure. We observe that the cascaded system composed of two touching π-structures (d = 0) exhibits similar near-field distribution (Fig. 4(b)) with the cascaded structure composed of two separated π-structures with a distance, d = 100 nm, as shown in Fig. 2(a). The near-field intensity enhancement capabilities of the asymmetric design is further improved, reaching to enhancement values of 550 at air/metal interface when the two individual π-structures are touched one another. We observe that at the EIT-like dip, the enhanced near-fields are concentrated at the corners of the middle rod. Figure 4(c) shows the charge distribution of the cascaded design with two merged π-structures (d = 0). We observe that the dipole moment of the middle rod is twice as big as that of the left and right vertical rods. Therefore, the cascaded structure with a middle metal rod twice as big as the other two can also exhibit the EIT-like behavior as the one composed of separated individual π-shaped structures.

Fig. 4 (a) Numerical and experimental reflection data for the double π-shaped structures with different d values. In figure inset, SEM image of the fabricated structure with d = 0 is shown. (b) Total magnetic field, |H|², and (c) charge distribution at the calculated EIT-like resonance dip for the double π-structure composed of two merged π-shaped structures (d = 0). The corresponding parameters are: W = 100 nm, L = 400 nm, s = 200 nm, h = 50 nm and t = 30 nm.

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Since the cascaded system, composed of two merged π-structures (d = 0), exhibits the similar EIT-like behavior with the cascaded one composed of separated π-structures, we investigate the role of the middle rod in the overall EIT-like behavior. To realize a more compact system, we replace the large middle metal strip with the one identical to the others. Hence, the cascaded double π-structure turns into a compact design composed of identical three parallel and two horizontal metal strips as sown in Fig. 5(b) . SEM image of the fabricated structure is shown in Fig. 5(c). It is important to note that, as shown in Fig. 5(a), the EIT-like dip is still observable for the compact π-structure. We also determine the corresponding charge distribution at the calculated EIT-like resonance dip as in Fig. 5(d). We observe that the dipole moment of the middle rod is still twice as big as the other two while the charge distribution is minimum in the dipolar antennas. Since there is a minimum charge accumulation in the dipolar antennas, nearly the whole field is concentrated in the middle rod as shown in the near-field distribution (Fig. 5(e)). It is interesting that with our plasmonic design, we can concentrate the light in the middle rod oriented perpendicular to polarization direction of the illumination source. Furthermore, we can achieve high field intensity enhancement localized at a very small area. In addition to this, since we are at the EIT-like resonance dip, there is a minimum amount of absorption in the structure. In the compact structure, all other antennas funnel the incident field to the middle rod which decreases the mode volume of the overall structure. The mode volume can be calculated from the commonly used formula as given in [28]:

V = \frac{\int ε | E (r) |^{2} d V}{\max [ε | E (r) |^{2}]}

where ε is the dielectric constant. In comparison with the single π-structure, the compact π-structure funnel the incident light to the middle rod while in single-π structure, the field enhancement is localized at both two horizontal rods. Therefore, it supports a mode volume half of the one supported by the single π-structure:

Fig. 5 (a) Numerical and experimental reflection data for the compact double π-structure with the corresponding parameters: W = 100 nm_, L = 400 nm, s = 200 nm, h = 50 nm and t = 30 nm. (b) Schematic view of the compact π-structure. (c) SEM image of the fabricated compact π-structure. (d) Charge and (e) total magnetic field distribution, |H|², at the calculated EIT-like resonance dip for the compact π-structure.

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\frac{V (c o m p a c t - π)}{V (single - π)} \approx 0.494

This result shows that, compare to the conventional π-structures, we can localize the near-field enhancements in a much smaller volume with the compact π-structures. We observe that the compact π-structure also supports larger field enhancements compare to the single π-structure. We observe that near-fields are concentrated at the corner of the middle rod with an enhancement value of 850.

When the width of the middle rod of the compact π-structure is decreased, we observe that field intensity enhancement can be further localized to a smaller volume. The procedure is schematically illustrated in inset in Fig. 6(a) . In the calculated spectral response, both left and right peaks in the reflectance spectrum are red-shifted with decreasing width of the middle rod, a. We also fabricate the structure to experimentally demonstrate the far-field response. Figure 6(b) shows the SEM image of the compact π-structure without a middle rod (a = 0). We observe that the experimental results correlate well with the calculated spectra. Here, the discrepancy between numerical and experimental results is due to the fabrication imperfections in the experiments. The field distribution, determined at the EIT-like resonance dip, indicates that for the compact double π-structures with different middle rod widths, the illumination light is always funneled to the middle rod. The simulation results in Fig. 6(c), the left and middle one, correspond to a = 50 and 20 nm, respectively. Since the field enhancement is mainly concentrated in the middle rod, with decreasing middle rod width, smaller mode volumes can be achieved. As a demonstration, we compare the mode volume of two compact π-structures with middle rod widths, 50 and 100 nm. We observe that, when the middle rod width is half in size, the mode volume can be reduced by approximately 35% with higher near-field enhancement as large as 1350.

Fig. 6 (a) Numerical and experimental reflection data for the compact double π-shaped structure with middle metal strips of different widths. In figure inset, the middle rod adjustment is illustrated. (b) SEM image of the structure without the middle rod (a = 0) is shown. (c) Total magnetic field distribution, |H|², at the calculated EIT-like resonance dip for the compact π-structure with different ‘a’ values (For a = 0, the field distribution is calculated at the reflection peak). The corresponding parameters are: W = 100 nm_, L = 400 nm, s = 300 - a, h = 50 nm and t = 30 nm.

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\frac{V (a = 50 n m)}{V (a = 100 n m)} \approx 0.63

This controllable small mode volume is highly desirable for the applications requiring strong coupling between matter and light. However, when the middle rod is removed (a = 0), the EIT-like dip totally disappears as shown in Fig. 6(a). Here, the field distribution (at the most right illustration), calculated at the corresponding reflection peak, indicates that only dipolar antennas are coupled to the incident light and support high near-field enhancement Fig. 6(c).

4. Conclusion

In conclusion, we propose a composite metamaterial consists of two π-structures located asymmetrically in a single unit for controlling the EIT-like spectral behavior and field intensity enhancement location. The structure enables fine-tuning of hot spot location with high near-field intensities by varying the geometrical parameters. Analyzing the coupling between two individual π-structures in the composite system, we achieve a more compact metamaterial, composed of two merged π-structures. We show that this structure also possesses the similar EIT-like behavior with the asymmetric double π-shaped structure. Interestingly, this compact structure funnels the incident light in a smaller spot which depends on the geometrical parameters of the center metal rod. Hence, it provides a small mode volume controlled by the width of the middle rod. These two structures enable high field intensity enhancement with minimum absorption due to suppression of radiation damping. Possessing tunable hot spot locations and small mode volumes, the proposed metamaterials can be used in wide range of applications including enhancement of non-linear processes, bio-sensing, spectroscopy, optical filters, modulators and ultrafast switching devices.

Acknowledgments

We gratefully acknowledge support from National Science Foundation (NSF) CAREER Award (ECCS-0954790), Office of Naval Research Young Investigator Award (Grant 11PR00755-00 P00001), Massachusetts Life Science Center New Investigator Award, NSF Engineering Research Center on Smart Lighting (EEC-0812056), Photonics Center, DoD/Army Research Laboratory (Grant W911NF-06-2-0040) as well as Scientific and Technological Research Council of Turkey (TUBITAK) for supporting M.T.

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Plasmon induced transparency in cascaded π-shaped metamaterials

Abstract

1. Introduction

2. Cascaded π-shaped structure

3. More compact cascaded structure

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (6)

Equations (6)

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