Fano resonance with high local field enhancement under azimuthally polarized excitation

Being an enabling technology for applications such as ultrasensitive biosensing and surface enhanced spectroscopy, enormous research interests have been focused on further boosting the local field enhancement at Fano resonance. Here, we demonstrate a plasmonic Fano resonance resulting from the interference between a narrow magnetic dipole mode and a broad electric dipole mode in a split-ring resonator (SRR) coupled to a nanoarc structure. Strikingly, when subjected to an azimuthally polarized beam (APB) excitation, the intensity enhancement becomes more than 60 times larger than that for a linearly polarized beam (LPB). We attribute this intensity enhancement to the improved conversion efficiency between the excitation and magnetic dipole mode along with improved near-field coupling. The APB excited Fano structure is further used as a nanoruler and beam misalignment sensor, due to the high sensitivity of intensity enhancement and scattering spectra to structure irregularities and excitation beam misalignment. Interestingly, we find that, regardless of the presence of structural translations, the proposed structure still maintains over 60 times better intensity enhancement under APB excitation compared to LPB excitation. Moreover, even if the APB excitation is somewhat misaligned, our Fano structure still manages to give a larger intensity enhancement than its counterpart excited by LPB.

to now, it has been demonstrated that cylindrical vector beams (CVBs) can excite a much brighter "hot spot" in plasmonic lens [27][28][29] , multimers [30][31][32][33] and SRRs 34-37 than their counterparts produced by linearly polarized beams (LPBs). CVBs exemplified by radially and azimuthally polarized beams (APBs) can be generated and reconfigured by a spatial light modulator (SLM) at ease [38][39][40] . Therefore, it can provide a much more flexible and effective approach to excite a giant local field by matching the polarization states of the illumination to the eigenmodes of the plasmonic structures.
In this paper, we propose a method to boost the intensity enhancement of a SRR and nanoarc combined Fano structure subjected to APB excitation. In contrast to the conventional excitation with LPB, our scheme can increase the local field intensity by more than 60 times. Moreover, with the excitation of APB, we obtain a 3 times larger local field enhancement for our Fano structure compared to the individual SRR. We further evaluate the performance of the APB excited Fano structure when served as a nanoruler and beam misalignment sensor. Simultaneously, we investigate the APB produced intensity enhancement under the consideration of the structural translations of the Fano structure and the misalignment between excitation beam and structure. Our results provide a new possibility to control the near-field properties of Fano resonance, and could find applications in SERS and biosensing.

Results and Discussions
Figure 1(a) shows a schematic diagram of the proposed Fano structure, which is composed of a gold SRR and a nanoarc coaxially. The SRR has an angular gap α, inner radius r 1 , and outer radius r 2 . Similarly, the nanoarc has a central angle β, inner radius r 3 , and outer radius r 4 . The thickness T of the structure is kept as a constant (40 nm) throughout this paper. Figure 1(b) displays a typical intensity profile of an APB, which has the polarization direction aligned along the azimuthal direction.
The optical response of the designed structure is numerically calculated by using the finite-difference time-domain (FDTD) method 41 . We start our discussion with scattering spectrum of the SRR-nanoarc structure under the excitation of an LPB at normal incidence, whose polarization is indicated in the lower insets of Fig. 2.
Here, geometrical parameters are taken as: r 1 = 35 nm, r 2 = 60 nm, r 3 = 90 nm, r 4 = 190 nm, α = 45° and β = 160°. Figure 2, from the left to right panels, displays the scattering spectra of the individual SRR, nanoarc, and the combined structure. The scattering spectra of the individual SRR and nanoarc are dominated by a narrow and a broad resonances, respectively. We attribute these two resonances as the magnetic and electric dipole modes 20 , which can be confirmed by their charge distributions in the upper insets of Fig. 2. The magnetic dipole mode experiences weak radiation loss, therefore, it can be considered as a collection of "discrete" states. On the contrary, the electric dipole mode is highly radiative, and thus it is treated as a "continuum" state. The interference between these two modes leads to a pronounced spectral dip located at 1.37 μm in the scattering spectrum of the combined structure, which indicates the occurrence of Fano resonance. The origin of this Fano resonance when interpreted within the framework of hybridization theory 42 , can be attributed to the interference between bonding (~1.45 μm) and anti-bonding modes (~1.15 μm) shown in the right panel of Fig. 2.
In following analysis, we choose an APB with diameter of 700 nm at normal incidence as the excitation 43 . The red curve in Fig. 3(a) shows the scattering spectrum of the SRR-nanoarc when illuminated by the APB. Different from its counterpart produced by LPB [the red curve in Fig. 2], the APB excited Fano spectral lineshape exhibits a much stronger bonding mode resonance and a weaker anti-bonding mode resonance. Qualitatively, this can be attributed to the matching between the polarization state of APB and plasmonic modes. In term of field distribution, the APB has a better overlap with the azimuthally distributed Fano structure. Therefore, as a driving force, APB can effectively excite and enhance the oscillations along the same azimuthal direction (bonding mode), but decrease the oppositely aligned azimuthal oscillations (anti-bonding mode). As shown in Fig. 3(b), the enhancement factor (EF), defined by the ratio of near-field intensity at the gap center of SRR [as indicated in the insets of Fig. 3(b)] compared to the situation without SRR-nanoarc, is further examined. It is shown that the EF is significantly increased for the SRR-nanoarc structure illuminated by APB [red solid curve in Fig. 3 Fig. 3(b)]. Especially, with the excitation of APB, the EF has an over 60 times increase at the wavelength region where the bonding mode exists. In addition, with the excitation of APB, our SRR-nanoarc Fano structure exhibits a 3-fold larger local field enhancement compared to the individual SRR [black solid curve in Fig. 3(b)]. This obvious intensity enhancement effect can be exploited for applications such as ultrasensitive biosensing and SERS.

(b)] compared with that illuminated by LPB [black dashed curve in
In order to provide a deeper understanding of our system, a coupled oscillator model is employed to describe the Fano resonance of the SRR-nanoarc structure excited by LPB and APB. The two oscillators provide the anti-bonding and bonding modes, which are characterized by the resonance frequencies ω a , ω b , nonradiative  damping efficiencies γ a , γ b and radiation coupling efficiencies η a , η b . The equation governing the motions of the two oscillators can be written as 26,44 γ ω η η η γ ω η η η  The scattering coefficient of the system can be described by σ sca = I 0 + |C a + C b | 2 with I 0 accounting for the background, which is used to fit the scattering spectra excited by LPB and APB with the same excitation power over the structure. A good agreement between the theory (red solid curves) and simulation (black dots) is achieved, as depicted in Fig. 4(a) and (b). The fitting parameters are listed in Table 1, from which two emerging features are found. (1) There is an increase in η b under the excitation of APB, which suggests that the APB has a better coupling with the bonding mode. This results in an enhanced scattering in long wavelength regime, exhibiting a more profound asymmetric spectral lineshape as shown in Fig. 4(b). (2) A significant increase in coupling constant g is found in our system with the excitation of APB. This leads to the enhanced near-field intensity of the SRR-nanoarc structure, which can be confirmed by comparing the near-field intensity distributions at the top surface of the structure with LPB and APB illumination [see Fig. 4

(c) and (d)].
Owing to the enhanced scattering and more profound asymmetric spectral lineshape obtained from the Fano structure when illuminated by APB, it becomes much easier to detect and characterize the spectrum signal in practical applications. In the following, we demonstrate our system can serve as a nanoruler, which is important for determining nanoscale distances within chemical or biological species 45,46 . Here, the APB excitation is kept coaxially with the SRR and the nanoarc has an in-plane displacement along x and y directions as illustrated in Fig. 5(a) and (b). Figure 5(c) and (d) show the scattering spectra of SRR-nanoarc structure with the translations along x direction from −20 nm to 20 nm and y direction from 0 nm to 20 nm, respectively. It can be found that the SRR-nanoarc structure causes an obvious spectral lineshape shifting even down to the nanometer scale of structural translation. The resonance peak position and scattering intensity of bonding mode depend on in-plane displacement are depicted in Fig. 5(e) and (f), which allow us to evaluate the magnitudes as well as the directions of structural translations. Such high sensitivity to structural translations results from the SRR-nanoarc  gap dependent coupling strength, which is exponentially reduced when gap size increases [the red triangles in Fig. 5(g) and (h)], decreasing the spectral overlapping between the bonding and anti-bonding modes. It also suggests that the variation of coupling strength dominates the change on intensity EF shown as black dots in Fig. 5(g) and (h), which correspond to EF for the structural translations along the x and y directions, respectively. Interestingly, despite having imperfections in geometry, the APB excited SRR-nanoarc structure exhibits an EF that is regularly over 60 times larger than its LPB excited counterpart [the blue rectangles in Fig. 5(g) and (h)], and robustly maintains more than 1.5 × 10 5 . Apparently, the maximum near-field intensity enhancement is obtained for coaxial overlap between the APB and SRR-nanoarc structure. However, such registration is quite difficult in nanoscale regime and some misalignment might occur in practice. In order to study the impact of intensity enhancement subjected to the in-plane misalignment between excitation beam and structure, displacements of APB along x and y directions are taken into account, as depicted in Fig. 6(a) and (b). The EF decreases as APB has a displacement from the SRR-nanoarc as shown in Fig. 6(c). Nevertheless, intensity enhancement of SRR-nanoarc under APB is more than 5 times larger than its LPB excited counterpart even for a misalignment of 100 nm (over half the outer radius of nanoarc) between APB and the structure. In addition to this high sensitivity of intensity EF to the displacement between excitation beam and center of the structure, scattering intensity of bonding mode is also changed when the beam is misaligned, as illustrated in Fig. 6(d). The scattering intensities change inversely as APB transforms along x and y directions. According to the near-field intensity enhancement and far-field scattering spectra, our system can potentially serve as a beam misalignment sensor.

Conclusion
In summary, we have demonstrated the Fano resonance in a gold SRR-nanoarc structure. Our results show that, compared with LPB illumination, a much more asymmetric Fano lineshape is obtained under APB excitation. Moreover, the APB excited Fano resonance shows a more than 60 times larger intensity EF than its counterpart excited by LPB. Surprisingly, compared to the LPB, APB can produce a much stronger intensity enhancement even if the Fano structure is subjected to in-plane translation deviations and excitation beam is misaligned. Our results may find applications in nanoscale distances measurement, surface enhanced spectroscopy and ultrasensitive biosensing.

Methods
Simulation. The transverse electric field of the APB can be expressed as 39 x y 01 10 where HG 01 and HG 10 represent two orthogonally polarized Hermite-Gauss modes with the unit vectors e x and e y , respectively. The Hermite-Gauss mode can be described as 39 is the Rayleigh range, q(z) = z − iz 0 is the complex beam parameter, ϕ mn = (m + n + 1) tan −1 (z/z 0 ) is the Gouy phase shift, r is the radial coordinate and k = 2π/λ is the wavenumber. According to Eq. (4), we define d max = 2(z 0 /k) 1/2 , which refers to the diameter of the maximum intensity circle of the incident field, to characterize the beam size of APB 36 .
In our FDTD simulations, perfectly matched boundaries are used to mimic single nanostructure in infinitely large free space. The nanostructure is swept-meshed with the minimum size of 5 nm. The structure is immerged in