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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
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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
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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
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AUTHOR SUBMITTED MANUSCRIPT - JOPT-104599.R2
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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.
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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
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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
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Page 2 of 6
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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
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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
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AUTHOR SUBMITTED MANUSCRIPT - JOPT-104599.R2
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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.
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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
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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
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4. Conclusions
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an
[8]
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the resonance peak. Figure 6(b) shows that if all No 10JCZDJC23600.
other parameters keep the same, with increasing of
the Si ring size, the peak position of the Fano References
resonance is red shifted slightly and the intensity of
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resonance.
In
conclusion,
we
have
achieved
polarization-independent magneto-electric Fano
resonance in hybrid hetero-cavity consisting of a Si
ring and an Au disk. 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.
[9]
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AUTHOR SUBMITTED MANUSCRIPT - JOPT-104599.R2
[17]
[18]
Acknowledgments
This work was supported by the key project of the
Natural Science Foundation of Tianjin City under Grant
[19]
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