Hybrid photonic-plasmonic molecule based on
metal/Si disks
Qing Wang, 1 Hang Zhao,1 Xu Du, 1 Weichun Zhang,1 Min Qiu,1, 2 and Qiang Li 1,*
1
State Key Laboratory of Modern Optical Instrumentation, Department of Optical Engineering, Zhejiang University,
310027, Hangzhou, China
2
School of Information and Communication Technology, KTH Royal Institute of Technology, Electrum 229, 16440,
Kista, Sweden
*
[email protected]
Abstract: Optical properties of two identical coupled disks forming a
“hybrid photonic-plasmonic molecule” are investigated. Each disk is a
metal-dielectric structure supporting hybrid plasmonic-photonic
whispering-gallery (WG) modes. The WG modes of a molecule split into
two groups of nearly-degenerate modes, i.e., bonding and anti-bonding
modes. The oscillation of quality factor (Q) with the inter-disk gap d and
significant enhancement at certain inter-disk gaps can be observed. An
enhanced Q factor of 1821 for a hybrid photonic-plasmonic molecule
composed of two 1.2 μm-diameter disks, compared with that for a single
disk, is achieved. The corresponding Purcell factor is 191, making the
hybrid photonic-plasmonic molecule an optimal choice for subwavelengthscale device miniaturization and light-matter interactions. Moreover, the
far-field emission pattern of the hybrid photonic-plasmonic molecule
exhibits an enhanced directional light output by tuning the azimuthal mode
number for both bonding and anti-bonding modes.
©2013 Optical Society of America
OCIS codes: (250.5403) Plasmonics;
Subwavelength structures, nanostructures.
(230.4555)
Coupled
resonators;
(310.6628)
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1. Introduction
Photonic molecules composed of a cluster of mutually-coupled optical microcavities have
aroused keen interest in the last decade [1]. Conventional configurations of photonic
molecules include two or more optical resonators, such as microdisks, microrings,
microspheres and point-defect cavities in photonic crystals, etc [2–12]. By playing with the
structures and the compositions of the microcavities, photonic molecules can be optimized to
exhibit many unique optical properties including light confinements in the wavelength-scale.
Therefore, the photonic molecule is regarded as one of key components for a variety of
optical applications, such as low-threshold semiconductor microlasers [3, 12, 13], optical
filters and switches [7, 14, 15], information processing [16], biochemical sensing [17, 18], et
al.
Most optical microcavities designed so far are based on dielectric materials. Hence a
further size reduction is hindered by the diffraction [19–21]. Moreover, as the size of a disk
cavity decreases, the total internal reflection of the microcavity becomes weak, resulting into
an increase in the mode radiation loss and an exponential decrease in the quality factor (Q)
[20]. Thus the desire for a high Q and that for device miniaturization seem contradictory.
Recently the plasmonic cavities, which are capable of further reducing the mode volume to
subwavelength scale while maintaining a relatively high Q due to the effect of surface
plasmon polaritons (SPPs), are proposed as an alternative [22–27].
Earlier efforts dedicated to the plasmonic microcavities mainly focused on a single disk
[22–27]. Few of them have investigated the coupling between plasmonic disks. Previous
studies on the hybrid photonic-plasmonic geometry have shown many functionalities [28–
32]. Ref [28] has shown cascaded nanoscale hot-spot intensity enhancement in a hybrid
photonic-plasmonic structure composed of an Au nanoparticle dimer and a dielectric
microcavity. Ref [29] has demonstrated significant enhancement and redistribution of the
magnetic field in the hybrid metallo-dielectric clusters. Ref [30] has shown a whisperinggallery-mode biosensor based on wavelength shifts of a hybrid photonic-plasmonic structure
composed of a gold nanoparticle and a silica microsphere. Ref [31] has demonstrated a
spectrally and spatially configurable hybrid photonic-plasmonic superlens composed of a
polystyrene microsphere and two Au nanodimers. In this paper, a hybrid photonic-plasmonic
molecule consisting of two identical metal/Si microdisks is investigated. Unlike previous
hybrid metallo-dielectric structures composed of nanoparticles and microcavities [28–32],
the hybrid photonic-plasmonic molecule reported here can achieve a good field confinement
and enhancement [27, 33, 34]. Moreover, the characteristics of whispering gallery (WG)
mode splitting can be observed in the hybrid photonic-plasmonic molecule. The single-disk
mode splits into red-shifted bonding modes and blue-shifted anti-bonding modes. The shift of
resonant wavelength decreases with inter-disk gap d varying from 0 to 1200 nm. Meanwhile,
a highly enhanced Q factor of 1821 corresponding to a high Purcell factor of 191 can be
achieved at the resonant wavelength of 1025 nm. This is an extremely large improvement
over conventional photonic molecules in terms of reducing the mode volume while
maintaining a relatively high Q factor [4, 19, 20]. In addition, the far-field emission patterns
in the H-plane and the E-plane for the bonding modes and the anti-bonding modes are
studied. The possibility of manipulating the emission pattern by tuning the azimuthal mode
number is demonstrated.
#186860 - $15.00 USD Received 12 Mar 2013; revised 23 Apr 2013; accepted 24 Apr 2013; published 29 Apr 2013
(C) 2013 OSA
6 May 2013 | Vol. 21, No. 9 | DOI:10.1364/OE.21.011037 | OPTICS EXPRESS 11039
2. The structure of the hybrid photonic-plasmonic molecule
The hybrid photonic-plasmonic molecule consists of two identical 1.2 μm-diameter disks on
a silica substrate. As shown in Fig. 1, the disk is a sandwich-like geometry, which is
composed of the top silver layer, the middle alumina and the bottom silicon. Numerical
simulation based on our home-made three-dimensional finite-difference time-domain
(FDTD) code is conducted to model the hybrid photonic-plasmonic molecule [35, 36]. The
total computation domain is 4.4 μm × 4 μm × 1.2 μm along the x, y and z directions. The
spatial resolution is 15 nm in the x and y direction and 10 nm in the z direction. The
absorbing boundary condition used in the simulation is perfectly matched layers (PMLs). The
permittivities of the silica substrate and the silicon layer are ε SiO = 2.1 and ε Si = 11.9,
2
respectively. The lower index layer is alumina with a permittivity of ε Al2 O3 = 3. The
dispersive permittivity of silver is modeled according to the Drude model which is fitted with
experimental data [37]. The heights of each layer are hSi = 250 nm, hAg = 100 nm and
hAl2 O3 = 50 nm, respectively. For a practical device, a layer of silica is usually deposited atop
to prevent it from oxidizing.
Fig. 1. Schematic diagram of the hybrid photonic- plasmonic molecule consisting of two
disks.
Two kinds of modes can be excited in the proposed structure, i.e., transverse electric (TE)
mode and transverse magnetic (TM) mode. For the hybrid photonic-plasmonic TM mode,
most portion of energy is confined in the low-index layer. While for the dielectric TE mode,
most portion of energy is stored in the silicon layer. Therefore, the TM mode is more
promising for achieving subwavelength application than the TE mode and we only discuss
the TM mode in this paper. Resonant WG modes in individual microdisk are double
degenerate and characterized by two mode numbers, corresponding to the radial mode
number (n) and the azimuthal mode number (m) [20]. The fundamental modes (with n = 1)
are mostly related to practical applications because of their high Q factors and small mode
volumes. So we only classify the modes of the hybrid photonic-plasmonic disks in terms of
the azimuthal mode number m.
3. Mode splitting in the hybrid photonic-plasmonic molecule
Similar to the photonic molecules, when two hybrid photonic-plasmonic atoms (disks) are
brought into proximity, their WG modes will couple and split into two double-degenerate
WG modes, i.e., bonding (even) and anti-bonding (odd) modes, depending on symmetry of
the mode with respect to the y-axis. If we consider the mode symmetry with respect to the xaxis further, the bonding (even) mode includes x-even/y-even (EE) mode and x-odd/y-even
#186860 - $15.00 USD Received 12 Mar 2013; revised 23 Apr 2013; accepted 24 Apr 2013; published 29 Apr 2013
(C) 2013 OSA
6 May 2013 | Vol. 21, No. 9 | DOI:10.1364/OE.21.011037 | OPTICS EXPRESS 11040
(OE) mode. While for the anti-bonding (odd) mode, it includes x-even/y-odd (EO) mode and
x-odd/y-odd (OO) mode. Figure 2 illustrates the mode-splitting behavior in a hybrid
photonic-plasmonic molecule composed of two 1.2 μm diameter disks. For a single disk,
there is a resonant mode with the azimuthal number m = 8 at the wavelength λ = 1025 nm.
When the two disks are brought together with an inter-disk gap of d = 120 nm, the singledisk mode splits into red-shifted bonding modes (resonant wavelength λ = 1028 nm (OE) and
λ = 1026 nm (EE)) and blue-shifted anti-bonding modes (resonant wavelength λ = 1023 nm
(OO) and λ = 1022 nm (EO)). The profile of the dominant electric field component Ez over
the x-y plane in the center of the alumina layer is shown in Fig. 2(a). Figure 2(b) shows the
profile of the electric field Ez in the x-z plane for EE mode. Most of the electric field is
confined within the disk edge of the middle layer, yielding a rather small mode volume.
Fig. 2. Mode splitting in a hybrid photonic-plasmonic molecule with an inter-disk gap d = 120
nm. (a) The profiles of the electric field Ez in the x-y plane of bonding (OE, EE) and antibonding (OO, EO) modes for m = 8. (b) The profile of the electric field Ez in the x-z plane for
EE mode.
To gain more insight into the mode splitting, the resonant wavelength against the interdisk gap is plotted in Fig. 3(a). The resonant wavelength differences decrease when the
distance increases from 0 to 320 nm due to an increasingly weakened coupling strength.
When the distance increases further from 320 nm to 1200 nm, oscillations of the resonant
wavelengths can be observed. The oscillations can be attributed to oscillatory behavior of the
evanescent field. This oscillatory behavior has also been shown in Refs [3, 4, 18, 19]. When
the inter-disk separation is large enough, the four split molecule modes converge to a single
resonant wavelength. The coupling strength between the WG modes of disks (which is
represented by the difference between the resonant wavelengths of the bonding and the antibonding modes) decreases with the increasing distance. The difference of the resonant
wavelength Δλ is also related to the azimuthal mode number. For increasing azimuthal mode
number, the resonant wavelengths of WG modes shift to short wavelengths, similar to the
case of photonic molecules demonstrated by previous study [3]. The hybrid photonicplasmonic molecule shows excellent ability to bind the short wavelength modes; therefore,
the coupling strength decreases as the azimuthal mode number increases. As shown in Fig.
3(b), the difference of the resonant wavelengths λOE–λOO decreases from 22 nm to 5 nm with
the azimuthal mode ranging from 4 to 8, while the λEE –λEO decreases from 20 nm to 4 nm.
#186860 - $15.00 USD Received 12 Mar 2013; revised 23 Apr 2013; accepted 24 Apr 2013; published 29 Apr 2013
(C) 2013 OSA
6 May 2013 | Vol. 21, No. 9 | DOI:10.1364/OE.21.011037 | OPTICS EXPRESS 11041
Fig. 3. (a) The resonant wavelengths of anti-bonding (OO, EO) and bonding modes(OE, EE)
as functions of the distance between the two atoms for the azimuthal-order m = 8, (b)
Wavelength differences between bonding modes and anti-bonding modes versus the
azimuthal mode number when d = 120 nm.
4. Q factor enhancement of hybrid photonic-plasmonic molecule modes
Optical performance of a resonator cavity is evaluated by three major parameters: 1) the
quality factor Q, which represents the power of the optical disks to enhance light-matter
interactions, is calculated using a combination of FDTD techniques and Padé approximation
with Baker's algorithm [35, 36]. 2) the effective mode volume Veff which is vital for the sizereduction of optical devices and 3) the Purcell factor FP, which is related to the ratio of the Q
factor and mode volume as [27]:
3
FP =
3  λ0   Q 


4π 2  n  V eff 
(1)
where λ0 is the resonant wavelength in free space and n is the refractive index of the lowerindex layer. The effective mode volume is calculated as [27]:
2
V eff =
 ε (x , y , z ) E (x , y , z ) dx dydz
(2)
.
2
max{ε (x , y , z ) E (x , y , z ) }
A cavity system with a high Q factor and a small mode volume and thus a high Purcell
factor is in favor of practical applications. Previous studies have shown that a resonator of a
larger size can achieve a higher Q factor and the Q factor increases with the azimuthal mode
number m [4, 27]. Here we investigate the case of a high-azimuthal-order (m = 8) in the
coupling system. The dependencies of the Q factors for the OE, OO, EE, and EO modes on
the distance between disks d are plotted in Fig. 4 and Q factors are found to oscillate with
respect to d, which can be explained by “loss splitting” due to an imperfect destructive
interference between the WG modes referred in [38]. The highest Q factor of 1821 is
obtained for the anti-bonding mode (OO) at d = 540 nm. This is a three times enhancement
with respect to that of an isolated hybrid photonic-plasmonic atom (Q = 608). We also plot
effective mode volume Veff against the azimuthal mode number ranging from 4 to 8 for all
modes at d = 120 nm and d = 540 nm. Figure 5 shows that the increase of effective mode
volume is nearly linear with respect to the increasing azimuthal number m. For the same
azimuthal mode, Veff keeps almost the same for different modes (OE, OO, EE, and EO
modes) at different inter-disk distances (120 nm and 540 nm). The effective mode volume of
the hybrid photonic-plasmonic molecule is approximately two times of that of the single
disk. So the effect of coupling between the two atoms in the hybrid photonic-plasmonic
#186860 - $15.00 USD Received 12 Mar 2013; revised 23 Apr 2013; accepted 24 Apr 2013; published 29 Apr 2013
(C) 2013 OSA
6 May 2013 | Vol. 21, No. 9 | DOI:10.1364/OE.21.011037 | OPTICS EXPRESS 11042
molecule on the mode volume is not significant. The mode volume is predominantly
determined by the azimuthal mode number and the number of disks in the coupling system.
Fig. 4. The Q factor as functions of the distance between disks for bonding modes (OE, EE)
and anti-bonding modes (OO, EO). The azimuthal-order m is 8. For comparison, the Q factor
of an isolated disk (m = 8) is also plotted (dash dot line).
5
0
((λ /2n)3)
6
Mode volume V
eff
4
3
2
OE d = 120 nm
OO d = 120 nm
EE d = 120 nm
EO d = 120 nm
OE d = 540 nm
OO d = 540 nm
EE d = 540 nm
EO d = 540 nm
single disk
1
0
4
5
6
7
Azimuthal mode number
8
Fig. 5. The effective mode volume Veff against the azimuthal mode number for the bonding
modes (OE, EE) and the anti-bonding modes (OO, EO) at d = 120 nm and 540 nm. For
comparison, the mode volume of a single disk is also plotted (triangle).
As shown in Fig. 4, the highest Q factor of the hybrid photonic-plasmonic molecule is Q
= 1821 at d = 540 nm. Correspondingly, a large Purcell factor FP = 191 can be realized for
the hybrid photonic-plasmonic molecule at 1025 nm resonant wavelength. Those properties
offered by the hybrid photonic-plasmonic molecule demonstrate a way of reducing the
microcavity size to the order of subwavelength scale while maintaining a relatively high Q
factor.
#186860 - $15.00 USD Received 12 Mar 2013; revised 23 Apr 2013; accepted 24 Apr 2013; published 29 Apr 2013
(C) 2013 OSA
6 May 2013 | Vol. 21, No. 9 | DOI:10.1364/OE.21.011037 | OPTICS EXPRESS 11043
5. The far-field pattern from hybrid photonic-plasmonic molecule
High directional radiation and selective mode enhancement are desirable for the applications
of microcavities [39–42]. For a single microcavity, the disadvantage of multi-beam emission
pattern hinders its further optical applications. When two identical disks are brought into
proximity, the far-field emission properties of the hybrid photonic-plasmonic molecule are
modified by near-field coupling. The exact emission patterns of the hybrid photonicplasmonic molecule can be quite different among different WG modes. Appropriate control
of the mutual coupling between individual cavities forming the hybrid photonic-plasmonic
molecule enables enhancement of the directional emission.
In our FDTD calculation, the whole structure is first enclosed in a cube to collect nearfield electromagnetic components at resonant wavelengths. Then the far-field patterns are
calculated from the Fourier transformed near-field electromagnetic components based on the
Green’s theorem [43]. The observed near-field distributions of the hybrid photonicplasmonic molecule are analogous to those of multi-dipoles (m = 7 and 8) arranged along the
edge of circle disks. Their far-field emission patterns results from the multi-dipoles (m = 7
and 8) of individual disk and the interactions between coupled disks. The radiations from
multi-dipoles of individual disk for m = 7 and m = 8 are different. The interactions between
coupled disks further complicate the radiation patterns, leading to a substantial difference
between the patterns for m = 7 and m = 8.
Figure 6 shows the normalized H-plane emission patterns of the WG modes of m = 7 for
individual atom and a hybrid photonic-plasmonic molecule. As for a single disk, there exists
multi-beam emission (Fig. 6(a)), while the number of main emission beams decreases in the
hybrid photonic-plasmonic molecule. There are main emission beams in the direction of φ =
90° and 270° for OE and EE modes, while these beams disappear for OO and EO modes.
Meanwhile, there are negligible emission beams in the direction of φ = 0° and 180° for OE
and OO modes. The far-field emission patterns of the hybrid photonic-plasmonic molecule
for m = 8 are shown in Fig. 7. The emission pattern for a single disk is similar to that of m =
7. In contrast to the case of bonding modes (OE and EE), the anti-bonding modes (OO and
EO) have a better directional emission with four main beams of emission shown in Fig. 7(c)
and 7(e).
Fig. 6. The far-field emission patterns of H-plane (a) for the individual disk of WG modes of
m = 7, (b), (d) the bonding modes (OE and EE) and (c), (e) the anti-bonding modes (OO and
EO) for hybrid photonic-plasmonic molecule.
#186860 - $15.00 USD Received 12 Mar 2013; revised 23 Apr 2013; accepted 24 Apr 2013; published 29 Apr 2013
(C) 2013 OSA
6 May 2013 | Vol. 21, No. 9 | DOI:10.1364/OE.21.011037 | OPTICS EXPRESS 11044
Fig. 7. The far-field emission patterns of H-plane (a) for the individual disk of WG modes of
m = 8, (b), (d) the bonding modes (OE and EE) and (c), (e) the anti-bonding modes (OO and
EO) for hybrid photonic-plasmonic molecule.
Figure 8 shows the normalized E-plane emission patterns of the WG modes of m = 7 for
individual hybrid photonic-plasmonic atom and a hybrid photonic-plasmonic molecule. From
Fig. 8, the E-plane emission concentrates mainly in the direction of φ = 0° and 180° for the
individual disk, OE and EE modes, whereas the electric field emit downward for OO and EO
modes. The E-plane emission patterns of m = 8 are shown in Fig. 9, which shows that the
directions of main emission beam slope are unique for the four modes. However, there is no
emission energy in the direction of φ = 90° and 270° for both a single disk and a hybrid
photonic-plasmonic molecule owing to the top silver layer.
Fig. 8. The far-field emission patterns of E-plane (a) for the individual disk of WG modes of
m = 7, (b), (d) the bonding modes (OE and EE) and (c), (e) the anti-bonding modes (OO and
EO) for hybrid photonic-plasmonic molecule.
#186860 - $15.00 USD Received 12 Mar 2013; revised 23 Apr 2013; accepted 24 Apr 2013; published 29 Apr 2013
(C) 2013 OSA
6 May 2013 | Vol. 21, No. 9 | DOI:10.1364/OE.21.011037 | OPTICS EXPRESS 11045
Fig. 9. The far-field emission patterns of E-plane (a) for the individual disk of WG modes of
m = 8, (b), (d) the bonding modes (OE and EE) and (c), (e) the anti-bonding modes (OO and
EO) for hybrid photonic-plasmonic molecule.
The far-field emission patterns of the hybrid photonic-plasmonic molecule can be
efficiently manipulated by varying the azimuthal mode number. Furthermore, the emission
pattern of OE mode m = 7 shows enhanced directivity in the H-plane.
6. Conclusions
A new type of coupled resonator named “hybrid photonic-plasmonic molecule” comprising
of two identical disks is studied. For the molecule, each azimuthal mode can split into two
groups of nearly-degenerate modes, i.e., the bonding (OE, EE) and anti-bonding (EO, OO)
modes. The coupling strength and shifted resonant wavelength of the two modes decrease
with the inter-disk distance. Compared with the photonic molecule, the hybrid photonicplasmonic molecule can acquire a high Purcell factor 191 accompanied by a Q factor of
1821. Moreover, the far-field emission patterns of the coupling WG modes are investigated.
The emission patterns of the hybrid photonic-plasmonic molecule show an enhanced
directivity in the H-plane with fewer main beams of emission for both bonding and antibonding coupling modes by varying the azimuthal mode number. Compared with photonic
molecule geometries, the hybrid photonic-plasmonic molecule cannot only further reduce the
cavity size to the subwavelength dimension but also lower the threshold of WG modes lasers,
while a high Q factor and a small mode volume are maintained. These capabilities drive its
potential applications in a single photon source, laser, optical memory, etc [20, 44]. For
example, when a quantum dot is embedded in the hybrid photonic-plasmonic molecule, the
optical cavities with increased local density of optical states can enhance the emission rate,
which is beneficial for single photon sources [45].
Acknowledgments
This work is supported by the National Natural Science Foundation of China (Grant Nos.
61205030, 61275030 and 61235007), the Opened Fund of State Key Laboratory of
Advanced Optical Communication Systems and Networks, the Opened Fund of State Key
Laboratory on Integrated Optoelectronics, the Fundamental Research Funds for the Central
#186860 - $15.00 USD Received 12 Mar 2013; revised 23 Apr 2013; accepted 24 Apr 2013; published 29 Apr 2013
(C) 2013 OSA
6 May 2013 | Vol. 21, No. 9 | DOI:10.1364/OE.21.011037 | OPTICS EXPRESS 11046
Universities (2012QNA5003), Doctoral Fund of Ministry of Education of China (Grant No
20120101120128), the Swedish Foundation for Strategic Research (SSF) and the Swedish
Research Council (VR).
#186860 - $15.00 USD Received 12 Mar 2013; revised 23 Apr 2013; accepted 24 Apr 2013; published 29 Apr 2013
(C) 2013 OSA
6 May 2013 | Vol. 21, No. 9 | DOI:10.1364/OE.21.011037 | OPTICS EXPRESS 11047