Band-pass plasmonic slot filter with band
selection and spectrally splitting capabilities
Feifei Hu, Huaxiang Yi, and Zhiping Zhou*
State Key Laboratory on Advanced Optical Communication Systems and Networks,
Peking University, Beijing, 100871, China
*zjzhou@pku.edu.cn
Abstract: An ultra-compact surface plasmon polaritons (SPPs) narrow
band-pass filter based on a slot cavity is proposed and numerically
investigated. Attributed to the coupled resonances in the cavity, the filter
demonstrates pass-band selection capability. Also, by varying the positions
of output waveguides, the filter shows the spectrally splitting function.
Moreover, the combination of the adjustments to the length/width of the slot
cavity and to the coupling distance provides more flexibility in design for
the locations and widths of the pass-bands of the proposed filter.
©2011 Optical Society of America
OCIS codes: (240.6680) Surface plasmons; (130.7408) Wavelength filtering; (130.3120)
Integrated optics devices.
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Received 13 Dec 2010; revised 12 Feb 2011; accepted 19 Feb 2011; published 28 Feb 2011
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1. Introduction
Surface Plasmons, which are propagating along a metal-dielectric interface with an
exponentially decaying field in both sides, have been considered as energy and information
carriers to overcome the diffraction limit of light in conventional optics [1–3]. Among various
SPPs based waveguides, metal-insulator-metal (MIM) structure [4,5] has attracted tremendous
interests of researchers in recent years, because of its potential applications to manipulate and
control light in nanoscale. Numerous MIM waveguide based structures have been numerically
and/or experimentally demonstrated, such as bends [6], splitters [7], Mach-Zehnder
interferometers [8], Y-shaped combiners [9], etc. In order to realize wavelength selection,
several Bragg reflectors of MIM structure [10–12] have been theoretically proposed. But most
of these structures have large sizes with a relatively high transmission loss. Subsequently,
some simple plasmonic waveguide filters have been proposed and demonstrated, such as
tooth-shaped waveguide filters [13,14], coupler-type filters [15], channel drop filters with disk
resonators [16], rectangular geometry resonators [17], and ring resonators [16]. Most of them
can overcome the complexity of fabrication of Bragg reflectors and operate as good band-stop
filters. More recently, F-P cavity [18], microring [19] and nanodisk [20] resonators through a
different coupling method have been proposed as band-pass filters. However, all above
mentioned can only modify their resonance wavelengths by adjusting the internal parameters
of the resonators.
In this paper, a narrow band-pass plasmonic filter based on a slot cavity is proposed and
analyzed. Compared with previous researches on plasmonic filters, new adjusting mechanisms
are introduced to the structure to expend and enhance the filtering characteristics. In the
proposed new filters, the resonance characteristics of the slot cavity and the out-coupling
strength can be effectively modified by selecting proper input and output waveguide positions.
These properties can be used to achieve the band selection/splitting (selecting the pass-band
locations) capabilities. Furthermore, the transmission spectra (including the resonance
wavelengths and bandwidths) of the filter can also be easily controlled by modulating the
geometrical parameters of the slot cavity and the coupling distance between the waveguides
and the slot cavity. The finite difference time domain (FDTD) method with a perfectly
matched layer (PML) absorbing boundary condition is employed to simulate and study the
property of the filter. Due to its subwavelength scale and very simple configuration, this
device can be easily fabricated and highly integrated with other micro/nano devices.
2. Device structure and theoretical model
As shown in Fig. 1, the plasmonic slot filter is composed of two MIM waveguides and a short
slot cavity. The materials in the blue and white areas are chosen to be silver and air (  d = 1).
The widths of input/output waveguides and slot cavity are w and wt , respectively. The length
of slot cavity is L , and the distance of the input and output waveguides apart from the central
line O of the slot cavity are L and h , respectively. d is the coupling distance between two
waveguides and slot cavity. Since the widths of the waveguides are much smaller than the
incident wavelength, only a single propagation mode TM 0 (only H y , E x , E z  0) can exist in
the structure [21], whose complex propagation constant  can be obtained by solving
following dispersion equation [10,21]:
 d km   m kd tanh(
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kd
w)  0,
2
(1)
Received 13 Dec 2010; revised 12 Feb 2011; accepted 19 Feb 2011; published 28 Feb 2011
14 March 2011 / Vol. 19, No. 6 / OPTICS EXPRESS 4849

where k d and k m are defined as kd   2   d k02

1/ 2

and km   2   m k02

1/ 2
.  d and  m
are, respectively, dielectric constants of the insulator and the metal. k0  2 /  is the freespace wave vector. The effective refractive index of the MIM waveguide can be represented
as neff   / k0 . The frequency-dependent complex relative permittivity of metal  m ( ) can
be characterized by Drude mode  m ( )      p /  (  i ) , where   stands for the
dielectric constant at the infinite frequency,  and  p are the electron collision frequency
and bulk plasma frequency, respectively.  is the angular frequency of incident light. The
parameters for sliver can be set as   = 3.7,  p = 9.1 eV,  = 0.018 eV, which fit the
experimental optical constant of silver [22] quiet well in the visible and near-infrared spectral
range. The stable standing waves can be exited within the slot cavity only when the following
resonance condition is satisfied:   m 2L  r  2m , where r  1  2 , 1 and 2 are,
respectively, phase shifts of a beam reflected on the upper and lower facets of the slot cavity.
Positive integer m is the number of antinodes of the standing waves in this slot cavity.  m is
the propagation constant of SPPs corresponding to the resonance mode of the mst order of the
cavity. Thus, the resonance wavelengths can be obtained as follows:
m  2neff L / (m  r /  ).
(2)
Given the arbitrary input position L in the structure, the input filed H in inside the slot
cavity is divided into two nearly identical portions H left and H right propagating in opposite
directions as depicted in Fig. 1. The relation between them is H left = H right = H in / 2 = H 0 .
We assume the loss coefficient of the slot cavity is  , which represents the dissipation of the
light propagating per round-trip in the cavity, including the absorbing loss by the metal and
the loss caused by the power coupled out of the cavity. Since the slot cavity is symmetric with
respect to the central line x = 0, we just need to consider the condition that the position of the
input waveguide changes above the central line ( x >0). Based on the superposition principle
of optics [23] and cavity model, we can describe H field inside the cavity with an arbitrary
input position L as follows:
H m ( x, t ) 
2 H 0 cos(  m x 

m L
2
)
3
  exp[ j (  m L   m L)]
2
1
 exp[ j (  m L   m L)]
2
(3)
 exp( jm t ),
where 0  L  L / 2 ,  m 2L  2m accords to the above resonance condition with a very
small parameter r . From the Eq. (3), we can see the H fields inside the cavity are in the
form of the standing waves along x direction at the resonance wavelengths. In this paper, we
only consider the first and second resonance mode of the slot cavity. Therefore, for the
resonance of the first order ( m = 1), we can obtain the H field inside the cavity as follows:

2 H 0 cos( 1 x  )
2 2sin(  L) exp( j t ).
H1 ( x, t ) 
1
1

(4)
For the resonance of the second order ( m = 2), the Eq. (3) can be written as follows:
H 2 ( x, t ) 
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2H0 cos(2 x   )

2cos(2 L) exp( j2t ).
(5)
Received 13 Dec 2010; revised 12 Feb 2011; accepted 19 Feb 2011; published 28 Feb 2011
14 March 2011 / Vol. 19, No. 6 / OPTICS EXPRESS 4850
Based on the formulas above, It can be found: when L  0 , the H field inside the cavity is
H1 ( x, t )  0 , which means that the first resonance mode can’t exist inside the slot cavity, only
the second resonance mode can be coupled into the cavity. Whereas, when L  L / 4 , one
can obtain the field H 2 ( x, t )  0 , that means the second resonance mode have been highly
suppressed in this case. This phenomenon of selectively suppressing the intrinsic resonance
mode of the slot cavity will be verified numerically and explained visually latter on.
Fig. 1. Schematic of the plasmonic slot filter.
3. Simulation results and analysis
In the following FDTD (commercial package) simulations, the grid size in the x and z
directions are set to be 4 nm × 4 nm for good convergence of the numerical calculations. The
fundamental TM mode of the MIM waveguide is excited by a pulse dipole source from the
left waveguide. Two power monitors P and Q are set to detect the reflected and transmitted
powers of Pref and Ptr at the locations, the transmittance and reflectance are defined as
T  Ptr / Pin and R  Pref / Pin , respectively. The absorption parameter is simply given by
A  1  R  T , which represents the dissipation of the power in the device. The parameters of
the structure are set to be w = wt = 50 nm, d = 15 nm, and L = 500 nm. Firstly, the
positions of input/output waveguides are fixed as L = h = 225 nm, which means they are
kept on the top end of the slot cavity. Figure 2(a) shows the spectra of the transmission,
reflection and the absorption of the proposed filter. It can be seen that two resonance peaks at
the wavelengths  = 0.74 μm and 1.47 μm are located in the wavelength range 0.6-1.7 μm of
interest, and the corresponding maximum transmittances are 70% (1.5 dB) and 46%

(3.37 dB), respectively. The quality factor (defined as Q 
, where  is the resonance

wavelength of the cavity and  is the full width at half maximum of transmission spectra
[10]) at 0.74 μm and 1.47μm are, respectively, 35 and 37 in this case ( d = 15 nm). It is also
shown that two peaks appear around the resonance wavelengths in the absorption curve,
because the SPPs coupled into the slot cavity would propagate backwards and forwards inside
the cavity and thus undergo great absorption caused by the metal. The counter profiles of
fields H y at the different wavelengths are depicted in Fig. 2(b)–2(d). According to the
Eq. (1), the effective index neff of the MIM waveguide at 0.74 μm and 1.47 μm are calculated
to be 1.41 and 1.376, respectively. Given the total phase shift r , one can estimate the
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Received 13 Dec 2010; revised 12 Feb 2011; accepted 19 Feb 2011; published 28 Feb 2011
14 March 2011 / Vol. 19, No. 6 / OPTICS EXPRESS 4851
resonance wavelengths from Eq. (2). Submitting 1 = 1.47 μm and neff = 1.376 into Eq. (2)
gives r = 0.22 for m = 1 and L = 500 nm. Therefore, the wavelength for m = 2 can be
approximately calculated as 0.73 μm for neff = 1.41 and r = 0.22 with the formula, which
agrees reasonable well with the simulation result for 2 = 0.74 μm. The deviation between
FDTD simulation and the result from Eq. (2) could be attributed to the neglecting of
wavelength dependence of r .
Fig. 2. (a)The spectra of the transmission and the reflection of the plasmonic slot filter. The
contour profiles of fields H y in the structure at different wavelengths (b)

= 1.0 μm, and (d)


= 0.74 μm, (c)
= 1.47 μm.
Based on the assumptions and analysis in above section, a few novel characteristics of the
proposed filter will be demonstrated as follows.
Firstly, in order to verify the phenomenon that the intrinsic resonance modes are
suppressed alternatively inside the slot cavity, the input waveguide is moved to the central
position O ( x = 0) and the output waveguide is kept still on the top end of the slot cavity.
Figure 3(a) shows the spectra of the transmission and the reflection of the structure in this
case. It can be seen that there is only one narrow dip in the curve of reflection at the second
resonance mode and that the first resonance mode is completely suppressed inside this cavity,
which is highly in conformity with our theoretical analysis above. Similarly, when input
waveguide position is chosen to be L = 132 nm, one can see clearly that the second intrinsic
resonance mode of the slot cavity is suppressed as depicted in Fig. 3(b), and that only the first
resonance mode at 1.47 μm can be coupled into the slot cavity. The simulation results ( L =
132 nm) are consistent with our theoretical analysis ( L = 125 nm) reasonably well. For
clarity, we can visually explain this phenomenon in detail from propagation behavior of SPPs
inside the slot cavity as shown in Fig. 1. Taking the first resonance mode at 1.47 μm for
example, when the input waveguide is located in the central position O , the input field H in is
divided into two equal parts H left and H right with the identical initial phase 0 . One portion
of field H left propagates to the upper facet of the slot cavity and returns back to the input
position O with a phase 0   , thus, it will couple and interfere with another part of filed
H right destructively due to phase difference  between them. The similar condition would
also happen for the second resonance mode at 0.74 μm when input waveguide moves to the
position L = 132 nm. These two resonances in opposite directions coupled with each other
are the physical reasons that the intrinsic resonance modes of the slot cavity can be
alternatively suppressed by choosing proper input waveguide positions, which have never
been explicitly studied in the previous researches on plasmonic filters [18–20]. By introducing
these coupled resonances to modify the resonance characteristics of the slot cavity, the passband selection can be achieved without changing the parameters of the cavity. Moreover, a
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Received 13 Dec 2010; revised 12 Feb 2011; accepted 19 Feb 2011; published 28 Feb 2011
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single channel pass-band transmission in a broad wavelength range can be obtained as
depicted in Fig. 3(a) and 3(b), which may have promising applications in photonics and
nanoscale optics.
L = 0, (b)
L = 132 nm, respectively, with w = wt = 50 nm, L = 500 nm, d = 15 nm, h = 225
Fig. 3. The spectra of the transmission and reflection of the slot cavity for (a)
nm.
Secondly, the parameter h , which stands for the distance of output waveguide apart from
the central line O of the slot cavity, is also an important factor influencing the output
characteristics of the proposed filter, because the out-coupling strength through the endcoupling method is strongly depending on the intensity of H field in the out-coupling regions.
In another word, the SPPs can hardly be coupled out from the cavity in the position with very
low intensity of H field. In order to verify the above theoretical analysis, let the input
waveguide on the top end of the slot cavity with other parameters unchanged to make sure that
two resonance modes exist inside the slot cavity. According to Eq. (3), one can easily find out
that the H field inside the slot cavity is in the form of standing waves and that the antinodes
of the standing waves for the first and second resonance are in the positions h = 0 and h =
125 nm, respectively, which is also seen in Fig. 2(b) and 2(d). Therefore, when two output
waveguides are put in the above positions of the antinodes as shown in Fig. 4(a), the two
resonance modes are separately coupled into two output waveguides as depicted in Fig. 4(b).
It can be seen that only the first (second) resonance mode could be coupled out from the slot
cavity in the position of the antinodes of the second (first) resonance. And the crosstalks
between the port 1 (0.74 μm) and port 2 (1.47 μm) are 16 dB for the port 1 and 25 dB for
the port 2, respectively. This characteristic can be utilized to realize a narrow band-pass filter
with spectrally splitting function.
Fig. 4. (a) Schematic of the plasmonic slot filter with two output waveguides at
h
= 125 nm, respectively. (b) The transmission spectra of two output waveguides at
h
= 0 and
h
h
= 0 and
= 125 nm, respectively.
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Received 13 Dec 2010; revised 12 Feb 2011; accepted 19 Feb 2011; published 28 Feb 2011
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Next, the influence of internal parameters of the slot cavity on the resonance wavelengths
is studied by FDTD method in detail. The input/output waveguides are fixed to the position
L = L / 2  w / 2 to make sure that both two resonance modes exist inside the slot cavity. At
the beginning, the length of the slot cavity is set as variable while the other parameters are
fixed as above. Figure 5(a) shows the transmission spectra of the structure corresponding to
different cavity lengths. The inset of Fig. 5(a) reveals the wavelengths of each resonance
modes have nearly linear relationships with the length of the slot cavity, but with different
slope factors (approximate to 1/ m ). This result is in accordance with the solution of Eq. (2).
Meanwhile, according to Eq. (2), the resonance wavelengths will also shift when altering the
width wt of the slot cavity, as shown in Fig. 5(b), resulting from the width-dependent
effective index of MIM waveguide. Based on the simulations and analysis above, it is seen
that the locations of the pass-bands of the filter can be easily designed by changing both the
length and width of the slot cavity.
Fig. 5. (a) Transmission spectra of the structure for different length L with other parameters
unchanged. Inset: Wavelengths of the resonance peaks versus the length of the slot cavity for
different resonance order m = 1 and m = 2. (b) The transmission spectra for different widths
of the slot cavity with
L = 500 nm, d = 15 nm, L = h = 225 nm.
Now, we study the influence of the coupling distance d on the transmission
characteristics of the proposed filter, which is also an important factor influencing the
intensities of transmission spectra near the resonance wavelengths. Figure 6 shows the
transmission curves would change with altering the coupling distance. It is obvious that the
resonance wavelengths exhibits slightly blue-shift and transmission peaks decrease
simultaneously with increasing the coupling distance, which is consistent with the results in
Refs. [15,19]. Moreover, the bandwidths of peaks become a bit of narrower with increased d
because a large coupling distance would result in small coupling strength which will enhance
the “cavity” effect due to small amount of energy coupled out of the slot cavity. Therefore, the
bandwidths ( Q factor) of the resonance spectra can be modified by controlling the coupling
distance d .
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Received 13 Dec 2010; revised 12 Feb 2011; accepted 19 Feb 2011; published 28 Feb 2011
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Fig. 6. Transmission spectra of the proposed filter for different coupling distance d between
the input/output waveguides and the slot cavity with
L = 500 nm, L = h = 225 nm.
Finally, we make a simple comparison of our proposed structure with those considered in
Refs. [15–20]. Since the wavelengths of SPPs correspond to the resonance peaks are allowed
to transport efficiently in the output waveguides, while others are forbidden. Our structure can
operate as plasmonic band-pass filters, which is very different from the band-stop filters in
Refs. [15–17] based on the parallel directional coupling method. Compared with all other
band-pass filters in the literature [18–20], the proposed slot filter has a very simple structure
and flexible input/output positions (the input/output waveguides can be designed in the same
side or different side of the slot cavity). Most importantly, the novel phenomena of
suppressing resonance mode and spectrally splitting light have been both theoretically
demonstrated and numerically verified for the first time in this paper. Besides, a single
channel transmission can be realized in a broad wavelength range, while it’s unachievable in
Refs. [18–20].
4. Conclusion
In conclusion, a subwavelength plasmonic slot filter is proposed and numerically analyzed by
using 2D FDTD method. Several adjustable parameters have been investigated to flexibly
modify the filtering characteristics of the proposed plasmonic filter. Both the theoretical
analysis and simulation results show the variation of the input/output waveguide positions is
an effective method to select pass-band and spectrally split light. Moreover, the transmission
spectra, including the resonance wavelength and bandwidth can also be adjusted by
modulating the internal parameters of the cavity and the coupling distance between the slot
cavity and input/output waveguides. The results above imply that it have potential
applications in nanoscale integrated photonic circuits on flat metallic surface.
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Received 13 Dec 2010; revised 12 Feb 2011; accepted 19 Feb 2011; published 28 Feb 2011
14 March 2011 / Vol. 19, No. 6 / OPTICS EXPRESS 4855