1. Introduction

Similar to achieving electric field enhancement in nanophotonics [1], now achieving magnetic field enhancement at optical frequencies is drawing increasing attention [2], owing to its potential applications in magnetic nonlinearity and magnetic sensors [3–6]. In the interactions of light with matter at optical frequencies, however, the magnetic contribution is generally neglected since the effect of light on the magnetic permeability is a factor 10⁻⁴ weaker than on the electric permittivity [7]. Thus, seeking new strategies to enhance magnetic fields becomes very important [8,9]. Recent studies have shown that metallic diabolo nanoantenna and nanowire structures [10,11], designed by applying Babinet’s principle to the metallic nanostructures such as nanobowties and nanogaps which were widely employed to obtain huge electric field enhancement at electric resonances [12,13], can produce highly confined and enhanced magnetic optical fields. For instance, magnetic field enhancement with a factor of 2900 has been achieved for the metallic diabolo nanoantenna structures at a wavelength of 2540 nm [11].

Another important approach to enhance magnetic optical fields is to pattern artificial magnetic atoms like SRRs [14–18] and rod or cut-wire pairs [19,20] into one- or two-dimensional (2D) arrays [21–23]. It has been shown that MP resonances in the periodic array of metallic nanowire pairs can be coupled to Bloch surface waves and waveguide modes, resulting in an avoided crossing and the formation of mixed MP resonances [21,22]. More recently, we have also shown that for the diffraction coupling between the MP resonances and lattice resonance mode of arrays in 2D periodic arrays of metallic rod-pairs, an enhancement factor as high as 450 could be achieved for magnetic field intensity at a visible wavelength of 780 nm [23]. We stress that in the above study, the metallic rod-pair arrays are assumed to be in a homogeneous medium (i.e., air). But, in experiment metallic nanoparticle arrays are commonly prepared on dielectric substrates. The presence of dielectric substrates will severely weaken the strength of diffraction coupling, and therefore prevent the formation of the narrow-band mixed mode [24,25]. Fortunately, by embedding the metamaterials into the substrate, we have shown that the strength of diffraction coupling can be strengthened enough to observe successfully the narrow-band mixed MP mode [26]. However, in some cases this approach inevitably has a major disadvantage for practical applications since the enhanced electromagnetic fields are mainly confined within the dielectric substrates.

In this letter, we for the first time present an approach to enhance the MP resonances of metamaterials composed of periodic arrays of U-shaped metallic SRRs for high-quality sensing. We observe that compared with the on-substrate metamaterials, the suspended ones lead to a narrow-band mixed MP mode with a great magnetic field enhancement, which arises from the interaction between the MP resonances of individual SRRs and the lattice resonance mode of periodic arrays. And for such a diffraction coupling, the magnetic field component of the lattice resonance mode must be parallel to the magnetic moment induced in the SRRs. Importantly, the sensitivity and the FOM of the suspended metamaterials can reach as high as 1300 nm/RIU and 40, respectively, much better than what have been reported [27]. These results suggest that the proposed metamaterials could pave a new way for high-performance refractive index sensing.

2. Results and discussions

As schematically shown in Fig. 1(a), the proposed metamaterials are composed of 2D arrays of U-shaped Ag SRRs lifted by silica pillars on silica substrate. The structural parameters of the Ag SRRs are set to be with the arm length l = 160 nm, the arm width w_a = 40 nm, the base-line width w_b = 80 nm, and the SRR height d = 30 nm. The silica pillars have the same planar size and a height of 600 nm. The refractive index of silica is taken to be n_SiO2 = 1.45. The relative permittivity of Ag is described by a Drude model: ε = 1−ω_p²/[ω(ω + iτ⁻¹)], where ω_p is the plasma frequency and τ is the relaxation time related to energy loss. The parameters are taken to be ħω_p = 9.2 eV and ħτ⁻¹ = 0.02 eV [28]. The coordinates are chosen such that the SRRs lie on the xoy plane, with its origin located at the center of one of the SRRs. The array periods along the x and y axes are P_x and P_y, respectively. The electric field E_in, magnetic field H_in, and wave vector K_in of the incident light are along the x, y, and z axes, respectively. This proposed metamaterials could be easily fabricated by current planar nanofabrication process. For instance, firstly, a 2D array of U-shaped SRRs pattern is exposed by electron beam lithography. Then silver U-shaped SRRs are formed by silver evaporation and lift-off processes. Finally, masking by the silver U-shaped SRRs, the periodic U-shaped silica array structure is etched by ICP dry-etching.

 

Fig. 1 (a) Schematic of a 2D rectangular array of U-shaped Ag SRRs suspended by silica pillars on silica substrate. (b) Normal-incidence transmission spectra of the suspended and on-substrate (the h = 0 nm case) Ag SRR arrays with P_x = 400 nm and P_y = 1100 nm. Red solid line shows the transmission spectrum of the suspended array, black dotted line shows the transmission spectrum of the on-substrate array, and the inset is the transmission spectrum of the U-shaped Ag SRR array with P_x = 400 nm and P_y = 400 nm.

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Figure 1(b) presents the normal-incidence transmission spectra of suspended and on-substrate (the h = 0 nm case) Ag SRR arrays with P_x = 400 nm and P_y = 1100 nm, calculated with the commercial software package COMSOL MULTIPHYSICS. For the suspended array, as shown by the red solid line in Fig. 1(a), two obvious dips located at 1020 nm and 1184 nm are observed. In order to exclude the effect of the diffraction within the spectral range of interest from 800 nm to 1600 nm, the transmission spectrum of the suspended U-shaped Ag SRR array with P_x = 400 nm and P_y = 400 nm is shown in the bottom inset of Fig. 1 (b). As can be seen, there is also a transmission dip centered at about 1020 nm marked with the black arrow. Thus, we can conclude that the transmission dip at 1020 nm arises from the excitation of MP resonance in individual SRRs because there exists no diffraction channel for such an array. Actually, our previous work has shown that the broad transmission dip (marked as dip 1) appearing at λ₁ = 1020 nm is due to the excitation of MP resonance in Ag SRRs, and the narrow transmission dip (marked as dip 2) centered at λ₂ = 1184 nm is owing to the excitation of a mixed MP mode resulting from the diffraction coupling of MP resonances [23]. For comparison, the transmission spectrum of the on-substrate (the h = 0 nm case) Ag SRR array (black dotted line) is also presented in Fig. 1(b). As can be seen, compared with the suspended array, the major difference for the on-substrate array is the disappearance of this mixed mode because of the inefficient diffraction coupling in the inhomogeneous medium. At the same time, the MP resonance of the single Ag SRRs is shifted to 1276 nm because of the effect of the substrate. Auguié et al. have shown that it is important to surround the nanoparticles by a homogeneous dielectric background to achieve an effective diffraction coupling of electric resonances [29]. We note that the suspended array is not in a fully homogeneous medium due to the presence of silica pillars and substrate, thereby the condition (i.e., a homogeneous medium around the Ag SRR array) for the formation of the mixed MP mode is less stringent than believed [25].

Figures 2(a) and 2(b) respectively present the corresponding normalized magnetic field intensity distributions for the dip 1 and dip 2 resonances, on the xoy plane intersecting the SRRs at their middle height. For the dip 1 resonance (centered at λ₁ = 1020 nm), the magnetic fields are highly confined within the inner area of the SRRs, which are characteristics of a MP resonance of single Ag SRRs. For the dip 2 resonance (centered at λ₂ = 1184 nm), the field pattern is almost the same as that of the dip 1 resonance, but the magnetic fields within the inner area of the SRRs become much stronger, with a nearly 21.2 times enhancement. Moreover, the maximum of magnetic field intensity is enhanced to be about 2283 times of the incident fields.

 

Fig. 2 (a) and (b) Normalized magnetic field intensity distributions (H/H_in)² on the xoz plane intersecting the SRRs at their middle height for the dip 1 and dip 2 resonances marked in Fig. 1(b). Black solid line outlines the regions of U-shaped Ag SRRs.

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To get a deeper insight into the nature of the narrow-band mixed MP mode in the suspended U-shaped Ag SRR arrays, in Figs. 3(a)-3(f) we plot the normalized x, y, and z components of the total electromagnetic fields on the xoy plane for the dip 2 resonance. It is clearly seen that, the magnetic field component of the lattice resonance mode is in the z direction, and its electric field is mainly distributed along the x direction. The lattice resonance mode has a magnetic field component of the same direction as the induced magnetic moment (along the z direction) in the Ag SRRs. Thus, the lattice resonance mode can strongly couple with the MP resonances in each metallic SRRs, when it grazes the surface of the metamaterials. Such a diffraction coupling can strongly suppress radiative damping because the electromagnetic fields of the lattice resonance mode are trapped in the 2D lattice [30,31], thereby resulting in the formation of the narrow-band mixed MP mode at the dip 2 resonance. Besides, by varying the array periods, we can selectively close the diffraction channel in the y direction, but open the diffraction channel in the x direction (not shown here). For this case, the magnetic field component of the lattice resonance mode is orthogonal to the induced magnetic moment in the Ag SRRs. As a result, the lattice resonance mode could not directly interact with MP resonances, and similar diffraction coupling of MP resonances will not appear.

 

Fig. 3 (a)-(c) Normalized electric field intensity components (E_x/E_in)², (E_y/E_in)² and (E_z/E_in)² on the xoy plane for the dip 2 resonance. (d)-(f) The same as (a)-(c), but for normalized magnetic field intensity components (H_x/H_in)², (H_y/H_in)² and (H_z/H_in)². Black solid line outlines the regions of U-shaped Ag SRRs.

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In our proposal, the metallic SRRs are exposed in air rather than buried within dielectric substrate, which will be helpful for applications in biomedical sensing, especially at the resonance of narrow-band mixed mode associated with a great magnetic field enhancement. Next, we detailedly investigated the refractive index (n) sensing with the designed metamaterials. As shown in Fig. 4, when n is varied from 1.30 to 1.38 in intervals of 0.2, obvious red-shifts of the two transmission dips are observed (please see Fig. 4(a)). The spectral positions of the two transmission dips with the refractive indices are shown in Fig. 4(b). The bulk index sensitivities (defined as dip shift (nm)/∆RIU) of 1300 and 1000 nm/RIU are achieved by linear fitting for the narrow-band mixed mode and MP resonance, respectively. For the practical applications, the FOM of a sensor is another important parameter to evaluate its performance, which is defined as the resonance shift upon a change in the refractive index of the dielectric medium normalized by the full width of half maximum of characteristic line [32]. The FOM of our proposed metamaterials can reach as high as 40 for the narrow-band mixed mode and 10 for the MP resonance, respectively. Because of the huge magnetic field enhancement and narrower resonance linewidth for the mixed mode, its FOM is enhanced up to 4 times higher than that of the MP resonance. Finally, we note that although we have not optimized our proposed metamaterials for biodetection applications, the high sensitivity and FOM achieved here reach the highest level of the recently reported plasmonic sensing [27].

 

Fig. 4 Refractive index sensor based on the suspended metamaterials. (a) Caculated normal-incidence transmission spectra of the suspended metamaterials immersed in different dielectric mediums, with the refractive index n varied from 1.30 to 1.38. (b) Relationships between the wavelengths of dip 1 (black) and dip 2 (red) and the refractive indices, achieved from the caculated data, respectively.

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3. Conclusion

In summary, we have proposed and demonstrated an efficient approach to enhance the magnetic resonances of metamaterials composed of periodic arrays of U-shaped metallic SRRs for high-quality sensing. It is shown that by suspending the metamaterials to reduce the substrate effect, the coupling between MP resonances of individual metallic SRRs and the lattice resonance mode of the arrays will give rise to a narrow-band mixed mode with a great magnetic field enhancement. For such a coupling to appear, the magnetic field component of the lattice resonance mode must be parallel to the induced magnetic moment in the metallic SRRs. Importantly, it is also shown that the sensitivity and the FOM of the suspended metamaterials can reach as high as 1300 nm/RIU and 40, respectively. We hope that both huge magnetic field enhancement and narrow-band mixed mode achieved in the suspended metamaterials could find broad applications in biomedical sensing.