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Metal-Dielectric Hybrid Dimer Nanoantenna: Coupling Between Surface Plasmons and Dielectric Resonances for Fluorescence Enhancement Song Sun, Mo Li, Qingguo Du, Ching Eng Png, and Ping Bai J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 30 May 2017 Downloaded from http://pubs.acs.org on May 31, 2017

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The Journal of Physical Chemistry

Metal-Dielectric Hybrid Dimer Nanoantenna: Coupling between Surface Plasmons and Dielectric Resonances for Fluorescence Enhancement Song Sun1,2*, Mo Li1, Qingguo Du3,4, Ching Eng Png,2 Ping Bai2* 1

Microsystem & Terahertz Research Center, China Academy of Engineering Physics,

No.596, Yinhe Road, Shuangliu, Chengdu, China 610200. 2

A*STAR Institute of High Performance Computing, Electronics and Photonics Department, 1

Fusionopolis Way, #16-16 Connexis (North), Singapore 138632. 3

School of Information Engineering, Wuhan University of Technology, 122 Luo Shi Road,

Wuhan, Hubei, China 430070. 4

Laboratory of Fiber Optic Sensing Technology and Information Processing (Wuhan University

of Technology), Ministry of Education, Wuhan, Hubei, China 430070.

ACS Paragon Plus Environment

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ABSTRACT. Dimers made of noble metal particles possess extraordinary field enhancements but suffers from large dissipation, whereas low loss dielectric dimers are limited by relatively weak optical confinement. Hybrid systems could take advantages from both worlds. In this contribution, we study the mode-coupling in a hybrid dimer with rigorous dipole-dipole interaction theory and explore its potential in fluorescence enhancement. We first discovered that the direct coupling between metal surface-plasmon-resonance and dielectric electric-dipole-mode creates a hybridized mode due to the strong electric-electric dipole-dipole interaction between the constituent nanoparticles, whereas the dielectric magnetic-dipole-mode can only indirectly couple to the plasmons based on the induced electric-magnetic dipole-dipole interaction. When an electric/magnetic quantum emitter couples to the hybrid dimer, the emitter selectively excites the electric/magnetic (magnetic/electric) resonant modes of the dimer for emitter orientation parallel (perpendicular) to the dimer axis. Our study shows that the hybrid dimer simultaneously possesses high field enhancement and low loss features, which demonstrates a fluorescence excitation rate 40% higher than that of the pure dielectric dimer and an average quantum yield 30% higher than that of the pure metallic dimer. On top of that, the unique asymmetrical structure of the hybrid dimer directs 20% more radiation towards the dielectric side, hence improving the directivity of the dimer as an antenna.


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1. INTRODUCTION A dimer nanoantenna comprises two elementary nano-components (e.g. sphere, rod, cylinder etc) that are brought in close proximity to each other.(1),(2) Owing to the strong near-field interaction between the constituent nano-components, the dimer nanoantenna has demonstrated unprecedented capabilities to confine light into deep-subwavelength regime,(3),(4) offering an incomparable advantage of a small footprint suitable for on-chip integration and miniaturization.(5),(6) Such confinement leads to a pronounced enhancement in the local electromagnetic field within the antenna gap, whose intensity can easily surmount that of an individual nano-component by orders of magnitudes.(7)-(10) Besides, the antenna resonant wavelength can be flexibly adjusted via controlling the gap distance of the dimer, providing excellent tunability over a broad spectral range from visible to near-infrared regime.(7),(11),(12) These intriguing properties make the dimer nanoantenna promising for a variety of emerging applications such as optical trapping,(13),(14) high-order harmonic nonlinear optical process,(15),(16) surface-enhanced Raman spectroscopy (SERS),(17),(18) and quantum emitter enhancement,(19)-(25) among others.(8),(26),(27) Up to present, dimer configuration has been successfully materialized in two sorts of platforms: noble metals (e.g. Au, Ag)(1)(7)-(9),(25)-(27) and high permittivity dielectrics (e.g. Si).(2),(28)-(34) For the metallic dimer, the free electron oscillation at the surface of each elementary nano-component (so called surface plasmon resonance (SPR)) can couple with that of the proximal one, creating a bonding- or anti-bonding hybridized mode depending on the incident light polarization that is analogous to the hybridization of atomic orbitals in molecules.(1),(7),(35) Although such hybridization (bonding-mode in particular) is able to create an extraordinary field enhancement in the gap region, metals naturally suffer large parasitic losses which in turn


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significantly increase the probability of nonradiative photon recombination and can be detrimental for applications such as quantum emitter enhancement(6),(36),(37) as well as high-order harmonic generation.(15),(16) This inevitable problem stimulates the research on the high permittivity low loss dielectric counterpart, whose optical confinement can be achieved through the generation of intensive displacement current inside the structure, leading to either an electricdipole mode (ED) or magnetic-dipole mode (MD) depending on the wavelength.(38),(39) Once brought together, the near field at the vicinity of the dielectric nano-component can also interact with each other, resulting in a field enhancement within the gap region similar to that of the plasmonic dimer.(2),(28),(40) Despite the advantage of low energy dissipation, the field enhancement capability of the dielectric dimer is considerably weaker (e.g. generally less than 50%)(2),(29),(30),(41) as compared to that of the metallic counterpart, thereby limiting its potential in applications such as SERS(17),(18) and quantum emitter enhancement. To simultaneously satisfy the growing demand in both high electric field enhancement and low loss features, a natural way is to construct a metal-dielectric hybrid dimer that could integrate the advantages of both platforms. A few experimental attempts have recently been conducted by mixing various metallic and dielectric structures such as hybrid bulls-eye,(42) metal-nanoparticle combined

with

planar-dielectric,(43)

metal-nanoparticle

coupled

with

large

dielectric

microsphere,(44) metal-patch plus dielectric-resonator,(45) metal-dielectric waveguide,(46) among others.(47) Despite the excellent performance reflected in these hybrid structures, the underlying coupling mechanism has yet been clearly elucidated. The ambiguity originates from the intrinsically different resonating natures between metal and dielectric, e.g. metal SPR can be approximated as a pure electrical system whereas dielectric in general consists of both electrical and magnetic resonances. On top of that, when the two platforms are incorporated together, the


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interaction between metal SPR and various dielectric resonances will further manipulate the overall spectral response of the hybrid structure, rendering the physics even more complicated. To our best knowledge, no thorough study has been performed to reveal the physical insight on the coupling mechanism between the two platforms. To fill this gap and unlock the principle in designing the hybrid system, herein, we carry out a fundamental study on the optical response of a metal-dielectric dimer. First, we systematically investigate how the metal SPR can couple to the dielectric electric- or magnetic-resonance under plane wave excitation. All the exhibited features in the spectrum are explained rigorously with the generalized dipole-dipole analytical formulation extended from the previous literature.(2),(28) After that, we exam the corresponding radiative decay rate to reveal how an electric/magnetic dipole emitter couples to these resonance modes of the hybrid dimer, mimicking the interaction between a quantum emitter (e.g. dyes, quantum dot etc) and the nanoantenna. Lastly, we compare the average emission enhancement of the hybrid dimer to that of the pure metallic or dielectric counterpart by incorporating the excitation rate, quantum yield as well as the far field pattern, so as to make a preliminary assessment on the potential of the hybrid dimer nanoantenna on fluorescence enhancement application and directivity manipulation.

2. METHODS Generalized dipole-dipole interaction for arbitrary dimer configuration. The origin of the dimer extinction spectra is rigorously elucidated with the generalized dipole-dipole interaction model, which is an extension from the formulation proposed by Aizpurua et al for a special case,(2) and applicable to any dimer configuration which comprises two arbitrary spherical nanoparticles (NP), regardless of the size and material of each constituent one. The beauty of


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adopting the spherical NP relies on the neat analytical interpretation of the mode composition governed by the Mie coefficient,(39) allowing us easily accessing the separate contributions of various resonances from the NP. Each NP can be approximated by a group of electric and magnetic dipoles. The assembling effect of electric-electric (e-e), magnetic-magnetic (m-m) and electric-magnetic (e-m) dipole-dipole interaction reproduce the main feature of the dimer’s extinction spectra. Assuming a plane wave incidents on the dimer propagating along the z-axis, whose electric field is either polarized along y-axis for E||dimer or along x-axis for E⊥dimer as shown in Figure 1(a) and 1(b) respectively, whereby “E||dimer” represents the incident plane wave polarization with the electric field E parallel to the dimer axis, and “E⊥dimer” for the case where E is perpendicular to the dimer axis. The gray and blue spheres indicate that the dimer could be made of two different constituent NPs.

Figure 1. Schematic dipole-dipole interaction model for (a) E||dimer: the incident plane wave polarized with electric field E parallel to the dimer axis, and (b) E⊥dimer: E is perpendicular to the dimer axis. Pure red (blue) symbols and arrows correspond to the primary electric (magnetic) dipoles induced directly by the incident plane wave. Mix-colored symbols and dashed arrows stands for the secondary dipoles induced by the primary field of the primary dipolar sources. The coupling between NPs is approximately resembled by the interaction between these dipoles.


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The overall spectrum response of the hybrid dimer can then be approximated via selfconsistently solving the dipole-dipole interaction between the two constituent NPs as(28) = + = + = − + = − −

= − + = − −

! "

! "

− #

(1)

− #

for E||dimer, and

# + #

# = − + #

# = − − # (2)

# = − # = − − = − − = −

for E⊥dimer, where Pj/mj is the electric/magnetic dipole moment excited in the jth (j = 1,2) NP. For E||dimer/E⊥dimer, Pjy/mjy is the primary electric/magnetic dipolar source excited by the incident plane wave along y-axis, Pjz/mjz is the secondary electric/magnetic dipole moment along the z-axis induced by the primary dipolar source in the other particle, mjx/Pjx is the overall magnetic/electric dipole moment along the x-axis induced directly by the external field as well as the secondary dipole moments in the other particle. ξ0 is the vacuum permittivity, ξr is the relative permittivity of the medium, k is the vacuum wavevector, Z is the vacuum impedance, αje = 6πi/k3aj1 and αjm = 6πi/k3bj1 are the electric and magnetic polarizability with a1 and b1 are the 1st order Mie coefficient.(38) gyy, gxx and gzx are the scalar green function. The overall dimer extinction coefficient can be expressed as,


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)* =

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4, ( + )2 = Im3)4 + )#4# + )4# 5 (3) Im / 0 + 1 − 4, 4,

where σe-e, σm-m and σe-m are associated with the e-e, m-m and e-m dipole-dipole interaction respectively. Solving Eq. (1) and (2) and rearranging in the format of Eq. (3), we obtain, )4 = )4# =

, )#4# =

7 87 89:: 7 7 49::

(489==

;

7 7

8 49== 49== ;

9>= ; ?4 7 8 ?9== 7 89>= 7 89== (47 8)@7 @

;

; ; )?8 0(49== 7 49>= )7 8(49>= 7 49== 8(9== 89>= ) 7 7 ) 1@

49>= ; ?7 0489== 1 8 ; ?049== 49>= 17 89== 09== 809== 89>= 1 7 1@7 @

(489== ; )?8 ; 0(49== 7 49>= )7 8(49>= 7 49== 8(9== 89>= ) ; 7 7 )1@

+

(4)

for E||dimer, and )4 =

7 87 49== 7 7 49== ; 7 7

)4# = (489

==

;

, )#4# =

889:: 49:: ;

9>= ; 047 (489== 7 ) 87 (489== 7 ) 7 1

; A ; ; ; 7 7 )(9== 7 7 4(89>= 7 )(489>= 7 )49== (7 7 8 ))

9>= ; A 7 7 (47 87 (489== 7 ))

(489== ; 7 7 )(9== ; A 7 7 4(89>= ; 7 )(489>= ; 7 )49== ; (7 7 8))

+

(5)

for E⊥dimer. Note that Eq. (4) and (5) are universal and can be applied to any dimer configuration which comprises two arbitrary spherical NPs, regardless of the size and material of each constituent one. When two NP are identical (e.g. α1e = α2e, α1m = α2m), Eq. (4) and (5) reduce into the specific case formulation in Ref. 2. In particular for the metal-dielectric dimer studied in this contribution, we can further assume metal SPR is a pure electric resonating system with negligible magnetic dipolar momentum α1m ≈ 0. Consequently, Eq. (4) and (5) can be simplified to )4 =

7 87 89:: 7 7

)4# = −

49:: ; 7 7

, )#4# = #

9>= ; 7

48 ; 7 (9== 7 89>= )

(6)

for E||dimer, and


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)4 =

)4# =

7 87 49== 7 7 49== ; 7 7

, )#4# = #

9>= ; 7 (489== 7 )

(489== ; 7 7 )(489== ; 7 7 89 ; 7 )

(7)

for E⊥dimer. Eq. (6) and (7) clearly indicates that there is a strong e-e interaction between metal and dielectric as both materials possess electric dipole moments. However, the m-m interaction is predominated by dielectric NP alone due to the negligible contribution from metal. In the dimer scheme, the e-m interaction is always presented regardless of the incident wave polarization, which can also manipulate the overall extinction response. Excitation rate, average quantum yield and average emission enhancement. Within the classical framework,(36),(48) the quantum emitter is commonly treated as an electric or magnetic dipole source, whose radiation can be represented as the summation of a group of coherent plane waves with different wave-vectors and polarizations.(40) The nanoantenna enhanced emission of a dipole source ηem/η0 can then be estimated as the product of the excitation rate γext/γ0 and the quantum yield q/q0, whereby the subscript ‘0’ represents the corresponding quantity in homogeneous medium. The excitation rate γext/γ0 = |E·P|2 indicates the ability of a dimer nanoantenna in boosting the electron from the ground state to the higher energy state in the dipole emitter under plane wave incidence, where E is the electric field at the location of the dipole emitter, and P is the orientation of the dipole emitter. The quantum yield F" /F!

F" /F! 8FH" /F! 8(4E! )/E!

E

E!

=

accounts the competition between radiative Γr/Γ0 and non-radiative Γnr/Γ0

component, which indicates the probability that a photon can emit to the far field instead of being absorbed by the structure, whereby the dipole emitter becomes the optical source. The radiative decay rate Γr/Γ0 is obtained by integrating the energy flux in the far field, whereas the non-radiative decay rate Γnr/Γ0 is obtained by evaluating the energy absorbed in the dimer


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antenna. q0 is the intrinsic quantum yield of the emitter, which is set as q0 = 1 throughout the paper. To mimic the experimental measurement, the emitter is modelled as a statistical ensemble of dipoles with random orientations, which is located along the dimer axis in the antenna gap. Assuming equal probability for all emitter orientations, the average quantum yield can be neatly written as(49)-(51) J 〈 〉= J

L L X

X

M ∙ cos S + M T ∙ sin S ∙ sin S YSYZ || || T ∙ sin S) (M ∙ cos S + M T ∙ sin S) + (MW ∙ cos S + MW ||

L L sin S YSYZ X

X

(8)

where θ is the polar angle with respect to the dimer axis, φ is the azimuth angle, and “||” (“⊥”) stands for the dipole orientation parallel (perpendicular) to the dimer axis. After some straightforward algebra, we get

J 1 X 1 〈 〉= \ ∙ sin S YS (9) J 2 1+]

where ] =

|| M_` 8M⊥ _` ∙abc d

M` 8M⊥ ` ∙abc d ||

. The average emission enhancement can be subsequently

obtained by multiplying the excitation rate γext/γ0 and the average quantum yield . Note that it is legitimate to treat the excitation rate and quantum yield independently since there is no coherence between the two processes. Finite-element-method (FEM). FEM with COMSOL MULTIPHYSICS is adopted to calculate the radiative Γr/Γ0 and non-radiative Γnr/Γ0 rates. The scattered-wave formulation has been implemented to compute the respective power quantities. Subsequently, the radiative (nonradiative) decay rate can be straightforwardly determined as Γr/Γ0 = Psca/P0, and Γnr/Γ0 = Pabs/P0,(48),(51) where Psca is the power scattered by the dimer in the far field, Pabs is the ohmic loss in the dimer, and P0 is the power radiated by a free dipole emitter in a homogeneous


10

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medium. The dimer extinction spectrum is also obtained using FEM with a direct plane wave illumination, which is used to compare the results from dipole-dipole interaction model. Details can be found in the Supporting Information (SI).

3. RESULTS Schematic of metal-dielectric dimer. Figure 2 illustrates the schematic of the hybrid dimer which consists of a metal NP with diameter Dm and a dielectric NP with diameter Dd. The distance between the two NPs is denoted as Dgap. Via properly controlling the size of each constituent NP, the peaks of the selected resonance modes (e.g. metal SPR, dielectric ED and MD) can be deliberately aligned at the same wavelength to achieve a maximum overlap while minimizing the influence from other modes. Consequently, the coupling mechanism between the metal SPR and the dielectric ED and MD can be clearly revealed. It is noteworthy that different sizes of metal and dielectric NP (e.g. Dm ≠ Dd) are in general required to align their respective resonance peaks at the same wavelength due to the different material properties. For illustration, Ag is used to represent the metal whose optical property is taken from the experimental measurement.(52) Other plasmonic metals can also be used. The dielectric NP is assumed with a high permittivity (= 25), offering well-resolved ED and MD so that the coupling effect between the metal SPR and the selected dielectric resonance can be clearly reflected in the dimer extinction spectrum. Other low permittivity dielectric (e.g. SiO2 & PMMA with permittivity < 4) used in the previous experiments,(42)-(46) is not considered here since its ED and MD are significantly overlapped. The medium is assumed to be air with permittivity = 1.


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Figure 2. The schematic of the hybrid dimer, which is composed of a metal spherical NP with diameter Dm and a dielectric NP with diameter Dd. The distance between the two NPs is denoted as Dgap.

Coupling between metal SPR and dielectric ED under plane wave excitation. To start with, the coupling between the metal SPR and the dielectric ED (denoted as SPR-ED here after) under E||dimer excitation is shown in Figure 3(a). The isolated metal SPR (black dashed line) and dielectric ED (red dashed line) are both designed to align at wavelength λ = 400 nm to achieve a maximum overlap. The corresponding diameters for the Ag and dielectric NP are Dm = 100 nm and Dg = 108 nm respectively. The detail mode composition can be found in Figure S1 in SI. Apparently, the metal SPR and the dielectric ED can couple with each other and form a new hybridized mode (HM||e-e), which red-shifts as the gap distance Dgap shrinks. Meanwhile, the dielectric MD remains almost unshifted at λ = 560 nm regardless of Dgap with a slight change in the extinction magnitude.


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Figure 3. (a) The coupling between the SPR and dielectric ED (SPR-ED dimer) for E||dimer illumination. A new hybrid mode HM||e-e is formed due to the electric-electric dipole-dipole interaction between the two NPs, which red-shifts as the gap distance Dgap reduces. The dielectric MD remains unshifted at λ = 560 nm due to the absence of the magnetic dipolar momentum in the metal NP. (b) The separate contributions from electric-electric (e-e), magneticmagnetic (m-m), and electric-magnetic (e-m) dipole-dipole interaction at Dgap = 10 nm. (c) & (d) The electric and magnetic field distribution of the HM||e-e (Dgap = 15 nm and λ = 450 nm), and the dielectric MD (Dgap = 15 nm and λ = 560 nm) respectively.


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To understand the nature of the resonances, we decompose the overall extinction spectra into electric-electric (e-e), magnetic-magnetic (m-m) and electric-magnetic (e-m) components by implementing the generalized dipole-dipole interaction formulation. Figure 3(b) shows the separate contributions of e-e, m-m, and e-m interaction respectively at Dgap = 10 nm. The summation of the three components is compared with the FEM full-wave results, which shows good agreement. Clearly, the overlap between the SPR and ED results in a strong direct e-e interaction because both the SPR and ED can be described as electric dipoles, which eventually leads to the hybridized mode HM||e-e in the spectra. In addition, as the magnetic dipolar contribution inside the metal NP is negligible, the direct m-m interaction is solely contributed by the dielectric MD alone, hence explains the unshifted feature of the MD. The strength of e-m contribution, in principle, depends on (i) the strength of the individual electric and magnetic dipole moments and (ii) the spectral overlap between the electric and magnetic resonances. For hybrid dimer, the e-m contribution becomes significant (even higher than that of the pure dielectric dimer) mainly within the narrow MD region because only the dielectric part of the hybrid dimer possesses the magnetic resonance to induce a distinguishable e-m interaction. On the contrary, the e-m interaction is negligible for pure metallic dimer due to the lack of magnetic dipole moment in the metal NP, whereas it is large over a wide spectrum range for the pure dielectric dimer since both constituent NPs possesses electric and magnetic resonance and they are overlapped.2 More detail can be found in Figure S2 in SI. For illustration, the electric and magnetic field distribution of HM||e-e at λ = 450 nm for Dgap = 15 nm is shown in Figure 3(c). The HM||e-e naturally establishes a strong electric field enhancement |E/E0| in the gap regime because of the head-to-head orientation of the electric dipole moments inside the metal and dielectric NPs, whereas its magnetic field distribution


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|H/H0| inside the dielectric NP demonstrates a distorted ED feature as compared to that in the isolated case due to the coupling with the metal SPR. The field distribution of an isolate dielectric NP is shown in Figure S3 in SI as a reference. The magnitude of |E/E0| of the hybrid dimer is significantly larger that of an individual metallic or dielectric nanoparticle owing to the near field interaction in the gap region. In addition, it is considerably larger than that of the pure dielectric dimer and comparable with that of the pure metallic dimer, which reflects that the strong field enhancement property of the metal SPR is partially integrated in the hybridize dimer configuration. Details can be found in Figure S4 in SI. Figure 3(d) depicts the field distribution of the dielectric MD at λ = 560 nm. As expected, both the |E/E0| and |H/H0| inside the dielectric NP resembles a similar MD feature as that in the isolated case. Interestingly, introducing the metallic NP at its close proximity still leads to a decent electric field enhancement |E/E0| in the dimer gap. Note that all the field distributions are recorded at E-H plane here and thereafter. In Figure 3 above, Dgap is controlled to be small so that the coupling between the metal SPR and dielectric ED is strong to establish a prominent hybridized-mode HM||e-e in the spectrum with a significant red-shift from the individual SPR/ED (λ = 400 nm). Continuing increasing Dgap will reduce the coupling strength because the near field decays rapidly away from the nanoparticle surface, which is the common point for the hybrid dimer, pure metallic dimer and pure dielectric dimer configurations. Figure 4(a) and 4(b) show the extinction spectra of SPR-ED dimers with small Dgap = 10 nm (strong coupling) and relatively large Dgap = 50 nm (weak coupling), respectively. The separated e-e, m-m and e-m contributions are illustrated. Obviously at large Dgap, the shift of HM||e-e with respect to the individual SPR/ED is diminished due to the reduced e-e interaction as compared to that at small Dgap. The e-m interaction strength also becomes weaker at large Dgap. Figure 4(c) depicts the extinction spectra over a broad range of Dgap with


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varied resonating intensities, which clearly show that when the gap distance is greater than 50 nm, there is a negligible shift of the SPR-ED hybridization due to the weak coupling strength. Note that the MD, however, always remains unshifted at λ = 560 nm regardless of Dgap for the hybrid dimer due to the lack of magnetic dipolar response in the metal nanoparticle, which is different from the pure dielectric dimer where both the electric and magnetic resonance will shift accordingly with respect to the change in Dgap.(2) Beside the change in the spectra, increasing Dgap will also dramatically reduce the near-field enhancement at the center of the gap as shown in Figure 4(d), which is similar to that of the pure metallic and dielectric dimer. Hereafter, we focus our investigation on the strong coupling regime with small Dgap.

Figure 4. The extinction spectra for (a) strong coupling at small gap distance Dgap = 10 nm and (b) weak coupling at relatively larger Dgap = 50 nm. At large Dgap, the shift of HM||e-e with respect to the individual SPR/ED is diminished due to the reduced e-e interaction as compared to


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that at small Dgap. The e-m interaction strength also becomes weaker. (c) Extinction spectra and (d) near field enhancement at the center of the gap over a broad range of Dgap. Alternatively, Figure 5(a) shows the extinction spectra of SPR-ED dimer under E⊥dimer illumination. Again, a hybridized-mode (HM⊥e-e) is formed based on the e-e interaction. In this case, the electric dipole momentums inside the metal and dielectric NPs orient parallel to each other which causes HM⊥e-e to blue-shift as compared to the individual metal SPR/dielectric ED. Likewise, the dielectric MD remains unshifted at λ = 560 nm since the m-m interaction is dominated by the dielectric MD alone. The separate contributions of e-e, m-m, and e-m interaction are illustrated in Figure 5(b). The deviation from the FEM results is attributed to the presence of the high-order modes (e.g. quadrupole modes) in the NPs, which are not captured in the dipole-dipole interaction model. The corresponding field distributions of HM⊥e-e are shown in Figure 5(c) at λ = 388 nm for Dgap = 15 nm. Moderate electric field enhancements |E/E0| are presented on the surfaces of both metal and dielectric NPs due to the e-e interaction, and the |E/E0| and |H/H0| inside the dielectric NP resembles the ED feature as that in the isolated case. Figure 5(d) records the field distributions at the dielectric MD, where |E/E0| is rather weak at the vicinity of the metal NP since the wavelength is away from HM⊥e-e, and the field distribution inside the dielectric NP resembles a clear MD feature as that in the isolated case.


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Figure 5. (a) The coupling between the SPR and dielectric ED (SPR-ED dimer) for E⊥dimer illumination. A new hybrid mode HM⊥e-e is formed due to the electric-electric dipole-dipole interaction between the two NPs, which blue-shifts as compared to the individual metal SPR and dielectric ED. The dielectric MD remains unshifted at λ = 560 nm due to the absence of the magnetic dipole momentum in the metal NP. (b) The separate contributions from electric-electric (e-e), magnetic-magnetic (m-m), and electric-magnetic (e-m) dipole-dipole interaction at Dgap = 10 nm. (c) & (d) The electric and magnetic field distribution of the HM⊥e-e (Dgap = 15 nm and λ = 388 nm), and the dielectric MD (Dgap = 15 nm and λ = 560 nm) respectively.


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Coupling between metal SPR and dielectric MD under plane wave excitation. The same procedure is repeated to explore the coupling between the metal SPR and the dielectric MD (denoted as SPR-MD here after), whereby the peaks of isolated metal SPR and dielectric MD are deliberately designed at wavelength λ = 400 nm, corresponding to a Dm = 100 nm Ag NP and a Dg = 78 nm dielectric NP respectively. The dimer extinction spectra under E||dimer incidence are shown in Figure 6(a). It is observed that the dielectric MD slightly blue-shifts ~ 4 nm with a diminishing magnitude as Dgap reduces. Meanwhile, a shoulder arises in the spectrum at a wavelength longer than MD, which becomes significant particularly at small gap distance Dgap ≤ 10 nm.


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Figure 6. (a) The coupling between the SPR and dielectric MD (SPR-MD dimer) for E||dimer illumination. The original dielectric MD slightly blue shifts with a diminishing magnitude due to the influence of the electric-magnetic (e-m) dipole-dipole interaction. A shoulder arises at a wavelength longer than the MD because of the e-e interaction between the metal SPR and the tail of the dielectric ED. (b) The separate contributions from electric-electric (e-e), magneticmagnetic (m-m), and electric-magnetic (e-m) dipole-dipole interaction at Dgap = 10 nm. (c) & (d) The electric and magnetic field distribution of the dielectric MD (Dgap = 15 nm and λ = 400 nm), and the shoulder (Dgap = 15 nm and λ = 450 nm) respectively.


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In principle, the primary metal SPR and dielectric MD induced by the incident light cannot directly couple with each other due to the different resonating natures as well as the mutually orthogonal orientations. However, these primary dipolar sources on one NP can induce the secondary resonances on the other NP, and the subsequent interaction between the primary and secondary sources (e.g. e-m interaction) is thereby able to influent the overall extinction spectrum.(2) Indeed, the pulse-shape response of e-m interaction shown in Figure 6(b) eventually contributes to the slight blue-shift as well as the reduction in the magnitude of the dielectric MD. Note that the relative contribution of the e-m interaction of SPR-MD dimer to the overall extinction spectrum is generally larger than that of SPR-ED case because the SPR and MD is deliberately designed to fully overlap in SPR-MD scenario to induce a more distinguishable e-m influence. In addition, the shoulder arisen in the spectrum essentially results from the e-e interaction between the metal SPR and the tail of the dielectric ED presented in the MD regime, which red-shifts as Dgap reduces and appears at the wavelength longer than MD. See Figure S1 in SI for more detail. Such e-e interaction is relatively weaker as compared to the SPR-ED case (see Figure 3(a)) where the metal SPR and dielectric ED are fully coupled; thereby it is more observable at a small gap distance Dgap ≤ 10 nm. Figure 6(c) illustrates the field distribution of dielectric MD at λ = 400 nm and Dgap = 15 nm, which resembles the feature as that in the isolated case. Figure 6(d) depicts the field distribution of the shoulder at λ = 450 nm and Dgap = 15 nm, which exhibits a moderate electric field enhancement |E/E0| in the gap due to the e-e interaction nature, whereas its magnetic field enhancement |H/H0| becomes much smaller since the wavelength is far away from the MD. Finally under E⊥dimer incidence, the spectral responses of SPR-MD dimer are plotted in Figure 7(a). The dielectric MD again remains unshifted and does not couple to the metal SPR.


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Here the e-e contribution is also not profound (see Figure 7(b)) due to the parallel orientations of the electric dipolar moments inside the NPs as well as the small overlap between the metal SPR and the tail of dielectric ED. In this situation, the pulse-shape response of the e-m interaction is better reflected in the spectrum which induces a small shoulder ~ 388 nm and a shallow valley around ~ 417 nm. The resultant field distribution of the dielectric MD is depicted in Figure 7(c) with a clear resemblance of the feature in the isolated case. On the other hand, the field distribution at the small shoulder exhibits a decent |E/E0| at the surface of the metal NP as shown in Figure 7(d), which can be understood as the superposition of the partial excited primary dipolar source induced by the incident light (e.g. e-e interaction) and secondary dipolar moment induced by the dielectric NP (e.g. e-m interaction). Meanwhile, |H/H0| inside the dielectric NP becomes relatively weaker because the wavelength is away from the MD.


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Figure 7. (a) The coupling between the SPR and dielectric MD (SPR-MD dimer) for E⊥dimer illumination. The pulse-shape response of the e-m interaction is better reflected in the spectrum which induces a small shoulder ~ 388 nm and a valley around ~ 417 nm. (b) The separate contributions from electric-electric (e-e), magnetic-magnetic (m-m), and electric-magnetic (e-m) dipole-dipole interaction at Dgap = 10 nm. (c) & (d) The electric and magnetic field distribution of the dielectric MD (Dgap = 15 nm and λ = 400 nm), and the shoulder (Dgap = 15 nm and λ = 388 nm) respectively.


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Excitation of the hybrid dimer modes under dipole emitter radiation. One of the applications for the dimer nanoantenna is to control the emission of the quantum emitter (e.g. organic dyes, quantum dots etc).(53)-(55) Understand how the emitter radiation couples to the various resonances of the dimer is the foundation in designing the antenna structure. Under classic framework, a quantum emitter is commonly treated as a dipole source whose interaction with the dimer antenna can be revealed by determining the corresponding radiative decay rate Γr/Γ0 with respect to the orientation of the emitter. The results are shown below in Figure 8 for the SPR-ED dimer (left panel) and SPR-MD dimer (right panel) respectively. The emitter is located at the center of the dimer gap.


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Figure 8. The coupling between a dipole emitter and the hybridized SPR-ED dimer (left panel) and the SPR-MD dimer (right panel) respectively. Depending on the orientation as well as the nature of the emitter (electric or magnetic), the dipole selectively excites certain resonant modes of the dimer nanoantenna. (a) & (d): the various resonance modes of the dimer nanoantenna under plane wave illumination as references, (b) & (e) the spectral response when the emitter aligns parallel to the dimer axis, and (c) & (f) the spectral response when the emitter aligns perpendicular to the dimer axis. The emitter is located at the center of the antenna gap. Figure 8(a) recaptures the extinction spectra of the SPR-ED dimer for both E||dimer and E⊥dimer plane wave incidence as references. When the electric dipole emitter aligns parallel to the dimer axis, it primarily excites the resonances modes that are electric in nature over a broad band range as shown in Figure 8(b), e.g. the hybrid modes HM||e-e ~ 450 nm and HM⊥e-e ~ 390 nm originated from e-e interaction as well as the high-order electric quadrupole ~ 350 nm. Meanwhile, the magnetic dipole emitter selectively excites the resonant modes that are magnetic in nature, e.g. dielectric MD ~ 560 nm and high-order magnetic quadrupole ~ 385 nm. The situation is more intricate when the emitter orientation is perpendicular to the dimer axis as shown in Figure 8(c). First, high-order electric and magnetic quadrupole modes in general can be excited by both electric and magnetic dipole emitter to a certain degree. Second, the electric dipole emitter this time mainly excites the dielectric MD, whereas its coupling to the dimer’s electric resonances has been suppressed. In contrast, the magnetic dipole emitter is now able to couple with the resonances that are electric in nature, resulting in an intermediate peak ~ 420 nm between HM||e-e and HM⊥e-e, while the excitation of the dielectric MD becomes relatively weak. Note that the occurrence of the intermediate peak is also observed in the pure dielectric dimer,(2) which could be attributed to the superposition of the excited HM||e-e and HM⊥e-e bands. Lastly,


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the magnitude of the radiative decay rate Γr/Γ0 for emitter perpendicular to the dimer axis is much smaller than that for emitter parallel to the dimer axis (see Figure 8(b)). Similar conclusions can also be drawn for the SPR-MD dimer, whose extinction spectra under E||dimer and E⊥dimer plane wave incidence are illustrated in Figure 8(d) for reference. Again when the emitter orients parallel to the dimer axis in Figure 8(e), the electric dipole selectively excites the dimer’s electric resonances including the shoulder ~ 450 nm due to e-e interaction and the high-order electric quadrupole ~ 350 nm, while the magnetic dipole mainly couples to the dielectric MD ~ 400 nm. When the emitter aligns perpendicular to the dimer axis in Figure 8(f), as expected, the high-order electric quadrupole can always be excited by both electric and magnetic dipole. In addition, the electric dipole emitter now mainly couples to the dimer’s magnetic resonance while the magnetic dipole could respond to the dimer’s electric resonance.

4. DISCUSSION Hybrid dimer antenna enhanced fluorescence emission. After understanding the resonating coupling under plane wave excitation as well as the dipole emitter radiation (see Figure 3-8), we now proceed to estimate the potential of the hybrid dimer as an antenna in the fluorescence emission enhancement, which can be obtained as a product of the excitation rate γext/γ0 and the quantum yield q/q0.(36),(48) To mimic the experiments, the emitter is now modelled as the statistical ensemble of electric dipoles with random orientations, which is placed in the antenna gap along the dimer axis. The average quantum yield and emission enhancement can be determined analytically via averaging the respective quantities over all possible orientations. Detail can be found in the Methods section.


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We select the SPR-ED scheme under E||dimer incidence (see Figure 3) whereby the metal SPR and dielectric ED are fully coupled. The resultant hybrid mode HM||e-e provides a large |E/E0| in the gap, which naturally leads to a large excitation rate γext/γ0. In addition, its dielectric MD also possesses strong |E/E0| owing to the near field interaction, thereby broadens the spectral band that can be utilized to excite the emitter. For illustration, we design the SPR-ED dimer with a 160 nm Si NP and a 110 nm Au NP, whereby the isolated metal SPR and dielectric ED are both aligned at 515 nm. Detail mode composition can be found in Figure S5 in SI. Here Si is used due to its high permittivity (~ 14 to 30) in the visible light regime.(56) Meanwhile, Au is used in lieu of Ag because Au generally possesses a profound SPR at wavelength > 500 nm.(1) The gap distance is Dgap = 20 nm to allow sufficient space for the emitter to set in. This particular design results in the dimer resonance modes (both HM||e-e and dielectric MD) beyond 550 nm which fall at the low conductivity regime of Si, hence naturally improving the average quantum yield and the resultant fluorescence emission . More details can be found in Figure S6 in SI. To obtain the largest , the location of the emitter has to be carefully controlled to achieve the optimal balance between the excitation rate γext/γ0 and quantum yield , particularly when the nanoantenna comprises metallic materials. Detrimental quenching effect(12),(17),(19) could arise when the distance between the emitter and the nanoantenna is too small that the non-radiative decay rate due to SPR absorption wins over the radiative decay rate and is diminished.(36),(57) In contrast to the pure metallic dimer whereby the emitter should routinely present at the center of the gap, the emitter should in principle locate closer to the dielectric side of the SPR-ED dimer to: 1) improve the average quantum yield by being away from the lossy metal NP; and 2) benefit from larger excitation rate γext/γ0 near the NP’s


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surface as compared to that at the center of the gap. In Figure 9, we compare the best scenario of the fluorescence emission enhancements from: 1) the above SPR-ED hybrid dimer with the emitter location at x = 5 nm; 2) the pure dielectric dimer consists of two identical 160 nm Si NPs at x = 5 nm; and 3) the pure metallic dimer comprises two identical 110 nm Au NPs at x = 0 nm, where x denotes the location of the emitter in the antenna gap and x = 0 nm indicates the center of the gap. The detail optimization for the three schemes can be found in Figure S7-S9 in SI. Note that altering the morphologies (e.g. sizes, shape, environment) of the constituent NPs could not only change γext/γ0 via changing the near field enhancement |E/E0|,(58),(59) but also change since the non-radiative decay rate is associated with the SPR absorption while the radiative decay rate correlates with the scattering properties of NPs.(60),(61) Moreover, the change in the SPR absorption can further influence the temperature of the medium by converting photon energy into thermal energy, which could modify the absorption/desorption kinetics of surface molecules, change the dielectric properties of the medium and NP, and thermally activate additional non-radiative channels due to the thermochromism effect.(61)-(63) From these perspectives, the optimal location of the emitter need to be revised for different nanoantenna designs.


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Figure 9. The comparison of the best scenario of the average emission enhancements from: the SPR-ED dimer made of one 110 nm Au NP and one 160 nm Si NP with emitter location at x = 5 nm; the pure dielectric dimer consists of two 160 nm Si NPs at x = 5 nm; and the pure metallic dimer comprises two 110 nm Au NPs at x = 0 nm, where x denotes the location of the emitter in the antenna gap and x = 0 nm indicates the center of the gap. The corresponding (a) the excitation rate γext/γ0, (b) the average quantum yield , and (c) the average emission enhancement are illustrated. (d) The normalized far field intensity of the SPR-ED hybrid dimer at λ = 650 nm. Regardless of the emitter orientation, the overall emission is more directed towards the dielectric NP side owing to the asymmetrical feature of the hybrid dimer. Through coupling between the metal SPR and the dielectric ED, the hybrid dimer indeed yields an excitation rate γext/γ0 40% higher than that of the pure dielectric dimer as shown in


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Figure 9(a), hence overcoming the limitation of the pure dielectric platform whose electric field enhancement is relatively weak. The pure metallic dimer still possesses the highest γext/γ0 because of the strong electron oscillation of the metal SPR. On the other hand, the average quantum yield of the SPR-ED dimer can achieve 30% higher than that of the pure metallic dimer owing to the existence of the low loss dielectric NP as shown in Figure 9(b), and it is only 8% smaller than that of the pure dielectric dimer. The low loss feature is clearly well-preserved in the SPRED dimer. Note that since the hybrid dimer combines both metal and dielectric NPs, the respective fluorescence excitation rate or average quantum yield is legitimately bounded between that of the pure metallic and dielectric dimer systems. Nevertheless, the ultimate fluorescence emission enhancement depends on the product of both fluorescence excitation and the quantum yield instead of the individual one. The hybrid dimer offers the possibility to achieve a better balance between the fluorescence excitation rate and quantum yield. Eventually, the SPR-ED dimer develops a strong average emission enhancement = 87 as shown in Figure 9(c), which is 30% higher than that of the pure dielectric dimer ( = 67) and very close to that of the metallic dimer ( = 90). Besides a promising fluorescence enhancement, the hybrid dimer is also able to enhance the directivity of the fluorescence emission as illustrated in the normalized far field pattern in Figure 9(d). The overall emission favors the dielectric NP side regardless of the emitter’s orientation, which is approximately 20% higher than that towards the metal NP side. Such directivity originates from the uniquely two-fold asymmetrical features of the hybrid dimer: 1) the dimer comprises a metallic NP with permittivity < 0 and a dielectric NP with permittivity > 0. This permittivity contrast modifies the radiation pattern of the emitter and directs the emission more towards the high permittivity dielectric side due to the conversion of the evanescent waves into


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propagating waves;(49) and 2) the sizes of the metallic and dielectric NPs are different to overlap the metal SPR and dielectric ED. This size contrast also directs the emission towards the larger dielectric NP side due to its larger extinction cross-section. Note that this feature generally does not exist for pure metal and dielectric dimers since they are made of two identical NPs. We speculate that by further optimizing the morphologies (e.g. the shape, size, materials) of each constituent NP of the hybrid dimer, an even higher exceeding that of the pure metallic counterpart can be potentially realized on the basis of three perspectives: 1) Si used in this paper has a permittivity less than 16 beyond 550 nm. If a dielectric material with high permittivity at operating wavelength is implemented, the overall fluorescence excitation rate of the hybrid dimer could be further improved; 2) within the visible wavelength, Si is not absolutely lossless particularly at short wavelength below 500 nm. Using a dielectric material with a smaller conductivity at the operating wavelength could further boost the overall quantum yield of the hybrid dimer; 3) in this paper, the average enhancement is obtained by assuming all the fluorescence emission can be collected to simplify the problem. In reality, for a typical CCD detection system, only part of the emission can be collected depending on the numerical aperture (NA) of the lens.(48) Therefore, a good directivity naturally implies higher collection efficiency and eventually higher detected fluorescence enhancement. We have already illustrated that a hybrid dimer made of spherical NPs can direct 20% more light towards the dielectric side than that towards the metallic side (Figure 9(d)). We believe adopting other NP morphologies (e.g. rod, bowtie, cube etc) may further enhance the directivity of the fluorescence emission, which could help to develop a higher detected fluorescence enhancement than that of pure metallic dimer.


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Other potential applications using hybrid dimer. Besides fluorescence enhancement, we speculate that the hybrid dimer antenna might also be useful in many other applications, such as: •

Nonlinear optics: the strong field enhancement within the dimer gap and the interaction between various resonant modes could be used to boost the high-order harmonic generation. The asymmetrical feature of the hybrid dimer could also be exploited to enhance the directivity of the high-order harmonic radiation.

•

Meta-surface: the hybrid dimer could be used as a building block to construct complex metasurfaces for flat optical applications such as beam-steering, beam-shaping, sensing etc. The co-existence of both electric and magnetic modes as well as the asymmetrical nature of the hybrid dimer provides excellent degree of freedom in designing various meta-surfaces.

•

Fano-resonance: by properly designing the constituent metal and dielectric NP of the hybrid dimer, it is possible to realize Fano-resonance feature in the spectrum, e.g. coupling the sharp metal SPR of Al/Ag with the broad dielectric ED of low permittivity dielectric NP.

5. CONCLUSION In this contribution, we have performed a comprehensive investigation on the optical response of a hybrid dimer nanoantenna comprising a plasmonic metal nanoparticle (NP) and a high permittivity dielectric NP. Backed up by the generalized dipole-dipole interaction theory, we first discovered that the coupling between metal surface-plasmon-resonance (SPR) and dielectric electric-dipole-mode (ED) creates a hybridized mode under plane wave excitation due to the strong electric-electric dipole-dipole interaction. The dielectric magnetic-dipole-mode (MD) remains almost unchanged due to the missing magnetic dipolar contribution in the metal NP. In addition, the interaction between the primary resonances directly excited by the incident light


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and the secondary resonances induced by the primary resonances can also manipulate the overall extinction spectrum, particularly when the SPR and MD are overlapped. When the hybrid dimer antenna is subsequently utilized to control the radiation of a quantum emitter, it is observed that the electric/magnetic dipole selectively excites the electric/magnetic (magnetic/electric) resonances of the dimer when the emitter orients parallel (perpendicular) to the dimer axis. Finally by placing the emitter closer to the dielectric side of the hybrid dimer, 40% higher electric field enhancement compared to the pure dielectric dimer and 30% lower loss compared to the pure metallic dimer can be simultaneously achieved. Preliminary results show a fluorescence enhancement 30% higher than that of the pure dielectric dimer and equivalent to that of the pure metallic dimer, albeit the performance can be further improved. On top of that, the unique asymmetrical structure (e.g. permittivity and size contrast between the constituent NPs) of the hybrid dimer can be further exploited to manipulate the directivity of the fluorescence emission (e.g. 20% more radiation towards the dielectric side). Our results clearly prove the feasibility to couple metal and dielectric to form an optical antenna which integrates the advantages of both platforms. The fundamental coupling mechanism between the metal SPR and dielectric resonances revealed here can also be extended to other structures, paving the way in the design and optimization of the complex hybrid systems.

ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website. Detail mode compositions of the isolated metal and dielectric NPs; the electric and magnetic field distribution of an isolated dielectric NP; extinction spectrum of the Au-Si SPR-ED dimer


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and Si material properties; optimization of the fluorescence enhancement for SPR-ED dimer, pure dielectric dimer and pure metallic dimer. (PDF)

AUTHOR INFORMATION Corresponding Author *Email: [email protected]. *Email: [email protected]. Orchid ID Sun Song: 0000-0003-2382-6481 Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT The authors would like to acknowledge funding support from Science Challenge Project, PRC China (grant No. TZ2016003), National Natural Science Foundation Committee (NSFC) of China (grant No. 51475347), Agency for Science and Technology Research (A*STAR) Singapore Pharos project: Dielectric Nanoantennas (grant No. 152-73-00025) and Quantum Technologies for Engineering (QTE) Program (grant No. A1685b0005).

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