High Figure of Merit Refractive Index Sensor Derived From the Axial Length Ratio of Elliptically Polarized Light of Chiral Plasmonic Structure Arrays

The refractive index sensor based on the Fano resonance effect (that is, Fano sensor) is one promising branch of plasmonic sensing applications owing to its narrow spectral line shape. Further improvement in the sensitivity and figure of merit (FOM) is the main issue in this field. In contrast to the Fano sensor, herein, we report a novel ultra-sensitive refractive index sensor based on the axial length ratio of transmitted elliptically polarized light of chiral plasmonic structure arrays (that is, ratio sensor). Compared with the optimized Fano sensor in the same asymmetric chiral plasmonic structure arrays, the proposed ratio sensor shows a better sensitivity performance of 556.9 nm/RIU, that is, 1.31 times higher than that of the optimized Fano sensor. Specifically, the quality factor of the spectral line shape and FOM of the proposed ratio sensor reach 121.6 and 60, respectively, that are 2.14 and 2.92 times higher than those of the optimized Fano sensor, respectively. Our study proposes a potential path to achieve high-quality ultra-sensitive refractive index sensing.


Introduction
The evanescent wave localized at the interface of the metallic nanostructure and dielectric environment, called localized surface plasmon oscillation [1], has a broad range of applications in energy harvest [2,3], subwavelength optical images [4][5][6][7], chemical sensors [8][9][10], biology detection [11][12][13], and medical diagnosis [14] owing to its large electric field enhancement factor and high sensitivity.Among them, the refractive index sensor is one pivotal application of the localized surface plasmon resonance (LSPR) effect in the field of sensing and detection [15][16][17][18][19].However, because of the large radiation loss of the metallic nanostructure itself, the optical spectral line, which is generally used to characterize refractive index changes, has a large line width (full width at half-maximum, FWHM), resulting in a low figure of merit (FOM) of the refractive index sensor and thus limiting its large-scale and rapid advancement.Therefore, ways to further increase the sensitivity (RIS, defined as the resonant wavelength shift (Δλ) per refractive index (n) unit (RIU) [20,21], RIS = Δλ/Δn) and FOM (defined as the ratio of refractive index sensitivity to spectral line width [21,22], FOM = RIS/FWHM) of the refractive index sensor are the main research directions in the field of refractive index sensing.
The Fano resonance effect formed by the coherent coupling of surface plasmon modes in metallic nanostructures generally presents narrow line width characteristics [23], which has been used and studied in the field of refractive index sensing (Fano sensors) [24][25][26].Considering the excellent spectral performance of Fano resonance effect, two dominate strategies exist to improve the RIS and FOM of the refractive index sensor.The first category is the continuous optimization of the Fano structures to narrow these spectral line characteristics [27][28][29][30].However, the manufacturing process limit of micro-nanostructures with minimal characteristics become the Achilles' heel of this strategy, inhibiting its diversity, flexibility, and advancement of the upper limit of devices.The second category is based on a different route of processing differential spectra to increase the RIS and FOM of the refractive index sensor [31][32][33][34][35][36][37].For example, Ptasinsk et al. demonstrated that the zerocrossing points in the difference curve of two differential transmission spectra, obtained from nanostructure arrays with two incident angles, could be tracked for sensing [31].Maccaferri et al. introduced a null point wavelength, obtained from the spectral dependence of the polarization ellipticity variation of the transmitted light, to detect changes in the refractive index [32].Jeong et al. used the circular dichroism (CD) spectra of chiral plasmonic particles to achieve high-quality detection of refractive index changes [33].Shen et al. reported an experimental ultra-high-Q plasmon resonance with a linewidth down to 2 nm (Q factor ≈ 350) and a resonance intensity of 51% in an ultrasmooth gold nanogroove array [38].Khani and Afsahi proposed a plasmonic refractive index sensors based on the PIT phenomenon; the maximum sensitivity and FOM of the main RIS obtain 725.1 nm/RIU and 91.78 RIU −1 , respectively [39].All these studies have enabled plasmonic sensors with high RIS and FOM.However, in application scenarios, the aforementioned strategies generally have certain limitations, such as complex operations and post-processing.Besides, 2D structures have greater potential in refractive index sensor structure selection due to better device integration compatibility and ease of processing characteristics compared to 3D structures.Therefore, developing 2D refractive index sensors with high RIS and FOM is of great importance for practical applications.
Herein, we propose an ultra-sensitive refractive index sensor with a high FOM based on the axial length ratio (the ratio of major/minor axis) spectra of transmitted elliptically polarized light of chiral plasmonic structure arrays.By constructing a refractive index sensor based on the optimized Fano resonance (that is, Fano sensor) and a refractive index sensor based on the axial length ratio (that is, ratio sensor,) in the same asymmetric Z-shaped chiral structures, we demonstrated and confirmed the excellent performance of our proposed ratio sensor.The numerical results showed that the constructed Fano sensor had an RIS of 423.7 nm/RIU, whereas the proposed ratio sensor displayed a better RIS of 556.9 nm/RIU, 1.31 times higher than that of its counterpart.Moreover, the quality factor (Q) of the axial length ratio spectral line shape and FOM of the proposed ratio sensor can reach 121.6 and 60, respectively, that were 2.14 (56.82) and 2.92 times (20.53) higher than those of the optimized Fano sensor, demonstrating the huge practical application potential of our proposed ratio sensor in high-quality ultrasensitive refractive index sensing.

Results and Discussion
To demonstrate the superiority of our proposed ratio sensor, we constructed a Fano sensor and ratio sensor in the same chiral plasmonic structure arrays by the finite difference time domain method (FDTD, Lumerical Solutions). Figure 1a shows a schematic of the designed unit cell of a complex Z-shaped structure with rotational asymmetry (denoted as AZ-l 2 -l 3 ), comprising by two gold (Au) nanorods and a Z-shaped structure with rotational symmetry (denoted as Z-shape) on a quartz (SiO 2 ) substrate.Specifically, a Z-shaped structure with several fixed parameters, l 0 , l 1 , w 0 , and w 1 , was positioned near two Au nanorods (l 0 = l 1 = 400 nm and w 0 = w 1 = 100 nm).l 2 and w 2 denote the length and width of the first Au nanorod, respectively, whereas l 3 and w 3 denote those of the second nanorod, respectively.The coupling gap, g, between all components was fixed at 20 nm.The array parameters, P x and P y , were the array structural periods in X-and Y-axes, respectively (P x = P y = 800 nm).The polarization of electric field, E, was parallel to the cantilever of the Z-shaped structure (that is, X-polarized incidence), and the propagation direction of the incident light was perpendicular to the SiO 2 substrate (the direction of wave vector k).The experimentally measured refractive index data of Au (Johnson and Christy) were used for numerical calculations.In the solutions, the transmission spectra were obtained from the frequency domain field, and the power monitor in simulation model was achieved using a plane wave source with a spectral range of 1000-2000 nm.A periodic boundary condition was set for X-Y dimensions, and the designed structure is covered by a discrete grid with 2 nm mesh in the X-Y dimensions and 3 nm in Z dimension.The surface charge distribution, electric field distribution, and polarization properties of the transmitted light were obtained from the analysis group of the simulation model.
We first calculated the transmission spectrum of the Z-shaped array, in which only a wide resonance dip could be observed, as shown by the black curve in Fig. 1b.As is well known, the Fano resonance system can be realized by breaking the structural asymmetry.Therefore, an Au nanorod was placed on the side of the Z-shaped structure to form a Z-shape with rotational asymmetry (denoted as AZ-l 2 ).A schematic of the designed unit cell of AZ-l 2 is shown in the inset of Fig. 1b.Width w 2 of the nanorod was fixed at 100 nm.With the continuous increase in l 2 , the entire AZ-l 2 structural system exhibited a complex transmission spectrum of four obvious dip features, denoted as A, B, C, and D. Dip A (represented by a black dashed arrow) presented an obvious Fano resonance characteristic, that is, an asymmetric line shape and a narrow line width, that is the result of coherent coupling between the plasmon modes of the structural system.The original wide resonance dip of the Z-shaped structure split into two sub-dips, dip B (represented by an orange dashed arrow) and dip C (represented by a purple dashed arrow).Dip C redshifted remarkably with an increase in l 2 , whereas the redshift speed of dip B was slow, suggesting their different sensitivities to the change in l 2 .Dip D (represented by a dark golden dashed arrow), around 1900 nm, was a newly appeared resonance mode with a weak response intensity that was weak and slightly redshifted as l 2 increased.
To better optimize the Fano dip and meet the requirements of subsequent mode analysis, parameter value l 2 related to the clear mode distribution and obvious Fano features was fixed at 330 nm to further study the influence of nanorod width w 2 on the dip position.As shown in Fig. 1c, with an increase in w 2 , dips B and D experienced a redshift with different magnitudes, whereas dip C exhibited an obvious blue shift.Combining the features of dip C in Fig. 1b, it is reasonable that dip C is dominated by the structural characteristics of the Au nanorods.Notably, as w 2 increases, the position of dip A (Fano dip, the object to be optimized) redshifted, and the corresponding FWHM is broadened owing to the significant radiation loss of wide nanorods.This change is detrimental to the improvement of the FOM of the refractive index sensor.Thus, we maintained w 2 = 100 nm and laid another Au nanorod with the same width (w 3 = 100 nm) to the left of the Au nanorod to strengthen the asymmetry of the AZ-l 2 structure and finally form an AZ-l 2 -l 3 structure.This optimization process not only modulates the oscillation phase of the right nanorod but also avoids the increase in radiation loss as much as possible.As shown in Fig. 1d,   all four response dips had a certain degree of redshift as l 3 increased.The depth of the Fano dip (dip A) first increased and then decreased, and its FWHM did not change; this was attributed to the essential principle of modulating the oscillation phase of the Au nanorod.
To clearly understand the dominant plasmon mode in the complex transmission spectrum features of the constructed Fano structure, the optimized transmission spectra of different structures were selected, as shown in Fig. 2a.The results showed that the depth of the Fano dip [40] (δ 2 ) constructed in the AZ-l 2 -l 3 structure was 0.37, 1.754 times that of the Fano dip constructed in the AZ-l 2 structure (δ 1 ).As shown in Fig. 2a, no obvious difference was observed between the transmission spectra shape of the AZ-l 2 and AZ-l 2 -l 3 structure arrays.Hence, instead of causing a more complicated mode hybridization process, the left Au nanorod only modulated the oscillation phase of the AZ-l 2 -l 3 structure.Therefore, the spectral features of the Z-shaped (I) and AZ-l 2 structures (II, III, IV, V, and VI) were selected for the plasmon mode analysis.Figure 2b shows the charge distribution (upper row) and electric field distribution (bottom row) at different spectral characteristic positions, shown in Fig. 2a.Systematic analysis revealed that five primitive modes existed in the entire structural system: the transverse dipole mode of the nanorod (TD), longitudinal dipole mode of the nanorod (LD), quadrupole mode of the nanorod (Q r ), dipole mode of the Z-shaped structure (D), and quadrupole mode of the Z-shaped structure (Q).A specific hybridization process according to the hybridization model of the surface plasmon modes is shown in Fig. 2c.The D (1320 nm) and LD modes hybridized to form a high-energy anti-bonding mode DLD AB (1314 nm and 1430 nm) and low-energy bonding mode DLD B (1525 nm).The D and TD modes hybridized to form a high-energy anti-bonding mode DTD AB and low-energy bonding mode DTD B (confirmed by the charge distribution and the electric field distribution at 1100 nm and 1230 nm).The Q and TD modes hybridized to form an anti-bonding mode QTD AB and a bonding mode QTD B (1919 nm).The D and Q r modes hybridized to form a bonding mode DQ r (1160 nm).Thus, the optimized asymmetrical line shape of the Fano dip in the transmission spectrum of the AZ-l 2 structure array was dominated by coherent coupling between the DQ r and DTD B modes.The sensing feature of the refractive index proposed in this study was the axial length ratio of transmitted elliptically polarized light under the incidence of linearly polarized light (LPIL).Therefore, to understand the optical properties of the chiral structures at a deeper level, the transmission spectra of the structures under different polarized light incident were systematically calculated.Figure 3a, b, c show the transmission spectra of three chiral structures under different types of incident polarizations (L represents left-handed circularly polarized incident light (CPIL), P represents LPIL, and R represents right-handed CPIL).The spectral response of the Z-shaped structure with the LPIL was stronger than that with the CPIL (Fig. 3a).With LPIL, the depth of the first two characteristic dips of the AZ-l 2 structure array was greater than that with the CPIL, and the response depth of the latter two characteristic dips was basically the same as that with the CPIL (Fig. 3b).As the asymmetry of the Z-shaped structure array further increased (Fig. 3c, AZ-l 2 -l 3 ), the difference in the depth of the first feature dip (Fano dip) under different polarization states was small, the depth of the second and third feature dips under the LPIL was greater, and the depth of the fourth dip was greater under the CPIL.In addition to the obvious difference in the transmission spectrum of the AZ-l 2 -l 3 structure array under different CPILs, the other two structures showed considerably little difference in the characteristic spectra under different CPILs.To more show the difference in spectral features of different CPILs, circular dichroism (CD), that is, the difference in the structural absorbance for left-handed and right-handed CPIL [41], was used to describe the chiral optical properties of different structures.As shown in Fig. 3d, the Z-shaped structure array had an extremum of CD around the resonance dip (located at 1351 nm).The AZ-l 2 structure array had an extremum around all feature dip positions (  large.The AZ-l 2 -l 3 structure array had three obvious extremums of CD (located at 1176, 1568, and 1974 nm), and the first two extreme features had larger CD values.Notably, the extreme value corresponding to the second resonance dip was missing because of the superposition of the CD values corresponding to the first and second resonance dips.Thus, the results showed that the structure array with greater rotational asymmetry had a greater CD value.The CD values reached 0.063 at the Fano dip position and 0.037 at the third response dip position in the AZ-l 2 -l 3 structure array.We now focus on the basic principle of the ratio sensor proposed in this work.The main idea is based on the polarization conversion ability of the chiral structure array to the LPIL.Through the analysis group in the simulated model, first, the axial length ratio curves of the transmitted elliptically polarized light of chiral structure arrays at different wavelengths were obtained.Then, the refractive index sensor (ratio sensor) was realized by the response of axial length ratio curve to the change in the refractive index.Figure 4a,  c, e, respectively, show the transmitted light phase difference of different chiral structures (Z-shape, AZ-l 2 , and AZ-l 2 -l 3 ) in the X-and Y-directions (red curves) and the corresponding angle of the major axis of transmitted elliptically polarized light (the angle between the major axis and X-axis) (blue curves).Figure 4b, d, f show the axial length ratio curves of the transmitted elliptically polarized light of the corresponding structure array and elliptical polarization state at different positions.As shown in Fig. 4, the maximum position of the phase difference (associated with different resonance dip positions) corresponded to a large axial length ratio, indicating that the chiral structure array had a small effect on the polarization state of the incident light.In other words, the polarization conversion ability of the chiral structure array was poor.The position with a sharp phase change (around 1300 nm, that is, the position where the state of transmitted elliptically polarized light changes) has a very narrow line in the axial length ratio curves.This can be used as a potential sensing feature in refractive index sensor.This is also the basic principle of the ratio sensor.Notably, the shape of the axial length ratio curve, phase difference curve, and major angle curve of the AZ-l 2 -l 3 structure array were slightly complicated at approximately 1160 nm, owing to the combined effect of the Fano resonance and lattice modes.
In addition, as shown by the results in Fig. 4, the AZl 2 -l 3 structure array had an optimized Fano dip characteristic around 1160 nm, and at the same time, the corresponding axial length ratio curve of the transmitted elliptically polarized light had a narrow line width of approximately 1300 nm.Thus, the sensing characteristics of the two sensors (Fano and ratio sensors) were constructed using the same chiral plasmon structure array.Figure 5a and b show the transmission spectra and axial length ratio curves of the transmitted elliptically polarized light of the AZ-l 2 -l 3 structure array with various environmental refractive indices.Figure 5c shows the dependence of the Fano dip position and the selected axial length ratio characteristic position of the transmitted elliptically polarized light on the environmental refractive index.The results showed that the sensing characteristics of the two sensors were linearly dependent on the refractive index.The RIS of ratio sensor reached an incredible high value of 556.9 nm/RIU that was 1.314 times than that of the optimized Fano sensor (423.7 nm/RIU).The FOM of the ratio sensor was as high as 60, and the Q of the ratio curves could reach 121.6 as n = 1; these were 2.92 times and 2.14 times higher than those of the optimized Fano sensor, respectively.The aforementioned results show that the proposed ratio sensor is a reasonable candidate to replace the traditional Fano sensor.At the same time, the high stability of refractive index sensor proposed in this paper based on excellent electromagnetic material properties could enhance the operational lifespan of the device and could be prepared by many processing methods such as "sketch and peel" lithography process [42][43][44][45].

Conclusion
In summary, we propose a new type of refractive index sensor based on the axial length ratio curve of transmitted elliptically polarized light.By comparing two refractive index sensors built in the same structure (the optimized AZ-l 2 -l 3 structure array), we concluded that the proposed ratio sensor had a greater refractive index sensitivity of 556.9 nm/ RIU, a higher FOM of 60, and a greater Q of 121.6; these were 1.314, 2.92 and 2.14 times than those of the optimized Fano-sensor, respectively.Our study provides a new design strategy for a potentially refractive index sensor and an optimization strategy for the Fano feature of a chiral structure with rotational asymmetry.

Fig. 1 ac
Fig. 1 a Schematic of the chiral structure unit used to compare the performance of the optimized Fano sensor and proposed ratio sensor.b Transmission spectra of the AZ-l 2 structure array with various l 2 .

2 Fig. 2 a
Fig. 2 a Transmission spectra of different structure arrays.b Charge distribution (upper row) and electric field distribution (bottom row) at different characteristic positions in a. c Hybrid schematics of various primitive modes in the AZ-l 2 structure

Fig. 3
Fig. 3 Transmission spectra of three chiral structures under different types of incident polarization.L, P, and R represent left-handed circularly polarized, linearly polarized, and right-handed circularly

2 AZ-l 2 -l 3 Fig. 4
Fig.4 Transmitted light phase difference of different chiral structures in the X-and Y-directions, the corresponding angle of major axis, and the axial length ratio curves of transmitted elliptically polarized light.a, b Z-shape.c, d AZ-l 2 .e, f AZ-l 2 -l 3

Fig. 5 a
Fig. 5 a, b Transmission spectra and the axial length ratio curves of the transmitted elliptically polarization light of the AZ-l 2 -l 3 structure array as the refractive index of dielectric environment increase from located at 1169, 1301, 1556, and 1926 nm), and the CD values of the first and third feature dips were relatively