1. Introduction

Fano resonances have been observed successfully from the electric transport in quantum wires and quantum dots [1,2] as well as the absorption in molecular systems [3]. They can be well understood as interference of a discrete state with a continuum state, and they have a sharp asymmetric profile [4]. Recently, Fano resonances in optical nano-structures became more and more popular because of their potential applications in areas of chemical or biological sensors, filters, lasers, and switchers [5,6]. Because of subwavelength confinements of surface plasmon polaritons (SPPs) in metallic nanostructures and their high sensitivities to surroundings, various plasmonic nanostructures have been widely proposed to generate Fano resonances. For example, nano-clusters [7–10], split-ring resonators [11], nano-rod dimers [12–16], planar metamaterials [17,18], nano-antennas [19], nano-cavities [20] and nano-hole quarters [21], were designed to realize Fano resonances by using the interference of local surface plasmon resonances (LSPRs) with different orders.

Since Fano resonances in subwavelength metallic nano-structures exhibit enormous field enhancements and high sensitivities to surrounding media, they have important applications in the area of sensing, such as monitoring refractive index changes [7–21]. The sensitivities of these Fano-based sensors ranged from S = 338 nm/RIU to S = 647 nm/RIU [7–21] in experiments. However, the linewidths of Fano resonances in these nanostructures were large (Δλ > 20 nm) [7–21] because of huge losses of LSPs (including radiative losses and absorption losses) in metallic nanostructures. The large linewidths hamper the observation and recognition of wavelength shifts in sensing processes [6]. To better evaluate the performances of optical sensors, the figure of merit (FOM = S/Δλ), which is defined as the ratio of the sensitivity (S) and linewidth (Δλ) [6,10,11,13,15,18,21–23] is introduced. Due to large bandwidths of LSPRs, the values of FOM were smaller than 15 in Fano sensors based on LSPRs [7–21].

High-FOM sensors play an important role in many areas, such as the detection of early disease and low concentration explosives [24–35]. To obtain a high-FOM sensor, surface plasmon polarization (SPP) modes were used to narrow Fano resonances [24–35]. SPP modes show weaker confinement than LSP modes [6], and thus SPP modes exhibit lower losses than LSP modes [6]. Hence, linewidths of Fano resonances based on SPP modes are reduced, and a higher FOM is promised to obtain. For example, by designing a period metallic array, narrow Fano resonances were generated due to interference of SPP resonant modes and directly transmitted (or reflected) light in periodic metallic nanostructures [24–29,31–35]. In a gold patch array [24], the linewidth of Fano resonances and FOM were measured to 14.0 nm and 23, which is greater than that (FOM < 15) based on LSPRs [7–21]. In a gold nano-slit array [25], the linewidth of Fano resonances was 8.0 nm, and FOM was increased up to 55 [25]. Recently, by using Wood’s Anomaly, which has much weaker field confinements than SPP modes [36], to decrease metal losses, Scheuer’s group obtained a narrower Fano resonance in a nano-groove array [30]. The linewidth of Fano resonances was as small as Δλ = 5.0 nm, and FOM was as high as 140 [30], which was about 3 times that in the Fano sensors based on SPP modes [25]. Magnetic resonances [37,38], surface lattice resonances [39,40], toroidal resonances [41,42], and bound-states in the continuum [43,44] have also been introduced to design dielectric [37,38,43,44] or metallic [39–42] nanostructures to improve the performance of sensing devices. For example, the value of FOM based on bound-states in the continuum [43] by using all-dielectric photonic crystal meta-surface is increased up to FOM = 297 in liquid. However, the bound-states in the continuum need symmetric refractive index surroundings in the system, limiting the sensing ranges of refractive index (ranging from 1.4000 to 1.4480) [43].

In the letter, we propose to tilt a metallic nano-groove array to reduce linewidths of Fano resonances in the scattered spectra. The Fano resonances stem from interference between narrow SPP resonant modes and a broad LSP mode in the metallic nano-groove array. Simulation results show that linewidths of Fano resonances can be shrunk to ∼1.1 nm when tilting the metallic nano-groove array. The phenomena of linewidth narrowing stem from new generations of Fano resonances, which compress the Fano resonance of interest. As a result, the value of FOM is predicted to be approximately 600. This value is more than 10 times that (FOM ≤ 55) of Fano sensors based on SPP modes [24–29,31–35], and it is even four times greater than that of the previous Fano sensor based on Wood’s Anomaly [30]. In experiments, the phenomena of linewidth narrowing in Fano resonances are observed by tilting the metallic nano-groove array, coinciding well with the simulation results. We experimentally obtain a narrow Fano resonance with a linewidth of Δλ = 2.5 nm, which is greater than the simulation results (∼1.1 nm) because our gold film is polycrystalline. By using the narrowed Fano resonances, a high-FOM refractive index sensor is demonstrated, and the value of FOM is measured to be FOM=263. This value is larger than those in the Fano sensors based on LSPRs [7–21], SPPs [24–29,31–35], and Wood’s Anomaly [30].

2. Results and discussion

A tilted metallic nano-groove array on a metal film is schematically shown in Fig. 1(a). The nano-groove antenna array possesses a period of p_x and a period of p_y. A rectangular coordinate system is also added in Fig. 1(a). The x-axis and y-axis are on the metal surface. The angle between the y-axis and nano-groove array is φ, as shown in Fig. 1(a). The nano-groove antenna on the metal surface has a width of w, a length of l, and a depth of d, as displayed in Fig. 1(b).

 

Fig. 1. (a) Schematic and geometrical parameters of a tilted metallic nano-groove antenna array. The tilting angle is φ. (b) Sectional view (top) and top view (bottom) of a single metallic nano-groove antenna. The geometrical parameters and incident angle are also given here. The unit cell and cross-section of the nano-groove antenna array are indicated by green dashed boxes in (a) and (b), respectively.

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A p-polarized plane wave (vacuum wavelength of λ and magnetic field along the y axis) illuminates the metallic nano-groove array with an incident angle of θ [Fig. 1(b)], and SPP resonant modes with narrow linewidths can be excited [24–35]. According to the condition of wave-vector matching, the resonant wavelength of the metallic nano-groove array can be expressed as follows [45]:

Here, m₁ and m₂ are the orders of the SPP resonant modes in the x-axis and y-axis, respectively. The vectors $\vec{k}$, $\vec{x}$, and $\vec{y}\; $ denote unit vectors along the wave vector, x-axis, and y-axis. The expression on the left side of Eq. (1) means the effective refractive index of SPPs on the metal surface [24–35]. ɛ_m and ɛ_d denote permittivity of the metal and dielectric. Based on Eq. (1), the resonant wavelength can be expressed as follows:

The plus-minus signs in Eq. (2) originate from the bidirectional propagation of SPP modes on the metal surface. C₁ and C₂ are independent with θ and φ. Based on Eq. (2), the SPP resonant wavelength λ₀ is not only determined by p_x and p_y but also affected by the incident angle of θ and tilted angle of φ. In the following, we focus on the resonances in the long-wavelength range (the first plus-minus sign being treated as a plus sign) because the sensitivity is proportional to the wavelength [6]. Meanwhile, the metallic nano-groove antennas also support LSP modes [7–21], whose linewidth is large because of large losses [7–21]. As a consequence, the interference between the narrow SPP resonant modes and the broad LSP mode produces Fano resonances in the scattered spectra.

The nano-groove antenna is designed to be small and shallow, and the periods are designed to be larger to reduce the duty ratio of the nano-groove antennas in the array. As a result, the scattered losses of the nano-groove antennas are decreased, and the losses of SPP modes in the nano-groove antenna array become small. To collect the weak signal scattered from the nano-groove antennas and obtain a high signal-to-noise ratio, we calculate the scattered spectra in the direction vertical to the surface of the metallic nano-groove by a Finite Difference Time Domain (FDTD) method. The results are shown in Fig. 2(a). Here, the structure parameters are w = 60 nm, l = 200 nm, d = 150 nm, p_x = 1200 nm, and p_y = 800 nm, respectively. The incident angle is θ = 40.0°, and the tilted angle of the metallic nanogroove array is φ = 0.0°. The medium above the metal surface is water, and its refractive index is n = 1.333. The metal is set to be gold, whose permittivity as a function of a wavelength is taken from the experimental results in the previous work [46].

 

Fig. 2. (a) Scattered spectrum of a gold nano-groove antenna array (θ = 40.0° and φ = 0.0°). Electric field distributions (|E|) of the (b) (3,0) [blue dashed line in (a)] and (c) (2,1) [orange dashed line] SPP mode above the metal surface in a unit cell of the gold nano-groove antenna array [denoted by the green dashed box in Fig. 1(a)]. Electric field distribution in z component (|E_z|) of the (d) (3,0) and (e) (2,1) SPP mode in the cross-section of the gold nano-groove antenna array (denoted by the green dashed box in Fig. 1(b)). Insets in (d) and (e) are the zoom-in field distributions.

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There are four peaks in the scattered spectrum, as shown in Fig. 2(a). The four peaks from left to right are the LSP mode, the (0,1) SPP mode, the (3,0) SPP mode, and the (2,1) SPP mode, respectively. The LSP mode has a broad linewidth (Δλ ≈ 50.0 nm). The high-order modes [(3,0) SPP mode and (2,1) SPP mode] in Fig. 2(a) exhibit narrow linewidths, whose electric field distributions |E| are displayed in Figs. 2(b) and 2(c). The nodes in the electric field distribution along the x-axis and y-axis correspond to the resonant orders m₁ and m₂ intuitively. Moreover, the electric field distributions (|E_z|) of the above modes are displayed in Figs. 2(d) and 2(e). |E_z| shows an exponential decay along the z-axis, and it has a decay length of a bit less than the wavelength, verifying the high-order modes are SPP modes. The low-order mode [(0,1) SPP mode] is not on our focus. In addition, strong electric fields confined in the nano-grooves can also be observed from insets in Fig. 2 due to the LSP mode (Δλ ≈ 50.0 nm) in the nano-groove antenna. The interference between the high-order SPP modes and the LSP mode generate Fano resonances, which are denoted by a blue dashed line and an orange line in Fig. 2(a).

We then tilt the metallic nano-groove antenna array, and the scattered spectra are measured, as shown in Fig. 3(a). Here, we fix the incident angle of θ = 40.0°. It can be found that the (3,0) SPP mode is slightly blue-shifted (denoted by a blue dashed line), while the (2,1) SPP mode splits into two branches in opposite directions (denoted by orange dashed lines). As a result, a new Fano resonance emerges, as shown in Fig. 3(a). The new Fano resonance approaches the (3,0) SPP mode with increasing φ, and the Fano resonance of interest is compressed. So that, the linewidth of the Fano resonance decreases. The resonant wavelengths of the (3,0) and (2,1) SPP modes in simulations are denoted by the blue and orange dots in Fig. 3(b). While the calculation data by Eq. (2) are displayed by the red and green solid lines in Fig. 3(b). The simulation results agree well with the calculation data. An overlap between the (3,0) and (2,1) SPP modes emerges at φ = 7.5° [denoted by the black dashed line in Fig. 3(b)].

 

Fig. 3. (a) Spectra of a gold nano-groove antenna array versus φ. Herein, θ is set to be 40.0°. (b) Resonant wavelengths of the (3,0) and (2,1) SPP mode versus φ, respectively. The blue and orange dots are the simulation results. The red and green solid lines are the calculation results based on Eq. (1). (c) Linewidth and ν of the left Fano resonance in (a) versus φ. (d) Linewidths and ν of the left Fano resonance in (a) with different θ.

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Next, we obtain the linewidth and visibility of the left Fano resonance [denoted by the blue line in Fig. 3(a), as shown in Fig. 3(c)]. The linewidth of the left Fano resonance is defined as the full width at half maximum (FWHM) [13,15,18,22,24,25,47,48]. The visibility ν is defined as follows [49,50]:

Finally, we simulate the linewidth Δλ and visibility ν of the left Fano resonance at different incident angles of θ to identify the universal of our proposal, and the results are shown in Fig. 3(d). The linewidths of the (3,0) SPP modes can be compressed to approximately Δλ≈1.1 nm when θ = 35°, 40°, and 45°. Meanwhile, a decrease of the incident angle of θ leads to a rise of the tilted angle of φ to obtain a minimum linewidth. Compared to the previous work based on Wood’s Anomaly [30], the linewidth obtained by our structure is narrower (Δλ≈1.1 nm), and the value of ν is doubled. The Fano resonance with a narrow linewidth and high visibility is good for the observation and recognition of wavelength shifts in sensing processes.

To test our proposal experimentally, the metallic nano-groove antenna array is fabricated by using focused ion beams (FIB) on a 200-nm-thick gold film, which is evaporated on a glass substrate. A scanning electron microscopy (SEM) image of the gold nano-groove antenna array is shown in Fig. 4(a), and a zoom-in image is inserted. The length, width, and depth of the nanogroove are measured to be approximately 60 nm, 200 nm, and 150 nm, respectively. The periods are measured to be approximately p_x = 1200 nm and p_y = 800 nm. The schematic of the experimental measurement system is shown in Fig. 4(b). We use a super-continuum white light source (Fianium) as an incident light. The incident light illuminates the sample with an incident angle of θ. Here, we can slightly change the position of the mirror on the right top of Fig. 4(b) to change the incident angle of θ. In addition, the titled angle of φ can be changed by an indexing rotation mount, where the sample is pasted. Then, we collect the scattered light in the vertical direction from the nanogroove array by an objective (Mitutoyo 20X and NA = 0.4). Finally, the scattered light is split into two paths by a splitter. One couples into a fiber that connects to a spectrograph (Andor), and the other enters Complementary Metal Oxide Semiconductor (CMOS). The tilting process of the sample is monitored by CMOS, as shown in Fig. 4(c).

 

Fig. 4. (a) SEM image of a gold nano-groove antenna array. Inset is a zoom-in image of an individual nano-groove antenna array. (b) Schematic of the experimental measurement system. (c) Process of tilting the sample. The images are captured by CMOS.

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Next, we fix an incident angle of θ = 36.2° and place the sample in water. Since the linewidth of the (3,0) SPP mode can be reduced to ∼1.1 nm by changing the tilting angle in different incident angles θ, the incident angle θ here is not chosen to be the same as that in the simulation. When titling the sample, the scattered spectra are measured, and the results are shown in Fig. 5(a). The (3,0) SPP mode and (2,1) SPP mode are marked by the blue and orange dashed lines in Fig. 5(a), agreeing well with the simulation results in Fig. 3(a). Note that, we only show a part of the spectra in Fig. 5(a) to observe wavelength shifts of the Fano resonances more clearly. When the Fano resonance [(2,1) SPP mode] approaches the (3,0) SPP mode with increasing φ, the Fano resonance of interest is compressed. As a result, the linewidth of Fano resonance (blue dashed line) decreases. The resonant wavelengths of the (3,0) and (2,1) SPP modes in the experiment are denoted by the blue and orange dots, while the calculation results based on Eq. (2) are given by the red and green solid lines in Fig. 5(b). The experiment results are coincident with the calculation results. Moreover, the linewidth Δλ and visibility ν of the left Fano resonance [denoted by the blue line in Fig. 5(a)] are shown in Fig. 5(c). The linewidth Δλ and ν show a decrease with increasing φ. The linewidth Δλ = 2.5 nm and visibility ν = 0.74 are obtained when φ = 8.0°. Compared to the previous work [24–35], the linewidth of Fano resonances reduces to one-third of that (>8.0 nm) based on SPP modes [24–35], and it is half of that (5.0 nm) based on Wood’s Anomaly [30]. The Q-factor is λ/Δλ = 850/2.5 = 340, and the dephasing time t_d is calculated to be 2ħ/δ = 1.32×10⁻¹⁵ eV/4.18×10^{- 3}eV = 0.32 ps. [51] The visibility (ν = 0.74) of the Fano resonances in our sample is approximately double that (ν<0.4) in previous works. [30,50].

 

Fig. 5. (a) Experimental spectra (wavelength from 830 nm to 920 nm) of the gold nano-groove antenna array versus φ. Herein, θ is set to be 36.2°. (b) Resonant wavelengths of the (3,0) and (2,1) SPP mode versus φ, respectively. The blue and orange dots are the measured results. The red and green solid lines are the calculation results based on Eq. (1). (c) Linewidth and ν of the left Fano resonance in (a) versus φ.

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Last, we use the narrow linewidth and high-ν Fano resonance to experimentally demonstrate a refractive index sensor. We first prepare 0%, 1%, 2%, 3%, 4%, 5% of NaCl solutions, whose refractive indexes are 1.32165, 1.32326, 1.32500, 1.32674, 1.32848, 1.33022, respectively [52,53]. We fix the incident angle θ = 36.2° and tilted angle φ = 8.0°, which are the same as those at bottom of the Fig. 5(a). The scattered spectra are measured when the sample is placed in NaCl solutions with different concentrations. The measured results are shown in Fig. 6(a). It can be observed that the left Fano resonance (denoted by a black dashed line) shows a remarkable linear red-shift with the increase of the concentration of the NaCl solutions. Then, we plot the wavelengths of the Fano resonances as a function of the refractive index, as shown by the black dots in Fig. 6(b). The red solid line in Fig. 6(b) is a fitting curve. The Fano resonance is linearly red-shifted with the increase of refractive index variations from the solutions. We can derive that the sensitivity S is S ≈ 657 nm/RIU. The sensitivity S≈657 nm/RIU is much greater than the experimental results based on magnetic resonances (S=86 nm/RIU) [38], surface lattice resonances (S=449 nm/RIU) [54], and bound-states in the continuum (S = 178 nm/RIU) [43], and it is comparable to the best result (S = 647 nm/RIU) of previous plasmonic sensors [7–29] based on Fano resonances.

 

Fig. 6. (a) Experimental results of the compressed Fano resonant spectra (wavelength from 830 nm to 900 nm) in 0%, 1%, 2%, 3%, 4%, 5% NaCl-H2O solutions. The black dashed line represents the Fano resonant peak. (b) Measured values in (a) with the refractive indexes ranged from 1.32165 to 1.33022 (black spots). The red solid line denotes the linear fitting curve.

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The FOM in our sample is approximately FOM = S/Δλ = 657/2.5≈263. The comparison between the measured results, simulated results, and calculated results is shown in Table 1. The sensitivities of the three results are in good agreement. However, the FOM in the experiment is lower than that in simulation, which attributes to our polycrystalline gold film. Even so, the FOM of our plasmonic sensor is more than 4.7 times that (FOM ≤ 55) of Fano sensors based on SPP modes [24–29,31–35], and it is twice that of the previous Fano sensor based on Wood’s Anomaly [30]. The FOM of our plasmonic sensor is even close to the experimental result (FOM = 297) based on bound-states in the continuum [43] by using all-dielectric photonic crystal meta-surface. However, the bound-states in the continuum need symmetric refractive index surroundings in the system, limiting the sensing ranges of refractive index (ranging from 1.4000 to 1.4480) [43]. Furthermore, compared to some sensors with multi-material and multi-layers nano-structures [30,25] or symmetric refractive index surroundings [43,44], our structure only needs one gold layer, revealing an easy fabrication and large sensing ranges (refractive index ranging from 1 to 3).

Table 1. Experimental, Simulated, and Theoretical Sensing Performances

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3. Conclusions

In summary, we narrowed the linewidth of the Fano resonance by tilting the metallic nanogroove array. Experimentally, a linewidth Δλ = 2.5 nm and ν = 0.74 of the Fano resonance were obtained. Furthermore, we obtained a plasmonic refractive sensor whose sensitivity S and FOM are 657 nm/RIU and 263, respectively. The sensitivity (S = 657 nm/RIU) of our sample is comparable to the best result (S = 647 nm/RIU) [8] in previous plasmonic Fano sensors. The value of FOM was greater than those in Fano sensors based on LSPRs [7–21], SPPs [24–29,31–35], and Wood’s Anomaly [30]. Compared to some sensors with multi-material and multi-layers nano-structures [30,25] or symmetric refractive index surroundings [43,44], our structure only needs one gold layer, revealing an easy fabrication and large sensing ranges. Such a high-FOM sensor with easy fabrication and large sensing ranges might find important applications in the areas of environmental monitoring, biomedical diagnostics, healthcare, food safety, security, and chemical reactions.