Resonant circuit model for efficient metamaterial absorber Alexandre Sellier,1 Tatiana V. Teperik,1,∗ and Andr´e de Lustrac1,2 1 Univ.
Paris-Sud, Institut d’Electronique Fondamentale, UMR 8622, Orsay F-91405, France, 2 Univ. Paris-Ouest, 92410 Ville d’Avray, France ∗ [email protected]
Abstract: The resonant absorption in a planar metamaterial is studied theoretically. We present a simple physical model describing this phenomenon in terms of equivalent resonant circuit. We discuss the role of radiative and dissipative damping of resonant mode supported by a metamaterial in the formation of absorption spectra. We show that the results of rigorous calculations of Maxwell equations can be fully retrieved with simple model describing the system in terms of equivalent resonant circuit. This simple model allows us to explain the total absorption effect observed in the system on a common physical ground by referring it to the impedance matching condition at the resonance. © 2013 Optical Society of America OCIS codes: (160.3918) Metamaterials; (300.1030) Absorption; (260.5740) Resonance.
References and links 1. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008). 2. B. Wang, T. Koschny, and C. M. Soukoulis, “Wide-angle and polarization-independent chiral metamaterial absorber,” Phys. Rev. B 80, 033108 (2009). 3. Y. Cheng, H. Yang, Z. Cheng, and B. Xiao, “A planar polarization-insensitive metamaterial absorber,” Photonics and Nanostructures Fundamentals and Applications 9, 8–14 (2011). 4. 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, 9401–9407 (2011). 5. T. V. Teperik, F. J. Garc´ıa de Abajo, V. V. Popov, and M. S. Shur, “Strong terahertz absorption bands in a scaled plasmonic crystal,” Appl. Phys. Lett. 90, 251910 (2007). 6. H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: Design, fabrication and characterization,” Opt. Express 16, 7181–7188 (2008). 7. D. Y. Shchegolkov, A. K. Azad, J. F. O’Hara, and E. I. Simakov, “Perfect subwavelength fishnetlike metamaterialbased film terahertz absorbers,” Phys. Rev. B 82, 205117 (2010). 8. L. Huang, D. R. Chowdhury, S. Ramani, M. T. Reiten, S.-N. Luo, A. J. Taylor, and Hou-Tong, “Experimental demonstration of terahertz metamaterial absorbers with a broad and flat high absorption band,” Optics Lett. 37, 154–156 (2012). 9. S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Efficient light absorption in metalsemiconductormetal nanostructures,” Appl. Phys. Lett. 85, 194 (2004). 10. J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, , and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96, 251104 (2010). 11. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010). 12. K. B. Alici, A. B. Turhan, C. M. Soukoulis, and E. Ozbay, “Optically thin composite resonant absorber at the near-infrared band: a polarization independent and spectrally broadband configuration,” Opt. Express 19, 14260– 14267 (2011). 13. M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79, 033101 (2009).
#194138 - $15.00 USD Received 17 Jul 2013; revised 26 Sep 2013; accepted 26 Sep 2013; published 10 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.00A997 | OPTICS EXPRESS A997
14. X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with nearunity absorbance,” Phys. Rev. Lett. 104, 207403 (2010). 15. T. Maier and H. Brueckl, “Multispectral microbolometers for the midinfrared,” Opt. Lett. 35, 3766–3768 (2010). 16. G. Dayal and S. A. Ramakrishna, “Metamaterial saturable absorber mirror,” Opt. Lett. 38, 272–274 (2013). 17. T. V. Teperik, F. Garc´ıa de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299 – 301 (2008). 18. P. Ding, E. Liang, G. Cai, W. Hu, C. Fan, and Q. Xue, “Dual-band perfect absorption and field enhancement by interaction between localized and propagating surface plasmons in optical metamaterials,” J. Opt. 13, 075005 (2011). 19. K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun. 2, 517 (2011). 20. J. Yang and Z. Shen, “A thin and broadband absorber using double-square loops,” IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS 6, 388–391 (2007). 21. A. F. Arya, M. Mishrikey, C. Hafner, and R. Vahldieck, “Radar absorbers based on frequency selective surfaces on perforated substrates,” J. Computational Theoretical Nanosci. 5, 704–710 (2008). 22. A. Fallahi, A. Yahaghi, H.-R. Benedickter, H. Abiri, M. Shahabadi, and C. Hafner, “Thin wideband radar absorbers,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 58, 4051–4058 (2010). 23. H. Oraizi, A. Abdolali, and N. Vaseghi, “Application of double zero metamaterials as radar absorbing materials for the re- duction of radar cross section,” Prog. Electromagn. Res. 101, 323–337 (2010). 24. R. F. Huang, Z. W. Li, L. B. Kong, L. Liu, and S. Matitsine, “Analysis and design of an ultra-thin metamaterial absorber,” Prog. Electromagn. Res. B 14, 407–429 (2009). 25. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010). 26. J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61 (2002). 27. J. Hao, L. Zhou, and M. Qiu, “Nearly total absorption of light and heat generation by plasmonic metamaterials,” Phys. Rev. B 83, 165107 (2011). 28. P. Bouchon, C. Koechlin, F. Pardo, R. Hadar, and J.-L. Pelouard, “Wideband omnidirectional infrared absorber with a patchwork of plasmonic nanoantennas,” Opt. Lett. 37, 1038–1040 (2012). 29. M. Pu, C. Hu, M. Wang, C. Huang, Z. Zhao, C. Wang, Q. Feng, and X. Luo, “Design principles for infrared wide-angle perfect absorber based on plasmonic structure,” Opt. Express 19, 17413–17420 (2011). 30. H. Wakatsuchi, S. Greedy, C. Christopoulos, and J. Paul, “Customised broadband metamaterial absorbers for arbitrary polarisation,” Opt. Express 18, 22187–22198 (2010). 31. W. Zhu, X. Zhao, B. Gong, L. Liu, and B. Su, “Optical metamaterial absorber based on leaf-shaped cells,” Appl. Phys. A 102, 147–151 (2011). 32. W. Zhu and X. Zhao, “Metamaterial absorber with dendritic cells at infrared frequencies,” J. Opt. Soc. Am. B 26, 2382–2385 (2009). 33. P. V. Tuong, V. D. Lam, J. W. Park, E. H. Choi, S. A. Nikitov, and Y. P. Lee, “Perfect-absorber metamaterial based on flower-shaped structure,” Photonics and Nanostructures - Fundamentals and Applications 11, 89–94 (2013). 34. http://www.comsol.com. 35. C. A. Balanis, Antenna Theory: Analysis and Designs (John Wiley & Sons, Inc., NY, 1997). 36. T. V. Teperik, V. V. Popov, and F. J. Garc´ıa de Abajo, “Void plasmons and total absorption of light in nanoporous metallic films,” Phys. Rev. B 71, 085408 (2005). 37. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
1.
Introduction
A large variety of metallic and semiconductor metamaterials have been recently found to exhibit total absorption (TA) of electromagnetic radiation. This effect has been reported in broad frequency range including microwave [1–4], THz [5–8], NIR [9–12], MIR [13–16] and visible [17–19] regions. A lot of diverse applications have been already proposed. Among them radar [20-23], electromagnetic compatibility [24], photovoltaics [25], biosensing [11], thermal source emission [13, 26], and thermal bolometer [15]. Although the structures that exhibit total absorption might differ considerably, they possess some common characteristics: the energy transmission through entire structure is forbidden, the structure possess an intrinsic resonance, and total absorption is achieved at a specific condition imposed on the geometry of the structure or on the material properties. One of the metamaterial structures widely discussed in literature in respect to the highly efficient absorber is a planar metamaterial with lattice of metallic patches separated from the
#194138 - $15.00 USD Received 17 Jul 2013; revised 26 Sep 2013; accepted 26 Sep 2013; published 10 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.00A997 | OPTICS EXPRESS A998
ground plane by absorptive layer. Such structure with subwavelength thickness can exhibit the effect of total absorption by trapping the electromagnetic radiation under the patch. Several geometries of the patch have been studied. Among them square [10, 15, 27, 28] and circular patches [11, 16, 29], cut wires [8, 30], closed-ring [4], split-ring [1, 6, 12], and cross-shaped resonators [14]. Even the leaf-shaped [31] and flower-shaped patch configurations [32, 33] have been considered. In each of this studies an exhaustive information about the resonant total absorption effect and even the formation of the absorption bands are presented although limited to a particular geometry. Nevertheless, they fail to offer the basic physical principles for parameter choice of a perfect metamaterial absorber. To date, in spite of extensive engineering search for the patch geometry the lack of general strategy is still observed. In this paper along with rigorous electromagnetic calculations we present a simple physical model describing the properties of planar metallic metamaterial in terms of equivalent oscillating-current resonant circuit. In this analytical approach we describe the absorptive layer squeezed between the periodic arrangement of metallic patches and ground plane by an effective load impedance. This allows us to go beyond the geometry and to find the universal ruler for TA effect to be achieved. The paper is organized as follows. We start from the simplest geometry of a square patch in order to tackle the problem and understand the physics behind. In Sec. II we show the results of the rigorous electromagnetic calculations performed with use of the commercial software COMSOL Multiphysics [34] based on the finite element method. In Sec. III we present a simple physical model that describes the resonant absorption in terms of equivalent resonant circuit. In Sec. IV we develop the condition for the perfect absorber and discuss the role of radiative and dissipative damping of resonant mode supported by a metamaterial in the formation of absorption spectra. Finally, we tested our model with the planar metamaterials with arbitrary patch geometry. 2.
Resonant absorption by a planar metamaterial
In Fig. 1 we present the structure under consideration (metasurface): it is a periodic arrangement of square metallic patches of length l located above a ground plane at a distance s
Paris-Sud, Institut d’Electronique Fondamentale, UMR 8622, Orsay F-91405, France, 2 Univ. Paris-Ouest, 92410 Ville d’Avray, France ∗ [email protected]
Abstract: The resonant absorption in a planar metamaterial is studied theoretically. We present a simple physical model describing this phenomenon in terms of equivalent resonant circuit. We discuss the role of radiative and dissipative damping of resonant mode supported by a metamaterial in the formation of absorption spectra. We show that the results of rigorous calculations of Maxwell equations can be fully retrieved with simple model describing the system in terms of equivalent resonant circuit. This simple model allows us to explain the total absorption effect observed in the system on a common physical ground by referring it to the impedance matching condition at the resonance. © 2013 Optical Society of America OCIS codes: (160.3918) Metamaterials; (300.1030) Absorption; (260.5740) Resonance.
References and links 1. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008). 2. B. Wang, T. Koschny, and C. M. Soukoulis, “Wide-angle and polarization-independent chiral metamaterial absorber,” Phys. Rev. B 80, 033108 (2009). 3. Y. Cheng, H. Yang, Z. Cheng, and B. Xiao, “A planar polarization-insensitive metamaterial absorber,” Photonics and Nanostructures Fundamentals and Applications 9, 8–14 (2011). 4. 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, 9401–9407 (2011). 5. T. V. Teperik, F. J. Garc´ıa de Abajo, V. V. Popov, and M. S. Shur, “Strong terahertz absorption bands in a scaled plasmonic crystal,” Appl. Phys. Lett. 90, 251910 (2007). 6. H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: Design, fabrication and characterization,” Opt. Express 16, 7181–7188 (2008). 7. D. Y. Shchegolkov, A. K. Azad, J. F. O’Hara, and E. I. Simakov, “Perfect subwavelength fishnetlike metamaterialbased film terahertz absorbers,” Phys. Rev. B 82, 205117 (2010). 8. L. Huang, D. R. Chowdhury, S. Ramani, M. T. Reiten, S.-N. Luo, A. J. Taylor, and Hou-Tong, “Experimental demonstration of terahertz metamaterial absorbers with a broad and flat high absorption band,” Optics Lett. 37, 154–156 (2012). 9. S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Efficient light absorption in metalsemiconductormetal nanostructures,” Appl. Phys. Lett. 85, 194 (2004). 10. J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, , and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96, 251104 (2010). 11. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010). 12. K. B. Alici, A. B. Turhan, C. M. Soukoulis, and E. Ozbay, “Optically thin composite resonant absorber at the near-infrared band: a polarization independent and spectrally broadband configuration,” Opt. Express 19, 14260– 14267 (2011). 13. M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79, 033101 (2009).
#194138 - $15.00 USD Received 17 Jul 2013; revised 26 Sep 2013; accepted 26 Sep 2013; published 10 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.00A997 | OPTICS EXPRESS A997
14. X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with nearunity absorbance,” Phys. Rev. Lett. 104, 207403 (2010). 15. T. Maier and H. Brueckl, “Multispectral microbolometers for the midinfrared,” Opt. Lett. 35, 3766–3768 (2010). 16. G. Dayal and S. A. Ramakrishna, “Metamaterial saturable absorber mirror,” Opt. Lett. 38, 272–274 (2013). 17. T. V. Teperik, F. Garc´ıa de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299 – 301 (2008). 18. P. Ding, E. Liang, G. Cai, W. Hu, C. Fan, and Q. Xue, “Dual-band perfect absorption and field enhancement by interaction between localized and propagating surface plasmons in optical metamaterials,” J. Opt. 13, 075005 (2011). 19. K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun. 2, 517 (2011). 20. J. Yang and Z. Shen, “A thin and broadband absorber using double-square loops,” IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS 6, 388–391 (2007). 21. A. F. Arya, M. Mishrikey, C. Hafner, and R. Vahldieck, “Radar absorbers based on frequency selective surfaces on perforated substrates,” J. Computational Theoretical Nanosci. 5, 704–710 (2008). 22. A. Fallahi, A. Yahaghi, H.-R. Benedickter, H. Abiri, M. Shahabadi, and C. Hafner, “Thin wideband radar absorbers,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 58, 4051–4058 (2010). 23. H. Oraizi, A. Abdolali, and N. Vaseghi, “Application of double zero metamaterials as radar absorbing materials for the re- duction of radar cross section,” Prog. Electromagn. Res. 101, 323–337 (2010). 24. R. F. Huang, Z. W. Li, L. B. Kong, L. Liu, and S. Matitsine, “Analysis and design of an ultra-thin metamaterial absorber,” Prog. Electromagn. Res. B 14, 407–429 (2009). 25. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010). 26. J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61 (2002). 27. J. Hao, L. Zhou, and M. Qiu, “Nearly total absorption of light and heat generation by plasmonic metamaterials,” Phys. Rev. B 83, 165107 (2011). 28. P. Bouchon, C. Koechlin, F. Pardo, R. Hadar, and J.-L. Pelouard, “Wideband omnidirectional infrared absorber with a patchwork of plasmonic nanoantennas,” Opt. Lett. 37, 1038–1040 (2012). 29. M. Pu, C. Hu, M. Wang, C. Huang, Z. Zhao, C. Wang, Q. Feng, and X. Luo, “Design principles for infrared wide-angle perfect absorber based on plasmonic structure,” Opt. Express 19, 17413–17420 (2011). 30. H. Wakatsuchi, S. Greedy, C. Christopoulos, and J. Paul, “Customised broadband metamaterial absorbers for arbitrary polarisation,” Opt. Express 18, 22187–22198 (2010). 31. W. Zhu, X. Zhao, B. Gong, L. Liu, and B. Su, “Optical metamaterial absorber based on leaf-shaped cells,” Appl. Phys. A 102, 147–151 (2011). 32. W. Zhu and X. Zhao, “Metamaterial absorber with dendritic cells at infrared frequencies,” J. Opt. Soc. Am. B 26, 2382–2385 (2009). 33. P. V. Tuong, V. D. Lam, J. W. Park, E. H. Choi, S. A. Nikitov, and Y. P. Lee, “Perfect-absorber metamaterial based on flower-shaped structure,” Photonics and Nanostructures - Fundamentals and Applications 11, 89–94 (2013). 34. http://www.comsol.com. 35. C. A. Balanis, Antenna Theory: Analysis and Designs (John Wiley & Sons, Inc., NY, 1997). 36. T. V. Teperik, V. V. Popov, and F. J. Garc´ıa de Abajo, “Void plasmons and total absorption of light in nanoporous metallic films,” Phys. Rev. B 71, 085408 (2005). 37. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
1.
Introduction
A large variety of metallic and semiconductor metamaterials have been recently found to exhibit total absorption (TA) of electromagnetic radiation. This effect has been reported in broad frequency range including microwave [1–4], THz [5–8], NIR [9–12], MIR [13–16] and visible [17–19] regions. A lot of diverse applications have been already proposed. Among them radar [20-23], electromagnetic compatibility [24], photovoltaics [25], biosensing [11], thermal source emission [13, 26], and thermal bolometer [15]. Although the structures that exhibit total absorption might differ considerably, they possess some common characteristics: the energy transmission through entire structure is forbidden, the structure possess an intrinsic resonance, and total absorption is achieved at a specific condition imposed on the geometry of the structure or on the material properties. One of the metamaterial structures widely discussed in literature in respect to the highly efficient absorber is a planar metamaterial with lattice of metallic patches separated from the
#194138 - $15.00 USD Received 17 Jul 2013; revised 26 Sep 2013; accepted 26 Sep 2013; published 10 Oct 2013 (C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.00A997 | OPTICS EXPRESS A998
ground plane by absorptive layer. Such structure with subwavelength thickness can exhibit the effect of total absorption by trapping the electromagnetic radiation under the patch. Several geometries of the patch have been studied. Among them square [10, 15, 27, 28] and circular patches [11, 16, 29], cut wires [8, 30], closed-ring [4], split-ring [1, 6, 12], and cross-shaped resonators [14]. Even the leaf-shaped [31] and flower-shaped patch configurations [32, 33] have been considered. In each of this studies an exhaustive information about the resonant total absorption effect and even the formation of the absorption bands are presented although limited to a particular geometry. Nevertheless, they fail to offer the basic physical principles for parameter choice of a perfect metamaterial absorber. To date, in spite of extensive engineering search for the patch geometry the lack of general strategy is still observed. In this paper along with rigorous electromagnetic calculations we present a simple physical model describing the properties of planar metallic metamaterial in terms of equivalent oscillating-current resonant circuit. In this analytical approach we describe the absorptive layer squeezed between the periodic arrangement of metallic patches and ground plane by an effective load impedance. This allows us to go beyond the geometry and to find the universal ruler for TA effect to be achieved. The paper is organized as follows. We start from the simplest geometry of a square patch in order to tackle the problem and understand the physics behind. In Sec. II we show the results of the rigorous electromagnetic calculations performed with use of the commercial software COMSOL Multiphysics [34] based on the finite element method. In Sec. III we present a simple physical model that describes the resonant absorption in terms of equivalent resonant circuit. In Sec. IV we develop the condition for the perfect absorber and discuss the role of radiative and dissipative damping of resonant mode supported by a metamaterial in the formation of absorption spectra. Finally, we tested our model with the planar metamaterials with arbitrary patch geometry. 2.
Resonant absorption by a planar metamaterial
In Fig. 1 we present the structure under consideration (metasurface): it is a periodic arrangement of square metallic patches of length l located above a ground plane at a distance s
