Simulation based characterization of negative

Science and Information Conference 2013 October 7-9, 2013 | London, UK

Simulation based characterization of negative permeability plasmonic structures at X band Amitesh Kumar, Arijit Majumder

Shantanu Das

Subal Kar

SAMEER Kolkata Centre Plot L2, Block GP, Sec-V, Salt Lake, Kolkata-91, India.

Reactor Control Division, Bhaba Atomic Research Centre (BARC), Mumbai, India.

Institute of Radiophysics and Electronics (IRPE), University of Calcutta, 92 A.P.C. Road, Kolkata - 700009, India

Abstract—This paper presents the simulation and its based characterization of five negative permeability inclusion plasmonic structures named as SRR (Split Ring Resonator), SSRR (Square Split Ring Resonator), TTSR (Two Turn Spiral Resonator), NBSR (Non Bi-anisotropic Spiral Resonator) and LR (Labyrinth Resonator) used in metamaterials. These structures are designed and simulated using commercial FEM (Finite Element Method) solver at X-band (8-12 GHz). Using simulation results, a standard scattering-parameter based retrieval method is applied to characterize theses structures. All the results have been compared for performance comparison.

view. Based upon this study, one can easily choose negative permeability plasmonic structure suitable for a desired application having some design constrains.

Metamaterials are the metal-dielectric composite materials having their effective permittivity or permeability or both negative in some frequency range. These artificially designed materials can have unique properties like negative refraction, reverse Snell's law, reverse Cherenkov radiation, and reverse Doppler Effect etc. These reverse properties are generally not found in natural occurring materials. Veselago [1] in 1968 first proposed the theory of metamaterials and Smith et. al. [2] in 2000 proposed the first metamaterial having both permittivity and permeability negative. Shelby et. al. [3] in 2001 first demonstrated the reversal of Snell's law using metamaterials.

II. NEGATIVE PERMEABILITY PLASMONIC STRUCTURES Five structures SRR, SSRR (Square Split Ring Resonator), TTSR (Two Turn Spiral Resonator), NBSR (Non Bianisotropic Spiral Resonator) and LR (Labyrinth Resonator) are shown in Fig.1 where "r" is the inner radius and "a" is the inner dimension. All structures have width of metal ring or strip equal to "w" and gap equal to "g". SRR structure is made of two split rings separated by some gap which introduces the capacitance. The detailed theory, numerical simulation and application of SRR can be found in [4-7]. In SSRR, instead of circular rings, square shaped metal strip is used for inductor realization and it's theory, model and applications can be found in [8-11]. In TTSR, two rings of SRR have cut on same side and two ends are cross joined for connectivity. The detailed theory and modelling of TTSR can be found in [6], [7] and [12]. NBSR is the symmetric version of TTSR where bi-anisotropy is reduced. It has been closely investigated [6], [7] and [13-15] in detail. LR is a fully symmetric plasmonic structure initially designed for high frequency applications. It has two cuts in each ring and hence lowering the overall capacitance. It modelling, detailed theory and applications can be found in [6] and [16-17].

Negative permeability without using magnetic materials was first realized by Pendry et. al. [4] in 1999 using the array of Swiss roll structure and SRR (Split Ring Resonator). SRR is a resonating particle having inductance due to ring and capacitance due to gap between two metals. When wave propagates through SRR and magnetic field is along the axis of SRR, an alternating current is generated in split ring at resonant frequency and hence a stop band behavior in obtained which indicates the negative permittivity region. Based upon this concept, SRR has been modified by various researchers for better performance in terms of higher or lower frequency application, bandwidth, losses, bi-anisotropy, homogeneity and realizability.

III. SIMULATION METHOD An FEM based full wave electromagnetic solver HFSS (High Frequency Structure Solver) from Ansys1 has been used for simulation of these negative permeability inclusion structures. Periodic boundary conditions have been applied in x and y directions to intimate an infinite array as shown in Fig.2. Floquet ports are assigned in z direction which excites TM electromagnetic waves in z direction and these ports are de-embedded up to unit cell substrate for determining exact phase of wave propagating through magnetic inclusion structure. Fig.3 represents the simulation of 10 units of magnetic inclusion structure in direction of propagation wave i.e. z-axis.

Keywords—plasmonic; metamaterials; negative permeability; bi-anisotropy; magnetic inclusion structure

I.

INTRODUCTION

After a literature survey, five important negative permittivity planer plasmonic structures have been chosen for investigation at X-band (8-12 GHz). These structures are numerically simulated and characterized. All these structures share the same substrate and same periodicity in all directions. All the results have been compared from designer point of

1

An Introduction to HFSS, Ansys Inc., 2010.

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Science and Information Conference 2013 October 7-9, 2013 | London, UK

Fig.1.

Schematic of unit cell of SRR, SSRR, TTSR, NBSR and LR

All negative permeability magnetic inclusion structures are designed and optimized at X-band using above mentioned simulation technique and dimensions of these are summarized in Table I. These structures are printed on a high performance 20 mil Rogers RT/duroid 5880LZ dielectric substrate having relative permittivity 1.96 and loss tangent 0.0019 at 10 GHz. All structures have periodicity of 2.5mm x 5mm x 5mm in x, y and z directions respectively.

Dimensions of different-2 magnetic inclusion structures Magnetic Inclusion Structure SRR SSRR TTSR NBSR LR

IV.

Dimensions Inner radius / Inner dimension r/a (mm) 0.9 0.6 0.5 0.9 1.4

Width of metal strip/ring w (mm) 0.25 0.3 0.25 0.25 0.3

Gap g (mm) 0.1 0.3 0.3 0.1 0.1

SIMULATION BASED CHARACTERIZATION

Characterization of the magnetic inclusion structures not only clearly determines the frequency band where permeability is negative but also the magnitude of negative permeability and loss in the structure. A scattering parameter based standard retrieval method is used which was introduced by Smith et.al. [18] in 2002. In this standard parameter retrieval based method, the effective refractive index "n" and impedance "Zn" of the sample of thickness "d" is determined using the following formulas [18].

Fig.2. HFSS

Simulation of single unit cell of magnetic inclusion structure in

(1)

Fig.3.

Simulation of 10 unit cells of magnetic inclusion structure in HFSS

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Science and Information Conference 2013 October 7-9, 2013 | London, UK

where S11 and S21 are the reflection and transmission coefficients of the sample. "k" is the free space wave vector that depends upon frequency. The sign of impedance and refractive index is determined using the fact that in passive samples Im[n]>0 and Re[Zn] >0 which is also applicable in the present scenario. It should be noted that for Real(n) have many solutions but as the thickness of sample under test is decreased, finding a unique solution becomes easy. Once the refractive index and impedance of sample is determined, the effective permeability can be determined by multiplying the refractive index with impedance of sample. An advanced parameter retrieval method [19] developed for asymmetric or inhomogeneous structures can also be used but in the present scenario, this is not necessary. Standard parameter retrieval method has been applied to characterize all eight magnetic inclusion structures. Scattering parameters are obtained through simulation and for minimizing the sample thickness, only single unit cell of magnetic inclusion structures have been simulated. Fig. 4 presents real and imaginary part of effective permeability plotted versus frequency for different-2 magnetic inclusion structures obtained using standard parameter retrieval method. All the structures show a clear negative permittivity frequency band where losses are high due to resonance.

Fig. 4a

Fig. 4c

TTSR

Fig. 4d

NBSR

Fig. 4e

LR

SRR

Fig.4. Real and imaginary part of effective permeability of different magnetic inclusion structures plotted vs frequency Fig. 4b

SSRR

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Science and Information Conference 2013 October 7-9, 2013 | London, UK

V. RESULTS AND DISCUSSION Fig.5 presents the simulated insertion loss through the array of 10 unit cells in direction of propagation of wave for different-2 magnetic inclusion structures. SRR structures shows more than one stop band which may be associated with coupling or extra electrical resonance or bi-anisotropy.

Fig. 5(d) NBSR

Fig. 5(a) SRR

Fig. 5(e) LR Fig.5. Fig. 5(b) SSRR

Insertion loss through different-2 magnetic inclusion structures

Table II shows the comparison of magnetic resonance frequency fm0, magnetic plasma frequency fmp, negative permeability percentage bandwidth, maximum effective negative permeability and maximum losses for all magnetic inclusion structures. LR structure has highest percentage bandwidth and highest losses while TTSR have the lowest percentage bandwidth, highest realized negative permeability and lowest losses. This behaviour is also observed in insertion loss (vide Fig. 5) where LR is broadband while TTSR is narrowband. SSRR is having lowest realized negative permeability and higher losses but have a good bandwidth. Based upon this table, one may choose a magnetic inclusion structure depending upon the priority which may be bandwidth or losses or realized negative permeability.

Fig. 5(c) TTSR

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Science and Information Conference 2013 October 7-9, 2013 | London, UK TABLE I. Magnetic Inclusion structure SRR SSRR TTSR NBSR LR

PERFORMANCE COMPARISON OF DIFFERENT-2 MAGNETIC INCLUSION STRUCTURES Property

Magnetic resonance frequency fm0 (GHz)

Magnetic plasma frequency fmp (GHz)

Bandwidth Δf = fmp- fm0 (GHz)

% bandwidth

Maximum µreff

Maximum loss - ί µreff

9.36 11.09 8.54 9.59 8.51

10 12.32 8.88 10.25 10.2

0.64 1.23 0.34 0.66 1.69

6.61 10.51 3.9 6.65 18.1

-3.4 -2.2 -3.43 -3.37 -2.87

10.3 12.3 8.75 9.49 12.67

VI. CONCLUSION AND FUTURE SCOPE In this paper, five negative permeability inclusion plasmonic structures namely SRR, SSRR, TTSR, NBSR and LR has been simulated and characterized at X band using 3D FEM solver and standard scattering-parameter based retrieval method. Their performance has been compared for various parameters. The experimental testing of this structure is in progress. This study can be used for choosing negative permeability plasmonic structure best suitable for a desired application. ACKNOWLEDGEMENT We are thankful to BRNS (Board of Research for Nuclear Science), Department of Atomic Energy, Govt. of India for funding this research work. We are also indebted to Dr. A. L. Das, Director, SAMEER for his help and encouragement for this work. [1]

[2]

[3] [4]

[5]

[6]

[7]

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