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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 8 — Apr. 22, 2013
  • pp: 9691–9702
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Multi-band metamaterial absorber based on the arrangement of donut-type resonators

Jin Woo Park, Pham Van Tuong, Joo Yull Rhee, Ki Won Kim, Won Ho Jang, Eun Ha Choi, Liang Yao Chen, and YoungPak Lee  »View Author Affiliations


Optics Express, Vol. 21, Issue 8, pp. 9691-9702 (2013)
http://dx.doi.org/10.1364/OE.21.009691


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Abstract

We propose multi-band metamaterial absorbers at microwave frequencies. The design, the analysis, the fabrication, and the measurement of the absorbers working in multiple bands are presented. The numerical simulations and the experiments in the microwave anechoic chamber were performed. The metamaterial absorbers consist of an delicate arrangement of donut-shape resonators with different sizes and a metallic background plane, separated by a dielectric. The near-perfect absorptions of dual, triple and quad peaks are persistent with polarization independence, and the effect of angle of incidence for both TE and TM modes was also elucidated. It was also found that the multiple-reflection theory was not suitable for explaining the absorption mechanism of our investigated structures. The results of this study are promising for the practical applications.

© 2013 OSA

1. Introduction

Metamaterials (MMs) are artificial, effectively homogeneous electromagnetic (EM) structures consisting of dielectrics and highly conducting metals, which are periodically arranged. The major advantage of MM over natural materials is that the unit-cell parameters can be tailored to have desired macroscopic properties. Although MMs started to get spotlight by fascinating the negative-refractive-index properties [1

1. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). [CrossRef] [PubMed]

, 2

2. D. Cheng, H. Chen, N. Zhang, J. Xie, and L. Deng, “Numerical study of a dualband negative index material with polarization independence in the middle infrared regime,” J. Opt. Soc. Am. B 30(1), 224–228 (2013). [CrossRef]

] in the beginning, the significance of concept of MMs is not restricted to only this [3

3. J. B. Pendry, “Perfect cylindrical lenses,” Opt. Express 11(7), 755–760 (2003). [CrossRef] [PubMed]

6

6. R. J. Singh, E. Plum, W. L. Zhang, and N. I. Zheludev, “Highly tunable optical activity in planar achiral terahertz metamaterials,” Opt. Express 18(13), 13425–13430 (2010). [CrossRef] [PubMed]

]. MMs are characterized by the electric permittivity ε(ω) and the magnetic permeability μ(ω), whose real and imaginary parts are adjusted to match the impedance of MM to that of free space, and to possess a large imaginary part of the refractive index to be qualified as MM absorber (MM-A) by engineering the structure and considering the material. Therefore, both transmission and reflection are minimized and a large loss results in [7

7. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). [CrossRef] [PubMed]

]. Obviously, the MM-A single-band high absorption is inapplicable in some areas. Therefore, the research on broadband or multi-band high-performance MM-A is necessary. Hence, it is not easy to combine multi-band MM-As with high efficiency, since the sensitive perfect absorption conditions are easy to be broken. Therefore, the achievement is still a significant issue in the MM-A researches. In spite of numerous studies, many issues remain to be explored, for example, to relax the working conditions and to increase the number of absorption peaks and the absorption bandwidth [8

8. P. V. Tuong, J. W. Park, V. D. Lam, K. W. Kim, H. Cheong, W. H. Jang, and Y. P. Lee, “Simplified perfect absorber structure,” Comput. Mater. Sci. 61, 243–247 (2012). [CrossRef]

24

24. D. V. Brazhnikov, A. V. Taichenachev, and V. I. Yudin, “Polarization method for controlling a sign of electromagnetically-induced transparency/absorption resonances,” Eur. Phys. J. D 63(3), 315–325 (2011). [CrossRef]

], as well as to switch the absorption properties [14

14. B. Zhu, Y. Feng, J. Zhao, C. Huang, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010). [CrossRef]

, 25

25. H. Y. Zheng, X. R. Jin, J. W. Park, Y. H. Lu, J. Y. Rhee, W. H. Jang, H. Cheong, and Y. P. Lee, “Tunable dual-band perfect absorbers based on extraordinary optical transmission and Fabry-Perot cavity resonance,” Opt. Express 20(21), 24002–24009 (2012). [CrossRef] [PubMed]

] from microwave to infrared frequencies, because of significant impact in the field of solar cells [26

26. J. N. Munday and H. A. Atwater, “Large integrated absorption enhancement in plasmonic solar cells by combining metallic gratings and antireflection coatings,” Nano Lett. 11(6), 2195–2201 (2011). [CrossRef] [PubMed]

], photodetectors [27

27. J. Rosenberg, R. V. Shenoi, T. E. Vandervelde, S. Krishna, and O. Painter, “A multispectral and polarization-selective surface-plasmon resonant midinfrared detector,” Appl. Phys. Lett. 95(16), 161101 (2009). [CrossRef]

], sensors [28

28. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010). [CrossRef] [PubMed]

], imaging devices [29

29. Y. Zhao, S. C. Lin, A. A. Nawaz, B. Kiraly, Q. Hao, Y. Liu, and T. J. Huang, “Beam bending via plasmonic lenses,” Opt. Express 18(22), 23458–23465 (2010). [CrossRef] [PubMed]

] and thermal emitters [30

30. M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79(3), 033101 (2009). [CrossRef]

].

There were several nice attempts to fabricate the MM-A with multiple bands and wide-range absorption peak. Shen et al. [10

10. X. Shen, T. J. Cui, J. Zhao, H. F. Ma, W. X. Jiang, and H. Li, “Polarization-independent wide-angle triple-band metamaterial absorber,” Opt. Express 19(10), 9401–9407 (2011). [CrossRef] [PubMed]

, 11

11. X. Shen, Y. Yang, Y. Zang, J. Gu, J. Han, W. Zhang, and T. J. Cui, “Triple-band terahertz metamaterial absorber: Design, experiment, and physical interpretation,” Appl. Phys. Lett. 101(15), 154102 (2012). [CrossRef]

] fabricated a polarization-insensitive, wide-angle, triple-band MM-A. Ding et al. [12

12. F. Ding, Y. Cui, X. Ge, Y. Jin, and S. He, “Ultra-broadband microwave metamaterial absorber,” Appl. Phys. Lett. 100(10), 103506 (2012). [CrossRef]

] prepared an ultrawide-band MM-A. To add new information in the area of MM-A, we suggest another design of multi-band MM-A which is composed of donut-type resonators. By the suitable arrangement and the proper parametric study, we achieve the absorption conditions for multi peaks which are even not sensitive to the polarization condition of incident EM wave. Both experiment and simulation were performed, and it is found that the results of simulation are in good accordance with those of experiment.

2. Simulation and experimental setup

The samples were fabricated by the conventional printed-circuit-board process with copper patterns (0.036 mm thick) on one side and the other side was backed by a copper layer with the same thickness and a size of 15 × 30 cm2. The substrate was FR4 with a thickness of 1.2 mm, and a dielectric constant of 4.3 and a dielectric loss tangent of 0.024. The lossy-metal model was used for copper with an electric conductivity of σ = 5.8 × 107 S/m. The reflection spectra (|S11|2) were measured in a microwave anechoic chamber using a Hewlett-Packard E8362B network analyzer connected to linearly-polarized microwave standard-gain horn antennas and calibrated by replacing the sample with a copper board of the same size as perfect reflector. Two horn antennas, which are 120 mm wide and 90 mm long, respectively, were used; one for illuminating the microwave beam on the sample and the other for receiving the reflected beam with an incident angle of 5° with a proper distance (sample to the middle point of two horn antennas: 2.0 m). By varying the incident angle of EM wave, not only the distance between sample and middle point of two horn antennas but also the tilting angle of two horn antennas were established properly for each case. A computational study was performed for the MM-A with a commercial program, CST MICROWAVE STUDIOTM. Unit-cell boundary conditions were used in x and y direction, and plane wave was incident downward on the MM-A with the electric field polarized along the y direction as the excitation source. Because the proposed structure is backed by a metallic sheet, the EM wave cannot transmit, and thereby the EM wave absorption is determined by A = 1 - |S11|2 - |S21|2 with |S21| = 0 where S11 and S21 are scattering parameters relevant to reflection and transmission, respectively.

3. Results and discussion

The schematic drawing of suggested MM-A is shown in Fig. 1(a)
Fig. 1 (a) Schematic of the proposed structure of MM-A. Photos of the fabricated samples with (b) 2 types and (c) 3 types of structure.
. The optimized pattern is composed of 3 donut-type structures which have different radii with a periodicity p = 25 mm. The radii (r1, r2 and r3) represent those for the outer circles of donuts. The optimum values for the radii come to be r1 = 5.0 mm, r2 = 4.7 mm and r3 = 4.5 mm, and the corresponding width is 1.8 mm for all. Although the size of unit cell is relatively large, the sizes of resonators, which determine the resonance frequency, are still suitable for deep sub-wavelength concept. We define 3-donut structures as donut 1, 2 and 3 in compliance with the same numbering for the radius. Each group of donuts are distinguished by virtue of position of the central point of donut, in other words, that of r1, r2 or r3 matches with the center, the corner or the middle of boundary line of the square unit cell, respectively. As shown in Figs. 1(b) and 1(c), 2 types of sample were fabricated for realization of 2 peaks (donuts 1 & 2) and 3 peaks (donuts 1, 2 & 3).

The aforementioned donut structures are added one by one to realize the multiple absorption bands. Figure 2
Fig. 2 (a) Simulated and (b) measured absorption spectra for the combinations of donuts.
presents progress of the combination at α = 0 where α is the angle between the y-axis and the electric field of incident radiation. In the simulation [Fig. 2(a)], we can clearly see triple absorption peaks at 6.5, 7.0 and 7.6 GHz with absorption of 99%, 98% and 99%, respectively. The experimental results also reveal multiple peaks at 6.51, 7.0 and 7.61 GHz with absorption of 98%, 98% and 98%, respectively, and any appreciable alteration by varying the polarization of EM wave was not detected [Fig. 2(b)]. It is confirmed that both simulation and experiment are in excellent coincidence. We might ascribe the minor difference between simulation and experiment to the imperfect fabrication. When donut 2 was positioned with donut 1 [Fig. 2(a)], the corresponding 2 peaks appear nearly independently. We kept adding donut 3 to the system of donuts 1 and 2 (Fig. 2). Because of little interaction between them, the slight peak shift was shown in progress of the combinations. As aforementioned, the absorption band is significantly narrower than that in [10

10. X. Shen, T. J. Cui, J. Zhao, H. F. Ma, W. X. Jiang, and H. Li, “Polarization-independent wide-angle triple-band metamaterial absorber,” Opt. Express 19(10), 9401–9407 (2011). [CrossRef] [PubMed]

, 11

11. X. Shen, Y. Yang, Y. Zang, J. Gu, J. Han, W. Zhang, and T. J. Cui, “Triple-band terahertz metamaterial absorber: Design, experiment, and physical interpretation,” Appl. Phys. Lett. 101(15), 154102 (2012). [CrossRef]

].

The expression of the absorption is A(w) = 1 – R(w) – T(w), where A(w), R(w) and T(w) are the absorption, the reflection, and the transmission as a function of frequency w, respectively. The frequency-dependent T(w) and R(w) are determined to be dependent on the complex index of refraction n(w)=ε(w)μ(w)=n1+in2 and the impedance z(w)=μ(w)/ε(w)=z1+iz2 . It is possible to absorb both the incident electric and magnetic fields remarkably by properly tuning ε(w)and ε(w) and to achieve perfect impedance matching with the free space [z(w)=μ(w)/ε(w)=1]. In [31

31. D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005). [CrossRef] [PubMed]

], the retrieved impedance equation is given as follow;

z(w)=(1+S11)2S212(1+S11)2+S212.
(1)

Previously, a theoretical interpretation based on interferences, among multiply reflected beams between two metallic layers, without considering the antiparallel arrangements of induced currents was proposed [11

11. X. Shen, Y. Yang, Y. Zang, J. Gu, J. Han, W. Zhang, and T. J. Cui, “Triple-band terahertz metamaterial absorber: Design, experiment, and physical interpretation,” Appl. Phys. Lett. 101(15), 154102 (2012). [CrossRef]

, 32

32. H. T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20(7), 7165–7172 (2012). [CrossRef] [PubMed]

]. To analyze the effect of interferences among the multiple-reflection beams between two metallic layers, we need 4 coefficients – 2 reflection coefficients (air-to-air and dielectric-to-dielectric), and the transmission coefficients (air-to-dielectric and dielectric-to-air) – and 4 phase shifts associated with the aforementioned coefficients. The rear metal plate functions as a reflector with reflection coefficient ~-1. According to the interference theory [11

11. X. Shen, Y. Yang, Y. Zang, J. Gu, J. Han, W. Zhang, and T. J. Cui, “Triple-band terahertz metamaterial absorber: Design, experiment, and physical interpretation,” Appl. Phys. Lett. 101(15), 154102 (2012). [CrossRef]

, 32

32. H. T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20(7), 7165–7172 (2012). [CrossRef] [PubMed]

], not only the phase difference but also the amplitude of the coefficients play the key role for absorption mechanism. To adopt the multiple-reflection theory for our structure and to exclude the magnetic resonance, we removed the rear metal plate from the structure of Fig. 1(a) (decoupled system) and investigated the reflection and the transmission coefficients because the magnetic resonance can be taken into account between the resonator array and the rear metal plate (coupled system). Differently from the results in [11

11. X. Shen, Y. Yang, Y. Zang, J. Gu, J. Han, W. Zhang, and T. J. Cui, “Triple-band terahertz metamaterial absorber: Design, experiment, and physical interpretation,” Appl. Phys. Lett. 101(15), 154102 (2012). [CrossRef]

], only a single dipole resonance of the array of donut resonators, as indicated by the deep transmission drop at 12.2 GHz [Fig. 4(b)
Fig. 4 (a) Schematic diagram for multiple-reflection theory with associated parameters. (b) Amplitude of the reflection and the transmission coefficients at the air-dielectric interference for the system of only resonator array and dielectric (decoupled model). (c) Normalized surface current distribution of the decoupled model at 12.2 GHz.
], was observed even though 3 kinds of metallic components were present. Distribution of the normalized induced current at a resonance frequency is presented in Fig. 4(c). It is shown that existence of the rear metal plate significantly affects the absorption mechanism of suggested MM-A. Therefore, we can safely argue that the multiple-reflection theory is not suitable for elucidation of the absorption mechanism of our structure.

Another schematic drawings of MM-A with 4 absorption peaks are shown in Fig. 5
Fig. 5 Schematics of the proposed structure of MM-A for quad peaks (left) and photos of the fabricated sample (right).
. The optimized pattern is composed of 4 donut-type structures which have different radii with a periodicity p = 16 mm. The radii (r1 ~r4) represent those for the outer circles of donuts. The optimum values for the radii come to be r1 = 4.5 mm, r2 = 4.0 mm, r3 = 3.5 mm and r4 = 3.0 mm, and the corresponding widths are w1 = w2 = 0.5 mm and w3 = w4 = 1.0 mm, and the sizes of resonators are still in the range that the MM concept is still applicable. As previously started, we define 4-donut structures as donut 1 ~donut 4 in compliance with the same numbering set of radii and widths.

The black dotted data in Fig. 6
Fig. 6 (a) Simulated and (b) measured absorption spectra of quad-peak MM-A according to polarization.
show the simulated [Fig. 6(a)] and the measured [Fig. 6(b)] absorption spectra with α = 0, where α is the angle between the y-axis and the electric field of incident radiation. In the simulation, we can clearly see four absorption peaks at 6.45, 7.4, 9.1 and 11.0 GHz with absorption of 97%, 98%, 98% and 98%, respectively. The experimental results also present multiple peaks at 6.5, 7.4, 9.2 and 11.0 GHz with absorption of 97%, 97%, 98% and 98%, respectively, which indicates that both simulation and experiment are in excellent coincidence. We might ascribe the minor difference between simulation and experiment to the imperfect fabrication which can lead to, for instance, the minute disparity in the width of ring. Compared with [10

10. X. Shen, T. J. Cui, J. Zhao, H. F. Ma, W. X. Jiang, and H. Li, “Polarization-independent wide-angle triple-band metamaterial absorber,” Opt. Express 19(10), 9401–9407 (2011). [CrossRef] [PubMed]

], the realized absorption peaks are relatively concentrated in a certain frequency range with more number of bands. Any appreciable alternation by varying the polarization of EM wave was not detected, as shown in Fig. 6.

The coupling effect was also noticed, which has space dependence between each resonator. To understand the effect of coupling between the element at the center of unit cell and that at the corner, we simulated the absorption spectra by varying the periodicity. The results were presented in Fig. 8
Fig. 8 (a) Unit cell only with donuts 1 and 2. (b) Absorption spectra for 2 different p's. (c) and (d) Normalized surface current distributions at low-frequency peak.
, based on donuts 1 and 2 only. As in Fig. 8(b), for p = 16 mm 2 peaks appear to be independent, similarly to the data for donuts 1 & 2 in Fig. 8(b). When both structures become closer (p = 14 mm), however, not only the absorption but also the resonance frequency are changed, similar to the case of [35

35. P. Ding, E. J. Liang, L. Zhang, Q. Zhou, and Y. X. Yuan, “Antisymmetric resonant mode and negative refraction in double-ring resonators under normal-to-plane incidence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(1), 016604 (2009). [CrossRef] [PubMed]

]. It means that the MM-A does not have the ideal effective parameters any more for the free-space impedance matching at a certain frequency, even each though individual resonator can perform high absorption. For better understanding, the surface-current distributions were obtained when the central structure was highly excited. Although the main contribution to the low-frequency peak comes from donut 1 due to the larger radius, we are able to detect clearly the surface current of donut 2 induced by donut 1, because of the closeness [Fig. 8(c)]. By increasing the separation between them, the interaction is diminished and the pure resonant mode of each structure appears. If p is outsized to avoid this coupling effect, the periodicity of inner-positioned elements (donuts 3 and 4) is influenced and, in turn, the high multiple absorption peaks are not realized. Therefore, the controlling space between each element should be tuned carefully when the MM-A is designed.

Finally, we examine the dependence of absorption on the incident angle. Figures 9(a)
Fig. 9 Dependence of the simulated absorption spectra on incident angle for (a) TE mode and (b) TM mode. (c) The corresponding measured absorption spectra for TE mode.
and 9(b) display the dependence of the simulated absorption spectra for the TE and the TM polarizations, respectively. We also measured the dependence for the TE polarization [see Fig. 9(c)]. Due to the experimental limitation, that is, not only fixation of the polarization but also uncontrollable tilting up or down of the receiving horn antenna, we were unable to measure the dependence for the TM polarization. The experimental results agree well with the simulations for the TE polarization. It is evident that the absorption is nearly independent of the incident angle up to 45°. This can be explained by the fact that the position of magnetic-resonance peak is not changed much by increasing the angle of incidence [34

34. J. W. Park, X. R. Jin, P. V. Tuong, J. Y. Rhee, K. W. Kim, D. Kim, and Y. P. Lee, “Magnetic resonance of a highly symmetric metamaterial at microwave frequency,” Phys. Status Solidi B. 249(4), 858–861 (2012). [CrossRef]

]. In the TM mode, minor shifts of the absorption peaks were observed. As the contact area of copper layer by the electric field decreases upon increasing the angle of incidence, it is rather difficult to drive the magnetic resonance. Therefore, the resonance frequency changes slightly, resulting in more change of absorption [34

34. J. W. Park, X. R. Jin, P. V. Tuong, J. Y. Rhee, K. W. Kim, D. Kim, and Y. P. Lee, “Magnetic resonance of a highly symmetric metamaterial at microwave frequency,” Phys. Status Solidi B. 249(4), 858–861 (2012). [CrossRef]

]. Although the suggested parametric conditions of MM-A were selected because of the experimental limitation, if the proportion between the width of donuts and the thickness of FR4 is adjusted carefully, more stable absorption properties would be achieved. In addition, the suggested MM-A can be realized even in the optical range by scaling down.

4. Conclusions

Acknowledgments

This work was supported by the ICT Standardization program of KCC, by the Korean Ministry of Science, ICT and Future Planning though the KCA, the Priority Research Center Program through the National Research Foundation (NRF) funded by the Korean Ministry of Education Science and Technology (MEST) (2011-0031392), MEST and PAL, Korea, and the NRF funded by the MEST (Nos. 2010-0029418, 2010-0025306 and 2012K1A2B2A07033424).

References and links

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2.

D. Cheng, H. Chen, N. Zhang, J. Xie, and L. Deng, “Numerical study of a dualband negative index material with polarization independence in the middle infrared regime,” J. Opt. Soc. Am. B 30(1), 224–228 (2013). [CrossRef]

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7.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). [CrossRef] [PubMed]

8.

P. V. Tuong, J. W. Park, V. D. Lam, K. W. Kim, H. Cheong, W. H. Jang, and Y. P. Lee, “Simplified perfect absorber structure,” Comput. Mater. Sci. 61, 243–247 (2012). [CrossRef]

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D. V. Brazhnikov, A. V. Taichenachev, and V. I. Yudin, “Polarization method for controlling a sign of electromagnetically-induced transparency/absorption resonances,” Eur. Phys. J. D 63(3), 315–325 (2011). [CrossRef]

25.

H. Y. Zheng, X. R. Jin, J. W. Park, Y. H. Lu, J. Y. Rhee, W. H. Jang, H. Cheong, and Y. P. Lee, “Tunable dual-band perfect absorbers based on extraordinary optical transmission and Fabry-Perot cavity resonance,” Opt. Express 20(21), 24002–24009 (2012). [CrossRef] [PubMed]

26.

J. N. Munday and H. A. Atwater, “Large integrated absorption enhancement in plasmonic solar cells by combining metallic gratings and antireflection coatings,” Nano Lett. 11(6), 2195–2201 (2011). [CrossRef] [PubMed]

27.

J. Rosenberg, R. V. Shenoi, T. E. Vandervelde, S. Krishna, and O. Painter, “A multispectral and polarization-selective surface-plasmon resonant midinfrared detector,” Appl. Phys. Lett. 95(16), 161101 (2009). [CrossRef]

28.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010). [CrossRef] [PubMed]

29.

Y. Zhao, S. C. Lin, A. A. Nawaz, B. Kiraly, Q. Hao, Y. Liu, and T. J. Huang, “Beam bending via plasmonic lenses,” Opt. Express 18(22), 23458–23465 (2010). [CrossRef] [PubMed]

30.

M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79(3), 033101 (2009). [CrossRef]

31.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005). [CrossRef] [PubMed]

32.

H. T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20(7), 7165–7172 (2012). [CrossRef] [PubMed]

33.

Y. Q. Ye, Y. Jin, and S. He, “Omnidirectional, polarization-insensitive and broadband thin absorber in terahertz regime,” J. Opt. Soc. Am. B 27(3), 498–504 (2010). [CrossRef]

34.

J. W. Park, X. R. Jin, P. V. Tuong, J. Y. Rhee, K. W. Kim, D. Kim, and Y. P. Lee, “Magnetic resonance of a highly symmetric metamaterial at microwave frequency,” Phys. Status Solidi B. 249(4), 858–861 (2012). [CrossRef]

35.

P. Ding, E. J. Liang, L. Zhang, Q. Zhou, and Y. X. Yuan, “Antisymmetric resonant mode and negative refraction in double-ring resonators under normal-to-plane incidence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(1), 016604 (2009). [CrossRef] [PubMed]

36.

Z. G. Dong, M. X. Xu, S. Y. Lei, H. Liu, T. Li, F. M. Wang, and S. N. Zhu, “Negative refraction with magnetic resonance in a metallic double-ring metamaterial,” Appl. Phys. Lett. 92(6), 064101 (2008). [CrossRef]

OCIS Codes
(260.5740) Physical optics : Resonance
(160.3918) Materials : Metamaterials
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:
Metamaterials

History
Original Manuscript: January 9, 2013
Revised Manuscript: March 16, 2013
Manuscript Accepted: April 2, 2013
Published: April 11, 2013

Citation
Jin Woo Park, Pham Van Tuong, Joo Yull Rhee, Ki Won Kim, Won Ho Jang, Eun Ha Choi, Liang Yao Chen, and YoungPak Lee, "Multi-band metamaterial absorber based on the arrangement of donut-type resonators," Opt. Express 21, 9691-9702 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-8-9691


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  30. M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B79(3), 033101 (2009). [CrossRef]
  31. D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(33 Pt 2B), 036617 (2005). [CrossRef] [PubMed]
  32. H. T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express20(7), 7165–7172 (2012). [CrossRef] [PubMed]
  33. Y. Q. Ye, Y. Jin, and S. He, “Omnidirectional, polarization-insensitive and broadband thin absorber in terahertz regime,” J. Opt. Soc. Am. B27(3), 498–504 (2010). [CrossRef]
  34. J. W. Park, X. R. Jin, P. V. Tuong, J. Y. Rhee, K. W. Kim, D. Kim, and Y. P. Lee, “Magnetic resonance of a highly symmetric metamaterial at microwave frequency,” Phys. Status Solidi B.249(4), 858–861 (2012). [CrossRef]
  35. P. Ding, E. J. Liang, L. Zhang, Q. Zhou, and Y. X. Yuan, “Antisymmetric resonant mode and negative refraction in double-ring resonators under normal-to-plane incidence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.79(1), 016604 (2009). [CrossRef] [PubMed]
  36. Z. G. Dong, M. X. Xu, S. Y. Lei, H. Liu, T. Li, F. M. Wang, and S. N. Zhu, “Negative refraction with magnetic resonance in a metallic double-ring metamaterial,” Appl. Phys. Lett.92(6), 064101 (2008). [CrossRef]

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