Microfabricated V-band left-handed transmission lines

Available online at www.sciencedirect.com

Metamaterials 2 (2008) 26–35

Microfabricated V-band left-handed transmission lines Chao Qin ∗ , Alexander B. Kozyrev, Abdolreza Karbassi, Daniel W. van der Weide Department of Electrical and Computer Engineering, University of Wisconsin, Madison, WI 53706 USA Received 29 August 2007; received in revised form 1 November 2007; accepted 1 November 2007 Available online 17 November 2007

Abstract We present the design, microfabrication, and characterization of V-band transmission lines, having a wide left-handed passband between 42 and 73 GHz. The mushroom structure and associated microfabrication method is further extended to build a 1-D lefthanded transmission line working at 100 GHz and a 2-D left-handed structure with 9 × 9 cells, enabling 2-D or even 3-D left-handed metamaterials at high frequencies. © 2007 Elsevier B.V. All rights reserved. PACS: 41.20.Jb Keywords: Electromagnetic bandgap structures; Left-handed; Metamaterials; Microfabrication; Transmission lines

1. Introduction Over the last decade, left-handed metamaterials, which are artificial structures featuring anti-parallel phase and group velocities, have drawn considerable attention in the microwave community due to their potential for novel devices and applications. The concept of left-handed materials was considered in detail by Veselago in 1968 [1]. In 2000, Smith et al. [2] developed the first experimental left-handed structure, which was composed of split-ring resonators and thin metal wires. Since then, the operating frequencies of these composite structures have been boosted into 100 GHz and even THz regions [3–5]. Another way to implement left-handed materials, known as the transmission line approach, was pro-

∗ Corresponding author. Tel.: +1 608 263 6815; fax: +1 608 262 1267. E-mail address: [email protected] (C. Qin).

1873-1988/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.metmat.2007.11.001

posed almost simultaneously by three different groups [6–8]. This approach allows for low-loss left-handed structures with broad bandwidth due to tightly coupled resonant components [9]. Many microwave applications based on these two approaches have already been implemented using a printed circuit board (PCB) fabrication [10–17]. While PCBs are inexpensive for relatively lowfrequency applications with large planar structures, the demand for higher operating frequencies favors the miniaturization of structure dimensions using on-wafer microfabrication. For example, a left-handed coplanar stripline periodically loaded with lumped capacitors and inductors was fabricated on a quartz substrate [18]. However, this approach requires aggressive fabrication process, such as e-beam lithography for sub-micron features. We recently demonstrated a scalable left-handed transmission line manufactured by a microfabrication method [19]. This transmission line is composed of a 1-D periodic array of a metallic mushroom structure that was first introduced as the building block of 2-D electromag-

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netic bandgap surfaces [20]. Later, it is demonstrated that this structure is essentially a composite right/left-handed transmission line, capable of exhibiting a negative refractive index [21,22]. The mushroom structure employed here offers much design and fabrication freedom, making very high frequency left-handed transmission lines possible with rather large fabrication tolerance. Moreover, the proposed microfabrication method can be used directly to construct 2-D structures, which are more attractive for use in practical applications. Here we present an optimized microfabrication process that results in high-performance V-band left-handed transmission lines with various lengths. The design considerations, including the structure dimensions, material selection, and the equivalent circuit model, are discussed in Section 2. In Section 3, the process flow, along with a novel method for the construction of very tall vertical conductors, is proposed. In Section 4, comprehensive characterization using S-parameter measurements, ADS modeling, and HFSS simulation are presented. Finally, a 1-D left-handed transmission line working at 100 GHz and a 2-D left-handed mushroom structure are demonstrated in Section 5, revealing the capabilities of the proposed method to be extended to higher operating frequencies and higher dimensions. 2. Design 2.1. Principle of operation The schematic of a mushroom-type left-handed transmission line is shown in Fig. 1(a). The structure consists of a series of metal caps connected by metal posts to ground (not shown). Metal patches under the caps are

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Fig. 2. Equivalent circuit of the unit cell of the mushroom structure.

employed to enhance the coupling between adjacent caps and to provide a convenient way to adjust the dispersion characteristics. Ground-signal-ground (GSG) probe pads are added at each end for measurement. Microstripto-coplanar waveguide (CPW) transitions are employed to connect the GSG pads and the intrinsic mushroom structures. The metallic mushroom structures are embedded in dielectric layers, which are omitted in Fig. 1(a) for clarity and are presented in Fig. 1(b) for the crosssectional view. The equivalent circuit for a unit cell of the mushroom structure is given in Fig. 2. The patch-enhanced mutual coupling formed by the adjacent mushroom caps introduces the series capacitance CL , while the metal post provides the shunt inductance LL . The distributed inductance of the cap introduces the series inductance LR , while the capacitance between the ground plane and the cap provides the shunt capacitance CR . The overall loss of the structure is represented by the resistance R. The dispersion relationship of the 1-D periodic lefthanded transmission line is calculated as follows:  (ω2 CL LR − 1)(ω2 CR LL − 1) βd = 2 arcsin (1) 4ω2 LL CL where β is the propagation constant, d the period of the mushroom structure, and ω the radian frequency. When a certain relationship among CL , LL , CR and LR is fulfilled, the mushroom transmission line circuit represents itself as a composite right/left-handed transmission line, which exhibits a left-handed passband [12]. 2.2. Material selection

Fig. 1. Schematic of mushroom-type transmission line. (a) Perspective view (dielectric layers not shown); (b) cross-sectional view.

As shown in Fig. 1(b), two dielectric layers are required to support the metallic patches, and to fill within the gap between the patch and cap layers, respectively. In order to obtain the left-handed response, the values of the left-handed components (i.e. CL and LL ) must be large enough to be comparable to their right-handed counter-

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parts (i.e. CR and LR ). While a large series capacitance CL requires a thin dielectric layer between the patches and caps, a large shunt inductance LL requires that the metal post has a high aspect ratio (height over diameter), which in turn necessitates a thick supporting dielectric layer beneath the patches. From a fabrication point of view, the main considerations for the selection of this supporting material are that: (1) its thickness can be easily varied to provide scalable structure dimensions, and hence adjustable left-handed operating frequencies; (2) high-aspect-ratio structures (i.e. metal posts) can be easily fabricated in it; and (3) it should be strong enough to survive the subsequent process steps. For our work, the metallic mushroom structures are embedded in SU-8 layers. SU-8 is a negative, epoxybased photoresist, capable of forming high-aspect-ratio microstructures with various thicknesses (e.g. from several microns to 1 mm) using standard UV lithography [23]. Moreover, cured SU-8 is thermally stable, mechanically strong and highly resistant to most chemicals. These properties make SU-8 an ideal candidate for being a permanent part of the device. 2.3. Dimension design The Ansoft HFSS commercial simulator is used to design the mushroom-type transmission lines. The main criteria for the selection of our structure dimensions are: (1) the highest possible operating frequencies within our measurement capability, and (2) the largest fabrication tolerance, provided that (1) is satisfied. Because a very thick SU-8 layer (i.e. the patch supporting layer) is required in the processing, several problems, such as edge beads, non-uniform resist thickness, and bowing of substrates, are often found during photoresist lithography. Consequently, a gap typically forms between the photo mask and the substrate and small features cannot be easily resolved due to large diffraction errors [24]. Thus, some critical features, such as the gap between adjacent caps, G, the distance between patch and post, g, and the post diameter, D, must be kept reasonably large when manipulating left-handed operating frequencies. In the final design, the cap size, C × C, is 210 ␮m × 210 ␮m and the gap between the adjacent caps, G, is 42 ␮m, resulting in a structure period of 252 ␮m. The patch size, C × P, is 210 ␮m × 150 ␮m. The distance between the patch and the post, g, is 39 ␮m. The post is 24 ␮m in diameter and 80 ␮m in height. The thickness of the thin and thick dielectric layer is 5 and 75 ␮m, respectively.

3. Fabrication 3.1. Ultra tall vertical conductors As shown in Fig. 1, very tall metallic posts providing the left-handed inductance are required in the mushroom-type transmission lines. Conventionally, such structures can be accomplished by a UV–LIGA process, using deep via holes formed by thick photoresist lithography and a subsequent metal electroplating process [25]. LIGA is a German acronym for Lithographie (lithography), Galvanoformung (electroplating), and Abformung (molding). However, several significant fabrication challenges are associated with this platingthrough-via approach. Firstly, the lithography process must be carefully optimized in order to form very deep via holes with small apertures. Secondly, uniform and stress-free electroplating of metal into deep via holes is very challenging. Thirdly, metal electroplating is a timeconsuming process because the plating time increases with the via hole depth. To avoid these problems, we form the metallic posts in a different way. Instead of making deep via holes, we fabricate post structures first. These posts are then covered by conformal deposition of a metal layer using DC sputtering. As long as the metal thickness is much larger than its skin depth δ (e.g. 0.29 ␮m at 50 GHz for copper), these metal covered posts can be considered electrically equivalent to solid metal posts made by the conventional plating-through-via method. There are several advantages of this approach: firstly, it is much easier to make a post than a via structure; secondly, DC sputtering is much easier and more uniform than electroplating method; thirdly, the metal deposition time (or equivalently, the metal thickness) is only determined by the skin depth, not by the post height. 3.2. Process flow The process flow is shown in Fig. 3. For our work, the entire structure is implemented on a silicon substrate. However, this process can also be applied to other semiconductor or glass substrates. The first step is to construct the metal posts using the method mentioned above. SU-8 2050 (MicroChem Corporation) is patterned into 85-␮m tall posts using regular UV (365 nm) lithography. The SU-8 posts are then covered by thick metal layers (Ti/Cu, 0.5 ␮m/2.0 ␮m) using DC sputtering. The thick metal layers deposited on the substrate naturally act as ground plane, as shown in Fig. 3(a).

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Fig. 4. Top view of a finished 5-cell left-handed transmission line.

Fig. 3. Process flow.

In Fig. 3(b), another layer of 85 ␮m SU-8 2050 is spun on. Viscous SU-8 2050 becomes very fluidic at the soft bake temperature (i.e. 100 ◦ C) and naturally forms a planar surface when cooled, having the metal covered posts embedded in it. Oxygen plasma etching is then performed to reduce the thickness of the SU-8 2050 by 10 ␮m, leaving the top portion of the posts exposed. In Fig. 3(c), the metal patches (Ti/Au, 0.05 ␮m/ 0.5 ␮m) are defined using a conventional liftoff process consisting of sequential steps of regular photoresist lithography, metal deposition, and solvent liftoff. In Fig. 3(d), a thin layer of SU-8 2005 (5 ␮m) is spun on. The 5-␮m SU-8 2005 can completely cover the metal patches but not the exposed posts, which are 10-␮m thick according to step (b). Thus, only a brief oxygen plasma etching is required to remove any residual SU-8 2005 on top of the metallic posts. The mushroom structure is finalized when the metal caps (Ti/Au, 0.05 ␮m/0.5 ␮m) are formed in the same way the patches are created, as shown in Fig. 3(e). Fig. 4 shows a photograph of a finished 5-cell mushroom-type transmission line. During the fabrication of mushroom structures, it is very critical to assure a good connection between the posts and the caps. This requires that the posts are well exposed after the thin dielectric layer (i.e. SU-8 2005) is spin coated in step (d). In [19], the posts are exposed by a via hole opening process, which is not easy due

to the large diffraction errors mentioned previously. As shown in Fig. 5, if any via hole is not well opened, the device will not function, or at least contact resistance between the posts and caps will increase, and hence the losses. Thus, this process greatly affects the loss, uniformity and yield of the mushroom transmission lines. To solve this problem, we use an optimized process here. In step (b) of Fig. 3, a great deal of the supporting SU-8 2050 layer is removed. As a result, the height of the metal posts is larger than the total thickness of SU-8 2050 and SU-8 2005 layers. Thus, the metal posts are naturally exposed after the thin dielectric layer (i.e. SU-8 2005) is coated. Consequently, good electrical contact between the posts and the caps is guaranteed. The loss performance, uniformity, and yield are all greatly improved. Another advantage of this new process is that it is less costly because one mask (for via hole opening) can be eliminated.

Fig. 5. A close-up view of the problematic step (d) and (e) in the process flow reported in [19]. The device will not function because the via hole is not opened and thus there is no contact between the cap and the post.

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4. Characterization 4.1. S-parameters Two-port S-parameter measurements are taken with an Agilent 8510C vector network analyzer, a Cascade Summit 9000 probe station, and 150 ␮m pitch probes. Before measurement, a Line–Reflect–Reflect–Match (LRRM) calibration is performed using Impedance Standard Substrate (ISS) from Cascade Microtech. Fig. 6 shows the S21 magnitude and unwrapped phase of 5-, 7- and 9-cell transmission lines. A distinct passband between 42 and 73 GHz is obtained. Compared to those reported in [19], both passband width and center frequency are enhanced in the current design. The loss performance is also significantly improved. For example, the minimum insertion loss for the 7-cell transmission line is reduced by 11.3 dB, which is a nearly 50% improvement. A significant part of the loss is introduced by the mismatch loss due to CPW to microstrip transitions at

the terminal ports. Since these transitions are only for measurement purpose, it is more reasonable to evaluate only the losses of the intrinsic mushroom structures. The loss per unit cell can be easily extracted by comparing minimum insertion losses of any two transmission lines. This translates into less than 1 dB loss per unit cell. Another source of the insertion loss is SU-8. Through HFSS simulations, the effect of SU-8 loss tangent is studied. When the SU-8 is assumed to be lossless, the simulated insertion loss of the 5-cell transmission line is quite small. Increasing the loss tangent of SU-8 will increase the insertion loss of the transmission line. When the simulated and measured 5-cell S21 parameters match with each other, the loss tangent is found to be 0.05. This value is similar to those reported in [26,27]. The small fluctuation of the measured S21 magnitude within the passband is essentially due to the impedance mismatch at the terminal ports. It is noteworthy that the magnitude peaks exactly correspond to the resonance modes of a N-cell half-wavelength resonator, which exist when the phase, φ = 0␲, −␲, −2␲, . . ., and thus, βd = 0␲, −1/N␲, −2/N␲, . . . [14]. For instance, the peaks on the 5-cell curve, which are located at 65.4, 56.4, and 49.2 GHz, precisely correspond to the resonant modes m = −1, −2, and −3, respectively. This result indicates that our mushroom structure is very uniform. The left-handedness of the passband can be verified by comparing the insertion phase difference between transmission lines having different lengths, as given by [28] ϕ = ϕ2 − ϕ1 =

Fig. 6. (a) Measured S21 magnitudes and (b) measured S21 phase of the 5-, 7-, and 9-cell transmission lines.

−ω × n(ω) × (l2 − l1 ) c

(2)

where ϕ1 and ϕ2 are the insertion phases, l1 and l2 the transmission line lengths, ω the radian frequency, c the speed of light in vacuum, and n(ω) the frequency dependent refractive index. In Fig. 6(b), the insertion phase of a longer transmission line is found to always be larger than that of a shorter line within the passband, thus indicating the negative refractive index within this region. In other words, the mushroom-type transmission lines exhibit left-handed behavior within this frequency band. It can also be seen in Fig. 6(b) that the difference of the total insertion phase between the 5- and the 7-cell transmission line or between the 7- and the 9-cell transmission line is nearly 2␲ at the lower end of the passband. This result is expected because the transmission line length difference is 2 unit-cells in either case.

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4.2. Circuit model extraction

Table 1 Extracted circuit model component values

The Agilent ADS circuit simulator is used to extract the circuit model of the mushroom structure. The ADS circuit model consists of two parts. The mushroom structures are represented by the cascade of unit-cell circuits shown in Fig. 2. The transitions at both ends are represented by regular lossy right-handed L–C networks, consisting of a series inductor, a series resistor, and a shunt capacitor. The strategy is then to look for the best match between the measured and the calculated Sparameters as we adjust the circuit model component values. The circuit model extraction is performed for the 5-, 7- and 9-cell transmission lines. Both S11 and S21 parameters, including magnitudes and phases, are perfectly matched between measured and ADS-simulated results. Due to limited space, Fig. 7 only shows the S21 results. For the purpose of clarity, phase comparison is presented only for 5-cell transmission lines in Fig. 7(b). The extracted component values are summarized in Table 1. The component values extracted from different trans-

Transmission lines

CL (pF)

LL (nH)

CR (pF)

LR (nH)

R ()

5-cell 7-cell 9-cell

0.069 0.062 0.063

0.024 0.028 0.026

0.108 0.098 0.108

0.071 0.080 0.077

2.43 2.68 2.87

mission lines are very close to each other. The results in Table 1 and Fig. 7 indicate that performance variations among different transmission lines are very little and our circuit model shown in Fig. 2 can represent the fabricated devices very well. The Bloch impedance ZB of the structure can be calculated by applying Bloch–Floquet periodic boundary condition on the circuit model. Fig. 8 shows the Bloch impedance calculated using component values extracted from the 5-cell transmission line. The maximum Bloch impedance is approximately 12  at the center of the LH passband. De-embedding is carried out by excluding the CPW to microstrip transitions. In order to reduce the reflection losses, input/output port impedance is matched with structure Bloch impedance, instead of using the standard value of 50 . The dashed lines in Fig. 7(a) show that the insertion losses of intrinsic mushroom transmission lines are actually very small. It can be seen that the loss per unit cell is approximately 1 dB, which is consistent with previous calculation. 4.3. Dispersion relationship Fig. 9 presents the dispersion characteristics of the mushroom-type transmission lines as calculated using HFSS eigen mode simulation and the circuit model. The HFSS unit cell dimensions are specified in Section 2. The dielectric constants of SU-8 2050 and SU-8 2005 are 3.3

Fig. 7. Comparison of simulated and measured S-parameters. (a) S21 magnitude of the 5-, 7-, and 9-cell transmission lines. (b) S21 phase of the 5-cell transmission line.

Fig. 8. Bloch impedance calculated from extracted circuit model.

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Fig. 9. Dispersion curves obtained from HFSS simulation and ADS circuit model. The structure period, d = 252 ␮m.

and 4.4, respectively. Circuit model component values are taken from the 5-cell transmission line in Table 1. The HFSS simulation curve is very close to the circuit model curve. Both curves clearly indicate that the mushroom-type transmission lines support backward waves (left-handed mode) with anti-parallel group velocity vg (= ∂ω/∂β) and phase velocity vp (= ω/β). The HFSS curve is comprised of both right-handed and left-handed aspects. At low frequencies, a righthanded air mode (dashed line) exists above the surface of the mushroom structure and has a free-space propagation constant β (= ω/c). When the frequency increases above the cut-off frequency (∼45 GHz in Fig. 9), a lefthanded backward mode is also supported, but inside the mushroom structure. When the frequency increases to the point where the air mode and the backward mode have equal phase velocity, these two modes begin to couple with each other and result in a stopband above the left-handed passband [22]. The dispersion curve calculated using ADS model, however, does not show the existence of any air mode. This is because the circuit model shown in Fig. 2 does not take into account this air mode. However, a distinct stopband below the cutoff frequency (Fig. 6) clearly indicates that the air mode is not strongly excited by the measurement system. Thus, the circuit model shown in Fig. 2 is a very good approximation of the fabricated mushroom structure.

caps, which can be achieved by employing smaller (or even removal of) patches, by increasing the gap between adjacent caps, or by increasing the distance between the patch and cap layers. A smaller LL can be obtained by employing shorter posts with wider diameters. From a fabrication point of view, all of the above mentioned measures result in easier processes with relaxed fabrication requirements. Thus, mushroom structures are very suitable for high frequency applications. As a demonstration, we have designed and fabricated mushroom-type left-handed transmission lines working at 100 GHz. Whereas operating frequencies are increased, the fabrication difficulties are not. To achieve higher operating frequencies, the patch layer is removed so that the coupling between the caps is significantly reduced. The process is greatly simplified in that not only is the patch layer excluded, but also the thin dielectric layer. The structure dimensions are as follows: the cap size, C × C, is 222 ␮m × 222 ␮m; the gap between the adjacent caps, G, is 30 ␮m; the post is 22 ␮m in diameter and 228 ␮m in height. We intentionally increase the post height in order to lower the operating frequencies to a range compatible with our measurement capability. Considering that the unit-cell sizes in current designs are quit large, the operating frequencies can be easily boosted to several hundred GHz by further reducing the structure sizes. Transmission lines with 5, 7, and 9 cells are characterized. For the purpose of clarity, Fig. 10 only shows the measured S21 magnitude and phase of a 9-cell line. The left-handed region starts at 78 GHz and exists until beyond 100 GHz. The insertion loss of this structure is higher than that of the structure presented in previous section, mainly due to very tall metal posts (228 ␮m) and very high working frequencies. The loss per unit cell of this structure is approximately 1.5 dB.

5. Advanced structures 5.1. Towards higher operating frequencies Qualitatively speaking, a high-frequency left-handed passband can be reached by reducing the left-handed component values, CL and LL . For mushroom structures, a smaller CL means weak coupling between the

Fig. 10. S21 magnitude and phase of a 9-cell transmission line working at 100 GHz.

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5.2. Towards higher dimensions The fabrication method used for the above described 1-D structures can be directly used to construct 2-D structures without any modification. Fig. 11(a) shows a plan view of a 2-D mushroom structure with 9 × 9 unit cells. There are five sets of probe pads on each side. Fig. 11(b) shows a close-up view of the structure. The patches (dark) beneath the caps are outlined by dashed squares. The arrangement of the patches is adopted from [21]. The unit-cell equivalent circuit of the 2-D structure is shown in Fig. 12, where the structure is assumed to be perfectly isotropic in x and y directions. However, at edges and corners, the circuit model has to be modified accordingly.

Fig. 12. Equivalent circuit of the unit cell of 2-D mushroom structure.

Fig. 13 shows the transmission characteristics between input port 1 and output port 2, 3, and 4, respectively. ADS simulation for the transmission between the two central ports (1 and 2) is also presented for comparison.

Fig. 11. (a) A plan view and (b) a close-up view of a 2-D mushroom structure. C = 217 ␮m; G = 37 ␮m; P = 130 ␮m; S = 50 ␮m.

Fig. 13. (a) Measured and simulated S21 magnitude and phase. (b) Measured S31 and S41 magnitude.

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From Fig. 13(a), the measured and simulated S21 parameters agree well with each other within the passband. The circuit component values are extracted as follows: CL = 0.031 pF, LL = 0.039 nH, CR = 0.05 pF, LR = 0.146 nH, R = 7.44 . When the 2-D component values are compared with 1-D values in Table 1, one should avoid looking for a direct match, although the two structures have similar unit-cell sizes. As a rule of thumb, when the x and y branches in Fig. 12 merge, and corresponding components (i.e. R, LR , and CL ) are combined in parallel, the 2-D unit circuit becomes the 1-D unit circuit shown in Fig. 2. Consequently, 1-D CL is twice as large as 2-D CL and 1-D LR is only half of 2-D LR , which is exactly the case for our extracted component values. The series components CR and LL are related to the height of the posts. We employed higher posts in the 2-D structure. Consequently, LL is increased and CR is decreased, as compared to 1-D values. According to Fig. 13(a) and (b), a passband exists between 38 and 68 GHz. However, due to limited structure size, and hence the existence of boundaries at the upper and lower edges of the structure, the transmission characteristics at the center and at the edge are very different. When the output port is located near the edge, the transmission band is split into several distinct peaks, which originate from the internal resonances. The transmission between central ports is, however, less affected by the boundaries. This boundary effect is also verified through ADS simulation, in which S21 , S31 , and S41 are almost identical when the structure becomes much wider in the direction perpendicular to transmission. Finally, it is worth mentioning that having successfully implemented 2-D left-handed structures, a 3-D, bulky left-handed metamaterial can then be realized through a layer-by-layer construction. 6. Conclusion In conclusion, mushroom-type left-handed transmission lines are successfully fabricated using an optimized process. The left-handed response is demonstrated in a broad frequency band between 42 and 73 GHz. The microfabrication approach here opens the door to further reduce the structure dimensions, and consequently, increase operating frequencies. Furthermore, this approach can be easily extended to the fabrication of 2-D or even 3-D media, which would be more attractive for use in practical applications. Moreover, the incorporation of the nonlinear components into such structures will enable parametric generation, amplification and various other nonlinear phenomena to occur

[15,16], thus giving rise to novel active devices operating in microwave and THz frequency regions. Acknowledgments This work was supported by AFOSR through MURI program under grant no. F49620-03-1-0420. We thank Professor John H. Booske and Dr. Vladimir Joshkin for useful discussions on the early stage of the work and Alan D. Bettermann for assistance with manuscript preparation. References [1] V.G. Veselago, The electrodynamics of substances with simultaneously negative values of ε and μ, Sov. Phys. Usp. 10 (1968) 509–514. [2] D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, S. Schultz, Composite medium with simultaneously negative permeability and permittivity, Phys. Rev. Lett. 84 (2000) 4184– 4187. [3] M. Gokkavas, K. Guven, I. Bulu, K. Aydin, R.S. Penciu, M. Kafesaki, C.M. Soukoulis, E. Ozbay, Experimental demonstration of a left-handed metamaterial operating at 100 GHz, Phys. Rev. B 73 (2006) 193193. [4] W.J. Padilla, A.J. Taylor, C. Highstrete, M. Lee, R.D. Averitt, Dynamical electric and magnetic metamaterial response at terahertz frequencies, Phys. Rev. Lett. 96 (2006) 107401. [5] T.J. Yen, W.J. Padilla, N. Fang, D.C. Vier, D.R. Smith, J.B. Pendry, D.N. Basov, X. Zhang, Terahertz magnetic response from artificial materials, Science 303 (2004) 1494–1496. [6] C. Caloz, T. Itoh, Application of the transmission line theory of left-handed (LH) materials to the realization of a microstrip LH transmission line, IEEE AP-S Int. Symp. Dig. 2 (2002) 412–415. [7] A.K. Iyer, G.V. Eleftheriades, Negative refractive index metamaterials supporting 2-D waves, in: IEEE MTT-S International Microwave Symposium Digest, Seattle, WA, 2002, pp. 1067–1070. [8] A.A. Oliner, A periodic-structure negative-refractive-index medium without resonant elements, in: IEEE AP-S/URSI International Symposium Digest, San Antonio, TX, 2002, p. 41. [9] G.V. Eleftheriades, Analysis of bandwidth and loss in negativerefractive-index transmission-line (NRI-TL) media using coupled resonators, IEEE Microw. Wireless Compon. Lett. 17 (2007) 412–414. [10] A. Grbic, G.V. Eleftheriades, Overcoming the diffraction limit with a planar left-handed transmission-line lens, Phys. Rev. Lett. 92 (2004) 117403. [11] G.V. Eleftheriades, Enabling RF/microwave devices using negative-refractive-index Transmission-line metamaterials, Radio Sci. URSI Bull. 312 (2005) 57–69. [12] A. Lai, C. Caloz, T. Itoh, Composite right/left-handed transmission line metameterials, IEEE Microw. Mag. 5 (2004) 34–50. [13] C. Caloz, A. Sanada, T. Itoh, A novel composite right-/left-handed cupled-line directional coupler with arbitrary coupling level and broad bandwidth, IEEE Trans. Microw. Theory Tech. 52 (2004) 980–992. [14] C.A. Allen, K.M.K.H. Leong, T. Itoh, Design of microstrip resonators using balanced and unbalanced composite right/left-

C. Qin et al. / Metamaterials 2 (2008) 26–35

[15]

[16]

[17]

[18]

[19]

[20]

[21]

handed transmission lines, IEEE Trans. Microw. Theory Tech. 54 (2006) 3104–3112. A.B. Kozyrev, H. Kim, A. Karbassi, D.W. van der Weide, Wave propagation in nonlinear left-handed transmission line media, Appl. Phys. Lett. 87 (2005) 121109. A.B. Kozyrev, H. Kim, D.W. van der Weide, Parametric amplification in left-handed transmission line media, Appl. Phys. Lett. 88 (2006) 264101. F. Martin, J. Bonache, F. Falcone, M. Sorolla, R. Marques, Split ring resonator-based left-handed coplanar waveguide, Appl. Phys. Lett. 83 (2003) 4652–4654. T. Crepin, J.F. Lampin, M.F. Foulon, L. Desplanque, X. Melique, D. Lippens, Left handed CPS transmission lines at terahertz frequency, in: 2005 European Microwave Conference, vol. 2, 2005, 4 pp. C. Qin, A.B. Kozyrev, A. Karbassi, V. Joshkin, D.W. van der Weide, Microfabricated left-handed transmission line operating at 50 GHz, in: IEEE MTT-S International Microwave Symposium Digest, Honolulu, Hawaii, 2007, pp. 1145–1148. D. Sievenpiper, L. Zhang, R.F.J. Broas, N.G. Alexopolous, E. Yablonovitch, High-impedance electromagnetic surfaces with a forbidden frequency band, IEEE Trans. Microw. Theory Tech. 47 (1999) 2059–2074. A. Sanada, C. Caloz, T. Itoh, Planar distributed structures with negative refractive index, IEEE Trans. Microw. Theory Tech. 52 (2004) 1252–1263.

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[22] A. Grbic, G.V. Eleftheriades, Dispersion analysis of a microstrip based negative refractive index periodic structure, IEEE Microw. Wireless Compon. Lett. 13 (2003) 155–157. [23] K. Jiang, M.J. Lancaster, I. Llamas-Garro, P. Jin, SU-8 Ka-band filter and its microfabrication, J. Micromech. Microeng. 15 (2005) 1522–1526. [24] Y. Cheng, C.-Y. Lin, D.-H. Wei, B. Loechel, G. Gruetzner, Wall profile of thick photoresist generated via contact printing, IEEE J. Microelectromech. Sys. 8 (1999) 8–26. [25] H. Lorenz, M. Despont, N. Fahrni, N. LaBianca, P. Renaud, P. Vettiger, SU-8: a low-cost negative resist for MEMS, J. Micromech. Microeng. 7 (1997) 121–124. [26] R. Osorio, M. Klein, H. Massler, J.G. Korvink, Micromachined strip line with SU-8 as the dielectric, in: Gallium Arsenide Applications Symposium, Munich, Germany, 2003, pp. 179– 182. [27] F.D. Mbairi, H. Hesselbom, High frequency design and characterization of SU-8 based conductor backed coplanar waveguide transmission lines, in: International Symposium on Advanced Packaging Materials: Processes, Properties and Interfaces, Irvine, CA, 2005, pp. 243–248. [28] O.F. Siddiqui, M. Mojahedi, G.V. Eleftheriades, Periodically loaded transmission line with effective negative refractive index and negative group velocity, IEEE Trans. Antennas Propag. 51 (2003) 2619–2625.