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Actively tunable Fano resonances based on colossal magneto-resistant metamaterials Jie-Bing Tian,1 Chang-Chun Yan,1,* Cheng Wang,1 Ying Han,1 Rong-Yuan Zou,1 Dong-Dong Li,1 Zheng-Ji Xu,2 and Dao-Hua Zhang2 1
2
Jiangsu Key Laboratory of Advanced Laser Materials and Devices, School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore *Corresponding author: [email protected] Received November 21, 2014; revised January 22, 2015; accepted January 24, 2015; posted February 23, 2015 (Doc. ID 228288); published March 20, 2015 In this Letter, a periodic structure in which each unit cell consists of one manganese oxide (La0.7 Ca0.3 MnO3 ) strip and two gold strips is designed. By simulating the electromagnetic responses of the structure, we confirm that Fano resonances can be actively controlled in the infrared region by modulating the intensity of the external magnetic field applied to the structure. This is due to the colossal magneto-resistance of the La0.7 Ca0.3 MnO3 material. Furthermore, a transmission phase can also be effectively tuned. The phase has a shift of ΔΦ 1.05 rad at a frequency of 130 THz when the intensity of the external magnetic field varies from 5083 to 5193 kA∕m. Such a tunable method has potential applications in controllable photoelectric elements. © 2015 Optical Society of America OCIS codes: (160.3918) Metamaterials; (260.5740) Resonance; (050.1755) Computational electromagnetic methods. http://dx.doi.org/10.1364/OL.40.001286
Fano resonances found in metamaterials and plasmonic structures have become a key focus of research in recent years [1]. By analyzing the production mechanisms of Fano resonances, it was found that these structures could be divided into either electric or magnetic plasmonic structures. An electric plasmonic structure was first proposed by Zhang et al. [2]. It is composed of an array of two metal rods in a transverse arrangement and one metal rod in a longitudinal arrangement. Subsequently, ring/disk cavities [3,4] and an array of metal nanoparticle clusters [5,6] were also suggested as electric plasmonic structures. Zheludev et al. were the first to use a magnetic plasmonic structure to produce Fano resonances [7,8]. Their resonance unit cell consists of two sections of weakly asymmetric concentric metallic arcs. After that, different magnetic plasmonic structures [9,10] were demonstrated. However, the Fano resonances that are generated are non-tunable. If the resonance frequencies of these Fano resonances are adjusted, the structures will often need to be redesigned or refabricated, which limits their applications to a certain extent. In order to make the functions of these structures flexible, the metamaterials and plasmonic structures need to be actively tunable. Efforts by researchers in this regard have been progressing well. Thus far, there are about five actively tunable methods for Fano resonances: a voltage driving method [11–13], an optical excitation method [14–16], a thermal stimulus method [17], a stretching control method [18], and a magnetic field control method [19,20]. In the magnetic field control method, the tunable Fano resonances originate from the changes in the effective permeability of the ferrite-based structures acted on by various external magnetic fields. In this Letter, we introduce manganese oxide (La0.7 Ca0.3 MnO3 ) with a colossal magneto-resistance (CMR) effect into our design structure. When the intensity of the external magnetic field applied to the structure is tuned, the conductivity of La0.7 Ca0.3 MnO3 varies accordingly. The Fano resonance produced in the structure 0146-9592/15/071286-04$15.00/0
is therefore tuned. As evidenced by our experiment, its tunable mechanism differs from that described in [21,22]. As shown in Fig. 1, a unit cell of the structure designed consists of three strips in a parallel arrangement surrounded by air. The middle and right strips are the same in length, and are slightly longer than the left strip. This setup has been optimized to obtain a more obvious resonance phenomenon. The other dimensions remain the same. The three strips are symmetrical in the x direction. The middle strip is made of La0.7 Ca0.3 MnO3 with a CMR effect, while the other strips are composed of gold. We used the La0.7 Ca0.3 MnO3 material because its resistance changes considerably with the increase of the external magnetic field, even as that field changes from a dielectric field to a conductor. We can also easily obtain the exact parameters of the La0.7 Ca0.3 MnO3 material used in the simulations done by [23]. The detailed geometric dimensions are shown in the caption of Fig. 1. A plane wave is normally incident to the top surface of the structure, with its electric field E, magnetic field H, and wave vector k along the x, y, and z directions, respectively. Since the structure is periodic, we only consider one unit cell with periodic boundary conditions in the simulations. The two-paired surfaces of the unit cell in the
Fig. 1. (a) Schematic of one unit cell of the structure where the period p 5 μm. (b) Schematic of the three strips consisting of gold and La0.7 Ca0.3 MnO3 in the unit cell with the dimensions of a 2.9 μm, b 3 μm, k 800 nm, c 200 nm, and d 100 nm. © 2015 Optical Society of America
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two periodic arrangement directions are set to periodic boundary conditions, while the two surfaces of the unit cell in the propagation direction of the electromagnetic wave are set to ports. In addition, an external magnetic field H 0 is applied along the x direction. From the current distributions shown below, we can see that the directions of the currents are mainly along the x axis. To avoid the impact of the Lorentz force on the resonance [24–29], we made the direction of the external magnetic field the same as the directions of the currents. The permittivity of gold comes from the experimental data found in [30]. Following the work done in [23], La0.7 Ca0.3 MnO3 is an electric-resistant material, the resistivity of which has an approximate relationship as a result of the functions of the temperature and intensity of the external magnetic field. We refer to the following equation: ρH 0 ; T 0 ρm expf−MH 0 ; T 0 ∕M 0 g;
(1)
where ρ is the resistivity of the La0.7 Ca0.3 MnO3 , H 0 the intensity of the external magnetic field, and T 0 is the temperature. ρm is the constant related with ρm 21 3 mΩ · cm, MH 0 ; T 0 is the magnetization of the La0.7 Ca0.3 MnO3 , and M 0 is the initial intensity of the magnetization with 4πM 0 2.02 0.02 kG. With Eq. (1) and the experimental data from [23], we can determine the range of the ρ values and also retrieve ρ for different values of H 0 and T 0 . As is well known, conductivity is the reciprocal of resistivity. We computed the range of the conductivity as being from 5.6 × 103 to 1.36 × 106 S∕m. In this range, we employ the three conductivities of 105 , 1.2 × 105 , and 106 S∕m for simulations, which corresponds to the H 0 values of 5083, 5105, and 5193 kA∕m at T 0 272 K, respectively. The occurrence of the CMR effect generally needs the excitation of the strong external magnetic field, while the magnetic field of the plane wave is much weaker than the former. We thus neglect the influence of the plane wave on the CMR effect. By analyzing a material made of magnetite, it is found that the real parts of its permeability approaches unity in the high-frequency range [31]. For simplicity, the permeability of La0.7 Ca0.3 MnO3 is set to 1, and its magnetic loss is neglected in this Letter. The Ansoft high-frequency structure simulator software was used in the simulations. We calculated transmission and reflectivity as functions of the frequency for the three different conductivities mentioned previously. The corresponding results are shown in Fig. 2. It can be seen from the curve for the H 0 values of 5083 kA∕m that only one resonance exists. However, for the other two cases, there is one weak resonance in addition to the main resonance. The line shape of the main resonance is characterized by symmetry, and the resonance is called dipole oscillation. For the two weak resonances displayed in the curves for the H 0 values of 5105 and 5193 kA∕m, both of the line shapes clearly exhibit a characteristic of asymmetry. These are the Fano resonances. Their physical mechanism will be addressed later on in this Letter. From Fig. 2, we also find that the positions of the Fano resonances change as H 0 increases. Their resonance intensities also vary. Our additional simulations show that when the value of H 0 is less than
Fig. 2. (a) Transmission and (b) reflection as functions of the frequency for the H 0 values of 5083, 5105, and 5193 kA∕m.
5083 kA∕m (i.e., the conductivity is lower than 105 S∕m), the Fano resonances do not occur. This signifies that the Fano resonances can be effectively controlled by properly changing the external magnetic field. Additionally, the transmission phases for the three cases in which H 0 5083, 5105, and 5193 kA∕m were also calculated. The corresponding results are shown in Fig. 3. It is obvious that the transmission phases at resonances vary with the increasing value of H 0 . At 130 THz, the phase shift almost reaches a maximum of ΔΦ 1.05 rad, when the intensity of the external magnetic field increases from 5083 to 5193 kA∕m. Hence, the phase of the structure can be well tuned by the external magnetic field. Next, we will explore the cause of the tunable phenomena in Fig. 3, and then we will simulate the current distributions with different phases in the unit cell for different conductivities. The simulated results are shown in Figs. 4 and 5. Figure 4 shows the current distributions with the phases of 0°, 45°, 90°, 135°, and 180° for the conductivity
Fig. 3. Transmission phase as a function of the frequency for the H 0 values of 5083, 5105, and 5193 kA∕m.
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Fig. 6. Electric field distributions in the unit cell with phases of (a) 0°, (b) 45°, (c) 90°, (d) 135°, and (e) 180° for the value of H 0 of 5193 kA∕m.
Fig. 4. Current distributions in the three strips with phases of (a) 0°, (b) 45°, (c) 90°, (d) 135°, and (e) 180° for the H 0 value of 5193 kA∕m.
of 106 S∕m at the resonance of 134 THz, while Fig. 5 shows the current distributions for the conductivity of 105 S∕m with the same phases when the value of H 0 is 5083 kA∕m. From Fig. 4, it can be seen that there are no currents distributed in the La0.7 Ca0.3 MnO3 strip, and that the currents converge in the gold strips. By analyzing the directions of the currents, we can mark the charges distributed in the strips. Electric quadrupoles are shown in Figs. 4(a) and 4(b). These quadrupoles have a characteristic of non-radiation and form a dark mode. When the phase is converted to 135°, only the electric dipoles exist. The electric dipoles can radiate energy to the far field, and are thus viewed as a bright mode. When the phase increases to 180°, the case is similar to that when the phase is 0°. Their differences are the reversal of the charge distributions. From the half period of phase distributions, we can find that there exists the coupling between the dark mode and the bright mode, which induces the Fano resonances observed above. By comparing Fig. 5 with Fig. 4, we can see that electric quadrupoles do not occur in Fig. 5, and that only electric dipoles exist in that figure. This is why only dipole oscillation appears for the case of conductivity of 105 S∕m shown in Fig. 2.
Fig. 5. Current distributions in the three strips with phases of (a) 0°, (b) 45°, (c) 90°, (d) 135°, and (e) 180° for the H 0 value of 5083 kA∕m.
To further comprehend the mechanism of the Fano resonances, we also simulated the electric field distributions in the plane 10 nm away from the top surface of the unit cell, corresponding to the cases shown in Figs. 4 and 5. The simulation results are displayed in Figs. 6 and 7. From Fig. 6, we can see that the electric field in the La0.7 Ca0.3 MnO3 strip is very strong. This indicates that there is energy stored in the area. Such an energy storage process is necessary for the generation of Fano resonances. This is the formation process of the dark mode (or dark atoms). It is similar to that mentioned in [2]. Unlike the case shown in Fig. 6, almost no electric field is distributed in the La0.7 Ca0.3 MnO3 strip for the case shown in Fig. 7. This is because there is no energy storage during the process, and the electromagnetic energy is radiated outward by the electric dipole oscillation. Fano resonances are often accompanied by analogues of electromagnetically induced transparency (EIT). We therefore investigated the electromagnetic absorption of the structure for the H 0 values of 5083, 5105, and 5193 kA∕m. According to the reflection R and the transmission T, the resulting electromagnetic absorption can be calculated by 1 − T − R. The simulation results are
Fig. 7. Electric field distributions in the unit cell with phases of (a) 0°, (b) 45°, (c) 90°, (d) 135°, and (e) 180° for the value of H 0 of 5083 kA∕m.
Fig. 8. Absorption as a function of the frequency for the H 0 values of 5083, 5105, and 5193 kA∕m.
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shown in Fig. 8. It is found that almost no EIT occurs. There is one exception: the absorption curve for H 0 5105 kA∕m exhibits a very weak EIT. This is because the resistivity of the La0.7 Ca0.3 MnO3 material is still relatively high, despite the fact that it decreases significantly under the influence of strong external magnetic field. This decrease makes the Ohmic loss stronger than the coupling energy between the electric dipoles and electric quadruples. Thus, it is difficult to observe an analogue of EIT. In conclusion, a periodic structure, each unit cell of which is composed of one La0.7 Ca0.3 MnO3 strip with a CMR effect and two gold strips, is discussed in this Letter. The simulation results demonstrate that the structure exhibits a characteristic of tunable Fano resonances. The reason for the tunability is that the conductivity of La0.7 Ca0.3 MnO3 changes considerably with increasing intensity of the external magnetic field. The simulation results also demonstrate that the transmission phase of the structure is effectively tuned. The phase shift reaches ΔΦ 1.05 rad at 130 THz when the external magnetic field varies from 5083 to 5193 kA∕m. Such a structure has the potential for practical applications in controllable photoelectric devices. The project is supported by the Graduate Innovation Project of Jiangsu Normal University (2013YYB138), the National Natural Science Foundation of China (61401182 and 61372057), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), China. References 1. B. Luk'yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010). 2. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, Phys. Rev. Lett. 101, 047401 (2008). 3. F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, ACS Nano 3, 643 (2009). 4. Y. Sonnefraud, N. Verellen, H. Sobhani, G. A. E. Vandenbosch, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, ACS Nano 4, 1664 (2010). 5. J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, Science 328, 1135 (2010). 6. M. Hentschel, M. Saliba, R. Vogelgesang, H. Giessen, A. P. Alivisatos, and N. Liu, Nano Lett. 10, 2721 (2010).
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7. V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, Phys. Rev. Lett. 99, 147401 (2007). 8. N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, Nat. Photonics 2, 351 (2008). 9. N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, Appl. Phys. Lett. 94, 211902 (2009). 10. S. D. Jenkins and J. Ruostekoski, Phys. Rev. Lett. 111, 147401 (2013). 11. N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, Nano Lett. 14, 78 (2014). 12. H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, Nano Lett. 14, 4581 (2014). 13. F. Zhang, X. Hu, C. Wu, H. Yang, and Q. Gong, Appl. Phys. Lett. 105, 181114 (2014). 14. Y. B. Zhang, X. Y. Hu, Y. L. Fu, H. Yang, and Q. H. Gong, Appl. Phys. Lett. 100, 031106 (2012). 15. Z. Chai, X. Y. Hu, Y. Zhu, F. Zhang, H. Yang, and Q. H. Gong, Appl. Phys. Lett. 102, 201119 (2013). 16. F. Zhang, X. Y. Hu, Y. Zhu, H. Yang, and Q. H. Gong, Appl. Phys. Lett. 103, 191116 (2013). 17. M. Tomita, K. Totsuka, R. Hanamura, and T. Matsumoto, J. Opt. Soc. Am. B 26, 813 (2009). 18. Y. Cui, J. Zhou, V. A. Tamma, and W. Park, ACS Nano 6, 2385 (2012). 19. J. M. Laskar, B. Raj, and J. Philip, Phys. Rev. E 84, 051403 (2011). 20. F. Fan, S. Chen, W. Lin, Y. P. Miao, S. J. Chang, B. Liu, X. H. Wang, and L. Lin, Appl. Phys. Lett. 103, 161115 (2013). 21. L. Kang, Q. Zhao, H. Zhao, and J. Zhou, Opt. Express 16, 17269 (2008). 22. K. Bi, J. Zhou, H. Zhao, X. Liu, and C. Lan, Opt. Express 21, 10746 (2013). 23. M. F. Hundley, M. Hawley, R. H. Heffner, Q. X. Jia, J. J. Neumeier, J. Tesmer, J. D. Thompson, and X. D. Wu, Appl. Phys. Lett. 67, 860 (1995). 24. D. J. Bergman and Y. M. Strelniker, Phys. Rev. Lett. 80, 857 (1998). 25. Y. M. Strelniker and D. J. Bergman, Eur. Phys. J. Appl. Phys. 7, 19 (1999). 26. Y. M. Strelniker and D. J. Bergman, Phys. Rev. B 59, R12763 (1999). 27. Y. M. Strelniker and D. J. Bergman, Phys. Rev. B 67, 184416 (2003). 28. Y. M. Strelniker, Phys. Rev. B 76, 085409 (2007). 29. Y. M. Strelniker and D. J. Bergman, Phys. Rev. B 77, 205113 (2008). 30. D. W. Lynch and W. R. Hunter, Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, 1985). 31. J. Verwell, Magnetic Properties of Materials, J. Smit, ed. (McGraw-Hill, 1971).
OPTICS LETTERS / Vol. 40, No. 7 / April 1, 2015
Actively tunable Fano resonances based on colossal magneto-resistant metamaterials Jie-Bing Tian,1 Chang-Chun Yan,1,* Cheng Wang,1 Ying Han,1 Rong-Yuan Zou,1 Dong-Dong Li,1 Zheng-Ji Xu,2 and Dao-Hua Zhang2 1
2
Jiangsu Key Laboratory of Advanced Laser Materials and Devices, School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore *Corresponding author: [email protected] Received November 21, 2014; revised January 22, 2015; accepted January 24, 2015; posted February 23, 2015 (Doc. ID 228288); published March 20, 2015 In this Letter, a periodic structure in which each unit cell consists of one manganese oxide (La0.7 Ca0.3 MnO3 ) strip and two gold strips is designed. By simulating the electromagnetic responses of the structure, we confirm that Fano resonances can be actively controlled in the infrared region by modulating the intensity of the external magnetic field applied to the structure. This is due to the colossal magneto-resistance of the La0.7 Ca0.3 MnO3 material. Furthermore, a transmission phase can also be effectively tuned. The phase has a shift of ΔΦ 1.05 rad at a frequency of 130 THz when the intensity of the external magnetic field varies from 5083 to 5193 kA∕m. Such a tunable method has potential applications in controllable photoelectric elements. © 2015 Optical Society of America OCIS codes: (160.3918) Metamaterials; (260.5740) Resonance; (050.1755) Computational electromagnetic methods. http://dx.doi.org/10.1364/OL.40.001286
Fano resonances found in metamaterials and plasmonic structures have become a key focus of research in recent years [1]. By analyzing the production mechanisms of Fano resonances, it was found that these structures could be divided into either electric or magnetic plasmonic structures. An electric plasmonic structure was first proposed by Zhang et al. [2]. It is composed of an array of two metal rods in a transverse arrangement and one metal rod in a longitudinal arrangement. Subsequently, ring/disk cavities [3,4] and an array of metal nanoparticle clusters [5,6] were also suggested as electric plasmonic structures. Zheludev et al. were the first to use a magnetic plasmonic structure to produce Fano resonances [7,8]. Their resonance unit cell consists of two sections of weakly asymmetric concentric metallic arcs. After that, different magnetic plasmonic structures [9,10] were demonstrated. However, the Fano resonances that are generated are non-tunable. If the resonance frequencies of these Fano resonances are adjusted, the structures will often need to be redesigned or refabricated, which limits their applications to a certain extent. In order to make the functions of these structures flexible, the metamaterials and plasmonic structures need to be actively tunable. Efforts by researchers in this regard have been progressing well. Thus far, there are about five actively tunable methods for Fano resonances: a voltage driving method [11–13], an optical excitation method [14–16], a thermal stimulus method [17], a stretching control method [18], and a magnetic field control method [19,20]. In the magnetic field control method, the tunable Fano resonances originate from the changes in the effective permeability of the ferrite-based structures acted on by various external magnetic fields. In this Letter, we introduce manganese oxide (La0.7 Ca0.3 MnO3 ) with a colossal magneto-resistance (CMR) effect into our design structure. When the intensity of the external magnetic field applied to the structure is tuned, the conductivity of La0.7 Ca0.3 MnO3 varies accordingly. The Fano resonance produced in the structure 0146-9592/15/071286-04$15.00/0
is therefore tuned. As evidenced by our experiment, its tunable mechanism differs from that described in [21,22]. As shown in Fig. 1, a unit cell of the structure designed consists of three strips in a parallel arrangement surrounded by air. The middle and right strips are the same in length, and are slightly longer than the left strip. This setup has been optimized to obtain a more obvious resonance phenomenon. The other dimensions remain the same. The three strips are symmetrical in the x direction. The middle strip is made of La0.7 Ca0.3 MnO3 with a CMR effect, while the other strips are composed of gold. We used the La0.7 Ca0.3 MnO3 material because its resistance changes considerably with the increase of the external magnetic field, even as that field changes from a dielectric field to a conductor. We can also easily obtain the exact parameters of the La0.7 Ca0.3 MnO3 material used in the simulations done by [23]. The detailed geometric dimensions are shown in the caption of Fig. 1. A plane wave is normally incident to the top surface of the structure, with its electric field E, magnetic field H, and wave vector k along the x, y, and z directions, respectively. Since the structure is periodic, we only consider one unit cell with periodic boundary conditions in the simulations. The two-paired surfaces of the unit cell in the
Fig. 1. (a) Schematic of one unit cell of the structure where the period p 5 μm. (b) Schematic of the three strips consisting of gold and La0.7 Ca0.3 MnO3 in the unit cell with the dimensions of a 2.9 μm, b 3 μm, k 800 nm, c 200 nm, and d 100 nm. © 2015 Optical Society of America
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two periodic arrangement directions are set to periodic boundary conditions, while the two surfaces of the unit cell in the propagation direction of the electromagnetic wave are set to ports. In addition, an external magnetic field H 0 is applied along the x direction. From the current distributions shown below, we can see that the directions of the currents are mainly along the x axis. To avoid the impact of the Lorentz force on the resonance [24–29], we made the direction of the external magnetic field the same as the directions of the currents. The permittivity of gold comes from the experimental data found in [30]. Following the work done in [23], La0.7 Ca0.3 MnO3 is an electric-resistant material, the resistivity of which has an approximate relationship as a result of the functions of the temperature and intensity of the external magnetic field. We refer to the following equation: ρH 0 ; T 0 ρm expf−MH 0 ; T 0 ∕M 0 g;
(1)
where ρ is the resistivity of the La0.7 Ca0.3 MnO3 , H 0 the intensity of the external magnetic field, and T 0 is the temperature. ρm is the constant related with ρm 21 3 mΩ · cm, MH 0 ; T 0 is the magnetization of the La0.7 Ca0.3 MnO3 , and M 0 is the initial intensity of the magnetization with 4πM 0 2.02 0.02 kG. With Eq. (1) and the experimental data from [23], we can determine the range of the ρ values and also retrieve ρ for different values of H 0 and T 0 . As is well known, conductivity is the reciprocal of resistivity. We computed the range of the conductivity as being from 5.6 × 103 to 1.36 × 106 S∕m. In this range, we employ the three conductivities of 105 , 1.2 × 105 , and 106 S∕m for simulations, which corresponds to the H 0 values of 5083, 5105, and 5193 kA∕m at T 0 272 K, respectively. The occurrence of the CMR effect generally needs the excitation of the strong external magnetic field, while the magnetic field of the plane wave is much weaker than the former. We thus neglect the influence of the plane wave on the CMR effect. By analyzing a material made of magnetite, it is found that the real parts of its permeability approaches unity in the high-frequency range [31]. For simplicity, the permeability of La0.7 Ca0.3 MnO3 is set to 1, and its magnetic loss is neglected in this Letter. The Ansoft high-frequency structure simulator software was used in the simulations. We calculated transmission and reflectivity as functions of the frequency for the three different conductivities mentioned previously. The corresponding results are shown in Fig. 2. It can be seen from the curve for the H 0 values of 5083 kA∕m that only one resonance exists. However, for the other two cases, there is one weak resonance in addition to the main resonance. The line shape of the main resonance is characterized by symmetry, and the resonance is called dipole oscillation. For the two weak resonances displayed in the curves for the H 0 values of 5105 and 5193 kA∕m, both of the line shapes clearly exhibit a characteristic of asymmetry. These are the Fano resonances. Their physical mechanism will be addressed later on in this Letter. From Fig. 2, we also find that the positions of the Fano resonances change as H 0 increases. Their resonance intensities also vary. Our additional simulations show that when the value of H 0 is less than
Fig. 2. (a) Transmission and (b) reflection as functions of the frequency for the H 0 values of 5083, 5105, and 5193 kA∕m.
5083 kA∕m (i.e., the conductivity is lower than 105 S∕m), the Fano resonances do not occur. This signifies that the Fano resonances can be effectively controlled by properly changing the external magnetic field. Additionally, the transmission phases for the three cases in which H 0 5083, 5105, and 5193 kA∕m were also calculated. The corresponding results are shown in Fig. 3. It is obvious that the transmission phases at resonances vary with the increasing value of H 0 . At 130 THz, the phase shift almost reaches a maximum of ΔΦ 1.05 rad, when the intensity of the external magnetic field increases from 5083 to 5193 kA∕m. Hence, the phase of the structure can be well tuned by the external magnetic field. Next, we will explore the cause of the tunable phenomena in Fig. 3, and then we will simulate the current distributions with different phases in the unit cell for different conductivities. The simulated results are shown in Figs. 4 and 5. Figure 4 shows the current distributions with the phases of 0°, 45°, 90°, 135°, and 180° for the conductivity
Fig. 3. Transmission phase as a function of the frequency for the H 0 values of 5083, 5105, and 5193 kA∕m.
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Fig. 6. Electric field distributions in the unit cell with phases of (a) 0°, (b) 45°, (c) 90°, (d) 135°, and (e) 180° for the value of H 0 of 5193 kA∕m.
Fig. 4. Current distributions in the three strips with phases of (a) 0°, (b) 45°, (c) 90°, (d) 135°, and (e) 180° for the H 0 value of 5193 kA∕m.
of 106 S∕m at the resonance of 134 THz, while Fig. 5 shows the current distributions for the conductivity of 105 S∕m with the same phases when the value of H 0 is 5083 kA∕m. From Fig. 4, it can be seen that there are no currents distributed in the La0.7 Ca0.3 MnO3 strip, and that the currents converge in the gold strips. By analyzing the directions of the currents, we can mark the charges distributed in the strips. Electric quadrupoles are shown in Figs. 4(a) and 4(b). These quadrupoles have a characteristic of non-radiation and form a dark mode. When the phase is converted to 135°, only the electric dipoles exist. The electric dipoles can radiate energy to the far field, and are thus viewed as a bright mode. When the phase increases to 180°, the case is similar to that when the phase is 0°. Their differences are the reversal of the charge distributions. From the half period of phase distributions, we can find that there exists the coupling between the dark mode and the bright mode, which induces the Fano resonances observed above. By comparing Fig. 5 with Fig. 4, we can see that electric quadrupoles do not occur in Fig. 5, and that only electric dipoles exist in that figure. This is why only dipole oscillation appears for the case of conductivity of 105 S∕m shown in Fig. 2.
Fig. 5. Current distributions in the three strips with phases of (a) 0°, (b) 45°, (c) 90°, (d) 135°, and (e) 180° for the H 0 value of 5083 kA∕m.
To further comprehend the mechanism of the Fano resonances, we also simulated the electric field distributions in the plane 10 nm away from the top surface of the unit cell, corresponding to the cases shown in Figs. 4 and 5. The simulation results are displayed in Figs. 6 and 7. From Fig. 6, we can see that the electric field in the La0.7 Ca0.3 MnO3 strip is very strong. This indicates that there is energy stored in the area. Such an energy storage process is necessary for the generation of Fano resonances. This is the formation process of the dark mode (or dark atoms). It is similar to that mentioned in [2]. Unlike the case shown in Fig. 6, almost no electric field is distributed in the La0.7 Ca0.3 MnO3 strip for the case shown in Fig. 7. This is because there is no energy storage during the process, and the electromagnetic energy is radiated outward by the electric dipole oscillation. Fano resonances are often accompanied by analogues of electromagnetically induced transparency (EIT). We therefore investigated the electromagnetic absorption of the structure for the H 0 values of 5083, 5105, and 5193 kA∕m. According to the reflection R and the transmission T, the resulting electromagnetic absorption can be calculated by 1 − T − R. The simulation results are
Fig. 7. Electric field distributions in the unit cell with phases of (a) 0°, (b) 45°, (c) 90°, (d) 135°, and (e) 180° for the value of H 0 of 5083 kA∕m.
Fig. 8. Absorption as a function of the frequency for the H 0 values of 5083, 5105, and 5193 kA∕m.
April 1, 2015 / Vol. 40, No. 7 / OPTICS LETTERS
shown in Fig. 8. It is found that almost no EIT occurs. There is one exception: the absorption curve for H 0 5105 kA∕m exhibits a very weak EIT. This is because the resistivity of the La0.7 Ca0.3 MnO3 material is still relatively high, despite the fact that it decreases significantly under the influence of strong external magnetic field. This decrease makes the Ohmic loss stronger than the coupling energy between the electric dipoles and electric quadruples. Thus, it is difficult to observe an analogue of EIT. In conclusion, a periodic structure, each unit cell of which is composed of one La0.7 Ca0.3 MnO3 strip with a CMR effect and two gold strips, is discussed in this Letter. The simulation results demonstrate that the structure exhibits a characteristic of tunable Fano resonances. The reason for the tunability is that the conductivity of La0.7 Ca0.3 MnO3 changes considerably with increasing intensity of the external magnetic field. The simulation results also demonstrate that the transmission phase of the structure is effectively tuned. The phase shift reaches ΔΦ 1.05 rad at 130 THz when the external magnetic field varies from 5083 to 5193 kA∕m. Such a structure has the potential for practical applications in controllable photoelectric devices. The project is supported by the Graduate Innovation Project of Jiangsu Normal University (2013YYB138), the National Natural Science Foundation of China (61401182 and 61372057), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), China. References 1. B. Luk'yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010). 2. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, Phys. Rev. Lett. 101, 047401 (2008). 3. F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, ACS Nano 3, 643 (2009). 4. Y. Sonnefraud, N. Verellen, H. Sobhani, G. A. E. Vandenbosch, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, ACS Nano 4, 1664 (2010). 5. J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, Science 328, 1135 (2010). 6. M. Hentschel, M. Saliba, R. Vogelgesang, H. Giessen, A. P. Alivisatos, and N. Liu, Nano Lett. 10, 2721 (2010).
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