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Split Ring Resonator

Phase modulation using dual split ring
Iftekhar O. Mirza*, Shouyuan Shi, and Dennis W. Prather
Dept of Electrical and Computer Engineering, University of Delaware, 151 Evans Hall Newark, Delaware 19716

See the attached file below with the full Descripiton of Phase Modulation using duel Split Ring-
Abstract: In this paper, we studied phase modulation numerically using
metamaterials such as stacked structures of dual split ring resonators
(DSRRs). To demonstrate the modulation, a vertical and a planar design
were considered, where the wave vectors were parallel and perpendicular to
the proposed structures creating 70 degrees and 80 degrees of phase change,
respectively. In both of the designs modulation was brought about by
changing the effective index of the structure through switching between the
open and short states of the DSRRs while maintaining high transmission.
One of the attractive features of our design was the thin layers of DSRRs,
where for the vertical and planar models the DSRRs layers were 5 mm and
2.28 mm respectively. The numerical results obtained by simulation
matched well with the theoretical prediction.
© 2009 Optical Society of America
OCIS codes: (160.3918) Metamaterials; (060.5060) Phase Modulation; (070.5753)
References and links
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#106965 - $15.00 USD Received 30 Jan 2009; revised 4 Mar 2009; accepted 13 Mar 2009; published 16 Mar 2009
(C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5089
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1. Introduction
Recently metamaterials have drawn a lot of attention in the research arena [1, 2, 20]. The
ability of this class of materials to respond to an electromagnetic field and bring about
changes in a material’s fundamental properties has opened up doors for new applications such
as flat lens, antenna miniaturization and artificial magnetic conductors to name a few [3, 16,
17]. One of the advantages of these artificial materials is that they can also be tuned over a
frequency range by effectively changing the substrate properties, the geometry of the
resonating metamaterial structure, or by changing the external fields with non linear
dielectrics [4, 6, 7, and 8]. Another effective way of tuning resonating metamaterials such as
the split ring resonators is by changing the resistance properties of the rings using capacitors
that can be controlled by an applied voltage [11]. As these tunable structures are scalable with
the wavelength, they can be used for modulation for any desired frequency range. In
particular, a Terahertz modulator was demonstrated where the metamaterials were grown on a
conductive substrate and the amplitude of the incoming wave was modulated using electrical
controls to change the resistivity of the metamaterial on a GaAs substrate [9, 15]. Also
recently, another research group demonstrated phase shifting with tunable negative refractive
index metamaterials using variable external magnetic field [12]. Similar work was also done
with negative index material by means of photoconductive coupling [10]. Complementary
split ring resonators and their applicability in tuning frequency has also been studied [13].
Although these works had been successful in bringing out the idea of frequency and
amplitude modulation, little investigation has been carried out in terms of phase modulation
using metamaterials. Also a major challenge in working with metamaterials has been the
inherent loss that arises from their resonating nature. To address such issues, in this paper we
demonstrated phase only modulation using tunable metamaterials, namely the DSRRs. We
mitigated the issue of material loss by employing thin resonating metamaterials operating at
an off-resonant frequency to demonstrate a high degree of phase modulation with very
minimal loss. Particularly, in our paper we demonstrated phase modulation using two
#106965 - $15.00 USD Received 30 Jan 2009; revised 4 Mar 2009; accepted 13 Mar 2009; published 16 Mar 2009
(C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5090
different polarizations for the DSRRs: in the first configuration, the polarization of magnetic
field, H, was perpendicular to the DSRRs as shown in Fig. 1 (a), whereas in the second
configuration, shown in Fig. 1(b), the wave vector k was perpendicular to the ring. The
DSRRs consisted of single split rings packed very closely where the adjacent rings’ split gaps
were alternated in orientation. The key advantage of the DSRRs in the first configuration was
that the rings could provide an off-resonance high permeability value when excited by the
magnetic field [18]. Whereas in the second configuration the symmetric nature of the
alternate rings could avoid electric coupling from the magnetic resonances that might lead to
cross-polarization effects [21] when excited by the electric field .The key advantages in both
of our designs were the constituent elements which could be readily manufactured using
standard lithography processes and simple electrical connections could be used to regulate
between the two states of the modulation using very thin layers of DSRRs in the propagation
direction. Compared to conventional phase modulators, metamaterial-based phase modulators
operating in transmission mode, promise to produce enhanced phase modulation in terms of
exhibiting a high degree of phase change within a small volume. Moreover, being physically
small it can ensure ease of structural integration and can offer scalability with wavelength that
can reduce design constraints while operating in different frequencies. We believe these
modulators can be the building block for spatial light modulators in the microwave frequency
regime that can add significant advantage over conventional modulators by simplifying future
Digital Micromirror Devices (DMD) and phased array antenna design by controlling each
element of the array or pixel electronically [22, 25].
The first step in the recipe to build a tunable phase modulator was to design the DSRRs
that could provide the resonant frequency around which the phase modulation would occur.
Standard numerical techniques were used to retrieve the constitutive parameters and the
effective refractive index information of the unit cell of the DSRRs for the two different states
of modulation: electrically open and closed rings [5]. The difference in the value of the
effective index for the two different states was used to calculate the phase change. We also
calculated the change in phase using the volumetric field data obtained inside the
computational region and explained the differences with the calculated theoretical result. In
the following sections we will provide the details of the numerical setup, extraction of the
relevant parameters to calculate the modulation and discuss the simulated results with a
conclusion for improvement and our plan for experimental verification.
Transmission plane Reflection plane Transmission plane
Reflection plane
3.81 mm
5 mm
15 mm
15 mm
(a) (b)
3.63 mm
Fig. 1. (a). Configuration 1: H-field perpendicular to the DSRR. (b) Configuration 2: k vector
perpendicular to the DSRR
#106965 - $15.00 USD Received 30 Jan 2009; revised 4 Mar 2009; accepted 13 Mar 2009; published 16 Mar 2009
(C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5091
2. Design and modeling
The DSRRs needed to be designed in such a way so that it could operate for a particular
frequency where the values of the effective permeability and permittivity of the DSRR’s
would meet the following criteria: a) numerically large to create appreciable phase change
through a change in the effective index, b) impedance matched interface, and c) minimize the
power loss. This is formalized in terms of the Figure Of Merit (FOM) = nreal / nimaginary, where
nreal and nimaginary are the real and imaginary parts of the refractive index respectively. The
goal will be to achieve a high FOM for each state for both of the configurations.
In order to meet these requirements we carried out several numerical simulation using the
commercial software HFSS to obtain an optimal design. Two different orientations of the
DSRRs with respect to the wave vector were considered: case1) wave vector, k, parallel to the
structure and case 2) wave vector, k, perpendicular to the structure. The setup in Fig. 1(a),
shows the unit cell analysis for the configuration 1 which will be discussed in the following.
The dimensions of the DSRR were 3 mm x 3 mm with a gap and strip width of 0.33 mm. The
thickness of the metal was 0.02 mm printed on a 0.25 mm thick Duroid substrate (ε = 2.2).
The unit cell of dimension 5 mm x 1 mm x 3.63 mm was placed in between the waveports
with a perfect magnetic conductor (PMC) boundary condition in the y-direction and
perpendicular to the ring and a perfect electric conductor (PEC) boundary condition in the z-
direction and parallel to the ring. By doing so, we were able to simulate a two dimensional
periodic structure along both y and z directions with minimal computation. A similar setup
was used in [4]. Based on this orientation, the DSRRs were excited by the magnetic field
which was perpendicular to the DSRRs. The dense stack of DSRRs acted as metalsolenoid
which helped to concentrate the magnetic flux inside the structure giving rise to a strong
magnetic resonance. Similar design was considered and discussed in [18] where it was
highlighted that the main benefit of this design was that a high value of permeability could be
obtained away from the resonance. The large off-resonance permeability value leads to a
large effective index at the same frequency for the DSRRs which could be exploited for
maximum phase modulation. The reflection/transmission spectra results obtained from the
simulation were used to extract the effective index of the DSRR using the formulation
described in [4, 5].
For a normally incident wave in free-space, at the air-sample boundary the scattering
parameters, namely the S11 and S21 can be related to the reflection ( Γ ) and transmission (T)
coefficients [5] as:
Γ = R ± R2 −1 (1)
 S 2 − S 2 +1
R = 0.5  11 21  (2)
 
 S + S −Γ 
T =  11 21  (3)
 1 − ( S11 + S21 )Γ 
ncomplex = nreal + nimag ,
Following this, the complex refractive index can be formulated as
2mπ − arg(T ) − log(| T |)
nreal = and nimag = . The parameter d indicates the slab
dk0 dk0

, where λ0 is the operational
thickness in the direction of propagation and k0 =
#106965 - $15.00 USD Received 30 Jan 2009; revised 4 Mar 2009; accepted 13 Mar 2009; published 16 Mar 2009
(C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5092
wavelength in free space. In our studies, m was set to zero as the wavelength inside the
DSRRs was larger than the slab thickness. Detailed discussion of the parameter m can be
found in [4]. The extracted data are shown in Fig. 2(a), where the real and imaginary parts of
the effective index for the open and closed cases of the DSRRs were plotted. From the graph,
at 4 GHz the real part of the effective index was 5.9 for the open state DSRRs while for the
closed state the value of the real part of the effective index was 1.6. The closed state had a flat
real part response and minimal loss since the DSRRs were off-resonance within the frequency
range of 3.5 – 4.5 GHz. The closed state for the DSRR was achieved by effectively shorting
the gaps in the DSRRs by placing a piece of metal inside the gap. Due to the large index
difference between the two states, we chose a frequency band centered at 4 GHz for our phase
modulation application. Although, at resonance the real index was at a maximum which
would provide the maximum phase modulation, the imaginary part which indicated the loss of
the structure was also very high that could potentially degrade the overall performance of the
device. In particular, the transmission data as shown in Fig. 3(a) indicated that for
configuration 1 the transmission was -1.6 dB and -2.8 dB for the open and short case
respectively. The value of the imaginary parts for both the cases at this frequency was
negligibly low and the difference in the real parts of the effective index was calculated as 5.9-
1.6 = 4.3. The calculated FOM for the open state was 5.9/0.325 = 18.2 and for the closed state
the FOM was 1.6/0.0003 = 5.3 x 103. As expected the FOM was much higher for the closed
state because of the absence of a resonance.
Freq: 4GHz

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