Tunable plasmon-induced transparency in hybrid waveguide-magnetic resonance system Jiakun Song, Yuzhi Song, Kangwen Li, Zuyin Zhang, Xin Wei, Yun Xu, and Guofeng Song* Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China *Corresponding author: [email protected] Received 16 December 2014; revised 10 February 2015; accepted 10 February 2015; posted 11 February 2015 (Doc. ID 230867); published 13 March 2015
We present a hybrid waveguide-magnetic resonance system with split ring resonators (SRRs) periodically arranged on top of a waveguide layer. Due to the destructive interference between the electric coupling to the magnetic resonance mode generated in the SRRs and the TE/TM waveguide modes supported by the waveguide layer, double plasmon-induced transparency is obtained at the infrared wavelength. Furthermore, the PIT resonance can be dynamically tuned by the incident angle. An ultranarrow PIT window with an FWHM of 7 nm is observed at the wavelength of 1.448 μm. The group index at the narrow PIT window can reach up to 100. We also demonstrate that the refractive index sensitivity and the figure of merit value can reach up to 640 nm∕RIU and 64 in the sensing range, respectively. The proposed hybrid waveguide-magnetic resonance system with a high-quality factor PIT window is promising for efficient optical sensing, optical switching, and slow-light device design. © 2015 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (310.6628) Subwavelength structures, nanostructures; (260.2110) Electromagnetic optics. http://dx.doi.org/10.1364/AO.54.002279
1. Introduction
Plasmon-induced transparency (PIT) as a result of the quantum interference effect in metallic nanostructures has drawn much attention since it was investigated for its extraordinary characters, such as room temperature operation, large bandwidth, and easy integration into nanoplasmonic circuits. Similar to the electromagnetically induced transparency in an atomic system, plasmon-induced transparency can be considered as the coupling of the bright–dark mode or the bright–bright mode. Up to now, a variety of structures and systems have been proposed to realize PIT resonance, such as optical antennas [1], optical resonances [2–4], and plasmon-waveguide systems [5–7]. Usually, the bandwidth of the PIT window is broad, which blocks their applications in 1559-128X/15/092279-04$15.00/0 © 2015 Optical Society of America
high-performance sensing and modulation. In pursuit of a high-quality PIT window, more efficient nanostructures and coupled systems were experimentally or theoretically demonstrated [8–10]. For example, Liu et al. proposed a hybrid waveguideplasmon system, which serves as a high-performance refractive index sensor with a notable figure of merit (FOM) value of 28.8 [5], and Wang et al. proposed a novel planar metamaterial design for electromagnetically induced transparency and slow light with the group index, and the quality (Q) factor can reach up to 1.2 × 103 and 97, respectively [11]. Usually, the frequency of plasmon-induced resonance is no longer changed, as long as the geometrical dimensions of the nanostructure are confirmed [12]. While the realization of active manipulation of the plasmoninduced transparency would be much desired in practical application, such as filters and swich devices, up to now, several approaches have been proposed to achieve dynamic tunability of PIT 20 March 2015 / Vol. 54, No. 9 / APPLIED OPTICS
2279
effects [13–16]. In this article, we propose a waveguide-magnetic resonance system to realize plasmon-induced transparency, which consists of split ring resonators (SRRs) periodically arranged on top of a waveguide layer. Due to the destructive interference between the electric coupling to the magnetic resonance (EEMR) mode and the TE/TM waveguide modes, double plasmon-induced transparency resonance is obtained. We also demonstrate that the coupling between the EEMR and the waveguide modes can be dynamically tuned by the incident angle. At the incident angle of 60°, an ultranarrow PIT window with an FWHM of 7 nm (Q factor ∼207) is obtained at the wavelength of 1.448 μm, which is much desired in light-slowing devices and high-performance refractive index sensors. The group index at the narrow PIT window can reach up to 100. Furthermore, the refractive index sensitivity (S) and the FOM value can reach as large as 640 nm∕RIU and 64 in the sensing range, respectively. 2. Structure Design and Simulation Method
Figure 1(a) shows the tilt view of our proposed hybrid waveguide-magnetic resonance system with SRRs squarely arranged on top of a waveguide layer (ε 3.8). The unit cell of the structure with geometrical parameters indicated are shown schematically in Fig. 1(b). The thickness of the SRRs is 50 nm. As the electric field component of the incident light parallel to the bottom part of the SRR, the low-quality factor EEMR mode is excited [17]. The resonance frequency of the EEMR mode can be tuned by the geometrical parameters of the SRR structure. The permittivity of Au is described by the Drude model, with plasmon frequency ωp 1.37e16 Hz and damping constant ωt 8.143e13 Hz [18]. Below the SRR structures is a 300 nm dielectric waveguide layer. A high-quality factor waveguide mode can be excited in the waveguide layer due to the momentum conservation produced by periodicity of the lattice. Rigorous coupled wave analysis is performed in the simulation to obtain the absorption and transmission spectra of the designed structure.
Fig. 2. (a) Calculated transmission as a function of incident light frequency and transverse wave vector of the hybrid waveguidemagnetic resonance system. Black and green dashed lines are the dispersion curves of the TE and TM waveguide mode in a three-layer symmetry slab waveguide, respectively. (b) Transmission, reflection, and absorption spectra of the hybrid waveguidemagnetic resonance system at the incident angle of 40°. Magnetic field (c) distribution at the wavelength of 1.161 μm and the electric field (d) distribution at the wavelength of 1.330 μm in the x–z plane.
resonance structure as a function of transverse wave vector and frequency. The broad transmission dip around 0.693 μm−1 is the typical EEMR mode, which is not affected by the transverse wave vector [19]. Desired EEMR resonance frequency can be obtained by appropriate optimizing the geometrical parameters of the SRR structure [20]. With the periodic lattice produced by the SRRs sitting on the waveguide layer, waveguide modes are generated in the waveguide layer. The eigenvalue equation of TE and TM waveguide modes in a three-layer symmetry slab waveguide are given by γ1d γ mπ arctan 2 ; 2 γ1
(1)
Figure 2(a) shows the simulated transmission dispersion of the hybrid waveguide-magnetic
γ1d ε1 γ 2 mπ arctan ; ε2 γ 1 2
(2)
Fig. 1. (a) Tile view of the hybrid waveguide-magnetic resonance system with the SRRs periodic sitting on the top of the waveguide layer. (b) Unit cell of the SRR structure with geometrical parameters indicated. Geometrical parameters are w 160, l 200, d 60, h 100, and Px Py 600 nm.
where γ 21 k20 ε1 − β2 , γ 22 β2 − k20 ε2 , m is an integer, d is the thickness of the waveguide layer, and β is the propagation constants. The black and green dashed lines shown in Fig. 2(a) correspond to the TE and TM waveguide modes in a three-layer symmetry slab waveguide, respectively. At the increase of the transverse wave vector, the waveguide modes gradually overlap with the EEMR mode. Due to the destructive interference between the EEMR mode and the TE/ TM waveguide modes, typical double PIT resonance is observed. Figure 2(b) shows the transmission, reflection, and absorption spectra of the hybrid waveguide-magnetic resonance structure at the
3. Simulation Results
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incident angle of 40°, which corresponds to the blue dashed line in Fig. 2(a). The two absorption peaks correspond to the hybrid TE and TM waveguide modes as a result of the interaction between the EEMR mode and the TE/TM waveguide modes. To further understand the characteristic of the resonances, electromagnetic field distributions of the EEMR mode and the hybrid TE and TM waveguide modes are investigated. Inset of Fig. 2(b) shows the EEMR mode with magnetic (H z ) field mainly localized within the SRR gap. The EEMR mode couples strongly with the incident light and serves as the bright mode. Furthermore, the incident angle does not have an effect on the resonance frequency of the EEMR mode. The magnetic field (H y ) distribution shown in Fig. 2(c) and electric field (Ey ) distribution shown in Fig. 2(d) on the x–z plane are hybrid TM and TE waveguide modes, respectively. According to momentum conservation given by 2π β k0 sinθ m 2π Px n Py , the TE and TM waveguide modes can be tuned by the period of the SRRs and the incident angles. While, the EEMR resonance frequency is not affected by the changing of the period of the SRRs and the incident angles. As a result, the hybrid waveguide-magnetic resonance frequencies can be tuned to the desired frequency by optimizing the period of the SRRs. Furthermore, the interaction between the EEMR mode and waveguide mode can be dynamically tuned by the incident angle. Figure 3(a) shows the transmission spectra of the structure with Px Py 0.6 μm at different incident angles. As the incident angle increases from 0° to 80° with 20° steps, the TE and TM waveguide modes gradually shift to longer wavelengths and couple with the EEMR resonance mode. At large incident angles, typical double PIT resonances generate, and the quality of the PIT windows are improved. Simply by varying the incident angle, the transmission spectra of the hybrid waveguidemagnetic resonance system can be dynamically tuned from single transmission dip to double PIT windows, which is promising for active slow-light devices, tunable sensors, and switcher designs. The influence of the period Px and Py on the coupling between TE/TM waveguide modes and EEMR mode is illustrated in Figs. 3(b) and 3(c), respectively. At the incident angle of 60°, the hybrid TE and TM resonance wavelengths increase with Px for fixed Py 0.6 μm and have not change with Py for fixed Px 0.6 μm.
Fig. 3. (a) Calculated transmission spectra of the hybrid waveguide-magnetic resonance system with Px Py 0.6 μm at different incident angles. Transmission spectra of the hybrid waveguide-magnetic resonance system with fixed Py 0.6 μm (b) and fixed Px 0.6 μm (c) at the incident angle of 60°.
transmission phase and group index are shown in Fig. 4(b). Strong transmission phase dispersion is observed around the PIT windows, which results in a
4. Application for Slowing Light and Refractive Index Sensing
Figure 4(a) shows the transmission, reflection, and absorption spectra of the structure with Px Py 0.6 μm at the incident angle of 60°. An ultranarrow PIT window at a wavelength of 1.448 μm with an FWHM of 7 nm (Q factor ∼207) is obtained. Furthermore, the transmission intensity at the PIT window can reach up to 90%. The corresponding
Fig. 4. (a) Transmission, reflection, and absorption spectra of the hybrid waveguide-magnetic resonance system with Px Py 0.6 μm at the incident angle of 60°. (b) Corresponding transmission phase and group index. (c) Transmission peak shifting with the surrounding refractive index increase from 1 to 1.5. 20 March 2015 / Vol. 54, No. 9 / APPLIED OPTICS
2281
large group index. The group index can be evaluated from the relation: ng −
c0 dφω d dω
where c0 is the speed of light in the free space, d is the thickness of the structure in the z direction, and ϕ is the transmission phase as a function of the angular frequency ω. The group index of the right narrow PIT window can reach up to 100, which can be used to design slow-light devices. The sensing performance of the hybrid waveguidemagnetic resonance system is also investigated for its particularly narrow PIT window. Figure 4(c) shows the transmission peak shifting Δλ of the structure with Px Py 0.6 μm at the incident angle of 60° as a function of refractive index change Δn in the sensing range of 1–1.5. The refractive index sensitivity can reach up to about 640 nm per refractive index unit (RIU). A small refractive index change of 0.01 can also be detected. The corresponding FOM S∕FWHM value is about 64. The high sensitivity and large FOM value would be desired in a high-performance refractive index sensor. 5. Conclusion
In conclusion, we have proposed a hybrid waveguidemagnetic resonance system to realize plasmoninduced transparency. Due to the coupling between the TE/TM waveguide modes and the magnetic resonance mode, two typical PIT windows are observed in the broad absorption band in the infrared wavelength. The PIT resonances can be tuned by the period of the SRRs and dynamically tuned by the incident angle. At the incident angle of 60°, an ultranarrow PIT window with an FWHM of 7 nm is observed at the wavelength of 1.448 μm. Meanwhile, the transmission intensity of the long wavelength PIT window can reach up to 90%. The proposed hybrid waveguide-magnetic resonance system with an ultranarrow PIT window is promising for lightslowing devices and sensing device design. This work is supported by the National Basic Research Program of China (nos. 2011CBA00608, 2012CB619203, 2015CB351902, 2015CB932402) and the National Key Research Program of China under grant no. 2011ZX01015-001. The National Natural Science Foundation of China under grant nos. 61036010, 61177070, 11374295, and U1431231 are acknowledged. References 1. A. Pors, M. Willatzen, O. Albrektsen, and S. I. Bozhevolnyi, “Detuned electrical dipoles metamaterial with bianisotropic response,” Phys. Rev. B 83, 245409 (2011).
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2. D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004). 3. J. B. Khurgin and P. A. Morton, “Tunable wideband optical delay line based on balanced coupled resonator structures,” Opt. Lett. 34, 2655–2657 (2009). 4. Q. F. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. H. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006). 5. J. T. Liu, B. Z. Xu, J. Zhang, and G. F. Song, “Double plasmoninduced transparency in hybrid waveguide-plasmon system and its application for localized plasmon resonance sensing with high figure of merit,” Plasmonics 8, 995–1001 (2013). 6. V. Yannopapas, E. Paspalakis, and N. V. Vitanov, “Electromagnetically induced transparency and slow light in an array of metallic nanoparticles,” Phys. Rev. B 80, 035104 (2009). 7. J. Zhang, W. L. Bai, L. K. Cai, Y. Xu, G. F. Song, and Q. Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett. 99, 181120 (2011). 8. L. Qin, K. Zhang, R. W. Peng, X. Xiong, W. Zhang, X. R. Huang, and M. Wang, “Optical-magnetism-induced transparency in a metamaterial,” Phys. Rev. B 87, 125136 (2013). 9. X. Duan, S. Chen, H. Cheng, Z. Li, and J. Tian, “Dynamically tunable plasmonically induced transparency by planar hybrid metamaterial,” Opt. Lett. 38, 483–485 (2013). 10. H. Cheng, S. Q. Chen, P. Yu, X. Y. Duan, B. Y. Xie, and J. G. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103, 203112 (2013). 11. J. Q. Wang, B. H. Yuan, C. Z. Fan, J. N. He, P. Ding, Q. Z. Xue, and E. J. Liang, “A novel planar metamaterial design for electromagnetically induced transparency and slow light,” Opt. Express 21, 25159–25166 (2013). 12. H. Lu, X. Liu, G. Wang, and D. Mao, “Tunable high-channelcount bandpass plasmonic filters based on an analogue of electromagnetically induced transparency,” Nanotechnology 23, 444003 (2012). 13. J. Q. Gu, R. Singh, X. J. Liu, X. Q. Zhang, Y. F. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. G. Han, and W. L. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012). 14. W. Cao, R. Singh, C. H. Zhang, J. G. Han, M. Tonouchi, and W. L. Zhang, “Plasmon-induced transparency in metamaterials: active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103, 101106 (2013). 15. C. Zeng, J. Guo, and X. M. Liu, “High-contrast electro-optic modulation of spatial light induced by graphene-integrated Fabry–Perot microcavity,” Appl. Phys. Lett. 105, 121103 (2014). 16. C. Zeng, Y. Cui, and X. Liu, “Tunable multiple phase-coupled plasmon-induced transparencies in graphene metamaterials,” Opt. Express 23, 545–551 (2015). 17. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004). 18. B. Kante, Y. S. Park, K. O’Brien, D. Shuldman, N. D. Lanzillotti-Kimura, Z. Jing Wong, X. Yin, and X. Zhang, “Symmetry breaking and optical negative index of closed nanorings,” Nat. Commun. 3, 1180 (2012). 19. T. Tomioka, S. Kubo, M. Nakagawa, M. Hoga, and T. Tanaka, “Split-ring resonators interacting with a magnetic field at visible frequencies,” Appl. Phys. Lett. 103, 071104 (2013). 20. C. Jeppesen, N. A. Mortensen, and A. Kristensen, “Capacitance tuning of nanoscale split-ring resonators,” Appl. Phys. Lett. 95, 193108 (2009).
We present a hybrid waveguide-magnetic resonance system with split ring resonators (SRRs) periodically arranged on top of a waveguide layer. Due to the destructive interference between the electric coupling to the magnetic resonance mode generated in the SRRs and the TE/TM waveguide modes supported by the waveguide layer, double plasmon-induced transparency is obtained at the infrared wavelength. Furthermore, the PIT resonance can be dynamically tuned by the incident angle. An ultranarrow PIT window with an FWHM of 7 nm is observed at the wavelength of 1.448 μm. The group index at the narrow PIT window can reach up to 100. We also demonstrate that the refractive index sensitivity and the figure of merit value can reach up to 640 nm∕RIU and 64 in the sensing range, respectively. The proposed hybrid waveguide-magnetic resonance system with a high-quality factor PIT window is promising for efficient optical sensing, optical switching, and slow-light device design. © 2015 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (310.6628) Subwavelength structures, nanostructures; (260.2110) Electromagnetic optics. http://dx.doi.org/10.1364/AO.54.002279
1. Introduction
Plasmon-induced transparency (PIT) as a result of the quantum interference effect in metallic nanostructures has drawn much attention since it was investigated for its extraordinary characters, such as room temperature operation, large bandwidth, and easy integration into nanoplasmonic circuits. Similar to the electromagnetically induced transparency in an atomic system, plasmon-induced transparency can be considered as the coupling of the bright–dark mode or the bright–bright mode. Up to now, a variety of structures and systems have been proposed to realize PIT resonance, such as optical antennas [1], optical resonances [2–4], and plasmon-waveguide systems [5–7]. Usually, the bandwidth of the PIT window is broad, which blocks their applications in 1559-128X/15/092279-04$15.00/0 © 2015 Optical Society of America
high-performance sensing and modulation. In pursuit of a high-quality PIT window, more efficient nanostructures and coupled systems were experimentally or theoretically demonstrated [8–10]. For example, Liu et al. proposed a hybrid waveguideplasmon system, which serves as a high-performance refractive index sensor with a notable figure of merit (FOM) value of 28.8 [5], and Wang et al. proposed a novel planar metamaterial design for electromagnetically induced transparency and slow light with the group index, and the quality (Q) factor can reach up to 1.2 × 103 and 97, respectively [11]. Usually, the frequency of plasmon-induced resonance is no longer changed, as long as the geometrical dimensions of the nanostructure are confirmed [12]. While the realization of active manipulation of the plasmoninduced transparency would be much desired in practical application, such as filters and swich devices, up to now, several approaches have been proposed to achieve dynamic tunability of PIT 20 March 2015 / Vol. 54, No. 9 / APPLIED OPTICS
2279
effects [13–16]. In this article, we propose a waveguide-magnetic resonance system to realize plasmon-induced transparency, which consists of split ring resonators (SRRs) periodically arranged on top of a waveguide layer. Due to the destructive interference between the electric coupling to the magnetic resonance (EEMR) mode and the TE/TM waveguide modes, double plasmon-induced transparency resonance is obtained. We also demonstrate that the coupling between the EEMR and the waveguide modes can be dynamically tuned by the incident angle. At the incident angle of 60°, an ultranarrow PIT window with an FWHM of 7 nm (Q factor ∼207) is obtained at the wavelength of 1.448 μm, which is much desired in light-slowing devices and high-performance refractive index sensors. The group index at the narrow PIT window can reach up to 100. Furthermore, the refractive index sensitivity (S) and the FOM value can reach as large as 640 nm∕RIU and 64 in the sensing range, respectively. 2. Structure Design and Simulation Method
Figure 1(a) shows the tilt view of our proposed hybrid waveguide-magnetic resonance system with SRRs squarely arranged on top of a waveguide layer (ε 3.8). The unit cell of the structure with geometrical parameters indicated are shown schematically in Fig. 1(b). The thickness of the SRRs is 50 nm. As the electric field component of the incident light parallel to the bottom part of the SRR, the low-quality factor EEMR mode is excited [17]. The resonance frequency of the EEMR mode can be tuned by the geometrical parameters of the SRR structure. The permittivity of Au is described by the Drude model, with plasmon frequency ωp 1.37e16 Hz and damping constant ωt 8.143e13 Hz [18]. Below the SRR structures is a 300 nm dielectric waveguide layer. A high-quality factor waveguide mode can be excited in the waveguide layer due to the momentum conservation produced by periodicity of the lattice. Rigorous coupled wave analysis is performed in the simulation to obtain the absorption and transmission spectra of the designed structure.
Fig. 2. (a) Calculated transmission as a function of incident light frequency and transverse wave vector of the hybrid waveguidemagnetic resonance system. Black and green dashed lines are the dispersion curves of the TE and TM waveguide mode in a three-layer symmetry slab waveguide, respectively. (b) Transmission, reflection, and absorption spectra of the hybrid waveguidemagnetic resonance system at the incident angle of 40°. Magnetic field (c) distribution at the wavelength of 1.161 μm and the electric field (d) distribution at the wavelength of 1.330 μm in the x–z plane.
resonance structure as a function of transverse wave vector and frequency. The broad transmission dip around 0.693 μm−1 is the typical EEMR mode, which is not affected by the transverse wave vector [19]. Desired EEMR resonance frequency can be obtained by appropriate optimizing the geometrical parameters of the SRR structure [20]. With the periodic lattice produced by the SRRs sitting on the waveguide layer, waveguide modes are generated in the waveguide layer. The eigenvalue equation of TE and TM waveguide modes in a three-layer symmetry slab waveguide are given by γ1d γ mπ arctan 2 ; 2 γ1
(1)
Figure 2(a) shows the simulated transmission dispersion of the hybrid waveguide-magnetic
γ1d ε1 γ 2 mπ arctan ; ε2 γ 1 2
(2)
Fig. 1. (a) Tile view of the hybrid waveguide-magnetic resonance system with the SRRs periodic sitting on the top of the waveguide layer. (b) Unit cell of the SRR structure with geometrical parameters indicated. Geometrical parameters are w 160, l 200, d 60, h 100, and Px Py 600 nm.
where γ 21 k20 ε1 − β2 , γ 22 β2 − k20 ε2 , m is an integer, d is the thickness of the waveguide layer, and β is the propagation constants. The black and green dashed lines shown in Fig. 2(a) correspond to the TE and TM waveguide modes in a three-layer symmetry slab waveguide, respectively. At the increase of the transverse wave vector, the waveguide modes gradually overlap with the EEMR mode. Due to the destructive interference between the EEMR mode and the TE/ TM waveguide modes, typical double PIT resonance is observed. Figure 2(b) shows the transmission, reflection, and absorption spectra of the hybrid waveguide-magnetic resonance structure at the
3. Simulation Results
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incident angle of 40°, which corresponds to the blue dashed line in Fig. 2(a). The two absorption peaks correspond to the hybrid TE and TM waveguide modes as a result of the interaction between the EEMR mode and the TE/TM waveguide modes. To further understand the characteristic of the resonances, electromagnetic field distributions of the EEMR mode and the hybrid TE and TM waveguide modes are investigated. Inset of Fig. 2(b) shows the EEMR mode with magnetic (H z ) field mainly localized within the SRR gap. The EEMR mode couples strongly with the incident light and serves as the bright mode. Furthermore, the incident angle does not have an effect on the resonance frequency of the EEMR mode. The magnetic field (H y ) distribution shown in Fig. 2(c) and electric field (Ey ) distribution shown in Fig. 2(d) on the x–z plane are hybrid TM and TE waveguide modes, respectively. According to momentum conservation given by 2π β k0 sinθ m 2π Px n Py , the TE and TM waveguide modes can be tuned by the period of the SRRs and the incident angles. While, the EEMR resonance frequency is not affected by the changing of the period of the SRRs and the incident angles. As a result, the hybrid waveguide-magnetic resonance frequencies can be tuned to the desired frequency by optimizing the period of the SRRs. Furthermore, the interaction between the EEMR mode and waveguide mode can be dynamically tuned by the incident angle. Figure 3(a) shows the transmission spectra of the structure with Px Py 0.6 μm at different incident angles. As the incident angle increases from 0° to 80° with 20° steps, the TE and TM waveguide modes gradually shift to longer wavelengths and couple with the EEMR resonance mode. At large incident angles, typical double PIT resonances generate, and the quality of the PIT windows are improved. Simply by varying the incident angle, the transmission spectra of the hybrid waveguidemagnetic resonance system can be dynamically tuned from single transmission dip to double PIT windows, which is promising for active slow-light devices, tunable sensors, and switcher designs. The influence of the period Px and Py on the coupling between TE/TM waveguide modes and EEMR mode is illustrated in Figs. 3(b) and 3(c), respectively. At the incident angle of 60°, the hybrid TE and TM resonance wavelengths increase with Px for fixed Py 0.6 μm and have not change with Py for fixed Px 0.6 μm.
Fig. 3. (a) Calculated transmission spectra of the hybrid waveguide-magnetic resonance system with Px Py 0.6 μm at different incident angles. Transmission spectra of the hybrid waveguide-magnetic resonance system with fixed Py 0.6 μm (b) and fixed Px 0.6 μm (c) at the incident angle of 60°.
transmission phase and group index are shown in Fig. 4(b). Strong transmission phase dispersion is observed around the PIT windows, which results in a
4. Application for Slowing Light and Refractive Index Sensing
Figure 4(a) shows the transmission, reflection, and absorption spectra of the structure with Px Py 0.6 μm at the incident angle of 60°. An ultranarrow PIT window at a wavelength of 1.448 μm with an FWHM of 7 nm (Q factor ∼207) is obtained. Furthermore, the transmission intensity at the PIT window can reach up to 90%. The corresponding
Fig. 4. (a) Transmission, reflection, and absorption spectra of the hybrid waveguide-magnetic resonance system with Px Py 0.6 μm at the incident angle of 60°. (b) Corresponding transmission phase and group index. (c) Transmission peak shifting with the surrounding refractive index increase from 1 to 1.5. 20 March 2015 / Vol. 54, No. 9 / APPLIED OPTICS
2281
large group index. The group index can be evaluated from the relation: ng −
c0 dφω d dω
where c0 is the speed of light in the free space, d is the thickness of the structure in the z direction, and ϕ is the transmission phase as a function of the angular frequency ω. The group index of the right narrow PIT window can reach up to 100, which can be used to design slow-light devices. The sensing performance of the hybrid waveguidemagnetic resonance system is also investigated for its particularly narrow PIT window. Figure 4(c) shows the transmission peak shifting Δλ of the structure with Px Py 0.6 μm at the incident angle of 60° as a function of refractive index change Δn in the sensing range of 1–1.5. The refractive index sensitivity can reach up to about 640 nm per refractive index unit (RIU). A small refractive index change of 0.01 can also be detected. The corresponding FOM S∕FWHM value is about 64. The high sensitivity and large FOM value would be desired in a high-performance refractive index sensor. 5. Conclusion
In conclusion, we have proposed a hybrid waveguidemagnetic resonance system to realize plasmoninduced transparency. Due to the coupling between the TE/TM waveguide modes and the magnetic resonance mode, two typical PIT windows are observed in the broad absorption band in the infrared wavelength. The PIT resonances can be tuned by the period of the SRRs and dynamically tuned by the incident angle. At the incident angle of 60°, an ultranarrow PIT window with an FWHM of 7 nm is observed at the wavelength of 1.448 μm. Meanwhile, the transmission intensity of the long wavelength PIT window can reach up to 90%. The proposed hybrid waveguide-magnetic resonance system with an ultranarrow PIT window is promising for lightslowing devices and sensing device design. This work is supported by the National Basic Research Program of China (nos. 2011CBA00608, 2012CB619203, 2015CB351902, 2015CB932402) and the National Key Research Program of China under grant no. 2011ZX01015-001. The National Natural Science Foundation of China under grant nos. 61036010, 61177070, 11374295, and U1431231 are acknowledged. References 1. A. Pors, M. Willatzen, O. Albrektsen, and S. I. Bozhevolnyi, “Detuned electrical dipoles metamaterial with bianisotropic response,” Phys. Rev. B 83, 245409 (2011).
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