Journal of Optics ACCEPTED MANUSCRIPT Polarization-independent magneto-electric fano resonance in hybrid ring/disk hetero-cavity To cite this article before publication: Zhiqiang Hao et al 2017 J. Opt. in press https://doi.org/10.1088/2040-8986/aa952a Manuscript version: Accepted Manuscript Accepted Manuscript is “the version of the article accepted for publication including all changes made as a result of the peer review process, and which may also include the addition to the article by IOP Publishing of a header, an article ID, a cover sheet and/or an ‘Accepted Manuscript’ watermark, but excluding any other editing, typesetting or other changes made by IOP Publishing and/or its licensors” This Accepted Manuscript is © 2017 IOP Publishing Ltd. During the embargo period (the 12 month period from the publication of the Version of Record of this article), the Accepted Manuscript is fully protected by copyright and cannot be reused or reposted elsewhere. 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All third party content is fully copyright protected, unless specifically stated otherwise in the figure caption in the Version of Record. View the article online for updates and enhancements. This content was downloaded from IP address 129.59.95.115 on 27/10/2017 at 16:08 Page 1 of 6 Polarization-Independent Magneto-electric Fano resonance in Hybrid Zhiqiang Hao, Yune Gao, Zhenxian Huang and Xinyi Liang Department of Physics, School of Science, Tianjin University of Commerce, Tianjin 300134, People’s Republic of China E-mail: lxyhzhq@tjcu.edu.cn cri pt Ring/Disk Hetero-cavity an us Abstract In this work, we study the scattering properties of the hybrid ring/disk hetero-cavity and reveal the existence of polarization-independent magneto-electric Fano resonance. Such Fano resonance occurs through the destructive interference between the orthogonal electric and magnetic modes in hetero-cavity, where Si ring provides additional magnetic response. Furthermore, dipole radiative enhancement is used to analysis magneto-electric response of the hetero-cavity and the spectral features of cavity can be used to quantitatively characterize by coupled oscillator model. Generation of magneto-electric Fano resonance in such nanostructures does not require any symmetry breaking and presents clear advantages over their asymmetric counterparts, as it is easier to fabricate and can be used in a wider range of technological applications. dM Keywords: Surface plasmon resonance, Fano resonance, Magnetic resonance 1. Introduction one another, where the resonant circulating displacement current can induce the magnetic responses in the looped nanocluster, resulting in the magnetic-based Fano resonances [24–26]. Differing from the looped clusters, magnetic-based Fano resonances due to optically induced magnetic response of individual high-dielectric nanoparticle have also been realized in single silicon (Si) nanoparticle or oligomers [27–30], where Si nanoparticle supports both orthogonal electric and magnetic responses simultaneously. Similar to the case of electric dipole in plasmonic nanoparticles, the induced magnetic dipole in high-dielectric nanoparticles can be used to create complex nanostructures, such as directional optical antenna [31] and all-dielectric low-loss metamaterials [32]. However, magneto-electric Fano resonances are often excited by breaking the structural symmetry to realize enhanced electromagnetic interaction, inevitably showing the incident polarization-dependent optical responses. For many applications based on magneto-electric Fano resonances, for example, nonlinear switching [33], sensing [34, 35], and so on, polarization-independent magneto-electric Fano resonances are highly desirable but have been given little attention. In this letter, we theoretically demonstrate a polarization-independent magneto-electric Fano resonance in electromagnetically tunable hybrid hetero-cavity consisting of an Au disk inside the center ce pte Fano resonance is characterized by a distinct asymmetric line shape and has attracted considerable attention in recent years [1–3]. As a ubiquitous wave-inference phenomenon, the applications of Fano resonance spread rapidly from atomic physics, where it was first discovered [4], to plasmonics [5–7]. In near-degenerate levels, the wave-inference can lead to plasmon induced transparency of the nanostructure, displaying many promising advantages in actual applications such as Raman scattering [8, 9], biosensing [10] and slow light [11,12]. Recently numerous metallic nanostructures have been designed to generate pronounced Fano resonances, such as core/shell nanoparticles [13–15], mismatched dimers [16–18], ring/disk cavities [19–20], which provide important implications in biosensing [21], surface-enhanced Raman scattering [22], wave guiding [23], and so on. However, Owing to the optical response of an isolated metal nanoparticle is purely electric in nature, Fano resonances have mainly focused on purely electric response in metal nanostructures. Besides Fano resonance arising from pure electric field, considerable attention has been shifted to Fano resonances between electric and magnetic responses in dielectric or metallic nanostructures recently. It is possible to generate magnetic-based Fano resonances by arranging metallic nanoparticles in close proximity to Ac 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 AUTHOR SUBMITTED MANUSCRIPT - JOPT-104599.R2 1 AUTHOR SUBMITTED MANUSCRIPT - JOPT-104599.R2 inset. In contrast, the scattering spectrum for single Si ring shows an obvious resonance peak located at 408 nm, which can be attributed to the contribution of the magnetic dipole resonance. It can be easily verified by the calculated magnetic field enhancement distribution as shown in the inset, which is similar to the unity dipole resonance within the plane of the CdSe nanoplatelets [38]. The orthogonal electric and magnetic modes in the Au disk and Si ring can interference together with the same or nearly the same frequency. It is worth noting that the dipole response in the ring and disk is irrespective of the incidence polarization direction due to the high structural symmetry. cri pt of a Si ring as shown in figure 1. Differing from the pure metallic ring/disk cavity, the magnetic dipole resonance supported by the Si ring interferes with the electric dipole resonance supported by the Au disk, resulting in an apparent magneto-electric Fano dip in the total scattering spectrum in the visible region. Also the spectral features of cavity can be used to quantitatively characterize by coupled oscillator model. Further, Fano resonance does not require any symmetry breaking and can be tailored by varying the geometrical dimensions and inter-particle separation, providing promising applications in sensing, nonlinear and lasing devices. us 2. Structure description an Figure 1. (a) Schematic 3D illustration of the ring/disk (RD) hetero-cavity. (b) 2D layout of RD hetero-cavity with geometric parameters. Figure 2. (a) Scattering spectra of the individual Au disk (R 1 = 48 nm) and Si ring (R 2 /R 3 = 56, 78 nm) with H = 70 nm. The insets show the electric and magnetic field enhancement at resonance wavelengths indicated by blue arrows. pte dM The ring/disk (RD) hetero-cavity under consideration is illustrated in figure 1. The geometry is defined by four parameters as in figure 1: the radius of the Au disk R 1 , the inner and outer radius of the Si ring R 2 and R 3 , and cavity height H. The height of the disk is the same as that of the ring. For a finite size of the gap between disk and ring, we hence have R 1 <R 2 <R 3 . No significant dependence of scattering spectra on the detailed shape of the cross section was found, hence perfect ring and disk are used in the modeling. The dielectric constants of gold (Au) and Si in the hetero-cavity are taken from ref [36] and [37], respectively. The surrounding medium is air and the dielectric constant is set to 1. The polarization (E) and propagation (k) directions of incident light are denoted. The three-dimension finite-difference time-domain (FDTD) method is used to calculate the spectra. In the calculation of FDTD, a plane wave total field-scattered field (TFSF) source is used, and the computational domain is truncated by the perfectly matched layers of absorbing boundaries in all directions to simulate the infinite space surrounding the cavity. We assume a uniform grid, and the unit cell size is 1 × 1 × 1 nm3. Figure 3. Scattering spectrum (black dot line), and dipole radiative enhancement for magnetic dipole (red dot line) and electric dipole (green dot line) for the hetero-cavity with R 1 /R 2 /R 3 = 48/56/78 nm and H = 70 nm. ce As is well-known, the electric dipole mode, or the dipolar plasmon mode, of the Au disk is of surface type, while the magnetic dipole mode supported by the Si ring is of a cavity type where the magnetic field is confined inside the ring, and therefore, the resulting interaction is usually weak due to the nature of modes. However, one can finely tune the strength and frequency of these two dipole modes by carefully adjusting parameters such as the spacing of the hetero-cavity and the sizes of the disk or ring, whereby enhanced 3. Results and Discussion Figure 2 gives the scattering spectra for an individual Si ring and Au disk in free space, which is excited by a plane wave with linear polarization from top. For the individual Au disk, the scattering resonance centers at 551 nm, where the electric dipole contribution dominates the scattering in the Au disk, as shown in the Ac 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Page 2 of 6 1 Page 3 of 6 dip at 544 nm, which is different from the previously reported Fano resonances in metallic ring/disk cavity [39]. And Fano dip presents weak electric and magnetic dipole radiative enhancement simultaneously. Furthermore, the hetero-cavity does not depend on any symmetry breaking and can sustain polarization-independent magneto-electric Fano resonance in the visible spectrum. In order to verify the underlying mechanism of the magnetic and electric interaction and identify the modes related to the Fano resonance, the magnetic and electric near-field enhancements corresponding to the selected resonance wavelengths are shown in figure 4(a) and (b). To facilitate a direct comparison, the field maps in figure 4 are plotted in the same scale. Differing from metallic ring/disk cavity [19–20], the proposed hetero-cavity can induce remarkable electric and magnetic field intensity enhancements simultaneously within the gap between the ring and disk, as shown in figure 4(a) and (b). And the enhanced mechanism in this cavity is different from that in the metallic ring/disk cavity. Here, the enhanced near-field is caused by the strong coupling between the orthogonal electric and magnetic modes. The effects of near-field couplings can be ignored at 396 nm as the field enhancement is so small. The orthogonal magnetic field enhancement in figure 4(b) is mainly confined inside the Si ring, suggesting that formed magnetic response is contributed mostly from that of the individual Si ring, which is reasonable because the magnetic resonances of the Si ring is insensitive to the surrounding environment due to its cavity nature. The resonance at 544 nm shows the near-field properties around the spectral position of the pronounced Fano resonance, where one can find that the hybrid dipole-dipole mode is excited and can be treated as magnetic-electric dipole moments oriented along the orthogonal direction, ultimately leading to the Fano resonance. And at the 602 nm resonance peak, the magnetic and electric field distributions are similar to the case at 544 nm, resulting from the hybrid magnetic-electric dipole mode, but its intensity is largely enhanced. Obviously the largest magnetic and electric field enhancements occur at the 602 nm simultaneously. Further, figure 4(c) illustrates how the dipole resonances in individual Au and Si nanostructures hybridize to form the magnetic-electric dipole modes responsible for the Fano resonance. Together with the charge density distributions associated with various resonances, the electric dipole mode of dM an us cri pt interaction can be obtained via interference between the orthogonal electric and magnetic modes in the Au disk and Si ring with overlapping spectra. The black dot line in figure 3 represents the scattering spectrum of the hetero-cavity, and a pronounced Fano resonance appears at 544 nm accompanied by two clearly developed peaks at 396 nm and 602 nm. For the pure electric Fano resonances generated in plasmonic ring/disk cavity [39], symmetry breaking can lead to strong electric field interaction, which plays an important role in the coupling between electric modes. As for the hetero-cavity discussed here that has a high structural symmetry, considering the differences between metal and dielectric, that is, there are strong electromagnetic fields inside the dielectric cavity, where the orthogonal electric field in disk and magnetic field in ring can interfere and result in a prominent Fano dip at 544 nm. Figure 4. (a) Electric, (b) magnetic field intensity enhancement and (c) the charge density distributions at the central cross section of the hetero-cavity. ce pte To analyze magnetic and electric contribution to Fano resonance, magnetic and electric dipole light sources are used, which instead of the incident linearly polarized light and solely can excite magnetic or electric responses of the hetero-cavity. It is clearly observed that magnetic radiative enhancement (red dot line) compared with electric radiative enhancement (green dot line) contributes substantially to scattering spectrum. Two dipole radiative enhancements located at 430 nm and 598 nm represent magnetic dipole radiative enhancements, while the resonances at 428 nm and 584 nm stand for the electric dipole radiative enhancements. Noting that the dipole radiative enhancement in low energy is larger than that induced in the high energy, where the destructive interference between the orthogonal electric and magnetic responses results in the prominent Fano Ac 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 AUTHOR SUBMITTED MANUSCRIPT - JOPT-104599.R2 1 AUTHOR SUBMITTED MANUSCRIPT - JOPT-104599.R2 results agree well with each other, which implies that the formation of the Fano resonance in the hetero-cavity can be well explained by the coupled oscillator model. It is worth noting that the two spectra shown in figure. 5 diverge after 3.13 eV due to discount higher order resonances in coupled oscillator model and the electronic interband transitions in the FDTD calculation. us cri pt the Au disk and the magnetic dipole modes of the Si ring are clearly visible. The closeness in the energy levels of the monomers provides opportunity for the electric dipole mode of the Au disk to hybridize strongly with the magnetic dipole mode of the Si ring, forming a Fano dip at 544 nm, where the charges are grouped mainly on the side near the gap. an Figure 5. Simulated absorption spectra by FDTD (black dot line) and calculated power absorption in the oscillator model (red dot line). The inset shows two coupled interacting oscillators representing the optical responses of the hetero-cavity. pte dM Qualitatively, the spectral response of the proposed hetero-cavity can be modeled by a system of coupled oscillators, as shown in the inset of figure 5. As an analogue of the optical excitation of the electric and magnetic dipole modes, oscillator |ED⟩ and |MD⟩ are taken to be driven by two harmonic forces, respectively. Suppose the mass value of all oscillators equals to one, the equations of motion of the two oscillators can be written as [13]: ̈ () + ̇ () + 2 () − () = − (1) 2 ̈ () + ̇ () + () − () = − (2) where x i (t) (i =e, m) is the displacement of each oscillator from their respective equilibrium position, ω i hangs on the position of resonances and is the oscillation frequency of the oscillator; γ i is the friction coefficients which are used to account for the energy dissipation and rests with the line width of resonance; F e and F m is excitation coefficient and accounts for the excited intensity of resonances; and k ij represents the coherent coupling coefficient and determines the the strength of interaction between the pumping oscillator and the oscillator modeling the cavity, so the k ij and k ji are mutual and equal. Figure 5 shows the comparison between absorbed powers of the oscillator system calculated by Eqs. (1) and (2) and the FDTD simulated absorption of the hetero-cavity, and the calculation Figure 6. (a) Scattering spectra of the hetero-cavity with (a) varying Si disk R 1 (R 2 /R 3 = 56/83 nm, H = 70 nm), (b) varying ring radius R 3 (R 1 /R 2 = 48/56 nm, H= 70), (c) varying height H (R 1 /R 2 /R 3 = 48/56/83 nm). Geometric variation of the hetero-cavity enables significant tailor the electric/magnetic resonances of Si ring and Au disk to modulate the Fano resonance. We first consider the dependence of the gap on the Fano resonance of hetero-cavity with fixed parameters of ring. Figure 6(a) shows the effects of the gap between the ring and the disk. Along with the increase of the disk R1, the gap has become smaller and smaller, which results in stronger interaction. And the stronger interaction between the ring and disk results in increased spectral intensity of Fano resonance as well as red-shift of ce Ac 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Page 4 of 6 1 Page 5 of 6 4. Conclusions Plasmons in strongly coupled metallic nanostructures Chem. Rev. 111, 3913–61 Wang J Q, Zhang J, Tian Y Z, Fan C Z, Mu K J, Chen S, Ding P,. Liang E J 2017 Theoretical investigation of a multi-resonance plasmonic substrate for enhanced coherent anti-stokes raman scattering Opt. Express 25, 497 Yuan B H, Zhou W J, Wang J Q 2014 Novel h-shaped plasmon nanoresonators for efficient dual-band sers and optical sensing applications J. Opt. 16, 105013 Zhou W J, Wang X X, Wang J Q 2015 Polarization and angle quasi-independent metamaterial crystal with electromagnetically induced transparency based on plasmon hybridization J. Mod. 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Due to the high structural symmetry and strong magnetic-electric interaction between ring and disk, the destructive interference between the orthogonal electric and magnetic modes in hetero-cavity can sustain polarization-independent Fano resonance in the visible spectrum. Such Fano resonance is replicated by coupled oscillator model to simultaneously excite the electric and magnetic dipole modes. Compared with the previously reported Fano resonance in metallic nanoparticle, Fano resonance does not breaking the structural symmetry and the discrete magnetic dipole mode of the Si ring can be directly excited by normal incident wave. Furthermore, Fano resonance can be widely tuned by varying the geometrical dimensions and interparticles separation. Such mechanism of interference between the orthogonal electric and magnetic modes to achieve polarization-independent Fano resonance is not restricted to optics, and it can be applied to other fields, such as atomic and nuclear physics. 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