Detailed circuit parameters and dimensions of ML of the designed CRLH TLs.
In recent years, we have witnessed a rapid expansion of using metamaterials to manipulate light or electromagnetic (EM) wave in a subwavelength scale. Specially, metamaterials have a strict limitation on element dimension from effective medium theory with respect to photonic crystals and other planar structures such as frequency selective surface (FSS). In this chapter, we review our effort in exploring physics and working mechanisms for element miniaturization along with the resulting effects on element EM response. Based on these results, we afford some guidelines on how to design and employ these compact meta-atoms in engineering functional devices with high performances. We found that some specific types of planar fractal or meandered structures are particularly suitable to achieve element miniaturization. In what follows, we review our effort in Section 1 to explore novel theory and hybrid method in designing broadband and dual band planar devices. By using single or double such compact composite right-/left-handed (CRLH) atom, we show that many microwave/RF circuits, i.e., balun, rat-race coupler, power divider and diplexer, can be further reduced while without inducing much transmission loss from two perspectives of lumped and distributed CRLH TLs. In Section 2, we show that a more compact LH atom can be engineered by combining a fractal ring and a meandered thin line. Numerical and experimental results demonstrate that a subwavelength focusing is achieved in terms of smooth outgoing field and higher imaging resolution. Section 3 is devoted to a clocking device from the new concept of superscatterer illusions. To realize the required material parameters, we propose a new mechanism by combining both electric and magnetic particles in a composite meta-atom. Such deep subwavelength particles enable exact manipulation of material parameters and thus facilitate desirable illusion performances of a proof-of-concept sample constructed by 6408 gradually varying meta-atoms. Finally, we summarize our results in the last section.
- electrically small
- effective medium
- CRLH TL
- microwave/RF circuits
- super lens
1. Miniaturized CRLH atoms for compact microwave/RF circuits
Compact metamaterial element exhibits versatile features and merits over its conventional counterparts. One of the most important and direct features is that it enables more compact microwave/RF circuits. In this section, we will show this first benefit through a set of compact metamaterial transmission lines (TL), i.e., compact composite right/left-handed (CRLH) TLs. For a comprehensive study, two types of compact CRLH TLs, namely, lumped and distributed CRLH TLs, are investigated according to the realization manner. Of particular relevance and importance is the established design guideline, which paves the way for any microwave and millimeter wave integrated circuits and devices with high performances.
1.1. CAD design method for fractal lumped CRLH TL
To begin with, we first derive a general design mythology for the design of any compact CRLH element with fractal or meandered sections. Figure 1 depicts the CAD design flowchart of such CRLH TLs. For analysis convenience, the general circuit model (CM) of any CRLH TL is reproduced in Figure 1(a). The CRLH TL, with characteristic impedance of
(1) Determine and derive the circuit parameters of any CRLH TL according to the required phase response at operation frequency
(2) Given the computed values of LR and CR, the required electrical length of straight RH line (ML) for CRLH TL is determined by
Therefore, the physical length
(3) Design any fractal ML with specified phase shift. Since many chamfered bends are generated in iterative meandered process, the nonnegligible discontinuity reactance results in phase-shifting effect of RH line which should be properly evaluated and compensated. Here, a phase-equalizing method is developed. A slight physical length Δ
(4) Design the overall CRLH TL by taking into account the parasitic inductances and capacitances of SMT elements and soldering pad. This can be implemented by a close-loop precise optimization through dynamically comparing the phase response of real and ideal CRLH TLs. Here, the parasitic effects are evaluated through a direct comparison of measured transmission response of MLs with and without soldered SMT elements.
1.2. Broadband and dual band balun
1.2.1. Broadband balun using fully artificial fractal-shaped CRLH TL
In this subsection, a compact balun with bandwidth enhancement is realized based on the design methodology established in Section 1.1.
Balun, a three-port network, was commonly used to transfer the input unbalanced signal to two output balanced ones with 180° phase difference. It has been extensively studied for active amplifiers, balanced mixers, passive filter  and even antennas . Several types of baluns are available among the open literature, such as the Marchand balun [4–6], power-divider balun [7, 8], branch-line balun  and metamaterial balun . Highly integrated circuits with stable communication quality strongly require wideband and miniaturized RF/microwave devices. In this regard, several strategies have been proposed for miniaturization, e.g., by integrating coupled transmission line (TL) , using low temperature cofired ceramic technique  or fractal/meandered branches [9–11]. Although baluns achieved significant miniaturization in [4, 5], the multilayer design suffered thick profile, complicated structure and high-cost fabrication. As to the bandwidth enhancement of baluns, we have also witnessed several approaches such as using broadband Schiffman phase shifter , slot-coupled microstrip lines , substrate integrated waveguide , phase-adjusting CRLH TL  and metamaterial TL . Nevertheless, these baluns occupy a large circuit area. The lack of techniques regarding simultaneous bandwidth and miniaturization make the design of compact broadband balun a pressing task. Here, a compact broadband balun is proposed using fully artificial fractal-shaped CRLH TL  and we will begin with the theorem of CRLH TL for broadband objective.
Figure 2 shows the scheme of proposed balun along with the phase response of corresponding dual CRLH branches. Different from branch-line balun with two –90° and two –180° branches, our balun contains one +90° and three –90° TL branches. The characteristic impedance of +90° branch is denoted as
For simplicity, we select and
To maximize the bandwidth around
To mathematically guarantee above requirement, the first-order derivative of with respect to
The second derivative ensures the extremum of Eq. (5) to be a minimum. We have seven individual equations from Eqs. (4), (5) and (7) but have eight unknowns. Therefore, it is impossible to exclusively determine a group of solution. This additional degree of freedom can be utilized for other purpose in design of the broadband balun with fully artificial TLs.
For verification, we designed, fabricated and measured a proof-of-concept sample on F4B substrate with thickness of
The performance of developed balun is characterized through the dynamic links and solver of planar EM and circuit cosimulation in MOM-based Ansoft Designer and is measured by the
Measurement results reveal that return loss |
To sum up, the insertion loss mainly induced by fractal bends is moderate within the operation band. The hybrid technology of fractal and CRLH TL does not pose severe penalty on device performances but allows additional degree of freedom in developing devices with high integration, promising an elegant alternative for compact and multifunctional devices with high performances.
1.2.2. Dual band rat-race coupler
Rat-race coupler (RRC), see the circuit topology shown in Figure 5(a), is one type of 180° hybrids and one of the most important microwave passive devices. The four-port lossless reciprocal network consists of three –90° branches and one –270° branch with characteristic impedance of , where
Multiband components with miniaturized dimensions have aroused a wide of interest since they enable low cost, high reliability and integrity. Up to date, numerous approaches have been developed for compact RRCs, e.g., using capacitor  and periodic slow-wave loading , using periodic stepped-impedance ring resonators , T-shaped photonic bandgap (PBG) structures  and fractal strategy [17–19]. Although above RRCs feature compact, the lack of dual band (DB) performances deserves further improvements. To date, much fewer literatures were devoted to DB applications, e.g., using tri-section branch-line , stepped-impedance-stub units  and two T-shape open-stub units . However, the design and realization were tedious and typically featured large circuit size. The lack of literature concerning both the DB performance and size reduction makes the design of a compact DB RRC a pressing task.
In this work, we proposed a novel DB RRC based on the hybrid approach of fractals and CRLH TLs . A new scheme for DB design is proposed by combining two circuit topologies with different phased branches. We noticed that another two RRCs with topologies shown in Figure 5(b) and (c) also exhibit the same functionality. To develop a DB RRC, we consider combing two of them in one circuit board. Among all three possible combinations, the two networks shown in Figure 5(a) and (c) are examined as the exclusive solution for DB performance. Two types of CRLH branches with specified phases at two arbitrary frequencies are necessary to integrate these networks. This distinguishes our design from any previous DB synthesis for other devices [24, 25] which only required one set of CRLH branch. Consequently, DB RRC design is less direct and more complicated than any other DB device design, giving rise to the rarely reported work. In this particular design, the operation frequencies are designed at
In what follows, we begin with the dispersion of CRLH TL to briefly derive the fundamental DB theory. At
Combining Eqs. (4), (5) and (10), we can readily obtain explicit expressions of four circuit parameters as 
Following Eq. (12), the possible solution by combining circuit topologies shown in Figure 5(b) and (c) can ruled out for DB synthesis. Given determined circuit parameters, see Table 1, we can readily design the final RRC layout using the approach described in Section 1.1. The designed RRC is built on F4B substrate with
|PU||56 + 6.8||12||12 + 12|
Figure 6 shows the finally engineered layout of the fractal-shaped RRC. Again, we consider realizing the RH and LH part of the 70.7 Ω CRLH branches by MLs and SMT chip elements, respectively. In the former case, the MLs are configured in Koch shape of
For characterization, the eventually designed DB RRC is analyzed through the dynamic links and solver of planar EM and circuit cosimulation in Ansoft Designer. For verification, the fabricated RRC sample, see Figure 6(d) is measured by
Tables 2 and 3 detail the simulated and measured results for both in-phase and out-of-phase operation. In the former case, measured results indicate that |
|CF1||Sim.||18.2||2.9 and 3.3||33.1||0.35||–0.3|
|Meas.||24.2||3.4 and 3.1||28.3||–0.4||–4.2|
|CF2||Sim.||29.3||3.1 and 3.2||33.3||0.15||0.5|
|Meas.||19.9||3.2 and 3.5||28.5||0.6||–0.15|
|CF1||Sim.||21.6||3.27 and 2.97||33.1||–0.29||–0.29|
|Meas.||28.4||3.25 and 3.7||28.4||0.43||–3.3|
|CF2||Sim.||34.8||3.2 and 3.1||33.3||–0.15||–0.34|
|M||31.7||3.89 and 3.22||28.57||–0.67||0.6|
To sum up, a super compact CRLH RRC is successfully engineered with good DB performances based on proposed DB strategy and hybrid approach. The RRC features low insertion loss, modest operation bandwidth and good isolation between output ports. The 89.8% size reduction is believed to be one of the best miniaturizations in the open literature which should be highlighted.
1.3. Analysis and characterization of novel distributed CRLH atoms
Although lumped-element CRLH TL exhibits the merit of easy design and high degree of freedom, it is rigorously restricted to low-frequency operation due to self-resonant effects of chip components at high frequency. In this subsection, we will introduce a set of distributed resonant-type CRLH TLs made of novel complementary split ring resonators (CSRRs). Three types of CSRRs are involved in terms of compactness, namely complementary single split ring resonator (CSSRR) pair (CSSRRP), Koch-shaped CSSRRP (K-CSSRRP) and Koch-extended CSSRRP (K-ECSSRRP) [26, 27]. They are investigated in depth based on TL theory and electromagnetic (EM) response characterization, aiming to illustrate the novel working mechanism for miniaturization. Of particular irreverence is the dual-shunt branch circuit theory established for a new set of CRLH TLs.
1.3.1. CSSRRP-loaded CRLH atom
The topology of the first CSRRs-evolved CRLH element is shown in Figure 9(a). As is shown, the CSSRRP etched on the ground is composed of two CSSRRs with face-to-face splits beneath a capacitive gap. When the element operates in LH band where the backward propagation is supported, the CSSRRP responds to the time varying axial electric field and affords a negative permittivity. In the circuit model (losses have been excluded) shown in Figure 9(c), the CSSRRP is described by means of a parallel resonant tank formed by
Figure 10 depicts the frequency response of a CSSRRP- and CSSRR-loaded CRLH TLs obtained from EM full-wave simulation and electrical simulation (circuit model) in Ansoft Serenade. As is shown, the
The exotic EM behavior of the proposed CRLH atom can be analyzed based on equivalent circuit model inspired by Bloch theory. The series and shunt impedances are given by
The shunt admittance can be obtained immediately from Eq. (14):
As crucial parameters for circuit design, the electrical length
Thus, by insertion of Eqs. (13) and (14) into Eqs. (16) and (17), the propagation constant
In a similar manner, the transmission zero
When the parallel tank of CSSRRP resonates, we obtain the upper limit of the LH band by forcing Eq. (15) to be zero:
Here, Eqs. (18) and (20) are reasonable on assumption that . If
Referring to Figure 11,
Figure 12 illustrates the extracted effective constitutive parameters of the CSSRRP-loaded CRLH atom. Negative refractive index and propagation constant can be clearly observed within 2.74–3.94 GHz. The LH band that allows signals to be transmitted freely is observed within 3.56–3.94 GHz, where the imaginary parts of refractive index, permittivity and permeability approximate to zero. However, the imaginary parts associated with electric or magnetic loss are considerable within 2.74–3.56 GHz where the EM wave propagation is still not allowed. A further inspection reveals that an obvious electric resonance occurs around 3.6 GHz with negative permittivity. The vanished electric resonance for the meta-atom without CSSRRP illustrates that the new slot gives rise to the negative permittivity. Since the effective permeability is negative across the entire band, the simultaneous negative LH band is solely dependent on the negative permittivity band (3.56– 3.94 GHz). The retrieved
Our further numerical results (not included here for brevity) show that LH band shifts downwards when either width
1.3.2. KCSSRRP-loaded CRLH atom with balanced condition
Since the LH band of above CRLH atom is narrow, it is preferred for narrow-band filter applications. Moreover, the potential for further miniaturization of CSSRRP-loaded CRLH atom is still available. Here, we will improve the in-band bandwidth and demonstrate the zero-phase behavior by engineering a miniaturized balanced CRLH TL.
As discussed earlier, the position of RH band is much influenced by
In the first design example (see Figure 13), the K-CSSRRP is with partial fractal boundary only by constructing the two outmost vertical sides as Koch curves of third order. Figure 14 depicts the simulated
In the second design example (see Figure 15), the four-vertical and four-horizontal slots are constructed as Koch curves of quasi-second iteration order to roughly guarantee in a square configuration with full fractal boundary. In this regard, a balanced CRLH TL with bandwidth enhancement will be achieved as discussed above. To accommodate all fractal sections in a highly compact region for further size reduction, some Koch sections formed in the first-order iteration process are removed. The lumped-element circuit parameters are also extracted for theoretical analysis, see caption of Figure 16.
Figure 16 portrays the corresponding frequency response, along with representation of series impedance, shunt admittance and characteristic impedance. From Figure 16(a), it is obvious that
1.3.3. K-ECSSRRP-loaded CRLH atom with dual-shunt branch circuit
The objective of this subsection is to establish the theory and design of a new class of CRLH atoms that own dual-shunt branch circuit and enable compact RF/microwave devices with harmonic suppression. As a result, it is unnecessary to cascade a chain of CSRRs for harmonic suppression, which in turn leads to super compact devices.
Figure 17 shows novel dual-shunt brunch circuit model and the layout of novel CRLH atom evolved from previous CSSRRP-loaded CRLH structure. Here, previous CRLH atom, see Figure 17(a) is reproduced for comparison convenience. The major difference of novel CRLH atom lies in the K-ECSSRRP etched in the ground, see Figure 17(b). It is constructed by expanding each end-point of CSSRRP with an inner smaller slot made of three second-order Koch curves and one first-order Koch curve.
Similar to CSSRRP , the K-ECSSRRP beneath the capacitive gap excites current along the zig-zag boundary and generates two effects in response to the time varying axial electric field, i.e., the electric excitation to external CSSRRP and that to inner Koch slot. The electric excitation to inner slot is independent of external CSSRRP and thus also provides a shunt branch in the circuit model like CSSRRP. To guarantee effective excitation, the center area of the complementary resonator should be unoccupied. Both excitations contribute to the negative permittivity. In the CM shown in Figure 17(c) and (d), losses are irrespective of for analysis convenience.
To begin with, we perform numerical circuit analysis to identify the transmission zeros, cutoff frequencies, LH characteristic and balanced condition. Assume a two-port CRLH TL with
Although CRLH atoms are isotropic and periodic in this design for computational and fabrication convenience, it is unnecessary to require this condition in practice. The [
The calculation of
Apply the periodic boundary condition to the two-port network, we have and , where
The determinant of Eq. (25) should be zero to guarantee a nontrivial solution, which yields 
Insertion of Eq. (22) into Eq. (26), we can obtain the dispersion relation associated with
Take the condition of Brillouin zone (), we immediately have
The lower cutoff of LH band and the upper cutoff of RH band can be obtained by solving Eq. (28). In the same time, we obtain the equation of when take . In this regard, the upper limit of LH band and lower limit of RH band are achieved by solving the following equations:
Moreover, the Bloch impedance
Insertion of Eq. (22) into Eq. (31) yields
The and can be achieved by forcing Eq. (32) to be null. Moreover, two transmission zeros of the two shunt branches are determined when the denominator of Eq. (24) is null:
The CRLH TL is rigorously balanced only when which is particular interest for broadband design. In this case, the LH band (backward wave propagation) switches to the RH region (forward wave propagation) without a gap. Otherwise the continuous pass band is perturbed by a stop band. Rather than obtain cut-off frequencies from tedious analytical expressions by solving Eqs. (28), (29) and (32), we will illustrate them by means of representations of these equations, see Figure 18. Moreover, these cutoffs can also be ambiguously identified from transmission zeros of CRLH TLs with large number of cells, see Figure 19. Note that and do not correspond to the attenuation poles that the two shunt branches afford. In a general case, they fulfill the requirement of .
For characterization, Figure 18(a) illustrates the
Figure 19 depicts the
It should be emphasized that proposed meta-atom not only exhibits additional attenuation pole in the upper edge band but also has a miniaturized circuit which is on the order of 65% of the CRLH atom using CSSRRP. The extended current path on the ground due to the large compression ratio of Koch curves enhances considerably the LC values of lumped elements in parallel resonant tanks of CM. Further study shows that
1.4. Compact microwave device applications
1.4.1. Multiple-way and two-way Wilkinson power dividers
In this subsection, we will demonstrate the possibility of employing novel K-CSSRRP-loaded distributed CRLH TLs in the design of compact three-way fork power divider and a four-way series power divider by substituting zero phase-shift CRLH TLs for conventional 2
Since we only have three equations regarding the balanced condition, specified phase
Figure 20(a) depicts the schematic of the three-way fork divider. It is composed of two conventional 2
To examine the performances, Figure 21 plots the simulated and measured
For further application, a 1:4 series power divider is also designed and fabricated using the zero phase-shift CRLH atom shown in Figure 15. The corresponding schematic and the fabricated prototype are shown in Figure 22. As can be seen, the power divider consists of four series connected 2
For verification, Figure 23 portrays the full-wave simulated and measured
To sum up, a novel compact resonant-type CRLH atom along with equivalent circuit model is proposed. It features inherent balance condition, additional transmission zero above the RH band and a higher degree of freedom in design over previous CSRRs-loaded counterpart. The fractal perturbation in novel CRLH atom leads to a significant shrinking of LH and RH bands and thus is of particular interest in compact device applications with a super miniaturization factor. The high-performance of super compact three-way and series 1:4 power divider has qualified it a good candidate.
1.4.2. Harmonic suppressed diplexer
The additional transmission zeros of CRLH atom with dual-shunt branch circuit can be directly applied to design a diplexer with harmonics suppression and enhanced frequency selectivity. A diplexer used to make receiving and transmitting share a common antenna consists of three ports, a receiver (Rx) filter and a transmitter (Tx) filter. Here, we realize both the Rx and Tx filter utilizing single K-ECSSRRP-loaded CRLH atom with specified
Figure 25 illustrates the simulated and measured results of proposed diplexer. A reasonable agreement of results is observed in both cases. As shown in Figure 25(a), the bandwidth of the Tx filter is measured as 220 MHz (1.61–1.83 GHz), in which the return loss |
In summary, the theory of dual-shunt branch circuit has been numerically studied and experimentally vilified. Due to the inherent additional transmission zero of dual-shunt branch CRLH atom, the resulting devices can be engineered with enhanced harmonic suppression and selectivity without posing penalty on circuit dimension. Moreover, the compact CRLH atom further reduces the circuit size. The high performances of designed diplexer corroborate our proposal and above statements, promising potentials in transceiver front-ends of mobile and wireless local area network (WLAN) systems.
2. Compact LH atoms for three-dimensional super lens
Three-dimensional (3D) LH-TL super lens with free-space excitation is very fascinating in practical applications since it is unnecessary to embed the sources and fields in the TL network [29, 30]. Here, we propose a 3D super lens with super resolution  using fractal perturbed LH TL in printed circuit board (PCB) fabrication process. The distributed LH-TL lens allows geometry scalability and avoids the parasitic RH effects in soldering the lumped elements. Due to the space-filling feature of fractals, the operation frequency in terms of subwavelength resonance is drastically lowered down. Consequently, a compact LH-TL element is engineered with large inductance and capacitance (LC) values in a limited volume.
2.1. Analysis and characterization of fractal LH-TL metamaterial
Figure 26 portrays the schematic and equivalent circuit model of the TL atom and resulting 3D lens. The TL atom with a lattice of
In the model shown in Figure 26(c), similar to reference , the fractal ring is driven by the
For characterization, the commercial full-wave finite-element-method (FEM) solver Ansoft HFSS is employed. The fractal patterns are built on 1 mm thick F4B substrate with
2.2. Design and realization of super lens
Now, we show how to design the basic TL atom and resulting super lens. To lay a solid theoretical method for implementation of
Insertion of Eq. (39) into Eqs. (37) and (38) yields immediately the effective material parameters
The effective permittivity and permeability tensors of the TL lens can be written as
With above fundamentals known, we designed a 3D TL super lens working at
As shown in Figure 29, the effective parameters are retrieved as
2.2. Numerical and experimental results
To verify the subwavelength focusing, we numerically designed a TL lens using the extracted effective parameters. The simulation is conducted in Comsol Multiphysics™ software package, where a current source oriented along
Obvious focusing behavior is clearly suggested inside (interior focusing) and in front (exterior focusing) of the lens for both designed and ideal lens in either single-source or dual-source case. The evanescent wave amplification is clearly observed along the two-slab interfaces. The large field concentration on interfaces is attributable to plasmonic surface waves at the interface of LH and RH media. The nonideal material parameters away from –1 induce slightly asymmetric fields, discontinuous wave front and lower imaging intensity observed in practical lens due to slight loss and impedance mismatch at the interface of lens and free space. Nevertheless, the loss originated from imaginary parts of
For verification, the designed TL lens is fabricated and measured, see Figure 31(a). In fabrication, a total of 10 × 3 TL atoms are fabricated on FR4 substrate board using standard PCB technology. To sustain the bulk TL lens with desired air spacer, each substrate board is supported by a plastic foam of identical size with
For dual-source imaging, additional power-division circuit is necessary and wave interference of two closely distributed sources may degrade the focusing quality in terms of weak field intensity at focal point. Here, we only performed experiments for single-source imaging by measuring magnetic field intensity using loop antenna, see setup shown in Figure 33. The transmitting loop antenna (20 mm away from the slab), is stationary and illuminates at the front side of the lens (slightly larger than
3. Compact meta-atoms for superscatterer illusions devices
In this section, we conceptually proposed and experimentally demonstrated a superscatterer illusion device  with abundant functionality inspired by the concept of magnifying lenses [33, 34] using transformation optics (TO) theory. A new strategy to miniaturize the meta-atom is proposed by combining both electric and magnetic particles. Using such a compact building block, a proof-of-concept sample consisted by 6408 gradually varying meta-atoms is designed, fabricated and measured.
3.1. Scheme and theoretical design
The device which tightly wraps an original metallic object (denoted as yellow) in actual space, see Figure 35(a), is a shell (denoted as light green) embedded by four symmetrically located wing objects (denoted as light yellow). It functions to transform the metallic object into multiple isolated ghost objects with isotropic material properties () and an enlarged metallic object at center in virtual space, see Figure 35(b). In other words, the functional device enables the radar scattering signature of a metallic object to equal that of an enlarged metallic object and four symmetrically arranged ghost objects under EM wave illumination. The proposed scheme with complex and versatile functionality inherits the merits of both superscatterers and cognitive deception and is not confined to metallic objects but also suitable for dielectric objects.
In actual space, the radius of the object (also the inner radius of the ghost device), the inner and outer wings are denoted as
We derived the required material parameters in region I and II through a general transformation in 3D spherical coordinate (
In this particular design, the proposed superscatterer illusion functionality can be readily realized through following transformation:
where is a constant related to the magnifying factor that can be arbitrarily designed. By substituting Eq. (44) into Eq. (43), we immediately obtain the required permittivity or permeability tensor as
For 2D illusion device in the cylindrical coordinates (
where and are
The superscatterer illusion device is designed to work around 10 GHz in X band. Figure 36 portrays the required anisotropic and inhomogeneous material profile as a function of radius in both regions. Without loss of generality, two illusion devices with large and smaller magnifying factor of and are considered. From Figure 36, it is learned that the radial permeability
3.2. Metamaterial design and device fabrication
The above required gradient material profiles in both regions can be realized using compact meta-atoms. Since it is easy to fully cover a small scope of permeability using only one type of subwavelength elements, we consider implementing the superscatterer illusion in Case 2 with more relaxed slope of
In the fabricated prototype, the superscatterer illusion device is discretized into a total of 6408 grids (meta-atoms) each occupying an area of
|Number of Layers||Region I||Region II|
In the simulation setup shown in Figure 39(a),
3.3. Numerical and experimental results
Now, we carry out full-wave simulations in COMSOL Multiphysics to demonstrate the functionality of proposed superscatterer illusion device. For comprehensive study and not lose generality, the superscatterer illusion for a dielectric object is also studied. As shown in Figure 40, a line source (a monopole probe in experiment) is located 50 mm (1.67
To further quantitatively evaluate the superscatterer illusion performance, we compare the simulation results of scattered electric fields in actual and virtual spaces within the region −2
To validate the superscatterer illusion functionality, we measured 2D electric-field mappings in near-field parallel-plate waveguide measurement system (Figure 42). A monopole probe fixed inside the planar waveguide excites the sample over a discrete cluster of frequencies. The impinging EM wave interacts with thousands of particles and thus affords desired scattering signatures. Due to large size of the sample, the simulated and measured electric fields in horizontal plane are mainly recorded at rear side of the device (7
As shown in Figure 43(a) and (d), the simulated and measured scattering patterns are in reasonable agreement. The consistency can be further inspected from electric-field intensities shown in Figure 43(g), where the fields at 10.1 GHz are normalized to the maximum along the black dashed line
In summary, we have reviewed in this chapter our recent effort in synthesizing electrically small meta-atoms from effective medium perspective and utilizing compact meta-atoms to design microwave circuits and functional devices. Several strategies have been proposed for such a purpose and the mechanisms have been studied in depth. The advantages of compact meta-atoms can be classified in two categories. First, it can significantly reduce the circuit size without posing penalty on device performances. Second, it brings about additional degree of freedom for device design and broadband deep out-of-band signal inhibition which can be employed for harmonic suppression. Third, it enables manipulation of precise material parameters and smooth outgoing field which is preferable for functional devices with high performances and new physics demonstration with high-quality phenomena. Moreover, the precise-material parameters will improve the success rate of correct design. Our compact approach lays a platform and gives a promising alternative for both engineers and scientists to realize their devices or demonstrate their find using metamaterials.
This work was supported by National Natural Science Foundation China under Grant Nos. 61501499 and 61372034 and also Natural Science Foundation of Shaanxi Province under Grant 2016JQ6001. The authors deliver their special gratitude to Prof. Tie Jun Cui and his meta-group for the guidance, discussions and help afforded in the work of 3D super lens and illusion device.
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