Asymmetric band-pass plasmonic nanodisk filter
with mode inhibition and spectrally splitting
capabilities
Guangzhi Zhan, Ruisheng Liang,* Haitao Liang, Jie Luo, and Ruitong Zhao
Laboratory of Nanophotonic Functional Materials and Devices, School for Information and Optoelectronic Science
and Engineering, South China Normal University, Guangzhou 510006, China
*liangrs@scnu.edu.cn
Abstract: A compact wavelength band-pass filter based on metal-insulatormetal (MIM) nanodisk cavity is proposed and numerically investigated by
using Finite-Difference Time-Domain (FDTD) simulations. It is found that
the transmission characteristics of the filter can be easily adjusted by
changing the geometrical parameters of the radius of the nanodisk and
coupling distance between the nanodisk and waveguide. By extending the
length of input/output waveguides, the filter shows the resonant mode
inhibition function. Basing on this characteristic, a two-port wavelength
demultiplexer is designed, which can separate resonant modes inside the
nanodisk with high transmission up to 70%. The waveguide filter may
become a potential application for the design of devices in highly integrated
optical circuits.
©2014 Optical Society of America
OCIS codes: (240.6680) Surface plasmons; (140.4780) Optical resonators; (060.4230)
Multiplexing; (130.3120) Integrated optics devices.
References and links
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Received 20 Jan 2014; revised 4 Apr 2014; accepted 11 Apr 2014; published 17 Apr 2014
21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.009912 | OPTICS EXPRESS 9912
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1. Introduction
Surface plasmon polaritons (SPPs) are kinds of waves that spread along a metal-dielectric
interface with an index attenuation of electromagnetic field in both side, and because of the
prominent features that it can overcome the limit of traditional optical diffraction and
manipulate optical wave on sub-wavelength scales [1], it has been considered to be
information carriers in highly integrated optical circuits. By now, a number of SPPs
subwavelength optical waveguide devices, such as bend waveguide device [2], Bragg
reflectors [3,4], sensors [5], nano-particles [6], Y-shaped combiners [7], Mach-Zehnder
interferometers [8], V-grooves [9], and nanowires [10], have been investigated experimentally
or theoretically. The MIM waveguides are the hottest spot in recent years because of
miniaturization and high level of integration of optical circuits. At present, many researchers
are committed to the development of nanoscale MIM waveguide devices such as apertures
[11], wavelength selective waveguide [12], filters based on ring resonators [13], nanodisk
resonator [14], and all-optical switching [15]. Among the SPP-guiding structures mentioned
above, Band-pass and band-stop filters are vitall components of wavelength-selective devices
because of their practicability, symmetry, and simple manufacturing [16].
In some systems such as the wavelength division multiplexing (WDM) system, the bandpass filter [17–20] is of great significance. WDM plays an important role in signal processing
in optical communication technology. Therefore, how to realize wavelength selection is the
priority mission in plasmon devices. In this case, Bragg reflectors of MIM structure [21] have
been theoretically proposed. But most of them have a relatively large size and high
transmittance loss. Recently, nanoring resonators, nanodisk resonators [22], and rectangular
resonators [23] have been designed as bang-pass filters. However, almost all of the above
structures can only change their resonance wavelength by modifying the geometry of their
resonant cavity.
In this paper, a circular band-pass plasmonic filter based on a nanodisk resonant cavity is
proposed and its transmission properties are investigated numerically and analytically.
Comparing with previous filter researches, a new adjusting mechanism is applied to nanodisk
structure to enhance the filtering characteristics in transmittance and pulse width. In this new
filter structure, the resonance modes, inside the nanodisk, can be effectively suppressed by
selecting proper length in input and output coupling area and separated by putting the output
port in right place. Moreover, the transmission spectra (including the resonance wavelengths
and bandwidths) of the filter is easily adjusted by changing the geometric dimensioning of the
nanodisk and the coupling distance between the waveguides and the nanodisk. The
#205036 - $15.00 USD
(C) 2014 OSA
Received 20 Jan 2014; revised 4 Apr 2014; accepted 11 Apr 2014; published 17 Apr 2014
21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.009912 | OPTICS EXPRESS 9913
completely matched layer absorbing boundary conditions of finite difference method is used
in the simulation.
Fig. 1. (a) The schematic diagram of nanodisk filter (b) The transmission spectrum of the
nanodisk filter with r = 410nm, d = 8nm, t = 50nm.
2. Device structure and theoretical analysis
The illustration in Fig. 1(a) shows that the structure is composed of two slits, a nanodisk
resonator symmetrically placed between the two slits, and in a homogeneous metallic
background. The width of waveguides t is set as 50nm, the distance between the boundaries of
the waveguides and the cavity d is 8 nm and the radius of the disk cavity r is set as 410 nm.
The medium of the slits and nanodisk is assumed to be air whose refractive index is set to 1.
The surrounding metal is silver, whose frequency-dependent complex relative constant is
characterized by the Drude model [2,24]
ωD
2
ε m (ω ) = ε ∞ −
g LmωLm Δε
2
2
ω + iγ D ω
2
−
ω
m =1
2
− ωLm + i 2γ Lm ω
2
.
(1)
Here ε ∞ is the large-frequency limit of the permittivity with the value of 2.3646, and ω is
the angular frequency of the incident wavelength. γ D = 0.07489eV is the frequency of the
damped oscillation. ωD = 8.7377eV is the frequency of the majority of the plasma. ω =
4.3802eV, g L1 = 0.26663, γ L1 = 0.28eV, g L 2 = 0.7337, ωL 2 = 5.183eV, Δε = 1.1831, and
γ L 2 = 0.5482eV. These parameters listed above provide good description of permittivity data
for silver [25].
When the incident optical wave transmits through input waveguide, part of the energy will
be reflected and part of it coupled into nanodisk segment. When resonance condition is
reached, the stable standing wave in the nanodisk will be formed. The resonant condition can
be obtained by solving following equation [16,26]
L1
k
H
d
(1) '
n
m
H (k r)
n
Here
(k r)
(1)
m
'
=k
J (k r)
n
m
d
J (k r)
n
.
(2)
d
kd ,m = k (ε d ,m )1/2 are the wave vectors in the metal and the dielectric nanodisk,
respectively. ε m is the relative dielectric constant of the metal and ε d is the relative dielectric
constant of the dielectric, which can be obtained from the Drude model. k stands for the wave
number which includes a relatively small negative imaginary part, and the negative imaginary
part here stands for the loss. r represents the radius of the nanodisk cavity. H n(1) and
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H n(1)'
Received 20 Jan 2014; revised 4 Apr 2014; accepted 11 Apr 2014; published 17 Apr 2014
21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.009912 | OPTICS EXPRESS 9914
are the Hankel function with the order n. J n and J n' are the Bessel function with the order n,
respectively. The first and second order of Bessel and Hankel functions correspond to the first
and second order modes that resonate inside the nanodisk. From Eq. (2), one can find that the
resonance wavelength λ0 is determined by refractive index and the radius. By using the
coupled-mode theory [27], the transmission T near the resonant wavelength of the system is
described below
(
T=
1
τw
)
(ω − ω0 ) + (
2
2
1
τw
+
1
τi
.
)
(3)
2
Where ω stands for the frequency of the incident light, and ω0 is the resonance frequency.
τ w stands for the energy escaping from the waveguide and τ i is the decay rate of the
electromagnetic field because of the internal loss in the nanodisk. The transmittance formula
shows that if the incident light is far from resonance frequency, it will be completely
reflected. Thus, there is a transmitted peak at resonance frequency. From Eq. (3), the
resonance peak transmittance Tmax = (1 / τ w )2 / (1 / τ w + 1 / τ i )2 is close to 1 when 1 τ i is far
less than 1 τ w . Moreover, one can find that the transmission spectra around the resonant
frequency shows Lorentzian profiles.
Fig. 2. (a) Transmission spectra about different radii of the nanodisk cavity with d = 8nm, t =
50nm. (b) Relationship between peak resonance wavelengths and the radius of the cavity.
Fig. 3. (a) Transmission spectra about different distance between the boundaries of the
waveguides and the cavity d with r = 410, t = 50nm. (b) Relationship between the peak
resonance wavelengths and the distance of d.
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21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.009912 | OPTICS EXPRESS 9915
3. Simulation results and analysis
The FDTD method is used to simulate the transmission characteristics. The grid size in the x
and z directions are selected as 5 × 5nm, which has enough precision in the following
simulation. The SPPs enter into structure from left side. Figure 1(b) shows the numerical
simulation results of the transmission spectra when the gap between the disk and waveguide is
8nm. From it, one can see that there are two resonance modes (Mode 1 and Mode 2) at the
wavelengths of 956nm and 1550nm locating in the wavelength range from 0.75um to 2um,
and the corresponding maximum transmittances are 81% and 75%, respectively. The full
width at half-maximum (FWHM) of such two resonance modes are 37nm and 48nm,
respectively. The transmission peaks do not reach unity due to the waveguide loss in the metal
slits and the internal loss in the nanodisk. Both the maximum transmittance and FWHM are
better than the structure based on the nano-cavity resonators proposed by Huang et al. [28].
As shown in Fig. 1(b), the transmittance of mode 2 has higher value than mode 1. This
phenomenon happens because the resonant mode 2 has larger power escape than mode 1.
Figure 2(a) shows the transmission spectrum according to different radii of the nanodisk
cavity. It is obvious that the transmitted peak has a red-shift with the increasing radius. As
shown in Fig. 2(b), the wavelength-shifts of the resonant modes 1 and 2 almost have linear
relationship with the radius of the nanodisk cavity. The results of FDTD simulation is in
accordance with the solution of Eq. (2). According to the results and the above analysis, one
can easily manipulate the wavelengths of resonant modes by modifying the radius of nanodisk
resonator.
Fig. 4. The schematic diagram of an asymmetric nanodisk filter with d = 8nm, r = 410nm, and t
= 50nm.
In the next step of the research, we focus on the distance between the boundaries of the
waveguides and the cavity d, which is also an important factor influencing the characteristic
of transmission spectra near the resonant wavelength. With increasing the distance of
boundaries of the waveguides and the cavity, the external loss 1 / τ w will decrease rapidly
while the internal loss 1 / τ i is almost unchanged. Therefore, the peak of transmission will
decrease as the distance increasing. As shown in Figs. 3(a) and 3(b), the theoretic analysis is
verified by FDTD simulations. The transmission peaks can be controlled by adjusting the
distance between the boundaries of the waveguides and the cavity d. We also find that the
center wavelength has a slight blue shift. In addition, it is obvious that the FWHM of the
resonance spectrum markedly decrease with increasing the distance between the boundaries of
the waveguides and the cavity as shown in Fig. 3(a).
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Received 20 Jan 2014; revised 4 Apr 2014; accepted 11 Apr 2014; published 17 Apr 2014
21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.009912 | OPTICS EXPRESS 9916
Fig. 5. (a) Transmission spectra of different length of L from 0nm to 50nm. (b) Transmittance
contrast image between 0nm and 135nm of length of L.
Fig. 6. Magnetic fields of the band-pass filter with inhibiting structure for monochromatic light
at different wavelengths, (a) λ = 956nm, (b) λ = 1550nm, and all geometric parameters are
the same as used in Fig. 5(a).
4. Transmission properties of suppression mode band-pass filter
Figure 4 shows the schematic diagram of filter with the ability of inhibiting resonant mode.
We can see that the only difference between Fig. 1(a) and Fig. 4 is a section of waveguide
added on the output waveguide. In Fig. 4, we use L to stand for such segment of the
waveguide. As shown in Fig. 5(a), the transmission spectra almost the same with this segment
of the waveguide increasing from 0nm to 50nm. However, as this segment increasing and
reaching to 135nm, the transmittance of mode2 (956nm) has remarkable attenuation while the
transmittance of mode1 (1550nm) is almost unchanged. In Fig. 5(b), we can see that the
transmission spectra of original structure and new structure have a huge difference at the
wavelength of 956nm. This phenomenon can be explained by the following principle. When
the incident wideband SPPs waves are coupled into output waveguide from nanodisk, the
wave divided into two parts, the forward waves and backward waves. We use S1 and S2 to
stand for them, respectively. After backward waves are reflected at the end of output port, the
new coupled forward waves will encounter reflected waves (S2’). If such two waves satisfy
the phase conditions, it will reduce the intensity of some certain wavelength. Defining Δϕ to
be the phase delay of per round trip in the segment of the waveguide, one gets
Δϕ = k (ω ) × 2 L + ϕ r , where φr is the phase shift of the wave reflected at the end of the output
waveguide, and k (ω ) is the angular wavenumber of the wavelengths inside the waveguide at
the frequency of the light in vacuum. Obviously, some wavelengths will disappear when the
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Received 20 Jan 2014; revised 4 Apr 2014; accepted 11 Apr 2014; published 17 Apr 2014
21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.009912 | OPTICS EXPRESS 9917
following condition is satisfied Δϕ = (2m − 1)π , As
wavelength λm is given as follows [28]
λ =
m
4n L
eff
(2 m − 1) − ϕ / π
Re[ k (ω )] = 2π neff / λ
, the disappearing
.
(4)
r
Where λm is vacuum wavelength and neff is the real part of the effective index in the
waveguide. According to Eq. (4), we substitute the data of m = 1, neff = 1.5(according with
width of the waveguide t = 50nm), and L = 135nm into Eq. (4), then we can get the
disappearing wavelength of 952nm when assuming the phase shift φr with 0.15 π . In this
way, it is quite reasonable to compare theoretical analysis with simulation. Due to the
symmetry of the suppression mode band-pass filter, a similar result will get when using such
inhibiting structure at input waveguide instead of output waveguide. Furthermore, the
inhibiting structure can be used in the input and output waveguide at the same time to filter
out two different wavelengths. Figures 6(a) and 6(b) show the propagation of the field |Hz| for
incident light with the wavelength of 956nm and 1550nm. As for the output waveguide, it is
coupled to the antinode when the incident light are 956nm and 1550nm. However, the
wavelength of 956nm will be suppressed when the inhibiting structure is added in the output
waveguide. We can find the entirely different result from the field images and significant
effect by using the inhibiting structure at output waveguide.
Fig. 7. (a) Schematic diagram of a 1 × 2 wavelength demultiplexing structure based on
nanodisk cavity. (b) The transmission spectra of a 1 × 2 wavelength demultiplexing structure
with d = 8nm, r = 410nm, and t = 50nm.
5. The design of 1 × 2 wavelength demultiplexing
According to the above characteristics of the asymmetric plasmonic filter based on nanodisk
resonators, a 1 × 2 wavelength demultiplexing structure based on nanodisk is designed. Figure
7(a) shows the schematic diagram. This structure consists of two output ports at the bottom
and middle of the nanodisk, respectively. All of the distance between the boundaries of the
waveguides and the cavity is set as 8 nm. And the bottom output waveguide uses the
inhibiting structure. As shown in Fig. 7(b), the transmitted-peak wavelengths of two output
channels are 956nm and 1550nm, respectively. This is to say, the two resonant modes inside
the nanodisk are separated and exit from different channels, port 1 and port 2, respectively.
Figures 8(a) and 8(b) show the propagation of the field |Hz| for incident light with the
wavelength of 956nm and 1550nm. It is obvious that the incident light at 956nm and 1550 nm
can only pass through the corresponding port, respectively. As for port 2 without the
inhibiting structure, the wavelength of 956nm and 1550nm can be output and with a low
transmittance, but there is only the wavelength of 1550nm can be output when using the
#205036 - $15.00 USD
(C) 2014 OSA
Received 20 Jan 2014; revised 4 Apr 2014; accepted 11 Apr 2014; published 17 Apr 2014
21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.009912 | OPTICS EXPRESS 9918
inhibiting structure. This characteristic can be used to realize a band-pass filter with spectrally
splitting function.
Fig. 8. Magnetic fields of the 1 × 2 wavelength demultiplexing schematic diagram for
monochromatic light at different wavelengths, (a) λ = 956nm, (b) λ = 1550nm, and all
geometric parameters are the same as used in Fig. 5(a).
At last, comparing of our proposed structure with those considered in Refs [17–20], the
research in our work focuses on inhibition and separation of the modes inside the nanodisk.
Although separating the mode in a nano-cavity technique has been achieved [20], it is the first
time to put forward a feasible scheme to separate mode in a nanodisk cavity. Moreover, the
proposed method can overcome the problem of low transmittance in the most of filters
[17,18]. The transmittance in our proposed structure can be up to 80% without multiple
wavelength responses.
6. Summary
In this paper, a subwavelength plasmonic nanodisk filter is proposed and numerically
analyzed by utilizing FDTD method. The novel phenomena of suppressing resonance mode
and spectrally splitting light have been both theoretically demonstrated and numerically
verified in this paper. The desired wavelengths can be obtained by adjusting the radius of the
nanodisk resonator. The FWHM and transmittance can be tuned by modifying distance of the
coupling. In addition, the resonance modes inside nanodisk can be easily inhibited and
separated by adding a segment of waveguide at the input/output waveguide. The proposed
structures have important applications in highly integrated optical circuits and nanoscale
optics.
Acknowledgments
This work was supported by the National Natural Science Foundation of China Grants
No.61275059 and No.61307062.
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(C) 2014 OSA
Received 20 Jan 2014; revised 4 Apr 2014; accepted 11 Apr 2014; published 17 Apr 2014
21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.009912 | OPTICS EXPRESS 9919