Open Access
Add to BibSonomy
Abstract
In this paper, a hierarchical metamaterial (HMM) is reported to achieve compatible camouflage for laser, thermal infrared detectors, and radar. The HMM consists of an all-metallic metasurface array (AMMA) integrated with a microwave absorber. The top AMMA plays two roles. First, the gradient metasurface can reduce the specular reflection at the laser wavelength of 1.06 µm to less than 5% by tailoring the wavefronts and redirecting the reflected energy to non-specular angles. Second, the AMMA acts as an infrared shielding and microwave transparent layer, ultralow surface emissivity (∼5%) in the infrared atmosphere window of 3-5 µm and 8-14 µm can be realized, and incident microwave can perfectly pass through the top AMMA and then be absorbed by the bottom microwave absorber. The absorption efficiency is over 90% in the broadband of 7-12.7 GHz up to incident angles of 40° for both TE and TM polarizations. These excellent performances indicate that our proposed HMM has promising applications in multispectral camouflage fields.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Many efforts have been devoted to developing multispectral compatible camouflage technique [1,2], which is always a challenge and pursuit in electromagnetic applications. As to radar and laser camouflage materials, they need high absorptance and low reflectance, since microwave and laser detectors are working on active mode. In contrast, materials with low infrared emissivity are expected to camouflage against infrared detector, which means low absorptance and high reflectance is required for infrared invisibility based on Kirchhoff’s law [3]. Intuitively, it seems impossible to find materials that satisfy these conflicting parametric requirements simultaneously.
During the past decade, metamaterials have been widely studied due to their outstanding capacities in manipulating electromagnetic waves [4–6]. Metamaterial absorbers have attracted a growing attention in radar camouflage technology [7–10]. Through the near perfect absorption of incident microwave, the radar cross section can be dramatically reduced. Several metamaterial-based structures have been proposed to realize radar-infrared compatible camouflage [11–15]. The core idea to achieve the compatible camouflage is to cover a broadband microwave absorber with an infrared shielding and microwave transparent layer. Metamaterial absorbers are also used for achieving laser-infrared compatible stealth by designing narrow working band around the laser wavelengths [16]. Nevertheless, this approach has limited performance and cannot cope with laser detector with tunable frequency. As a two-dimensional version of metamaterial, metasurfaces provide another promising approach to realize invisibility [17–19]. By introducing phase mutation at the interface of two kinds of media to realize local clipping of surface electromagnetic response at the subwavelength scale, metasurfaces can achieve arbitrary control of light wavefronts [20–25]. Recently, all-metallic metasurfaces are presented to reduce both the specular reflection and infrared emissivity, resulting in simultaneous radar-infrared or laser-infrared invisibility [26,27]. As far as we know, there is still no relevant report about simultaneous laser, thermal infrared detectors and radar camouflage based on metamaterials.
In this paper, we present a strategy to achieve compatible camouflage for 1.06 µm laser, thermal infrared detectors and radar by using a hierarchical metamaterial (HMM) consisting of an all-metallic metasurface array (AMMA) integrated with a microwave absorber. The simulated results indicate that the top AMMA can contribute to both ultralow surface emissivity (<5%) in 3-14 µm and ultralow specular reflectivity (<5%) at 1.06 µm. Besides, the bottom absorber can realize wideband absorption from 7 to 12.7 GHz with attenuation efficiency larger than 90% up to incident angles of 40° for both TE and TM polarizations.
2. Design and results
A schematic of our proposed HMM is depicted in Fig. 1. On top of the HMM is an AMMA, which is composed of periodically arranged all-metallic phase gradient metasurfaces. The AMMA plays a dual role here. First, it can guide backscattered waves to four non-specular directions at the laser wavelength of 1.06 µm to suppress the echo signal. Second, the AMMA serves as an infrared shielding layer (ISL) with high transmittance at microwave band. Gold (Au) is chosen as the material of AMMA to realize high reflectance in the infrared regime. Periodic arrangement of micrometer-scale slit in the AMMA make it possible that the incident microwave can pass through the metasurface and then be absorbed by the bottom absorber. The other parts under the AMMA, including resistive sheets embedded in two FR4 spacers, which is used as microwave absorption layer, and copper ground.
Fig. 1. Schematic of a unit cell of the proposed HMM, showing the incident microwave, reflected infrared wave, and the electromagnetic scattering of incident laser in the upper half-space.
According to the generalized Snell’s law [25,28], abnormal reflection will occur by introducing abrupt changes of phase. The AMMA is used to redirect the reflected laser beams to other directions to suppress the specular reflection. The two basic unit cells of the AMMA are shown in Figs. 2(a) and 2(b). Unit cell I is a gold plate whose thickness is t = 0.2 µm, and the period is Λ = 0.8 µm. Unit cell II consists of a gold cube placed on a gold plate with the same thickness and period as unit cell I. The geometry parameters of the gold cube are d = 0.64 µm and h = 0.22 µm. Numerical simulations were conducted using commercial software CST Microwave Studio. The simulations are performed in frequency domain solver, unit cell boundary is applied in both x and y directions and open boundary is adopted in z direction, the minimal mesh is set to be λ/10, the permittivity of gold is from Ref. [29]. Because of their four-fold geometrical symmetry, the unit cells are insensitive to the polarization states of incident waves. Here, Floquet port with TE or TM mode (y or x polarization) is adopted. The simulated reflection phase of the two unit cells, as well as relative phase difference (ΔΦ = Φ2 - Φ1, where Φ1 and Φ2 are the reflection phases of unit cell I and unit cell II, respectively) between them are presented in Fig. 2(c). Figure 2(d) shows the wavelength dependence of the reflectance. One can see that ΔΦ is about π from 0.8 to 1.2 µm, and the corresponding reflectance is higher than 90% for both unit cells.
Fig. 2. Design of the unit cells. Three-dimensional schematic of the (a) unit cell I and (b) unit cell II. (c) Simulated reflection phases of the two unit cells, as well as relative phase difference between unit cell I and unit cell II. (d) Simulated reflectance of the two unit cells.
In the following, we focus on the full model design. As shown in Fig. 3(a), the chessboard-like metasurface consists of 2×2 intertwined supercells, and the two supercells are composed of two 3×3 arrays of the unit cell I and unit cell II, respectively. For this chessboard-like configuration, the reflection field direction (θ, φ) can be calculated by [30–32]
where λ is the wavelength of incident light, dx = dy = 2.4 µm are the dimensions of the supercell along the x- and y-axis. According to Eq. (1), φ = ±45° can be obtained, which indicates that the reflected energy is mainly concentrated on the 45° and 135° plane. The elevation angles are calculated to be θ = ±18.2° for incident wavelength of 1.06 µm. Therefore, the power reflected in specular direction can be dramatically reduced. Numerical calculations are performed to validate the performance of the metasurface. A subgroup containing 2×2 supercells [dashed box in Fig. 3(a), p = 2dx = 2dy = 4.8 µm] is simulated in time domain solver with periodic boundary in both x- and y-axis and open boundary in z-axis, a plane wave with x polarization propagating along the negative z-axis is used as the excitation. Far-field monitors at different frequencies are set to obtain the specular reflectance and far field scattering patterns. The simulated specular reflectance spectra of the metasurface and a gold plate are shown in Fig. 3(b), from which we can see that the reflectance of the metasurface is less than 0.05 from 0.8 to 1.2 µm. In comparison, the unpatterned gold plate has much higher specular reflectance. The three-dimensional far field scattering pattern at 1.06 µm is illustrated in Fig. 3(c). As described theoretically, the reflected energy is spilt into four diagonal directions in the 45° and 135° plane (φ = ±45°). The scattering pattern at φ = 45° (or 135°) plane is shown in Fig. 3(d). It is evident that the reflection elevation angles are θ = ±18°, which are in good agreement with the theoretical calculations, and the specular (θ = 0°) reflectance is near to zero. The above results confirm that the metasurface can realize remarkable reduction of laser radar cross section.Fig. 3. Numerical simulation results of the all-metallic gradient metasurface. (a) Front view of the designed metasurface containing periodically arranged subgroups. (b) Simulated specular reflectance spectra of the metasurface and a gold plate from 0.8 to 1.2 µm. (c) Three-dimensional far field scattering patterns of the metasurface at 1.06 µm. (d) Scattering pattern of the metasurface on φ = 45° plane at 1.06 µm.
As we mentioned previously, the AMMA is composed of periodically arranged all-metallic metasurfaces, which also serves as an ISL with high transmittance at microwave band. The infrared emissivity of the AMMA can be evaluated approximately by an empirical formula [13,14]
where εm is the emissivity of the metallic structure, εf = 0.955 is the emissivity of FR-4 in wavelengths ranging from 3 to 14 µm [14,33], t is the filling ratio of the metal parts in AMMA. The schematic of the AMMA is shown in Fig. 4(a), where the period is p1 = 121 µm, and the size of metal part is d1 = 120 µm. Thus, the filling ratio t can be calculated as 98.35%. In order to characterize the emissivity of the metallic structure (εm) accurately, full-wave simulations are performed in frequency domain solver, as illustrated in Fig. 4(b). For comparison, a pure Au plate without the metallic cubes is also simulated. We find there is a sharp absorption at about 3.4 µm for the metasurface, which is originated from the grating mode [34]. Because the absorption band is ultra-narrow, the metasurfac can still remain ultralow emissivity in the whole infrared atmosphere window. The average absorptivity/emissivity in 3-5 µm, 8-14 µm, and 3-14 µm is calculated to be 0.041, 0.023, and 0.033. Finally, according to Eq. (3), the average surface infrared emissivity of HMM is calculated to be 0.056, 0.039, and 0.048. In addition, microwave can pass through the AMMA. Because the height of the metallic cubes in the metasurface is on the order of micrometer, for the electromagnetic wave whose wavelength is on the order of centimeter, the AMMA can be equivalent to metallic patch array without the cubes [Fig. 4(c)], which acts as a capacitive frequency selective surface and is transparent to incident microwave. In order to verify this performance, a simulation is performed as shown in Fig. 4(d), from which one can see that the AMMA and metallic patch array have equal transmittance of near 100% in 5-20 GHz.Fig. 4. (a) Schematic of the AMMA. (b) Simulated absorptance/emissivity of the all-metallic metasurface and metallic plate in 3-14 µm. (c) Schematic of the patch array without the metallic cubes. (d) Simulated transmittance and reflectance of the AMMA and metallic patch array in the microwave range.
In the following, we simulate the microwave absorption performance of the HMM. As depicted in Fig. 5(a), different from Fig. 1, here the metallic cubes in the AMMA are neglected. Because there are 72 million metallic cubes located on the patch array (80 × 80 = 6400 patches) in a unit cell of the absorber, numerical calculations cannot be performed owing to our computer's computing power limitation if the metallic cubes are considered. Therefore, here we use the patch array without metallic cubes in the simulations, which is reasonable from the discussion for Fig. 4(d). Under the metallic patch array, periodic resistive sheet array with high impedance is used as the microwave absorption layer, two FR4 substrates are employed as the spacers to support the patch array and resistive sheets, and the copper ground provides a zero transmittance. We should note that this is a simple and common method for design of microwave absorbers [13–15]. The total thickness of the absorber is 3.517 mm, where the thickness of upper metal layer is 0.2 µm, the thickness of FR4 above and below the resistive sheets are t1 = 2 mm and t2 = 1.5 mm, respectively, and the thickness of copper layer is 15 µm. In the simulations, we set the material type of resistive sheets as an ohmic sheet with the resistance of 34 ohm/sq, which means one can use resistive film materials with same sheet resistance in the actual processing, such as nichrome, carbon, indium tin oxide (ITO) and so on. The FR4 has a relative permittivity of 4.4 and a loss tangent of 0.02. The front view of the resistive sheet layer is shown in Fig. 5(b), where the width d2 and period p2 are 6.5 mm and 9.68 mm, respectively. The simulations are performed in frequency domain solver and adaptive mesh refinement is used in the calculations. Figs. 5(c) and 5(d) illustrate the absorption spectra of the microwave absorber under different incidence angles for TE and TM polarizations. For TE mode, the absorptance remains higher than 90% in 6.5-13.4 GHz for all the incidence angles. For TM mode, when the incidence angle increases, the absorption bandwidth begins to decrease, while the microwave absorber still keep high absorptance above 90% between 7 and 12.7 GHz even under 40° oblique incidence. In order to further understand the absorption mechanism, the electric field, magnetic field and power loss density distributions at two resonant frequency of 7.5 GHz and 11.4 GHz are provided. As shown in Figs. 6(a) and 6(b), the electric fields are primarily concentrated on both the top and bottom sides of the resistive sheets, which produces capacitance. The intensity of the electric fields would follow a catenary curve, as indicated in the catenary electromagnetic theory [35,36]. As can be seen in Figs. 6(c) and 6(d), the magnetic fields are primarily focused on both the left and right sides of the resistive sheets, which produces inductance. Based on the equivalent circuit theory, the resonance absorption at the two resonant frequencies can be achieved [13,37]. From Figs. 6(e) and 6(f), one can see that the power loss of the incident microwave is mainly originating from the resistive sheets. These discussions demonstrate that the broadband absorption is attributed to the ohmic loss of the resistive sheets [38].
Fig. 5. (a) Unit cell of the microwave absorber, the total thickness is 3.517 mm (t1 = 2 mm, t2 = 1.5 mm, the thickness of gold and copper are 0.2 µm and 15 µm, respectively. (b) Front view of the resistive sheet layer, where p2 = 9.68 mm, d2 = 6.5 mm. (c)(d) Simulated absorption spectra under different incident angles in x-z plane for TE and TM polarizations, respectively.
Fig. 6. Simulated absorption characteristics of the microwave absorber. (a)(b) Electric field distributions at two absorptive peaks of 7.5 GHz and 11.4 GHz, respectively. (c)(d) Magnetic field distributions at two absorptive peaks of 7.5 GHz and 11.4 GHz, respectively. (e)(f) Power loss density distributions at two absorptive peaks of 7.5 GHz and 11.4 GHz, respectively.
3. Conclusion
In conclusion, we have demonstrated a HMM which can realize compatible camouflage for 1.06 µm laser, thermal infrared detectors and radar. The HMM consists of an AMMA integrated with a microwave absorber. The AMMA is composed of periodically arranged all-metallic gradient metasurfaces, which are utilized to reduce the specular reflection at the laser wavelength of 1.06 µm to less than 5%. The broadband specular reflection reduction in 0.8-1.2 µm is also demonstrated. In addition, the AMMA also serves as an ISL with high transmittance at microwave band. The microwaves in 7-12.7 GHz can pass through the AMMA and then be absorbed by the bottom microwave absorber with attenuation efficiency larger than 90% for both TE and TM polarizations even under 40° oblique incidences. These results indicate that our presented HMM is a good candidate for multispectral camouflage against three main detection technologies.
Funding
National Natural Science Foundation of China (61975210).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References
1. D. Qi, Y. Cheng, X. Wang, F. Wang, B. Li, and R. Gong, “Multi-layer composite structure covered polytetrafluoroethylene for visible-infrared-radar spectral Compatibility,” J. Phys. D: Appl. Phys. 50(50), 505108 (2017). [CrossRef]
2. T. Wang, J. He, J. Zhou, X. Ding, J. Zhao, S. Wu, and Y. Guo, “Electromagnetic wave absorption and infrared camouflage of ordered mesoporous carbon–alumina nanocomposites,” Microporous Mesoporous Mater. 134(1–3), 58–64 (2010). [CrossRef]
3. J.-J. Greffet and M. Nieto-Vesperinas, “Field theory for generalized bidirectional reflectivity: derivation of Helmholtz’s reciprocity principle and Kirchhoff’s law,” J. Opt. Soc. Am. A 15(10), 2735–2744 (1998). [CrossRef]
4. X. Luo, “Subwavelength Artificial Structures: Opening a New Era for Engineering Optics,” Adv. Mater. 31(4), 1804680 (2019). [CrossRef]
5. L. R. Meza, A. J. Zelhofer, N. Clarke, A. J. Mateos, D. M. Kochmann, and J. R. Greer, “Resilient 3D hierarchical architected metamaterials,” Proc. Natl. Acad. Sci. 112(37), 11502–11507 (2015). [CrossRef]
6. X. Zheng, W. Smith, J. Jackson, B. Moran, H. Cui, D. Chen, J. Ye, N. Fang, N. Rodriguez, and T. Weisgraber, “Multiscale metallic metamaterials,” Nat. Mater. 15(10), 1100–1106 (2016). [CrossRef]
7. T. Jang, H. Youn, Y. J. Shin, and L. J. Guo, “Transparent and flexible polarization-independent microwave broadband absorber,” ACS Photonics 1(3), 279–284 (2014). [CrossRef]
8. C. M. Watts, X. Liu, and W. J. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. 24(23), OP98–OP120 (2012). [CrossRef]
9. J. Zou, P. Yu, W. Wang, X. Tong, L. Chang, C. Wu, W. Du, H. Ji, Y. Huang, and X. Niu, “Broadband mid-infrared perfect absorber using fractal Gosper curve,” J. Phys. D: Appl. Phys. 53(10), 105106 (2020). [CrossRef]
10. P. Yu, L. V. Besteiro, Y. Huang, J. Wu, L. Fu, H. H. Tan, C. Jagadish, G. P. Wiederrecht, A. O. Govorov, and Z. Wang, “Broadband metamaterial absorbers,” Adv. Opt. Mater. 7(3), 1800995 (2019). [CrossRef]
11. S. Zhong, W. Jiang, P. Xu, T. Liu, J. Huang, and Y. Ma, “A radar-infrared bi-stealth structure based on metasurfaces,” Appl. Phys. Lett. 110(6), 063502 (2017). [CrossRef]
12. C. Zhang, J. Yang, W. Yuan, J. Zhao, J. Y. Dai, T. C. Guo, J. Liang, G. Y. Xu, Q. Cheng, and T. J. Cui, “An ultralight and thin metasurface for radar-infrared bi-stealth applications,” J. Phys. D: Appl. Phys. 50(44), 444002 (2017). [CrossRef]
13. C. Zhang, X. Wu, C. Huang, J. Peng, C. Ji, J. Yang, Y. Huang, Y. Guo, and X. Luo, “Flexible and Transparent Microwave–Infrared Bistealth Structure,” Adv. Mater. Technol. 4(8), 1900063 (2019). [CrossRef]
14. T. Hao, L. Hai-Tao, and C. Hai-Feng, “A thin radar-infrared stealth-compatible structure: Design, fabrication, and characterization,” Chin. Phys. B 23(2), 025201 (2014). [CrossRef]
15. T. Kim, J.-Y. Bae, N. Lee, and H. H. Cho, “Hierarchical Metamaterials for Multispectral Camouflage of Infrared and Microwaves,” Adv. Funct. Mater. 29(10), 1807319 (2019). [CrossRef]
16. C. Zhang, C. Huang, M. Pu, J. Song, Z. Zhao, X. Wu, and X. Luo, “Dual-band wide-angle metamaterial perfect absorber based on the combination of localized surface plasmon resonance and Helmholtz resonance,” Sci. Rep. 7(1), 5652 (2017). [CrossRef]
17. X. Ni, Z. J. Wong, M. Mrejen, Y. Wang, and X. Zhang, “An ultrathin invisibility skin cloak for visible light,” Science 349(6254), 1310–1314 (2015). [CrossRef]
18. M. Pu, Z. Zhao, Y. Wang, X. Li, X. Ma, C. Hu, C. Wang, C. Huang, and X. Luo, “Spatially and spectrally engineered spin-orbit interaction for achromatic virtual shaping,” Sci. Rep. 5(1), 9822 (2015). [CrossRef]
19. X. Ma, M. Pu, X. Li, Y. Guo, and X. Luo, “All-metallic wide-angle metasurfaces for multifunctional polarization manipulation,” Opto-Electron. Adv. 2(3), 18002301–18002306 (2019). [CrossRef]
20. M. Pu, Y. Guo, X. Ma, X. Li, and X. Luo, “Methodologies for On-Demand Dispersion Engineering of Waves in Metasurfaces,” Adv. Opt. Mater. 7(14), 1801376 (2019). [CrossRef]
21. M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015). [CrossRef]
22. X. Xie, K. Liu, M. Pu, X. Ma, X. Li, Y. Guo, F. Zhang, and X. Luo, “All-metallic geometric metasurfaces for broadband and high-efficiency wavefront manipulation,” Nanophotonics (2019), https://doi.org/10.1515/nanoph-2019-0415.
23. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014). [CrossRef]
24. A. Nemati, Q. Wang, M. Hong, and J. Teng, “Tunable and reconfigurable metasurfaces and metadevices,” Opto-Electron. Adv. 1(5), 18000901–18000925 (2018). [CrossRef]
25. X. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China: Phys., Mech. Astron. 58(9), 594201 (2015). [CrossRef]
26. X. Xie, X. Li, M. Pu, X. Ma, K. Liu, Y. Guo, and X. Luo, “Plasmonic Metasurfaces for Simultaneous Thermal Infrared Invisibility and Holographic Illusion,” Adv. Funct. Mater. 28(14), 1706673 (2018). [CrossRef]
27. X. Xie, M. Pu, Y. Huang, X. Ma, X. Li, Y. Guo, and X. Luo, “Heat Resisting Metallic Meta-Skin for Simultaneous Microwave Broadband Scattering and Infrared Invisibility Based on Catenary Optical Field,” Adv. Mater. Technol. 4(2), 1800612 (2019). [CrossRef]
28. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011). [CrossRef]
29. E. D. Palik, Handbook of Optical Constants of Solids (Academic press, 1998), 3.
30. J. C. I. Galarregui, A. T. Pereda, J. L. M. De Falcon, I. Ederra, R. Gonzalo, and P. de Maagt, “Broadband radar cross-section reduction using AMC technology,” IEEE Trans. Antennas Propag. 61(12), 6136–6143 (2013). [CrossRef]
31. W. Chen, C. A. Balanis, and C. R. Birtcher, “Checkerboard EBG surfaces for wideband radar cross section reduction,” IEEE Trans. Antennas Propag. 63(6), 2636–2645 (2015). [CrossRef]
32. X. Xie, M. Pu, X. Li, K. Liu, J. Jin, X. Ma, and X. Luo, “Dual-band and ultra-broadband photonic spin-orbit interaction for electromagnetic shaping based on single-layer silicon metasurfaces,” Photonics Res. 7(5), 586–593 (2019). [CrossRef]
33. Y. Pang, Y. Li, M. Yan, D. Liu, J. Wang, Z. Xu, and S. Qu, “Hybrid metasurfaces for microwave reflection and infrared emission reduction,” Opt. Express 26(9), 11950–11958 (2018). [CrossRef]
34. L. Meng, D. Zhao, Z. Ruan, Q. Li, Y. Yang, and M. Qiu, “Optimized grating as an ultra-narrow band absorber or plasmonic sensor,” Opt. Lett. 39(5), 1137–1140 (2014). [CrossRef]
35. M. Pu, X. Ma, Y. Guo, X. Li, and X. Luo, “Theory of microscopic meta-surface waves based on catenary optical fields and dispersion,” Opt. Express 26(15), 19555–19562 (2018). [CrossRef]
36. Y. Huang, J. Luo, M. Pu, Y. Guo, Z. Zhao, X. Ma, X. Li, and X. Luo, “Catenary electromagnetics for ultra-broadband lightweight absorbers and large-scale flat antennas,” Adv. Sci. 6(7), 1801691 (2019). [CrossRef]
37. J. Chen, Z. Hu, G. Wang, X. Huang, S. Wang, X. Hu, and M. Liu, “High-impedance surface-based broadband absorbers with interference theory,” IEEE Trans. Antennas Propag. 63(10), 4367–4374 (2015). [CrossRef]
38. F. Costa, A. Monorchio, and G. Manara, “Analysis and design of ultra thin electromagnetic absorbers comprising resistively loaded high impedance surfaces,” IEEE Trans. Antennas Propag. 58(5), 1551–1558 (2010). [CrossRef]
