second-order bandpass terahertz filter achieved by multilayer complementary metamaterial structures
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Second-Order Bandpass THz Filter Achieved by Multilayer Complementary Metamaterial Structures
M. Lu, W. Li, and E. R. Brown
accepted to Optics Letters
Second-Order Bandpass THz Filter Achieved by Multilayer
Complementary Metamaterial Structures
Mingzhi Lu,* Wenzao Li, Elliott R. Brown+
Department of Electrical and Computer Engineering, University of California,
Santa Barbara, CA, 93106, USA
+Now at Wright State University, Dayton, OH 45435
*Corresponding author: [email protected]
A multilayer complementary metamaterial structure is proposed, fabricated on a crystal quartz
substrate, and measured between 100 and 700 GHz. The concept of a second-order THz
bandpass filter is realized by this structure, and offers superior quality factor, steepness of skirts,
and out-of-band rejection. Physical limitations on quality factor and insertion loss have also been
studied, including the skin depth of metal and optical phonon resonance in quartz. Based on
them, a series of higher frequency filters have been designed and simulation results are
In recent years, much research on metamaterials has been carried out and new
characteristics of metamaterials have been discovered [1-4]. Some of the phenomena that cannot
be achieved by natural material is observed using metamaterials, such as invisible cloak  and
negative-index material . Their capability of manipulating electromagnetic waves makes
metamaterials a powerful tool of designing new devices. The application of metamaterial could
be found in antennas, free space lenses, absorbers , filters, polarizers , etc. Since most
microwave and optical devices do not scale well to the THz region, a new method of designing
becomes very important, and metamaterials provides such an option.
One of the most important devices in THz applications is bandpass filters, which could be
widely applied in imaging, spectroscopy, molecular sensing, security, drug identification, or
other systems. Some theoretical and experimental research has been done using traditional
frequency-selective surfaces (FSS), such as metal-mesh [5,6] or resonant-grid [6,7] structures.
The addition of surface plasmonic and trapped-mode effects have led to refined understanding of
such FSS-based structures using metamaterial principles, and interesting multilayer bandpass-
filter performance has been achieved [8,9].
In this paper, a second-order THz bandpass filter is proposed, fabricated, and
demonstrated based on a more recent, metamaterial building block – the four-split
complementary electric-LC (CELC) structure. Most of the metamaterial structures, such as split-
ring resonator (SRR) with single-split and electric-LC (ELC) structure with two splits , are
highly anisotropic geometrically and therefore electromagnetically. They show a plasmonic
forbidden band at the resonance frequencies. According to Babinet’s Principle, complementary-
structure ELCs or SRRs will have a passband at resonance . Taking the symmetry and
feasibility into consideration, the four-split CELC structure  turned out to be the best choice.
Its four-fold rotational symmetry ensures that the filter shows no polarization dependence for
radiation at normal incidence.
The layout of the filter design is shown in Fig. 1. It is a 90-by-90 square array of CELC
unit cells with a period 230 µm. We use 165-µm-thick Z-cut single crystal quartz as the substrate
because of its low loss at THz, and choose Ti/Pt/Au as the metallization for low loss and good
attachment to the substrate. The dielectric constant of the Z-cut quartz substrate is 4.41, and the
loss tangent is 0.0004 at 250 GHz [12,13]. The filter has a metal-dielectric-metal (MDM)
structure, and the metallic patterns on each side of the quartz substrate are identical. The
dimension of the design is shown in Fig 1(a), in which a = 230 µm, b = 180 µm, w = 20 µm, and
g = 16 µm. Fig 1(b) shows the layer structure and the geometry of 36 unit cells of the filter.
With a transverse electromagnetic (TEM) wave at normal incident, the scattering
parameters were computed using 3D full-wave electromagnetic solver Ansoft HFSS®, and the
result is shown in Fig. 2. Inspection of the S parameters clearly indicates that a bandpass filter
has been achieved with a fundamental passband ranging from 227 GHz to 283 GHz having an
average insertion loss of around 2 dB. Note that the fundamental passband is much flatter than
single-layer complementary metamaterial structures , and there are two intermediate peaks at
235 GHz and 275 GHz. The lower and upper skirts of the transmission profile (S21) have slopes
60-dB/octave and 100-dB/octave, respectively. The quality factors of these two poles are 11.8
at 235 GHz and 18.2 at 275 GHz. The small transmission peak at 410 GHz can be explained as
an etalon (i.e., Fabry-Perot) resonance effect. The metamaterial surface forms the reflector and
the slab of quartz acts as a cavity. To prove this we ran an HFSS® simulation with only one layer
of metal pattern on the same quartz substrate, and did not see the peak at 410 GHz. In Fig. 2
second passband occurs between 590 and 680 GHz that, unlike most optical filters such as
gratings and quarter-wavelength stacks, is not harmonically related to the first. This makes it
possible to achieve a filter having a single unique passband by cascading the CELC-MDM
structure with other filters, such as a tunable Fabry-Perot.
Our filter structures were produced by standard microfabrication techniques. The primary
steps were contact photolithography in photoresist, followed by e-beam deposition of Ti/Pt/Au,
and finally metal liftoff. Identical metal patterns were created on opposite sides of the quartz
substrate with good alignment and registered using backside alignment, taking advantage of the
excellent visible transparency of quartz. The effects of misalignment have also been investigated.
Simulation shows that even with 115 um misalignment (half of the period), the filter can still
work quite well.
The radiative transmission (|S21|2) of the filter was measured with a photomixing THz
spectrometer having a dynamic range of ~60 dB in the frequency range of interest. The
comparison of the measured data and the simulation result is also displayed in Fig. 2, which
shows that the measured transmission and the HFSS-predicted transmission agree almost
perfectly. The loss is quite low (~2 dB) across the fundamental passband, and the out-of-band
rejection is about -40 dB between 350 and 400 GHz. The rejection degrades at higher
frequencies to values around -18 dB at 500 GHz because of the spurious resonance at 410 GHz
and approaching to the second passband. While our filter has similar values of in-band insertion
loss compared to recent multilayer FSS-based bandpass filters with metamaterial refinement
[8,9], comparison of the out-of-band rejection is difficult because these other papers do not show
transmission on a logarithmic scale.
To gain a better understanding of the resonance mechanism of this filter, a circuit model
of coupled resonators [14,15] is applied [Fig. 3(a)] in which the metamaterial patterns on quartz
are two identical RLC resonators coupled and the quartz spacer (acting as short length of
transmission line) is represented by a pi lumped-element CLC circuit. In Fig. 3(a), R1=R2=1500
Ω, L1=L2=25.6 fH, C1+CT1=C2+CT2=18.8 fF, and LT =120.6 fH. The values were manually tuned
to achieve best fit of quality factor and fundamental passband. As shown in Fig. 3(b), the S21
parameter of the circuit matches the measured filter response quite well at the transmission peaks
and low frequencies as well. By changing the transmission-line component values, the distance
between the transmission peaks can be tuned, and by this we can control the bandwidth and the
ripple between the two peaks. We observed the same phenomenon when tuning the substrate
thickness in HFSS simulations. And because of the strong similarity with the known behavior of
a second order (or “two-section”) Chebyshev bandpass filter , we attribute a second-order
nature to our metamaterial filter.
The quality factor of this metamaterial filter has also been computed using HFSS® Field
Calculator. According to definition, at steady state the unloaded quality factor is
( )air quartzs
, where sW is the energy stored in and around the filter, incP is the
power of the incident wave, and airW and quartzW are the time-averaged energy stored in the air
near the filter and in the quartz substrate, respectively. incP , airW and quartzW are computed from
Poynting’s theorem. Assuming the incident power incP is 1 Watt, we computed at 235 GHz
122.24 10 JoulairW and 128.97 10 JoulquartzW . Hence, the quality factor is 16.8. Meanwhile,
we can see that quartz substrate carries 80% of the stored energy. The loss fraction in the quartz
then becomes 4''6 10
2 'lq quartz
. Another mechanism is the skin depth loss of
metal, which can be calculated by the integrated surface current as 2
P J ds
where surfJ is the surface current. In this case, the loss fraction of metal is 0.18.
Since most of the energy is stored in the quartz rather than in the air, the influence of
water vapor and moisture will be greatly suppressed compared to an open-resonator filter such as
a Fabry-Perot. Compared to humid air or most other dielectrics, quartz crystal has a relatively
low loss at THz frequencies. Thus, utilizing quartz as the substrate, metamaterial filters working
at even higher frequencies should be considered. Ref.  shows that the optical-phonon
resonance of quartz is at ~10 THz, and its low frequency “tail” comprises the dominant loss
mechanism at lower frequencies. Therefore, we have scaled the present filter design accordingly.
Up to at least 5 THz, the loss fraction of quartz substrate remains below 10%. Fig. 4 shows
several designs of quartz-based metamaterial filters working at the frequencies of 250 GHz, 500
GHz, 1 THz, 2 THz, 4 THz and 5 THz. The dimensions of the last five filters are linearly scaled
by a factor of 2, 4, 8, 16, and 20 for both metal pattern dimensions and quartz thickness. The
quality factors at transmission peaks of these filters are 16.8, 17.2, 16.5, 15.1, 12.2 and 13.4
respectively, and the loss fractions in quartz substrates are 6×10-4, 4.8×10-3, 8.7×10-3, 8.39×10-3,
0.059 and 0.017. The dielectric constants and loss tangents of quartz are obtained from Ref. ,
and the metallization is still 200/500/3000 Ǻ-thick Ti/Pt/Au. As shown in the figure, the one
working at 4 THz has a slightly larger insertion loss than the 5 THz one, mainly because of the
small optical phonon resonance in quartz .
In conclusion, a second-order metamaterial THz bandpass filter is proposed, analyzed,
fabricated and measured. In the experiments, the virtues of low insertion loss, flat transmission
in the passband, steep skirts and high out-of-band rejection are realized. Analysis of substrate
loss and metal loss indicates the feasibility in scaling the metamaterial MDM filer design up to at
least 5 THz.
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List of Figure and Captions
Fig. 1: (color online) (a) The schematics of the unit cell of the metamaterial MDM filter; (b) The
two-layer structure of the filter.
Fig. 2: (color online) Simulated and measured results of the S-parameters of the bandpass filter.
The small diagram on the right down corner is the zoomed-in picture of the simulation result.
Fig. 3: (color online) (a) Circuit model of the resonators coupled by a short-length of
transmission line (CT-LT-CT pi circuit shown in the dashed box); (b) The comparison of circuit
response and measured transmittance of the filter for the fundamental passband.
Fig. 4: (color online) The simulated transmittance of frequency-scaled, second-order