1. Introduction

Plasmonic sensing based on nanostructure metal is inherently sensitive to a small change in the refractive index (RI) of the dielectric environment, which offers a sensitive, real-time, label-free way to realize disease diagnosis [1–5], food safety [6] and environmental monitoring [7]. There are two kinds of conventional plasmonic sensors, based on surface plasmon resonance (SPR) and localized surface plasmon resonance (LSPR). SPR sensors benefit from a high sensitivity to refractive index changes of ~10⁶ nm/RIU with sensing distance of ~1000 nm and linewidth of typically ~50 nm [8]. However, SPR is not widely used due to the complexity of optical instrumentation to match momentum between the surface plasmon and a laser beam. LSPR sensors have emerged as an alternative to SPR primarily due to simple instruments for not requiring momentum matching. Although the refractive sensitivity of LSPR is ~10² nm/RIU, the highly confined electric field to tens of nanometers makes the detection level comparable to SPR sensor for biological molecule detection [9]. There are subtle differences between the bulk refractive index sensitivity and its surface detection sensitivity. To evaluate the surface-sensing capabilities of different nanostructures, the wavelength shift caused by the cover media on the surface can be expressed as [10]

The wavelength shift caused by the cover media can be improved while the electric field is more tightly confined on the metal surface. The surface sensitivity is a key merit for biological sensing where the RI changes are restricted at the interface of biosensor. Nevertheless, the figure of merit (FOM) of LSPR biosensors is usually less than 10 due to the broad linewidth of the spectra [11].

Among the metal nanostructure, the metal gratings have attracted extensive research due to its complex physics phenomena such as Surface Plasmon Polariton (SPP), cavity plasmon, Fano resonance and Rayleigh anomaly (RA) [12–15]. The electric fields of SPP and cavity plasmon are both confined on the metal surface, which is helpful to improve sensitivity of biosensor. However, the linewidth of both is broad [12,16]. The full-width at half maximum (FWHM) of gratings can be reduced by 60% using oblique incidence to generate Fano resonance by breaking the symmetry [17]. The interference between LSPR and SPP or RA results in a Fano resonance exhibits narrow linewidth of tens of nanometers [18]. However, the Fano resonance condition is very strict in structure design. Meanwhile, the position of Fano resonance is difficult to modulate only by changing incident angle. Rayleigh anomaly corresponding to a scattered wave tangential to the gratings surface is observed as a sharp dip in the reflection spectra with narrow linewidth of several nanometers. It is sensitive to the change in the surrounding refractive index [19,20]. Advantages of index sensor based on RA focus on the following points: (1) the sensitivity solely dependent on the period; (2) the spectral position excellently linear to the change in the environmental refractive index; (3) narrow linewidth; (4) large operation spectral range by changing incidence angle [21]. However, it is worth noting that the electric field enhancement extends far away from the gratings surface for RA [22]. Therefore, the surface sensitivity of RA deteriorates up to two orders compared with the corresponding bulk sensitivity due to large l_d in Eq. (1) [23], which is an obstruction for biosensor. To improve the biosensing capabilities, RA-based sensing with confined field is proposed by coupling RA on the detection side with the SPP on the substrate side [24]. However, the refractive index of the substrate must be smaller than that of the testing medium, which limits the device for practical application in detecting biological molecules. Another way to improve the performance of biosensor is coupling RA with other modes such as LSPR to achieve high confined field and narrow linewidth [20,21,25–27]. Nevertheless, the coupling condition is strict with narrow operation spectral range, which restricts application of the biosensor in different wavelengths.

To reduce the evanescent decay length, a novel label-free plasmonic biosensor based on metamaterials is performed with very high surface sensitivity to detect biomolecules. A plasmonic biosensor platform based on the hyperbolic metamaterials composing of 16 alternating thin films of Au and Al₂O₃ coupled of two-dimensional (2D) gold diffraction gratings have been developed with high sensitivity of 30000 nm/RIU and figure of merit (FOM) of 590 [28]. It utilized the guided mode with broad linewidth (~50 nm) to detect biomolecules. Whereas, the RA-based biosensor with much narrower linewidth of few nanometers has better performance than that of the guided mode.

Here we proposed a one-dimensional (1D) metal/dielectric multilayer grating sensor composing of 8-layer Au/Al₂O₃ stacks. The RA properties of Au/Al₂O₃ multilayer gratings, comparing with Au gratings, are explored by finite-difference time-domain (FDTD) method. For the Au/Al₂O₃ multilayer gratings, the electric field is bound to the gratings surface and limited in the several hundreds of nanometers from the surface. The surface sensitivity of the new structure increases 10 times compared with that of Au gratings under normal incidence when the thickness of detection media is less than 400 nm. Furthermore, for the Au/Al₂O₃ multilayer gratings, reflection dip is deeper with narrower linewidth. The improved surface sensitivity and the narrow linewidth make Au/Al₂O₃ multilayer grating a good candidate as biosensor based on RA. Furthermore, oblique incidence can modulate the wavelength of RA. Moreover, the electric field is confined more tightly to the surface when the light is oblique incidence, thus the surface index sensitivity can be improved 5 times than that at normal incidence when the thickness of cover media is 20 nm.

2. Design and simulation

The sensor composed of nano-patterned Au/Al₂O₃ multilayer is shown in Fig. 1. The multilayer consists of 8 Au/Al₂O₃ stacks and the thickness of each stack is 50 nm (Au 20 nm and Al₂O₃ 30 nm). The period and width of the 1D-grating are denoted as p and w, respectively. The reflection spectra and the electric field distribution are calculated by the two dimensional finite-difference time-domain (FDTD) method [29]. The structure is illuminated by transverse magnetic (TM) polarized light with the electric field perpendicular to the gratings propagating from the upside under incident angle of θ. The infinite structure is simulated using Bloch boundary conditions for oblique incidence and period boundary conditions for normal incidence along the x direction around the unit cell; perfectly matched layers is set along the y direction. The meshes have been refined to 2 nm to resolve all sharp features in the spectra. The monitors can directly gain the reflection spectra. The structure of multilayer grating is optimized by changing the layers of Au/Al₂O₃ stack, the width of slit and the proportion of thickness of Au to gain the deepest and narrowest reflection spectra. The property of the optimized Au/Al₂O₃ multilayer gratings and the Au gratings was compared in two aspect: reflection spectra and electric field. Besides, the surface sensitivity of multilayer gratings was explored with different thickness of cover media under different incident angle, which indicates the capability to detect small molecules.

 

Fig. 1 A scheme of nanostructure of multilayer gratings. consisting of nano-patterned 8 layers of Au (20 nm)/Al₂O₃ (30 nm) multilayer with the period of p = 500 nm and the width of w = 150 nm under TM incidence with angle of θ from upside.

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3. Results and discussion

3.1. Au gratings

The optical properties of Au gratings were explored by simulation in following three environments. (1) The Au gratings are freestanding and the surrounding media is water denoted as water-Au-water (case 1). (2) The Au gratings are surrounded by glass denoted as glass-Au-glass (case 2). (3) The Au gratings are sandwiched between water and glass with the slits in water denoted as water-Au-glass (case 3). The Au gratings were designed with period p = 500 nm, thickness of Au h = 400 nm and slit width w = 150 nm. The simulation based on the finite-difference time-domain method was carried out using the Lumerical FDTD software [29]. The frequency-dependent permittivity of Au is obtained by Palik database and the refractive index of glass substrate and water is taken as n_sub = 1.46 and n_water = 1.33, respectively. The light is normally illuminated from the upside of the gratings with electric field perpendicular to the slits. Periodic boundary conditions is set along the x direction; perfectly matched layer is set along the y direction.

The reflection of electromagnetic waves through the Au gratings mentioned above have been calculated as shown in the Fig. 2(a). There are three dips in the reflection spectra. For the shortest wavelength, the dip of spectra in case 3 is coincident with that in case 1, which suggests the dip is associated with the media on the upside and has no reaction with the substrate. For the other two dips, the dip of spectra in case 3 is in the middle of that in case 2 and case 1, but it is nearer to that in case 1 indicating the slit is associated with the two modes.

 

Fig. 2 The property of Au gratings. (a) The reflection spectra of Au gratings in three different environments. (b) Dispersion diagrams of Au gratings, i.e. measured reflection energy dispersion as a function of in-plan wave vector on Au surface. The full lines denote calculated SPP with Eq. (4), and dash lines represent calculated RA with Eq. (3) with n_d = 1.33 for black and n_d = 1.46 for red. (c) Percentage of space-integrated near-field intensity confined within a volume extending a distance t_d outside the Au grating surface. (d-f) The distribution of electromagnetic field of Au gratings with p = 500 nm, w = 150 nm and h = 400 nm at different wavelength 665 nm, 828 nm and 1520 nm respectively, corresponding to the reflection dips in Fig. 1(a) denoted by water-Au-glass.

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The resonance modes were analyzed further by the electric field distribution at the reflection dips in case 3 as illustrated in Figs. 2(d)–2(f). The electric field of the first dip at wavelength of 665 nm results from two combined effect: one is the interference of the incident and reflected beams in the vertical direction; the other is interference of the grazing diffraction propagating parallel to the substrate. Both interferences have a periodicity matching half of the period of gratings [30]. The linewidth of the narrow reflection dip caused by Rayleigh anomaly is only 2.6 nm. However, the electric field shown in Fig. 2(d) extends far away from the surface, which is an obstruction for biosensor. The other two dips are derived from the cavity mode. From Figs. 2(e)–2(f), it illustrates that the field is tightly confined near the surface of gratings where it is sensitive to the surface index change. As shown in Fig. 2(c), the percentage of space-integrated near-field electric intensity confined within a volume extending a distance t_d outside the Au gratings at the three reflection dips is calculated. The field of the two cavity modes is confined on the grating surface within tens of nanometers, while the first dip induced by RA is extended far away out of 1 μm. However, the linewidth of the cavity mode is very broad which decreases the accuracy of the dip wavelength. Thus, the figure of merit (FOM) of the two cavity modes is low, which is given by [31]

Angle-resolved reflection spectra was acquired by changing incident angle from $1°$ to $10°$ in step of $1°$. We converted wavelength vs. angle data to photon energy vs. in-plane wave vector (k_x) data to construct dispersion diagrams depicted in Fig. 2(b) [32]. The color bar represents the reflection intensity. The reflection dip of the shortest wavelength splits under oblique incidence. The position of the resonance dips is in good agreement with the simple dispersion relation (dash lines) of RAs, which indicates the dip originated from the RAs. RAs occur at wavelength λ_RA predicted by [33]

The Au gratings have good FOM of 194 at RA wavelength. Whereas, the surface sensitivity is poor due to the electric field extending far away from the surface. The reflection dip derived from cavity mode demonstrates good surface sensitivity due to tightly confined electric field on the surface, however, the broad linewidth lends to poor FOM.

3.2. Au/Al₂O₃ multilayer gratings

The multilayer gratings composing of 8 Au/Al₂O₃ stacks have the same lattice parameters with the Au gratings mentioned above with period p = 500 nm, gap w = 150 nm and each layer of Au/Al₂O₃ stack is 50 nm (Au 20 nm and Al₂O₃ 30 nm), as schematically shown in Fig. 1. The bulk sensitivity can be obtained by changing the bulk refractive index of the media on the gratings from 1.33 to 1.41 with step of 0.01. The reflection spectra of Au/Al₂O₃ multilayer gratings and Au gratings are described in Figs. 3(a) and 3(b), respectively. The graph of resonance wavelength of RA and refractive index in Figs. 3(c) and 3(d) are extracted from Figs. 3(a) and 3(b), respectively. The dip derived from RA is almost in the same position for the two structures and the bulk sensitivity are both ~500 nm/RIU equal to the period of the gratings as predicted by Eq. (3). Moreover, the dip of Au/Al₂O₃ gratings is much deeper than that of Au gratings and the FWHM is reduced from 2.6 nm to 1.8 nm. The FOM can reach 275 for bulk sensing in Au/Al₂O₃ gratings. The electric field of Au/Al₂O₃ multilayer gratings at the dip of 666 nm for n = 1.33 is demonstrated in Fig. 3(e). The electric field is confined more tightly on the surface and the electric intensity is much larger than that of Au gratings shown in Fig. 2(d). Au/Al₂O₃ multilayer gratings with narrow reflection dip and tightly confined electric field can be used as biosensor based on RA. In Fig. 3(f), the photonic band structure of the Au/Al₂O₃ multilayer gratings was acquired by changing incident angle from $1°$ to $35°$ in steps of $2°$. The highest branch associated with the dip of Fig. 3(a) is close to the energy of RAs denoted by the black dash lines, which illustrates the mode is induced by RAs. The lowest branch coincides with the coupled SPPs on the interface of Au and Al₂O₃ denoted by the red full line depicted by Eq. (4) setting ε_d as 3.1.

 

Fig. 3 Properties of Au/Al₂O₃ mulitlayer gratings compared with that of Au gratings. (a) The reflection spectra of Au/Al₂O₃ multilayer gratings changes with the bulk refractive index. The corresponding field distribution of the dip at n = 1.33 is demonstrated in (e). (b) The reflection spectra of Au gratings changes with the bulk reflcetive index. (c)The RA wavelength changes with refractive index of multilayer gratings extracted from (a). (d) The RA wavelength changes with refractive index of Au gratings extracted from (b). (f) Dispersion diagrams of Au/Al₂O₃ multilayer gratings. Calculated SPP were denoted by the full lines, with black for n_d = 1.33 of the surface media and red for n_d = 1.77 of Al₂O₃. Dash lines represent Rayleigh anomalies with black for surface media and red for Al₂O₃.

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To determine the best formation of the Au/Al₂O₃ multilayer grating, the reflection spectra was investigated by changing geometry parameters: layers (n) of Au/Al₂O₃ stacks; the width of slit (w); proportion of the thickness of Au (f_Au,). Thickness of each Au/Al₂O₃ stack is set to 50 nm. As shown in Fig. 4(a), with more layers of Au/Al₂O₃ stack, the linewidth of reflection spectra becomes narrower. There is little difference in 6-10 layers. Here 8 layers of Au/Al₂O₃ stack was set for investigating the sensitivity of the multilayer gratings considering that less or more layers have little influence on the reflection spectra, which can bear some fabrication error in experiment. Decreasing width of the slit can reach deeper reflection at the wavelength of RA demonstrating in Fig. 4(b). However, considering the difficulties in fabrication of sub-100 nm nanostructure, the multilayer gratings with the slit of width at 150 nm can be fabricated more easily. Changing the proportion of Au part in the multilayer while keeping the thickness of each Au/Al₂O₃ stack 50 nm, it is found that f_Au = 0.4 (i.e. the thickness of Au is 20 nm) is the best condition for deep and narrow reflection dip at RA depicted in Fig. 4(c). Therefore, 8 layers of Au/Al₂O₃ stack with width of slit w = 150 nm and thickness of Au 20 nm was determined to be the best formation of Au/Al₂O₃ multilayer gratings for the simulation considering the cost and difficulty of nano-fabrication.

 

Fig. 4 (a)-(c) The reflection spectra of the multilayer gratings with different layers (n) of Au/Al₂O₃ stack, width of slit (w) and proportion of the thickness of Au (f_Au,). (a) w = 150 nm and f_Au = 0.4 with different layers. (b) n = 8 and f_Au = 0.4 with different w. (c) n = 8 and w = 150 nm with different f_Au. (d) The transmission (T), reflection (R) and absorption (A) of multilayer gratings (f_Au = 0.4) and Au gratings (f_Au = 1) both with geometry of p = 500 nm, w = 150 nm and h = 400 nm.

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The transmission (T), reflection (R) and absorption (A) spectra of 8-layer Au/Al₂O₃ multilayer gratings with best formation and Au gratings of the same geometry (p = 500 nm, w = 150 nm and h = 400 nm) was demonstrated in Fig. 4(d). The transmission and reflection spectra were obtained directly by FDTD simulation; the absorption spectra was gained by formula A = 1-R-T. For multilayer gratings, the deep reflection dip with narrower linewidth is much more notable than transmission peak, thus sensitivity is explored through reflection spectra. The deep reflection dip is caused by strong absorption of Au due to evanescent electric field in Au layers. The transmission of multilayer gratings is low to 15%. The transmission of Au gratings with thickness of 400 nm is 36% with low absorption of 6%.

To investigate the surface sensitivity of the Au gratings and Au/Al₂O₃ multilayer gratings, the thickness of cover media was swept from 20 nm to 400 nm with different refractive index to obtain surface sensitivity as shown in Figs. 5(a) and 5(b). The surface sensitivity of RA-based Au gratings is less than 30 nm/RIU when the thickness of cover media is 400 nm that is 10 times less than bulk sensitivity of RA. The surface sensitivity of Au grating (w = 150 nm and p = 500 nm) with thickness of 160 nm (the same thickness of Au as multilayer gratings), 400 nm (the same geometry as multilayer gratings) and 500 nm shows little improvement by increasing thickness of Au. It is ineffective to improve surface sensitivity by changing the geometry of Au gratings because its electric field extends far away at RA wavelength. The surface sensitivity of Au/Al₂O₃ multilayer gratings under normal incidence improved 10 times compared with that of Au gratings when the thickness of detection media is less than 400 nm. This result can be explained by the field distribution in Fig. 3(e) and Fig. 2(d). The electric field is confined on surface of the Au/Al₂O₃ multilayer gratings while extended far away from the surface of Au gratings. Under the oblique incidence from 1° to 5° with step of 1°, the RA wavelength splits as depicted in Fig. 3(d). The graph of surface sensitivity of the blue-shift RA with thickness of cover layer t_d is demonstrated in Fig. 5(a); the red-shift branch is shown in Fig. 5(b). The blue-shift branch has better surface sensitivity than that under normal incidence and shows little higher sensitivity by increasing incident angle. Under incidence angle of 5°, the surface sensitivity can be 5 times larger than that of normal incidence when the thickness of cover media is 20 nm. The electric distribution of blue-shift RA under incidence angle of 5° is exhibited in Fig. 5(c). Compared with the electric field of RA under normal incidence shown in Fig. 3(e), the electric enhancement under oblique incidence confined stronger to the surface leads the surface sensitivity to improve further. Whereas, surface sensitivity of red-shift branch becomes lower by increasing incident angle. To quantify the extent of electric field confined to surface, the decay length of electric field under incident angle of 0° to 5° is obtained by fitting graphs of Figs. 5(a) and 5(b) using Eq. (1). The decay length of the blue-shift branch is reduced under oblique incidence to improve surface sensitivity. Whereas, the red-shift branch achieves best surface sensitivity under incidence of 1° and decreases with larger incident angle.

 

Fig. 5 The surface sensitivity of Au/Al₂O₃ multilayer gratings and electric field distribution at oblique incidence. (a) The surface sensitivity of blue-shift RA as function of the thickness t_d of cover media. (b) The surface sensitivity of red-shift RA as function of the thickness t_d of cover media. (c)The electric field of the blue-shifted RA under incident angle of 5° at 622 nm. (d) The decay length l_d calculated by fitting Figs. 5(a) and 5(b) using Eq. (1) changes with incident angle θ.

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4. Conclusion

The surface index sensitivity of Au/Al₂O₃ multilayer gratings proposed by us is improved 10 times compared with gold gratings at RA wavelength under normal incidence. Because the electric field enhancement of Au/Al₂O₃ multilayer gratings is tightly bound to the surface within several hundreds of nanometers. FOM reaches 275 in bulk sensing due to narrow linewidth of 1.8 nm, which is far better than conventional LSPR sensor. The improved surface sensitivity and good FOM of RA-based Au/Al₂O₃ multilayer gratings make it a good candidate as a biosensor. Furthermore, the wavelength of RA can be designed by changing the period of gratings and modulated by oblique incidence. This convenient way to control detection wavelength of biosensor broadens its application. More importantly, the surface index sensitivity can increase 5 times under oblique incidence owing to the electric field confined more tightly to the surface than that under normal incidence.