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Abstract
Magnetic plasmons (MPs) refer to the coupling of external electromagnetic waves with a strong magnetic response induced inside the nanostructures. MPs have been widely employed as artificial magnetic atoms to fabricate negative-permeability or negative-refractive-index metamaterials with peculiar electromagnetic properties. Here, we propose a refractive index sensing by utilizing the MP resonances excited in a simple one-dimensional (1D) metallic nanogroove array. We demonstrate a sensitivity up to 1200 nm/RIU with a figure of merit (FOM*) of 15 thanks to the MP resonances that are extremely sensitive to the surrounding media. Importantly, the influence of the local environment effects on the sensing ability is studied. An equivalent inductor-capacitor (LC) model is used to give a precise quantitative description of the sensing performance and reveal the underlying mechanism. Such a MP-based sensor with the ease of fabrication may provide great potentials in designing broadband sensing devices with high performance and compactness.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Surface plasmons(SPs), optical excitations at the metal-dielectric interface, carry significant potential for guiding and manipulating light on the nanoscale [1–4]. Being confined at the metal surface with strong field enhancement, SP resonances can be very sensitive to changes in the dielectric properties of the surrounding medium. With this unique property, SPs excited by various metallic nanostructures or metamaterials have been extensively applied in plasmonic sensing applications [2, 5–7]. Plasmonic refractive index sensors with sensitivity up to over 1000nm/RIU can be generally achieved [8].
Analogous to SP resonances excited in plasmonic nanostructures, strong magnetic response, also termed magnetic plasmons (MPs) [9–12], can be excited in some metamaterials like split-ring resonators (SRRs) [13], paired rods [14], nanodisks [15–17]. MPs, stemming from the coupling of external electromagnetic waves with a strong counteracting magnetic moment, have been widely employed as artificial magnetic atoms to fabricate negative-permeability or negative-refractive-index metamaterials. Consequently, enhancing and manipulating magnetic responses are drawing increasing attention owing to their promising applications in magnetic nonlinearity and magnetic sensors [18–22]. However, these tasks are still challenging due to the fact that in light-matter interactions, the magnetic contribution is negligible since the effect of light on the magnetic permeability is much weaker than on the electric permittivity.
Different types of metamaterials have been proposed to enhance the MP response including periodic array of metallic nanowire pairs [23, 24] and rod-pairs [10]. Our previous work has also demonstrated a considerable enhanced magnetic response by integrating a multilayered metal/dielectric metamaterials with a monolayer graphene [25]. Whereas, studies on utilizing MP enhancement for sensing are still lacking. More recently, a metamaterial consisting of a 2-dimensional (2D) array of U-shaped metallic split-ring resonators (SPPs) has been proposed to achieve great magnetic field enhancement for sensing at near-infrared (NIR) frequencies [22].
In this paper, we propose a high-quality refractive index sensing by utilizing the MP resonances excited in a simple 1D metallic groove array. We demonstrate a sensitivity up to 1200 nm/RIU with figure of merit (FOM*) of 15 resulting from the MP resonances that are extremely sensitive to the surrounding media. The sensitivity obtained here is better than that achieved in most plasmonic refractive index sensors [26]. This MP-based sensing device is featured by two main advantages: (i) the 1D nature and the simple geometrical configuration dramatically facilitate the practical fabrication with high compactness and integrability, and (ii) it shows high-quality sensing capability over a broadband wavelength range, which can be precisely described and explained in the framework of equivalent inductor-capacitor (LC) nanocircuit model. This provides an effective way of designing the highly tunable refractive index sensors working in desired wavelength range.
2. Results and discussions
The proposed structure, as depicted in Fig. 1(a), consists of an array of nanogrooves on a gold film with groove period p = 800 nm, groove width b = 50 nm and groove depth h = 150 nm. Under illumination of transverse magnetic(TM) wave with the magnetic component parallel along the groove (y-direction), an oscillating current can be produced around the grooves in the x–z plane. According to Lenz’s law, this induced current generates a diamagnetic response, which is then coupled to the gold groove to generate a strong MP resonance [18,27,28].
Fig. 1 (a) 3-dimensional schematic illustration of gold nanogroove array. The right part shows the cross section with the schematic of equivalent LC circuit. (b) Simulated absorptance of the nanogroove array with groove period p = 800 nm, groove width b = 50 nm and groove depth h = 150 nm under illumination of TM (red) and TE (blue) wave respectively. A strong MP resonance is excited at λMP = 1542 nm with the absorptance α = 0.79. (c) Distribution of magnetic field at MP resonance λMP = 1542 nm.
With the geometric parameters mentioned above, we performed full wave simulations by using the commercial finite element(FEM) solver COMSOL multiphysics. Figure 1(b) gives the simulated absorptance of the groove array at normal incidence. A strong resonance peak can be clearly seen at λMP = 1542 nm with a maximum absorptance of 0.79. This is a strong indication of MP excitation, which is confirmed by the strong localized magnetic field inside the groove at the resonance peak, as shown in Fig. 1(c).
To demonstrate the validity of this MP-based refractive index sensor, we have chosen different surrounding media on top of the nanogroove array including water and glucose solution with various concentrations, corresponding to refractive indices n ranging from 1.312 to 1.352. Figure 2(a) plots the simulated absorptance of the nanogroove array by varying n with small change of Δn = 0.01, where a considerable MP resonance peak shift can be clearly seen. It is noted that the peak is linearly red-shifted by approximately 12 nm with increasing n. To evaluate the sensing performance, we introduced a sensitivity S describing the peak wavelength shift per refractive index unit (nm/RIU), which can be expressed as [26]:
Here, dn represents the change of the refractive index, and dλMP denotes the corresponding MP resonance peak shift. Since dλMP is linearly proportional to dn, we take dn =1.332–1.312=0.02, which corresponds to the peak shift dλMP = 24 nm from 1542 nm to 1566 nm. Then a sensitivity as high as 1200 nm/RIU is obtained.Generally, a figure of merit (FOM), which is defined as sensitivity divided by the resonance linewidth (full width at half maximum, FWHM), is employed as another important parameter to evaluate the performance of a sensor [29,30]. This definition is valid for narrow spectral lines since it is easier to detect a given resonance shift for a single sharp plasmonic resonance. Whereas, the above concept of FOM is not appropriate for more complex plasmonic responses, which do not follow a simple Lorentz peak shape, for example, the plasmonic excitations in metamaterial structures based on an analog of electromagnetically induced transparency (EIT) [31]. Therefore, an improved figure of merit (FOM*) introduced by J. Becker [26, 32] is used here for a more accurate assessment of the sensing ability. It is defined by evaluating a resonance shift as a relative intensity change dI(λ)/I(λ) induced by a small index change dn at a fixed wavelength λ, which can be expressed as
Here, I(λ) is the absorptance and λ is chosen where FOM* has a maximum value. Figure 2(b) shows the relative intensity change dI(λ)/I(λ) with wavelength induced by a slight refractive index change dn = 0.02. Apparently, the FOM* of our structure reaches a maximum of about 15 at a wavelength of 1630 nm.
Fig. 2 (a) Simulated Absorptance with different refractive index n. (b) Calculated [dI(λ)/I(λ)]/dn as a function of wavelength with dn = 0.02. (c) MP resonance positions extracted from (a) (red squares) and the corresponding results calculated by LC model (blue triangles).
Now, we give a quantitative description of the changes in MP response under the influence of the surrounding medium by applying a modified equivalent inductor-capacitor(LC) nanocircuit model. Actually, LC nanocircuit model has been successfully used to describe the magnetic or plasmonic responses in a variety of nanostructures [25, 27, 33]. Consider a unit cell of the nanogroove array, the gold groove can be regarded as a nanocircuit with a capacitor and an inductor that are connected in series, as displayed in Fig. 1(a) (right). According to LC model, the inductance of gold can be calculated as LAu = Lk + Lm, where Lm is mutual inductance between two parallel walls and Lk represents the kinetic inductance. Their expressions are given as follows [34,35]:
Here, δ = 1/α represents the penetration depth of the electric field with α being the extinction coefficient. Here, h′ = 2h + b + 2δ is the total distance of current flows. ∊0 and μ0 denote the vacuum permittivity and permeability, respectively. The real (∊′Au) and imaginary (∊″Au) part of gold permittivity are given by Drude model [36]. When filled with a material n, the groove introduces an effective capacitor which can be calculated as CG = c1∊d∊0h/b, where ∊d = n2 is the permittivity of the medium and c1 is a numerical factor used to indicate the non-uniform of bound charges. By solving LC circuit resonance equation , we can obtain the wavelength of magnetic resonance for different filling medium. Here, c0 is the speed of light in vacuum. The calculated MP resonances, as shown in Fig. 2(c) (blue triangles), are in good agreement with the simulated results (red squares).Therefore, from the perspective of LC model, the MP-based sensing ability can be well explained as follows: the MP resonances are actually controlled by the groove-induced capacitor CG, which is directly relevant to the filling material ∊d. Considering the expressions of CG and ∊d, the dependence of MP resonance on the refractive index of the filling material can be given in a more explicit form:
Here, the frequency-dependent gold inductance LAu Eqs. (3) and (4) is a slowly varying quantity, which can be regarded as a constant in the interested wavelength range. With c1 representing the inhomogeneous distribution of bound charges, which is also almost invariant in our case, Eq. (5) clearly gives the MP wavelengths that are linearly proportional to the refractive index of the filling material n. This linear dependence is confirmed by the straight lines in Fig. 2(c).To give a deep insight into the sensing mechanism, we further investigate the local effects of our sensor, i.e., the influence of local environment change on the sensing ability. It is worth mentioning that the MP excitation is also featured by a strong electric field localization at the groove opening, which is crucial for determining the light-matter interaction within the surrounding material, thus governing the refractive index sensing performance. Figure 3(a) gives the distribution of electric field at the MP resonance λMP = 1542 nm with a strong field enhancement at the groove opening. We expect that a local change of refractive index at the place where a strong localized electric field occurs will lead to a better sensing ability. In contrast, variations of the refractive index at the region with weak electric field will cause small shift of the MP resonances with reduced sensing performance. To verify this, we have simulated two cases with local refractive index changes at two different places inside the groove. Figure 3(b) (blue) displays the result of the first case in which only the refractive index within a 50-nm-thick region at the groove bottom changes from 1.312 to 1.352, as shown in the left inset of Fig. 3(b). In this case, due to the weak electric field at the bottom, the MP resonance only shifts by 2 nm with respect to that with homogeneously filled material (n = 1.312). While for the second case, as illustrated in the right inset of Fig. 3(b), the material at the groove opening changes to n = 1.352. This results in a much larger MP resonance shift of 14 nm (red), corresponding to the high sensitivity of S = 1200 nm/RIU.
Fig. 3 (a) Distribution of electric field at λMP = 1542 nm with a strong field confinement at the groove opening. (b) Simulated absorptance for locally varying material inside the groove.
This strong local effect can be qualitatively understood in the framework of LC model. For the first case with the strong electric field localization at the groove opening, a certain amount of change in the refractive index Δn corresponds to a larger variation of CG, thus leading to a larger MP shift to red. In contrast, for the second case, the same amount of Δn results in a smaller CG due to the weak electric field distribution at the groove bottom. This definitely gives rise to a reduced sensing ability.
Another characteristic of this simple 1D nanostructure lies in the fact that the MP excitations are dependent on the geometrical configurations. Now we will show that high-quality sensing can be achieved over a broadband wavelength range by changing groove depth. Figure 4 demonstrates the simulated figure of merit as a function of groove depth. We can clearly see that the MP resonances are blue shifted with increasing sensing performance (larger FOM*) for shallower groove (smaller groove depth). By varying the groove depth from 120 nm to 200 nm, We have obtained a high-quality refractive index sensing over 500 nm in NIR region. Note that our simulations (data are not shown) also show that the MP resonances are not sensitive to the angle of incidence. Therefore, the sensing performance is almost independent of the angle of incidence. Importantly, the MP resonance positions and the corresponding sensing ability can be readily predicted and controlled via LC nanocircuit model, which is expected to facilitate the future design and practical realization of the NIR refractive index sensor.
Fig. 4 Calculated FOM* values at MP resonances over a broad wavelength range. The lower left and the upper right insets show the simulated absorptance for a groove depth of 120 nm and 200 nm, respectively. The red and blue lines represent the absorptance simulated with refractive indices of 1.312 and 1.332, respectively.
3. Conclusion
In summary, we have proposed a high-quality refractive index sensor based on a simple magnetic nanostructure consisting of an array of metallic nanogrooves. A sensitivity up to 1200 nm/RIU with FOM* of 15 has been obtained due to the MP resonances that are extremely sensitive to the surrounding media. An equivalent inductor-capacitor (LC) model is used to give a precise quantitative description of the sensing performance and reveal the underlying mechanism. We have also studied the influence of the local environment effects on the sensing ability. We expect that such a MP-based sensor with the ease of fabrication may provide great potentials in designing broadband sensing devices with high performance and compactness.
Funding
National Natural Science Foundation of China (No. 61675139, 11474207, 11374217); National Key R&D Program of China (2017YFA0303600).
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