- Email: [email protected]
Optical refractive nanosensor with planar resonators metamaterial
Optics Communications 338 (2015) 399–405
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Optical refractive nanosensor with planar resonators metamaterial Junqiao Wang a,n, Kaijun Mu a, Fengying Ma a, Huaping Zang a, Chunzhen Fan a, Jinna He a, Erjun Liang a, Pei Ding b a School of Physical Science and Engineering and Key Laboratory of Materials Physics of Ministry of Education of China, Zhengzhou University, Zhengzhou 450052, China b Department of Mathematics and Physics, Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou 450015, China
art ic l e i nf o
a b s t r a c t
Article history: Received 26 August 2014 Received in revised form 28 October 2014 Accepted 4 November 2014 Available online 12 November 2014
We numerically investigated the optical properties of planar resonators metamaterial that exhibits two narrow transmitted dips with quality factors of 23 and 50 in the optical regions. The results show that, both of the two resonances reveal a distinct plasmon shift with respect to a small fluctuation in the refractive index of the surrounding medium, and calculated average refractive index sensitivities are 900 nm/RIU and 493 nm/RIU, and corresponding figure of merits of two modes are 16 and 32 in vacuum, respectively. The sensing performance can be improved by changing the geometric parameters of planar metamaterial due to the plasmon modes coupling effect, which offer an excellent potential for optical nanosensing applications. & Elsevier B.V. All rights reserved.
Keywords: Metamaterials Sensors Resonance
Plasmonic nanostructures are of considerable current interest because of their unusual electromagnetic and optical characteristics and the prominent applications in surface enhanced Raman scattering (SERS) [1], biological and chemical sensing [2], perfect light absorption [3], optical antennas and switching [4], slow-light devices [5], and imaging and cloaking. [6,7] The unique ability of plasmon to focus incident light into subwavelength regions near metal nanostructure surfaces can lead to very large local field concentration. In addition to localized confinement of enhanced near-fields energy, plasmon resonances in nanostructures are sensitive to surrounding environments, and generally, the electromagnetic responses of plasmon resonances in metal nanostructures are commonly broad-band with large plasmon lifetime and low quality factor (Q factor) due to the significant radiation losses, which is unexpected in chemical/biological nanosensors. However, the resonant characteristics of metal nanostructures can be controlled by adjusting the shape, size and composition of nanostructure. As for sensing application, we appreciate the plasmon resonances with the both narrow optical spectra and large figure of merit (FOM), which indicate that the weak changes in surrounding environments can be perceived through direct observation of spectral shift of plasmon resonances. In the past few decades, conventional plasmon resonance sensors based on surface plasmon resonance for a thin metal film and the localized surface plasmon resonance(LSPR) supported on n
Corresponding author. E-mail address: [email protected] (J. Wang).
http://dx.doi.org/10.1016/j.optcom.2014.11.009 0030-4018/& Elsevier B.V. All rights reserved.
isolated nanoparticles have been of great attention and widely studied [8,9]. Anker et al. reviewed developments on improving the sensitivity of optical sensors based on metal nanoparticle arrays and single nanoparticles [10]. Furthermore, recently, a lot of efforts have been applied to identify the high sensitive nanosensors based on plasmonic metamaterial. Liu group and Li group introduced a novel plasmonic sensor which combined the concepts of a perfect metamaterial absorber and an LSPR sensor in near-infrared region [11,12]. Pryce et al. investigated how the mechanical deformation of compliant metamaterials can be used to create new types of tunable sensing surfaces, they used split ring resonator (SRR) metamaterial on polydimethylsiloxane to demonstrate refractive index sensing with FOM of up to 10.1 [13]. Ren et al. proposed a plasmonic sensor based on a spiral G-shaped metamaterial, they achieved a spectral shift sensitivity of 410 nm/ RIU and a FOM of 17 in the near-infrared region [14]. Mock et al. utilized the coupling between LSPR and propagating surface plasmon to probe the highly sensitive distance-dependent LSPR of the gaps [15]. In addition, Prodan et al. presented the plasmon hybridization concept in 2003, which can be used to describe the plasmon response of complex nanostructures of arbitrary shape [16]. Using the plasmon hybridization concept, the plasmon modes can be classified according to their irreducible representations, and a variety of nanostructures have been experimentally and theoretically exploited to improve performance of plasmonic nanosensors recognizing the variation of local refractive index [17– 19]. Furthermore, due to hybridization between broad superradiant modes (bright modes) and narrow subradiant modes (dark modes) can induce Fano resonance exhibiting an asymmetric
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sharp line shape and generating a large electromagnetic field congregation, many researchers have paid attention to plasmonic metamaterial that induces Fano resonances in their optical spectra as a sensing platform [20–27]. For example, Zhang et al. analyzed the plasmon mode interactions of a metallic nanocube on a dielectric substrate, and symmetry-breaking introduced by an adjacent semi-infinite dielectric can introduce coupling and hybridization of the plasmon modes of a metallic nanostructure, which provided a new insight for achieving plasmonic Fano-resonant LSPR sensors with FOM of 20 [23]. Furthermore, electromagnetically induced transparency (EIT) phenomenon with narrow transparency band can be manipulated by Fano resonances through symmetry breaking, which is desirable for sensing applications due to narrow spectral width. Liu et al. demonstrated that a plasmonic EIT analog could be achieved using a planar complementary metamaterial which consists of cut-out structures in a homogeneous gold film, however, this metamaterial sensor only has a small FOM of 3.8 in the near-infrared regions [28]. Dong et al. designed a planar metamaetial composed of three metal bars, which revealed the gain-assisted plasmonic analog of EIT for the purpose to enhance the sensing [29]. In this paper, we theoretically discussed the optical properties of a designed planar metamaterial with two sharp transmitted dips. The designed planar metamaterial is the recombination of paired SRRs and metallic cavity, and the hybridization of LC resonance and cavity plasmon leads to two distinct dips in transmitted spectrum. By adjusting the geometric parameters of designed metamaterial, the plasmon resonance modes reveal narrow line width and large FOM, which offer a potential for biosensing in the optical and near-infrared regions. In comparison to other plasmonic systems, the high sensing performance with large FOM can be achieved in this planar metamaterial by strong plasmon modes coupling effect, which provide further insight into designing the excellent plasmonic nanosensors. Fig. 1(a) and (b) shows a typically periodical array of the designed silver planar metamaterial and a sketch of a unit cell with relevant geometric parameters, respectively. The geometrical parameters are chosen as follows: P ¼540 nm, s¼ 120 nm, a ¼420 nm, w¼ 40 nm, l ¼110 nm and g ¼20 nm. The dielectric constants of silver measured by Palik are used to model the planar metamaterial, and the thickness is fixed as 60 nm [30]. The planar metamaterial is located on the SiO2 substrate of thickness 100 nm and dielectric constants ε ¼1.96. The metamaterial is illuminated by a normal incident plane wave with an electric field polarization parallel to the y-axis. The simulation is carried out by the time domain solver of 3-D electromagnetic package (CST Microwave Studio), where the computational domain is truncated by Perfectly Matched Layers in the z-direction and the periodic boundary conditions are used to truncate the unit cell in the x–y plane. During simulating, the good convergence for calculated result can be obtained by utilizing adaptive meshing technique to handle the structure boundaries and geometries that need large aspect ratios of meshes. Fig. 1(c) shows the simulated transmitted spectrum of the planar metamaterial as designated in Fig. 1(a) and (b). By using the structural parameters as described above, we obtained two narrow plasmon resonances around P1 ¼224 THz and P2 ¼385 THz, respectively, where the fitted full width at half maximum (FWHM) are about 9.9 THz and 7.7 THz, respectively. The calculated Q factor (Q¼ ω0/FWHM) of P1 and P2 modes are Q1 ¼ 23 and Q2 ¼ 50, respectively. In addition, due to the structure asymmetry of the metamaterial in x and y directions, the responses of x and y polarized light are different, and only one broadened resonance dip appears in spectrum with x polarized light. The plasmon resonances with the narrow line width and high Q factor are two appreciated characteristics for achieving high
sensing performance in metamaterial sensor. In order to investigate the sensing performance of the designed planar metamaterial, we calculated the transmitted spectra in different dielectric environments (i.e. keep the substrate and change the permittivity of the upper space) as presented in Fig. 2(a). With the increasing of the refractive index of dielectric environments, both of the plasmon resonances P1 and P2 exhibit a red-shift in transmitted spectra. This can be understood by the fact that the resonance wavelength is proportional to the refractive index [31]. Two resonance dips reveal distinct plasmon resonance shifts with respect to a small fluctuation in the refractive index of the dielectric environments, even for Δn ¼0.01. The refractive index sensitivities are defined as the wavelength shift per refractive index unit (RIU). As shown in Fig. 2(b), the average refractive index sensitivities of P1 and P2 modes are 900 nm/RIU and 493 nm/RIU, respectively. For sensing application, a high FOM (refractive index sensitivity/FWHW) is desired, which is usually applied to further evaluate the sensing performance. The calculated FOM of P1 and P2 modes are 16 and 32, respectively. Therefore, the P2 resonance has greater FOM than P1 due to the narrower line width. Both P1 and P2 modes in designed planar metamaterial reveal high refractive-index sensing sensitivity and FOM, which offer an excellent potential for biosensing in the optical and near-infrared regions. In order to insight the physical mechanism to induce the two plasmon resonances in the proposed planar metamaterial nanosensor, we plot the real part of electric field Ey [(a), (b)], magnetic field Hz [(c), (d)] and current C [(e), (f)] distributions in the x–y plane at resonance frequencies of P1 ¼238 THz and P2 ¼ 350 THz, respectively, as shown in Fig. 3. The electric field hot spots appear between the two gaps of U-shaped SRRs at two ends of designed structure at P1 ¼238 THz, and the negative charges locate at upper arm and positive charges at the lower one, as shown in Fig. 3(a). SRRs can be modeled as LC resonators in which the effective inductance arises from the loop formed by the U-shaped SRR and effective capacitance is due to the gap region between SRR arms. The LC resonances of SRRs can be excited with an E-field perpendicular to the SRR arms. The primary plasmon resonances of two U-shaped SRRs at two ends of the structure are in-phase and strongly confined, generating a huge net electric moment contributing to the resonance at P1 ¼238 THz. Moreover, the magnetic fields are mainly confined in the left and right regions of the structure, as shown in Fig. 3(c). Due to the out-of-phase current loops induced in the left and right ends of structure, shown in Fig. 3(e), the magnetic dipole moments induced in the two ends regions are opposite in the z-directions, as shown in Fig. 3(c). Therefore, the net magnetic moment of the whole structure is zero due to the cancellation effect in this structure. The mode at P1 ¼238 THz is therefore attributed to the LC resonance. On the other hand, as for the resonance at P2 ¼350 THz, the electric field hot spots appear at the middle square cavity region, and the negative and positive charges concentrate on top and down metal arms of metamaterial, as shown in Fig. 3(b). The concentrated charges locate around middle cavity, which can induce the cavity plasmon mode. One current node appeared at the middle arms refers to the excitation of the fundamental cavity plasmon mode. The high-order plasmon modes can be excited by extending of the length of the cavity, while the more current nodes appear. Due to the structure symmetry in y direction, the magnetic dipoles excited by out-of-phase current in the two parts of the middle regions have the opposite directions and same strength, which lead to cancellation effect. Therefore, the resonance at P2 ¼350 THz is a result of the fundamental cavity plasmon mode. In fact, we can comprehend the interaction between the designed metamaterial and light wave by considering the whole structure unit cell as the combination of two separate elements: one is a paired SRR, and the other is a metallic cavity. We plot the
J. Wang et al. / Optics Communications 338 (2015) 399–405
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Fig. 1. (a) Schematic of designed silver wires planar metamaterial with period P (green: silver structure, gray: SiO2 substrate); (b) a unit cell with geometric scales P¼ 540 nm, s ¼ 120 nm, a¼ 420 nm, w¼ 40 nm, l ¼ 110 nm, g ¼ 20 nm, and the silver nanostructure and SiO2 substrate thickness 60 nm and 100 nm, respectively; and (c) the simulated transmitted spectrum of planar metamaterial.
transmitted spectra of paired SRRs and metallic cavity in Fig. 4 (a) and (b), respectively, and corresponding electric field distributions at resonance dips are also plotted in insert maps of Fig. 4. To compare with Fig. 1(c) and Fig. 3(a) and (b), it is obvious that our designed planar metamaterial is the recombination of paired SRRs and metallic cavity, and the hybridization of LC resonance and cavity plasmon leads to two distinct dips in transmitted spectrum. For our designed nanostructure, the line width of transmission dip is sensitive to the gap distance between the metal nanorods, which are clearly shown in Fig. 5(a). With the increasing of gap distance, the transmitted dips broadened gradually due to large radiation loss. In case of actual possibility of fabricating the proposed sensor device, the gap between two nanorods is as small as 20 nm, which is difficult to fabricate accurately. The feature size
about g ¼50 nm might be able to be fabricated by electron beam lithography. In order to investigate the sensing performance of designed sensor device with larger gap distance, we calculate the variation of both plasmon modes with different refractive index environments as g ¼50 nm shown in Fig. 5(b). The fitted average refractive index sensitivities of P1 and P2 modes are 891 nm/RIU and 496 nm/RIU, respectively. The corresponding FOM of P1 and P2 modes are 11 and 22, respectively. Compared with the results of g¼ 20 nm shown in Fig. 2(b), both of two plasmon resonances show the refractive index sensitivities almost keep unchanged and corresponding FOMs decrease with larger gap distance due to the broadened transmitted dips. As for the fixed gap spacing g¼20 nm, the plasmon resonance frequency depends mainly on the length of the middle cavity, and the simulated transmitted spectra are shown in Fig. 6. While
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Fig. 2. The sensing performance of the designed planar metamaterial with different refractive indices n of surrounding dielectric environments (i.e. keep the substrate and change the permittivity of the upper space).
Fig. 3. The real part of electric field [(a), (b)], magnetic [(c), (d)] field and current [(e), (f)] components distributions at the resonances of P1 ¼ 238 THz [(a), (c), (e)] and P2 ¼ 350 THz [(b), (d), (f)] in the x–y plane, respectively.
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Fig. 4. The transmitted spectra of separated SRRs (a) and metallic cavity and (b), the inserted pictures are corresponding electric field patterns at the resonance frequencies.
keeping a ¼480 nm unchanged, the resonance dips will vary over the length of middle cavity s, as clearly shown in Fig. 6(a), and the electric fields of selected points in transmission map are plotted in Fig. 6(a). There are two transmission bands in intensity map, and we select different transmitted dips in two bands to investigate its electric fields. We can divide the transmission map into three regions: (I) s ¼0–80 nm, (II) s ¼80–350 nm, and (III) s¼ 350–400 nm. In region (I), the fundamental and high-order LC resonance modes of paired SRRs are dominant, and the representative resonance electric fields patterns as s ¼40 nm are shown in (A) and (a). In region (II), the B–C band is a result of LC resonance, and the b–c band reveals the cavity plasmon resonance. When s¼ 220 nm, the two resonance frequencies are closest to each other, and one of the resonance dip disappears and the field distribution of preserved resonance dip present both of the LC resonance and cavity plasmon mode, as shown in Fig. 6(b)-O; In region (III), the fundamental and high-order cavity plasmon modes are clearly shown in Fig. 6(b)-d and Fig. 6(b)-D. For the results in Fig. 6(a), we calculate the corresponding refractive index sensing sensitivities and FOMs of transmission dips for the different cavity length s, as shown in Fig. 7. In top picture of
Fig. 7, the short-wavelength transmission dips with maximum refractive index sensitivity (about 750 nm/RIU) and FOM (about 85) appears as s¼200 nm or 230 nm, which locates in the vicinity of the strongest coupling location (s ¼220 nm). Due to the strong coupling between two plasmon modes around the cross point, one resonance dip become narrow and sharp with large transmission shown in Fig. 6(a), which leads to the high sensing performance. As for long-wavelength transmission dip shown in Fig. 7 (bottom picture), the sensing capability changes slightly when cavity length s varies from 100 nm to 320 nm. On the contrary, the sensitivities and FOMs of long-wavelength transmission dips increases greatly as so100 nm or s4 320 nm. In addition, we also calculate the variation of transmission spectra with fixed s¼160 nm and different length a, and the corresponding results are plotted in Fig. 8. Two distinct transmission bands are observed for the structures with different length a, one of the transmission band (A–B band) is always located around 880 nm while the other one (a–b band) depends quite sensitively on the length a, it is a fact that the variations of length a mainly influence the LC mode of SRRs, and the plasmon cavity mode is not affected greatly. Furthermore, a pronounced disappearance of one
Fig. 5. (a) Simulated transmitted spectra of designed planar metamaterial with different gap g; (b) the sensing performance with different refractive indices n of surrounding dielectric environments for g ¼50 nm (i.e. keep the substrate and change the permittivity of the upper space).
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Fig. 6. (a) The transmission map of designed planar metamaterial with different structural parameters s and fixed a¼ 480 nm; and (b) the corresponding electric field patterns at different points indicated in (a).
Fig. 8. (a) The transmission map of designed planar metamaterial with different structural parameters a and unchanged s¼ 160 nm; and (b) the corresponding electric field patterns at different points signed in (a).
Fig. 7. The refractive index sensing sensitivities and corresponding FOMs of transmission dips for the different cavity length s. The sensing performance evaluation for the results in Fig. 6(a).
resonance dip is observed around a ¼365 nm, suggesting a strong interaction between two plasmon resonance modes. The corresponding electric field patterns of different points in transmission map of Fig. 8(a) are shown in Fig. 8(b). It is clear that A–B band is a result of cavity plasmon mode and a–b band originates from the LC
resonance. As a ¼365 nm, the electric field pattern reveals both of the LC resonance and cavity plasmon modes. For the transmission map shown in Fig. 8(a), we also investigate the corresponding refractive index sensitivities and FOMs of resonance dips for the different parameter a, which are clearly shown in Fig. 9. For short-wavelength transmission dips, the sensing performance increases greatly as a varies from 320 nm to 355 nm. Moreover, the average refractive sensitivity and corresponding FOM reach to 600 nm/RIU and 80 for a¼ 355 nm due to strong plasmon mode coupling effect, respectively. The refractive index sensitivities change slightly and corresponding FOMs decreases gradually as a4 390 nm. On the other hand, in case of long-wavelength transmission dips, the refractive index sensitivities increase gradually and corresponding FOMs keep almost unchanged (about 21). In conclusion, we proposed an optical nanosensor based on plasmonic resonators metamaterial revealing two narrow transmission dips with Q factor of 23 and 50. Moreover, two resonance modes show spectral shift sensitivity of 900 nm/RIU and 493 nm/RIU, and
J. Wang et al. / Optics Communications 338 (2015) 399–405
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References
Fig. 9. The refractive index sensing sensitivities and corresponding FOMs of transmission dips for the different geometric parameter a. The sensing performance evaluation for the results in Fig. 8(a).
corresponding FOM of them are 16 and 32. By changing the geometrical parameters of the planar metamaterial, a higher sensing performance can be achieved in designed planar metamaterial, which provides a good potential for biosensing applications. Apart from sensing, the plasmonic metamaterial with the dual or multiple narrow plasmon resonances has extensional practical applications by controlling the line-shape of resonances such as active plasmonic switching, slow-light optical devices, SERS, and narrow band filters. However, because of the innate Ohmic loss of metal, the Q factor of conventional plasmonic nanosensor cannot achieve very high. Dielectric metamaterials may be a good choice for significantly improving the performance of their plasmonic counterparts due to their lower absorption loss, resulting in sensing FOMs that far exceed previously demonstrated plasmonic sensors [32].
Acknowledgments This work was supported by the National Natural Science Foundation of China (Nos. 11104252, 11404290, and 61307019), the Ministry of Education of China (No. 20114101110003), Henan Educational Committee Natural Science Foundation (Grant nos. 13A140693 and 14A140004).
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Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Optical refractive nanosensor with planar resonators metamaterial Junqiao Wang a,n, Kaijun Mu a, Fengying Ma a, Huaping Zang a, Chunzhen Fan a, Jinna He a, Erjun Liang a, Pei Ding b a School of Physical Science and Engineering and Key Laboratory of Materials Physics of Ministry of Education of China, Zhengzhou University, Zhengzhou 450052, China b Department of Mathematics and Physics, Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou 450015, China
art ic l e i nf o
a b s t r a c t
Article history: Received 26 August 2014 Received in revised form 28 October 2014 Accepted 4 November 2014 Available online 12 November 2014
We numerically investigated the optical properties of planar resonators metamaterial that exhibits two narrow transmitted dips with quality factors of 23 and 50 in the optical regions. The results show that, both of the two resonances reveal a distinct plasmon shift with respect to a small fluctuation in the refractive index of the surrounding medium, and calculated average refractive index sensitivities are 900 nm/RIU and 493 nm/RIU, and corresponding figure of merits of two modes are 16 and 32 in vacuum, respectively. The sensing performance can be improved by changing the geometric parameters of planar metamaterial due to the plasmon modes coupling effect, which offer an excellent potential for optical nanosensing applications. & Elsevier B.V. All rights reserved.
Keywords: Metamaterials Sensors Resonance
Plasmonic nanostructures are of considerable current interest because of their unusual electromagnetic and optical characteristics and the prominent applications in surface enhanced Raman scattering (SERS) [1], biological and chemical sensing [2], perfect light absorption [3], optical antennas and switching [4], slow-light devices [5], and imaging and cloaking. [6,7] The unique ability of plasmon to focus incident light into subwavelength regions near metal nanostructure surfaces can lead to very large local field concentration. In addition to localized confinement of enhanced near-fields energy, plasmon resonances in nanostructures are sensitive to surrounding environments, and generally, the electromagnetic responses of plasmon resonances in metal nanostructures are commonly broad-band with large plasmon lifetime and low quality factor (Q factor) due to the significant radiation losses, which is unexpected in chemical/biological nanosensors. However, the resonant characteristics of metal nanostructures can be controlled by adjusting the shape, size and composition of nanostructure. As for sensing application, we appreciate the plasmon resonances with the both narrow optical spectra and large figure of merit (FOM), which indicate that the weak changes in surrounding environments can be perceived through direct observation of spectral shift of plasmon resonances. In the past few decades, conventional plasmon resonance sensors based on surface plasmon resonance for a thin metal film and the localized surface plasmon resonance(LSPR) supported on n
Corresponding author. E-mail address: [email protected] (J. Wang).
http://dx.doi.org/10.1016/j.optcom.2014.11.009 0030-4018/& Elsevier B.V. All rights reserved.
isolated nanoparticles have been of great attention and widely studied [8,9]. Anker et al. reviewed developments on improving the sensitivity of optical sensors based on metal nanoparticle arrays and single nanoparticles [10]. Furthermore, recently, a lot of efforts have been applied to identify the high sensitive nanosensors based on plasmonic metamaterial. Liu group and Li group introduced a novel plasmonic sensor which combined the concepts of a perfect metamaterial absorber and an LSPR sensor in near-infrared region [11,12]. Pryce et al. investigated how the mechanical deformation of compliant metamaterials can be used to create new types of tunable sensing surfaces, they used split ring resonator (SRR) metamaterial on polydimethylsiloxane to demonstrate refractive index sensing with FOM of up to 10.1 [13]. Ren et al. proposed a plasmonic sensor based on a spiral G-shaped metamaterial, they achieved a spectral shift sensitivity of 410 nm/ RIU and a FOM of 17 in the near-infrared region [14]. Mock et al. utilized the coupling between LSPR and propagating surface plasmon to probe the highly sensitive distance-dependent LSPR of the gaps [15]. In addition, Prodan et al. presented the plasmon hybridization concept in 2003, which can be used to describe the plasmon response of complex nanostructures of arbitrary shape [16]. Using the plasmon hybridization concept, the plasmon modes can be classified according to their irreducible representations, and a variety of nanostructures have been experimentally and theoretically exploited to improve performance of plasmonic nanosensors recognizing the variation of local refractive index [17– 19]. Furthermore, due to hybridization between broad superradiant modes (bright modes) and narrow subradiant modes (dark modes) can induce Fano resonance exhibiting an asymmetric
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sharp line shape and generating a large electromagnetic field congregation, many researchers have paid attention to plasmonic metamaterial that induces Fano resonances in their optical spectra as a sensing platform [20–27]. For example, Zhang et al. analyzed the plasmon mode interactions of a metallic nanocube on a dielectric substrate, and symmetry-breaking introduced by an adjacent semi-infinite dielectric can introduce coupling and hybridization of the plasmon modes of a metallic nanostructure, which provided a new insight for achieving plasmonic Fano-resonant LSPR sensors with FOM of 20 [23]. Furthermore, electromagnetically induced transparency (EIT) phenomenon with narrow transparency band can be manipulated by Fano resonances through symmetry breaking, which is desirable for sensing applications due to narrow spectral width. Liu et al. demonstrated that a plasmonic EIT analog could be achieved using a planar complementary metamaterial which consists of cut-out structures in a homogeneous gold film, however, this metamaterial sensor only has a small FOM of 3.8 in the near-infrared regions [28]. Dong et al. designed a planar metamaetial composed of three metal bars, which revealed the gain-assisted plasmonic analog of EIT for the purpose to enhance the sensing [29]. In this paper, we theoretically discussed the optical properties of a designed planar metamaterial with two sharp transmitted dips. The designed planar metamaterial is the recombination of paired SRRs and metallic cavity, and the hybridization of LC resonance and cavity plasmon leads to two distinct dips in transmitted spectrum. By adjusting the geometric parameters of designed metamaterial, the plasmon resonance modes reveal narrow line width and large FOM, which offer a potential for biosensing in the optical and near-infrared regions. In comparison to other plasmonic systems, the high sensing performance with large FOM can be achieved in this planar metamaterial by strong plasmon modes coupling effect, which provide further insight into designing the excellent plasmonic nanosensors. Fig. 1(a) and (b) shows a typically periodical array of the designed silver planar metamaterial and a sketch of a unit cell with relevant geometric parameters, respectively. The geometrical parameters are chosen as follows: P ¼540 nm, s¼ 120 nm, a ¼420 nm, w¼ 40 nm, l ¼110 nm and g ¼20 nm. The dielectric constants of silver measured by Palik are used to model the planar metamaterial, and the thickness is fixed as 60 nm [30]. The planar metamaterial is located on the SiO2 substrate of thickness 100 nm and dielectric constants ε ¼1.96. The metamaterial is illuminated by a normal incident plane wave with an electric field polarization parallel to the y-axis. The simulation is carried out by the time domain solver of 3-D electromagnetic package (CST Microwave Studio), where the computational domain is truncated by Perfectly Matched Layers in the z-direction and the periodic boundary conditions are used to truncate the unit cell in the x–y plane. During simulating, the good convergence for calculated result can be obtained by utilizing adaptive meshing technique to handle the structure boundaries and geometries that need large aspect ratios of meshes. Fig. 1(c) shows the simulated transmitted spectrum of the planar metamaterial as designated in Fig. 1(a) and (b). By using the structural parameters as described above, we obtained two narrow plasmon resonances around P1 ¼224 THz and P2 ¼385 THz, respectively, where the fitted full width at half maximum (FWHM) are about 9.9 THz and 7.7 THz, respectively. The calculated Q factor (Q¼ ω0/FWHM) of P1 and P2 modes are Q1 ¼ 23 and Q2 ¼ 50, respectively. In addition, due to the structure asymmetry of the metamaterial in x and y directions, the responses of x and y polarized light are different, and only one broadened resonance dip appears in spectrum with x polarized light. The plasmon resonances with the narrow line width and high Q factor are two appreciated characteristics for achieving high
sensing performance in metamaterial sensor. In order to investigate the sensing performance of the designed planar metamaterial, we calculated the transmitted spectra in different dielectric environments (i.e. keep the substrate and change the permittivity of the upper space) as presented in Fig. 2(a). With the increasing of the refractive index of dielectric environments, both of the plasmon resonances P1 and P2 exhibit a red-shift in transmitted spectra. This can be understood by the fact that the resonance wavelength is proportional to the refractive index [31]. Two resonance dips reveal distinct plasmon resonance shifts with respect to a small fluctuation in the refractive index of the dielectric environments, even for Δn ¼0.01. The refractive index sensitivities are defined as the wavelength shift per refractive index unit (RIU). As shown in Fig. 2(b), the average refractive index sensitivities of P1 and P2 modes are 900 nm/RIU and 493 nm/RIU, respectively. For sensing application, a high FOM (refractive index sensitivity/FWHW) is desired, which is usually applied to further evaluate the sensing performance. The calculated FOM of P1 and P2 modes are 16 and 32, respectively. Therefore, the P2 resonance has greater FOM than P1 due to the narrower line width. Both P1 and P2 modes in designed planar metamaterial reveal high refractive-index sensing sensitivity and FOM, which offer an excellent potential for biosensing in the optical and near-infrared regions. In order to insight the physical mechanism to induce the two plasmon resonances in the proposed planar metamaterial nanosensor, we plot the real part of electric field Ey [(a), (b)], magnetic field Hz [(c), (d)] and current C [(e), (f)] distributions in the x–y plane at resonance frequencies of P1 ¼238 THz and P2 ¼ 350 THz, respectively, as shown in Fig. 3. The electric field hot spots appear between the two gaps of U-shaped SRRs at two ends of designed structure at P1 ¼238 THz, and the negative charges locate at upper arm and positive charges at the lower one, as shown in Fig. 3(a). SRRs can be modeled as LC resonators in which the effective inductance arises from the loop formed by the U-shaped SRR and effective capacitance is due to the gap region between SRR arms. The LC resonances of SRRs can be excited with an E-field perpendicular to the SRR arms. The primary plasmon resonances of two U-shaped SRRs at two ends of the structure are in-phase and strongly confined, generating a huge net electric moment contributing to the resonance at P1 ¼238 THz. Moreover, the magnetic fields are mainly confined in the left and right regions of the structure, as shown in Fig. 3(c). Due to the out-of-phase current loops induced in the left and right ends of structure, shown in Fig. 3(e), the magnetic dipole moments induced in the two ends regions are opposite in the z-directions, as shown in Fig. 3(c). Therefore, the net magnetic moment of the whole structure is zero due to the cancellation effect in this structure. The mode at P1 ¼238 THz is therefore attributed to the LC resonance. On the other hand, as for the resonance at P2 ¼350 THz, the electric field hot spots appear at the middle square cavity region, and the negative and positive charges concentrate on top and down metal arms of metamaterial, as shown in Fig. 3(b). The concentrated charges locate around middle cavity, which can induce the cavity plasmon mode. One current node appeared at the middle arms refers to the excitation of the fundamental cavity plasmon mode. The high-order plasmon modes can be excited by extending of the length of the cavity, while the more current nodes appear. Due to the structure symmetry in y direction, the magnetic dipoles excited by out-of-phase current in the two parts of the middle regions have the opposite directions and same strength, which lead to cancellation effect. Therefore, the resonance at P2 ¼350 THz is a result of the fundamental cavity plasmon mode. In fact, we can comprehend the interaction between the designed metamaterial and light wave by considering the whole structure unit cell as the combination of two separate elements: one is a paired SRR, and the other is a metallic cavity. We plot the
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Fig. 1. (a) Schematic of designed silver wires planar metamaterial with period P (green: silver structure, gray: SiO2 substrate); (b) a unit cell with geometric scales P¼ 540 nm, s ¼ 120 nm, a¼ 420 nm, w¼ 40 nm, l ¼ 110 nm, g ¼ 20 nm, and the silver nanostructure and SiO2 substrate thickness 60 nm and 100 nm, respectively; and (c) the simulated transmitted spectrum of planar metamaterial.
transmitted spectra of paired SRRs and metallic cavity in Fig. 4 (a) and (b), respectively, and corresponding electric field distributions at resonance dips are also plotted in insert maps of Fig. 4. To compare with Fig. 1(c) and Fig. 3(a) and (b), it is obvious that our designed planar metamaterial is the recombination of paired SRRs and metallic cavity, and the hybridization of LC resonance and cavity plasmon leads to two distinct dips in transmitted spectrum. For our designed nanostructure, the line width of transmission dip is sensitive to the gap distance between the metal nanorods, which are clearly shown in Fig. 5(a). With the increasing of gap distance, the transmitted dips broadened gradually due to large radiation loss. In case of actual possibility of fabricating the proposed sensor device, the gap between two nanorods is as small as 20 nm, which is difficult to fabricate accurately. The feature size
about g ¼50 nm might be able to be fabricated by electron beam lithography. In order to investigate the sensing performance of designed sensor device with larger gap distance, we calculate the variation of both plasmon modes with different refractive index environments as g ¼50 nm shown in Fig. 5(b). The fitted average refractive index sensitivities of P1 and P2 modes are 891 nm/RIU and 496 nm/RIU, respectively. The corresponding FOM of P1 and P2 modes are 11 and 22, respectively. Compared with the results of g¼ 20 nm shown in Fig. 2(b), both of two plasmon resonances show the refractive index sensitivities almost keep unchanged and corresponding FOMs decrease with larger gap distance due to the broadened transmitted dips. As for the fixed gap spacing g¼20 nm, the plasmon resonance frequency depends mainly on the length of the middle cavity, and the simulated transmitted spectra are shown in Fig. 6. While
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Fig. 2. The sensing performance of the designed planar metamaterial with different refractive indices n of surrounding dielectric environments (i.e. keep the substrate and change the permittivity of the upper space).
Fig. 3. The real part of electric field [(a), (b)], magnetic [(c), (d)] field and current [(e), (f)] components distributions at the resonances of P1 ¼ 238 THz [(a), (c), (e)] and P2 ¼ 350 THz [(b), (d), (f)] in the x–y plane, respectively.
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Fig. 4. The transmitted spectra of separated SRRs (a) and metallic cavity and (b), the inserted pictures are corresponding electric field patterns at the resonance frequencies.
keeping a ¼480 nm unchanged, the resonance dips will vary over the length of middle cavity s, as clearly shown in Fig. 6(a), and the electric fields of selected points in transmission map are plotted in Fig. 6(a). There are two transmission bands in intensity map, and we select different transmitted dips in two bands to investigate its electric fields. We can divide the transmission map into three regions: (I) s ¼0–80 nm, (II) s ¼80–350 nm, and (III) s¼ 350–400 nm. In region (I), the fundamental and high-order LC resonance modes of paired SRRs are dominant, and the representative resonance electric fields patterns as s ¼40 nm are shown in (A) and (a). In region (II), the B–C band is a result of LC resonance, and the b–c band reveals the cavity plasmon resonance. When s¼ 220 nm, the two resonance frequencies are closest to each other, and one of the resonance dip disappears and the field distribution of preserved resonance dip present both of the LC resonance and cavity plasmon mode, as shown in Fig. 6(b)-O; In region (III), the fundamental and high-order cavity plasmon modes are clearly shown in Fig. 6(b)-d and Fig. 6(b)-D. For the results in Fig. 6(a), we calculate the corresponding refractive index sensing sensitivities and FOMs of transmission dips for the different cavity length s, as shown in Fig. 7. In top picture of
Fig. 7, the short-wavelength transmission dips with maximum refractive index sensitivity (about 750 nm/RIU) and FOM (about 85) appears as s¼200 nm or 230 nm, which locates in the vicinity of the strongest coupling location (s ¼220 nm). Due to the strong coupling between two plasmon modes around the cross point, one resonance dip become narrow and sharp with large transmission shown in Fig. 6(a), which leads to the high sensing performance. As for long-wavelength transmission dip shown in Fig. 7 (bottom picture), the sensing capability changes slightly when cavity length s varies from 100 nm to 320 nm. On the contrary, the sensitivities and FOMs of long-wavelength transmission dips increases greatly as so100 nm or s4 320 nm. In addition, we also calculate the variation of transmission spectra with fixed s¼160 nm and different length a, and the corresponding results are plotted in Fig. 8. Two distinct transmission bands are observed for the structures with different length a, one of the transmission band (A–B band) is always located around 880 nm while the other one (a–b band) depends quite sensitively on the length a, it is a fact that the variations of length a mainly influence the LC mode of SRRs, and the plasmon cavity mode is not affected greatly. Furthermore, a pronounced disappearance of one
Fig. 5. (a) Simulated transmitted spectra of designed planar metamaterial with different gap g; (b) the sensing performance with different refractive indices n of surrounding dielectric environments for g ¼50 nm (i.e. keep the substrate and change the permittivity of the upper space).
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Fig. 6. (a) The transmission map of designed planar metamaterial with different structural parameters s and fixed a¼ 480 nm; and (b) the corresponding electric field patterns at different points indicated in (a).
Fig. 8. (a) The transmission map of designed planar metamaterial with different structural parameters a and unchanged s¼ 160 nm; and (b) the corresponding electric field patterns at different points signed in (a).
Fig. 7. The refractive index sensing sensitivities and corresponding FOMs of transmission dips for the different cavity length s. The sensing performance evaluation for the results in Fig. 6(a).
resonance dip is observed around a ¼365 nm, suggesting a strong interaction between two plasmon resonance modes. The corresponding electric field patterns of different points in transmission map of Fig. 8(a) are shown in Fig. 8(b). It is clear that A–B band is a result of cavity plasmon mode and a–b band originates from the LC
resonance. As a ¼365 nm, the electric field pattern reveals both of the LC resonance and cavity plasmon modes. For the transmission map shown in Fig. 8(a), we also investigate the corresponding refractive index sensitivities and FOMs of resonance dips for the different parameter a, which are clearly shown in Fig. 9. For short-wavelength transmission dips, the sensing performance increases greatly as a varies from 320 nm to 355 nm. Moreover, the average refractive sensitivity and corresponding FOM reach to 600 nm/RIU and 80 for a¼ 355 nm due to strong plasmon mode coupling effect, respectively. The refractive index sensitivities change slightly and corresponding FOMs decreases gradually as a4 390 nm. On the other hand, in case of long-wavelength transmission dips, the refractive index sensitivities increase gradually and corresponding FOMs keep almost unchanged (about 21). In conclusion, we proposed an optical nanosensor based on plasmonic resonators metamaterial revealing two narrow transmission dips with Q factor of 23 and 50. Moreover, two resonance modes show spectral shift sensitivity of 900 nm/RIU and 493 nm/RIU, and
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References
Fig. 9. The refractive index sensing sensitivities and corresponding FOMs of transmission dips for the different geometric parameter a. The sensing performance evaluation for the results in Fig. 8(a).
corresponding FOM of them are 16 and 32. By changing the geometrical parameters of the planar metamaterial, a higher sensing performance can be achieved in designed planar metamaterial, which provides a good potential for biosensing applications. Apart from sensing, the plasmonic metamaterial with the dual or multiple narrow plasmon resonances has extensional practical applications by controlling the line-shape of resonances such as active plasmonic switching, slow-light optical devices, SERS, and narrow band filters. However, because of the innate Ohmic loss of metal, the Q factor of conventional plasmonic nanosensor cannot achieve very high. Dielectric metamaterials may be a good choice for significantly improving the performance of their plasmonic counterparts due to their lower absorption loss, resulting in sensing FOMs that far exceed previously demonstrated plasmonic sensors [32].
Acknowledgments This work was supported by the National Natural Science Foundation of China (Nos. 11104252, 11404290, and 61307019), the Ministry of Education of China (No. 20114101110003), Henan Educational Committee Natural Science Foundation (Grant nos. 13A140693 and 14A140004).
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