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The independent excitation and tuning of double plasmonic waves are realized in a free-standing graphene-spacer-grating-spacer-graphene (GSGSG) hybrid slab, which consists of two graphene field effect transistors placed back-to-back to each other. Resulted from the high transparency and the tight confinement of surface plasmonic mode for the graphene, double plasmonic waves can be independently excited by guided-mode resonances (GMRs). Theoretical and numerical investigations are performed in the mid-infrared band. Furthermore, the tuning of individual GMR resonant wavelengths with respect to the system parameters is studied. The results provide opportunities to engineer the proposed hybrid slab for wavelength selective and multiplexing applications.
© 2016 Optical Society of America
1. Introduction
Over the past decades, there has been a growing interest in the understanding and application of guided-mode resonance (GMR) [1,2]. GMR refers to the electromagnetic energy exchange between the externally propagating light fields and the waveguide modes. In addition to strongly confining the electromagnetic energy within the waveguide or grating structure, it produces rapid variations on the transmission and reflection spectrum of the externally incident light. Complex resonant line shapes are thus emerged, leading to wide-range applications such as filter optics, modulators, switches, spectroscopy and sensors.
In recent years, GMR was utilized to excite the surface plasmonic modes, and the corresponding photonic devices based on noble metal nanostructures were proposed and investigated [3–5]. Moreover, created by diffractive grating, GMR can efficiently couple the normal-incidence light to the plasmonic wave propagating in-plane along a monolayer graphene, which is only one atom thick [6,7]. Graphene plasmonics has attracted tremendous research attentions, resulted from not only its extremely strong field confinement and low propagation loss, but also the fast and efficient electrically tunability on its plasmonic properties over broad wavelength band [8]. The unique properties of graphene make the active control of GMR more feasible.
On the other hand, for the sake of different applications, the research interest in GMR was extended from a single channel to double or multiple channels. Dual-channel GMR has attracted considerable attention due to their potential applications in the all-optical wavelength division multiplexing networks [9], dual-wavelength laser emission [10,11], multiplexing photodetector [12], and sensing systems [13,14]. Many efforts have been devoted to realizing double-channel GMR with two resonance peaks/dips on the spectrum. By increasing the waveguide thickness to admit additional leaky modes, the phase matching of diffracted light to various order waveguide modes can be fulfilled, and the resonance reflectance peaks with double, triple, and multiple channels can be obtained [15–17]. The dual or multiple bands can also be achieved by the anticrossing phenomenon that occurs between the GMR and the Fabry-Pérot resonances [18]. Moreover, by shaping a resonator composed of two sub-cavities with different size parameters, GMR can couple incident light into these cavity resonances and dual-band absorptance peak will appear [19,20]. However, in these techniques, the two GMR resonances for the double channels were highly interrelated to each other. The tuning of one resonant wavelength would accordingly influence the other. Their tuning range was limited by the geometry as well. These disadvantages will prevent the double-channel GMR from practical applications.
In this paper, we present the concept of independent excitation of double plasmonic waves in a free-standing graphene-spacer-grating-spacer-graphene (GSGSG) hybrid slab in the mid-infrared band. In this proposed hybrid slab, two graphene field effect transistors (GFETs) are placed back-to-back to each other. This configuration enables two graphene sheets to share not only the same gate electrode, but also the same diffractive grating. Unlike noble metals that are opaque in mid-infrared range, graphene is highly transparent. The absorptance of light is 2.3% for free-standing graphene [21,22]. Light can travel through the first graphene layer to reach the grating structure and couple its energy to both the graphene surface plasmonic (GSP) waveguides above and below the grating. In the meantime, the tight confinement of GSP modes, together with the screening effect of metal, prevent any crosstalk between the two modes. Independent excitation and tuning of double plasmonic waves can thus be realized. We herein investigate the relation between the double GMR resonances and the system parameters, e. g., the Fermi level of the graphene sheets, the geometrical parameters, and the refractive indices of the surrounding media. The results provide opportunities to engineer this dual-band GMR resonance for various applications, e. g., wavelength selective or multiplex optical filtering and sensing.
2. Geometry configuration and design consideration
The proposed free-standing graphene-spacer-grating-spacer-graphene (GSGSG) hybrid slab consists of two graphene field effect transistors (GFETs) arranged back-to-back to each other. GFET is the classical configuration to enable dynamic tuning on the graphene’s Fermi level, which determines its electromagnetic property of surface conductivity. For each GFET, a dielectric spacer is inserted between the graphene and the gate electrode. The gate electrode is fabricated to be grating structure. Conductor/semiconductor with nanostructure has been widely reported as transparent electrode [23,24]. Consequently, these two GFETs share not only the same grating component for the excitation of guided mode resonance (GMR), but also the same gate electrode for the electrical tuning, as shown in Fig. 1(a). Two bias voltages, VA and VB, are applied to the two GFETs to tune the graphene Fermi levels independently.
Fig. 1 (a) Schematic of the proposed free-standing graphene-spacer-grating-spacer-graphene (GSGSG) hybrid slab, and (b) cross sectional view with geometrical parameters. VA and VB are bias voltages between the graphene and the gate electrode. (c) The phase matching mechanism for GMRs on the GSGSG hybrid slab.
The geometrical parameters of the GSGSG hybrid slab are then depicted in Fig. 1(b) with the grating periodicity of p, the grating height of h, and the width of the grating as w. w/p is the occupation ratio. The thickness and refractive index of the spacer are dA (dB) and nA (nB) for GFET A (GFET B), respectively. In order to distinct the two GMRs in the spectrum, the spacer materials are assigned to be different, which are nA = 1.5 and nB = 1. The background material is the air. A plane wave with its E-field direction perpendicular to the grating lines incidents normally from above or below the hybrid slab. Throughout this work, we have it incidenting along the −z direction.
For the plasmonic TM (transverse magnetic) mode in a continuous graphene, the wave vector of the graphene surface plasmonic (GSP) waveguide can be determined by [25]
where ω is the angular frequency of light, ε0 is the vacuum permittivity, εr1 and εr2 are the dielectric constants of the cladding materials above or below the graphene, and σ(ω) is the surface conductivity of graphene described by local random phase approximation of the Kubo formula [26,27]. The real parts of ksp(ω) for graphene A and graphene B in the mid-infrared range were thus plotted in Fig. 1(c), with the temperature T = 300 K, the charge carriers scattering rate Γ = 0.43 meV [28], and the Fermi level EF = 0.6 eV for both of them. It should be noted that Γ is a phenomenological parameter. The value we chosed here corresponds to a carrier mobility of 1.6 × 105 cm2/(V · s), which is smaller than the theoretical estimation of the maximum mobility (2×106 cm2/(V · s)) in graphene [29]. Additional losses from optical phonons can be neglected since the simulated frequencies are below the threshold of 1667 cm−1.In order to couple the normally incident optical wave to the GSP modes in the graphene, GMRs are created by the presence of the diffractive grating, as indicated in Fig. 1. The phase of the first-order diffraction can be given by
To satisfy the phase matching (PM) condition in the mid-infrared wavelength, the grating periodicity was chosen to be p = 200 nm. As shown in Fig. 1(c), the phase of the grating intersects with the dispersion curves of the GSP mode A and B at 6.87 µm and 5.43 µm, respectively. This PM mechanism not only predicts the GMR resonant wavelengths, but also implies the possibility to adjust two GMR resonances independently.
The optical response of the proposed GSGSG hybrid slab was then numerically simulated by the frequency-domain finite element algorithm using the commercial software COMSOL Multiphysics™. Unlike the conventional methods that treated the graphene as a volumetric dielectric with artificial finite thickness and corresponding equivalent permittivity [6,28], in this work, we model it as an infinitesimally thin, local two-sided surface. To include the surface conductivity of the graphene into Maxwell’s equations, a surface current density boundary condition is exploited. This technique avoids the inexact and instable results, as well as the enormously expensive computations arising from the extrafine meshing on the graphene elements [30,31].
The grating geometry are w/p = 0.5, and h = 100 nm, while the grating material is silver Ag with its optical constants from Palik et al [32]. In order to better demonstrate the concept of independent excitation and tuning of double plasmonic waves, the spacer thicknesses are taken as dA = 10 nm and dB = 6 nm, respectively. Discussions about geometrical dependence of the double GMRs can be found in Section 3.2. Figure 2(a) showed the transmission spectra of four hybrid slabs composed of the graphene A only (red), the graphene B only (blue), the both (dark yellow), and the none (black dashed). When the hybrid slab comprises only one graphene, the incident wave will excite one GSP mode, and will produce a resulting resonant dip on the spectrum which is with no graphene. The line shapes resemble the Lorentz curves, and the full-heights are as large as unity. Both of GMR resonances happen with no mode hybridization to grating structure, for the grating has too large geometry mismatch to support any photonic mode when comparing to the wavelength of the incident light.
Fig. 2 (a) Transmission spectra for four hybrid slabs composed of the graphene A only (red), the graphene B only (blue), the both (dark yellow), and the none (black dashed). (b) and (c) Electric field distributions of the GSGSG hybrid slab at the resonant wavelength points I and II, corresponding to the GMR resonance A and B, respectively. The black solid lines sketch the profile of different materials, while the two magenta dashed lines denote two graphene sheets.
After both of graphene introducing into the hybrid slab, two resonant dips from their corresponding GMR resonances superimpose linearly, as indicated by the the dark yellow spectrum. Dual-band phenomenon emerges on the spectrum, with the resonant wavelengths and the linewidths keeping unchanged. This phenomenon is resulted from the high transparency and zero reflectance of the graphene monolayer. The externally propagating light can thus efficiently travel through the first graphene to reach the grating structure and couple its energy to the GSP waveguide either above or below the grating.
The simulated resonant wavelengths from Fig. 2(a) are 9.73 µm and 8.48 µm, as indicated by points I and II, respectively. Although the double PM mechanisms occurred, their resonant wavelengths did not agree well with the prediction of Fig. 1(c). The reason lies in the small spacer thickness of the proposed device. The interaction between the Ag grating and the GSP mode results in a red shift of the resonant wavelength comparing to the predicted one. Figures 2(b) and 2(c) presented the electric field intensity for the GSGSG hybrid slab at the resonant wavelength points I and II, corresponding to the GMR resonance A and B, respectively. It can be seen that the field patterns tend to be concentrated and enhanced in the regions between the Ag grating and the graphene. The increasing of the spacer thickness will resume the field pattern of a GSP mode and the simulated resonant wavelengths will match those predicted by the PM mechanism indicated in Fig. 1(c).
On the other hand, as demonstrated by Figs. 2(b) and 2(c), GMR A localizes its electromagnetic energy around graphene A without any overlap to graphene B, so does GMR B. Meanwhile, the field distributions are similar to those of the hybrid slabs consisted of only one graphene (not shown here). These are attributed to the tight field confinement of the GSP mode, which typically possesses a decay length of < 25 nm [6]. No interfering or coupling between the two graphene. This provides the possibility of independent manipulation on individual GMR resonances. In the following section, we investigate the independent tuning of the double GMR resonances on the proposed hybrid slab, and discuss their corresponding application.
3. Results and discussion
In this section, the independent tuning of the double plasmonic waves is investigated, and the results are obtained within the design space of the Fermi level, the geometrical parameters, and the refractive indices of the surrounding media.
3.1. Electrical tuning of the double GMRs
The electrical tuning of the double plasmonic waves was investigated by adjusting the Fermi level of each graphene separately. Figure 3(a) gave the transmission spectra of the proposed GSGSG hybrid slab with various Fermi levels of each graphene. The geometrical parameters from Fig. 2 were adopted. First of all, the Fermi level in graphene A was fixed at EFA=0.6 eV, while that of graphene B rose from 0.4 eV to 0.6 eV in steps of 0.1 eV. It can be seen that the resonant dip generated by the GMR B is blue-shifted as the increase of the EFB, while the one related to the GMR A keeps constant, as indicated by the red dashed line. Separate tunability of the double plamonic waves is feasible by adjusting the Fermi level in one of the graphene.
Fig. 3 (a) Transmission spectra with various Fermi levels in each graphene. The red dashed line indicates the independence of the GMR A on Fermi level EFB, while the red dotted line indicates the invariance of the GMR B with respect to EFA. (b) Dependence of double resonant wavelengths on the corresponding Fermi level. The dotted lines labelled by “theory” represents the analytically estimate results by Eq. (4). (c) Electric field distribution at the wavelength point where two resonance merges.
The Fermi level EFB in the graphene B was further modulated in a broader range, and the resonant wavelength λB of the GMR B was fitted and plotted in Fig. 3(b). It can be seen that the λB is the function against the reciprocal square root of the EFB. To analytically obtain the GMR resonant wavelength as a function of the Fermi level, a semi-classical model for the graphene surface conductivity was employed and written as [25]
where e is the electric charge, ħ is the reduced Planck constant, and τ is the carrier relaxation time, τ = 2πħΓ−1. For Fermi level and wavelength of interest, the contribution from interband transition can be neglected, and the this model can well describe graphene. Equation (3) was then inserted into Eq. (1). Under the phase matching mechanism between Eq. (1) and Eq. (2), the GMR resonant wavelength can be theoretically predicted by The simulated results in Fig. 3(b) thus comply with the reciprocal square root behavior exhibited by Eq. (4), which was plotted as well. Within the tuning range of EF, the simulated results have red shifts. They are caused by the small spacer thickness between graphene and grating, which had been discussed in Section 2. Frequency doubling can be readily achieved by rising the EFB from 0.2 eV to 0.8 eV.Similar to those of GMR B, the λA of GMR A shows blue shifts as the increase of EFA, in a reciprocal square root behavior. Broad tuning range of the wavelength λA is also available. The red dotted line in Fig. 3(a) suggests the invariance of the GMR B with respect to EFA, which is ranging from 0.6 eV to 0.8 eV. When EFA= 0.8 eV, EFB = 0.6 eV, the two resonances linearly merge into one dip. The electric field distribution was presented in Fig. 3(c) for the wavelength point where two resonances overlapped. Two GMR resonances coexist and have no disturbance to each other. Additionally, we performed the EFA (EFB) tuning under different EFB (EFA), which were not shown here for simplicity. The λA (λB) dependence on the EFA (EFB) will not be affected by the choice of EFB (EFA), suggesting that the two GMRs can be independently tuned by their corresponding Fermi level. This provides more flexibility in the design of dual-wavelength filter.
Lastly, the line shapes of the double resonances were discussed. Since the material property of graphene is dispersive with respect to the Fermi level, the line shapes would inevitably change during the electrical tuning. The full-width-half-maximum (FWHM) and the full-height (FH), determined from the Lorentz fit of a resonant dip, are two parameters concerned in the filter design. Figure 4 gave the dependence of FWHMs and FHs of the double GMR resonances on the corresponding Fermi level. The FWHMs of both GMR resonances decrease as the rise of their corresponding Fermi level. The decrement is 45.2% for GMR A, while that of GMR B is 51.4%. On the other hand, the FHs increase and approach to unity during these processes. Although there shows different trends about the FWHMs and the FHs, the origin lies in the same fact that the graphene’s surface conductivity decreases as the rise of its Fermi level on the mid-infrared range.
3.2. Geometrical dependence of the double GMRs
Besides the material property of graphene, the spacer thickness can also tune the resonant wavelengths of the GMRs, resulting from the confinement of plasmonic wave in the region where the spacer is located at. The dependence of resonant wavelength on the spacer thickness was illustrated in Fig. 5(a). Transmission spectra were calculated by changing the spacer thickness dB of GFET B from 3 nm to 10 nm, while keeping other parameters the same as those of Fig. 2. There is a clear blue shift of GMR B on the spectra with the enlarging dB, together with the narrowing of the FWHM. In contrast, the resonance of GMR A keeps immobile because of the invariance of dA. When dB = 4 nm, the two resonances linearly merge, and their mode patterns coexist, having the same electric field distribution as that of Fig. 3(c).
Fig. 5 (a) Transmittance of the proposed GSGSG hybrid slab as the function of wavelength and spacer thickness dB. (b) Dependence of FHs of double GMR resonances on the occupation ratio w/p. Both first-order and second-order cases are presented.
GMR resonances by higher-order diffraction of grating sneak in from the short-wavelength region of Fig. 5(a). The intensities are weak comparing to their first-order counterparts. Occupation ratio w/p of grating is the commonly used parameter to adjust the intensities of higher-order resonances [6]. Figure 5(b) showed the dependence of the FHs on w/p, in which both first-order and second-order cases are presented. It can be seen that the FHs of the second-order GMR resonances have minima which are close to zero when w/p = 0.45, and they strength themselves dramatically as w/p increases. On the other hand, although the first-order FHs have maxima when w/p = 0.8, they are almost equal to unity for w/p > 0.5. We use occupation ratio of 0.5 throughout this work, while this parameter can be used as a design parameter for various application.
Furthermore, we discussed the effect of the grating height h and the spacer thickness d (dA=dB=d) on the spectral intensities, i.e., transmittance, reflectance and absorptance, which are extracted from the spectra at the resonant wavelength point. The results of GMR A were given in Fig. 6(a), while those of GMR B were in Fig. 6(b). The h is ranging from 3 nm to 50 nm, while the d adopts some designated value between 5 nm and 50 nm. With the increase of the grating height h, the transmittances drop exponentially, and the reflectances have an opposite behavior. They both saturate after the h reaching a threshold, which is ~7 nm for GMR A and ~4 nm for GMR B. The larger h is, the less disturbance from the counterpart GMR resonance. Consequently, The spectral intensities would keep constant as long as the grating is thick enough.
Fig. 6 Dependence of transmittance, reflectance and absorptance on the grating height h. Investigation on different spacer thickness d is also presented. dA=dB=d. (a) GMR A, and (b) GMR B. Data are extracted at the resonant wavelength point. The use of solid line and dashed line indicates different dependence of absorptance on h and d.
Another interesting phenomenon of the geometrical dependence is that the relationship between the absorptances and the spacer thickness d. It can be seen that during the process of the enlarging d, the absorptances elevate first, and then drop after reaching a ceiling value of ~50%. This phenomenon agrees well with the temporal coupled mode model of a hybrid system, as proposed in [33]. Based on this model, there exists a critical spacer thickness which makes the absorptance the largest, and the thickness depends on the intrinsic loss of a GSP mode. Although the material properties of the two graphene are the same, GSP mode A and B have different intrinsic losses due to their different cladding materials. It can be seen from Fig. 6 that the critical spacer thickness is 30 nm for GMR A and 20 nm for GMR B, respectively. In the mean time, the results in our work confirmed the largest absorptance of 50%. The ceiling value on the absorptances limits the application of the proposed hybrid slab in the fields of dual-band absorber and photodetector.
3.3. Refractive index sensing
The GMR wavelength is also very sensitive to the refractive index (RI) changes of surrounding media. In this subsection, we examined the performance of the proposed GSGSG hybrid slab as an RI sensor, which is an emerging research topic in recent years [34]. The sensing of pure bulk dielectric will be studied first, and then that of dielectric films with nanoscale thickness will be discussed. Parameters are kept the same as those of Fig. 2 unless otherwise stated.
Due to the free-standing geometry, the proposed hybrid slab can either sense the medium beneath the graphene A by GMR A, or that above the graphene B by GMR B. The RIs of the sensing media are referred as nSA and nSB, respectively. By changing the sensing medium from nS = 1 to nS = 1.333, RI sensitivity (RIS) of both GMR resonances can be numerically estimated by measuring the resonant wavelength shift per RI unit (RIU). The results were plotted in Fig. 7(a). Clear reciprocal square root dependence on the corresponding Fermi level can be found for both GMR A and B. This behavior can also be validated by an analytical formula, which is determined by the partial derivative of Eq. (4) with respect to the RI of the sensing medium,
εr2 in this equation is the dielectric constant of the cladding material which is not used for sensing. The reciprocal square root relationship between the RIS and the Fermi level proves the validity of the numerically estimated results. On the other hand, RIS for GMR B is more sensitive than that of GMR A, resulting from the smaller εr2 of GMR B.Fig. 7 (a) Bulk sensitivities of the proposed GSGSG hybrid slab as the function of the corresponding Fermi level. The dotted lines labelled by “theory” represent the analytically estimate results by Eq. (5). (b) Dependence of FoM factors on the corresponding Fermi level.
To quantify the sensing performance of an RI sensor, a figure of merit (FoM) value is introduced, which is defined as the ratio of the RIS and the FWHM of probing signal. FoM factors were presented in Fig. 7(b). Optimal FoMs can be found, which are 5.1 for GMR A and 8.07 for GMR B, both with the Fermi levels of 0.4 eV. The FoMs of the proposed GSGSG hybrid slab are comparable to that of sensors based on graphene ribbon arrays in the mid-infrared range, implying the great potential for practical application [14,35].
Next, the thin film sensitivity was investigated by covering a dielectric film with finite thickness on top of the graphene B. In this scenario, GMR B with a Fermi level of 0.4 eV was utilized as the probing signal. The results were shown in Fig. 8. It can be seen that at the thickness of the sensing film tSB = 100 nm, the RIS is 2.237 µm/RIU, which is close to the bulk sensitivity of GMR B. As the thickness decreases, the thin film sensitivity decays exponentially, and drops to 0.21 µm/RIU for tSB = 2 nm. However, one should consider it as a high sensitivity to sense the thin film medium, for the ratio between the operational wavelength and the film thickness is extremely high, which is ~ 4840. The transmission spectra were given in the inset of Fig. 8 as well. As tSB decreases, the resonant wavelength of GMR B is blue shifted, leading to the decay of the RIS sensitivity. On the other hand, during this process, the line shape of GMR B keeps almost unchanged, indicating the feasibility of the probing signal in the thin film sensing. Together with the previous analysis, the proposed GSGSG hybrid slab can be applied not only in the gas and environmental monitoring, but also in the assay of the biomolecular film, whose dimension is usually < 10 nm.
Fig. 8 Thin film sensitivities as the function of the target film thickness. GMR B was utilized as the probing signal. The inset shows the transmission spectra for the proposed hybrid slab covered by dielectric thin films with constant nSB = 1.333 and various thicknesses tSB = 2 nm, 4 nm, 8 nm, 10 nm, 20 nm, 50 nm, and 100 nm.
4. Conclusion
We have demonstrated the independent tuning of the double plasmonic waves in a free-standing graphene-spacer-grating-spacer-graphene hybrid slab. Due to the high transparency and the tight confinement of surface plasmonic mode of graphene, two resonant dips from their corresponding guided-mode resonances can be excited and tuned independently on the transmission spectrum, with the resonant wavelengths and the lineshapes unrelated to each other. We investigate this phenomenon theoretically and numerically in the mid-infrared band. Furthermore, the influence of system parameters on the individual plasmonic waves is studied in detail. The independent tuning of the two resonant wavelengths by the Fermi level or the geometrical parameters provides the guideline for the design of dual-band filter, while the sensitivity of the resonant wavelengths to the refractive indices of surrounding media implies the potential applications for both the bulk and thin film sensing.
Acknowledgments
This work was supported in part by National Natural Science Foundation of China (41390453, 11504305, 11501481), Key Scientific Project of Fujian Province in China (2015H0039), and Fundamental Research Funds for the Central Universities, Xiamen University (20720160104).
References and links
1. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993). [CrossRef] [PubMed]
2. S. H. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]
3. P. B. Catrysse, G. Veronis, H. Shin, J. T. Shen, and S. Fan, “Guided modes supported by plasmonic films with a periodic arrangement of subwavelength slits,” Appl. Phys. Lett. 88(3), 031101 (2006). [CrossRef]
4. R. Magnusson, H. G. Svavarsson, J. Yoon, M. Shokooh-Saremi, and S. H. Song, “Experimental observation of leaky modes and plasmons in a hybrid resonance element,” Appl. Phys. Lett. 100(9), 091106 (2012). [CrossRef]
5. L. J. Meng, D. Zhao, Z. C. Ruan, Q. Li, Y. Q. Yang, and M. Qiu, “Optimized grating as an ultra-narrow band absorber or plasmonic sensor,” Opt. Lett. 39(5), 1137–1140 (2014). [CrossRef] [PubMed]
6. W. L. Gao, J. Shu, C. Y. Qiu, and Q. F. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012). [CrossRef] [PubMed]
7. W. L. Gao, G. Shi, Z. H. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. F. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13(8), 3698–3702 (2013). [CrossRef] [PubMed]
8. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012). [CrossRef]
9. D. Sadot and E. Boimovich, “Tunable optical filters for dense wdm networks,” IEEE Commun. Mag. 36(12), 50–55 (1998). [CrossRef]
10. B. M. Walsh, “Dual wavelength lasers,” Laser Phys. 20(3), 622–634 (2010). [CrossRef]
11. X. Z. Wang, Z. F. Wang, Y. K. Bu, L. J. Chen, G. X. Cai, and Z. P. Cai, “A 1064-and 1074-nm dual-wavelength Nd:YAG laser using a fabry-perot band-pass filter as output mirror,” IEEE Photonics J. 6(4), 1501607 (2014). [CrossRef]
12. S. C. Song, Q. Chen, L. Jin, and F. H. Sun, “Great light absorption enhancement in a graphene photodetector integrated with a metamaterial perfect absorber,” Nanoscale 5(20), 9615–9619 (2013). [CrossRef] [PubMed]
13. Y. P. Zhang, T. T. Li, B. B. Zeng, H. Y. Zhang, H. H. Lv, X. Y. Huang, W. L. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double fano resonances,” Nanoscale 7(29), 12682–12688 (2015). [CrossRef] [PubMed]
14. D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. G. de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349(6244), 165–168 (2015). [CrossRef] [PubMed]
15. Z. S. Wang, T. Sang, L. Wang, J. T. Zhu, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance brewster filters with multiple channels,” Appl. Phys. Lett. 88(25), 251115 (2006). [CrossRef]
16. A. Greenwell, S. Boonruang, and M. G. Moharam, “Control of resonance separation over a wide spectral range in multiwavelength resonant grating filters,” Appl. Opt. 46(25), 6355–6361 (2007). [CrossRef] [PubMed]
17. R. Magnusson, “Spectrally dense comb-like filters fashioned with thick guided-mode resonant gratings,” Opt. Lett. 37(18), 3792–3794 (2012). [CrossRef] [PubMed]
18. H. Yun, S. Y. Lee, and B. Lee, “Hybrid multibands of surface plasmon and Fabry-Pérot resonances,” IEEE Photonics Technol. Lett. 26(20), 2027–2030 (2014). [CrossRef]
19. K. Chen, R. Adato, and H. Altug, “Dual-band perfect absorber for multispectral plasmon-enhanced infrared spectroscopy,” ACS Nano 6(9), 7998–8006 (2012). [CrossRef] [PubMed]
20. R. Feng, W. Q. Ding, L. H. Liu, L. X. Chen, J. Qiu, and G. Q. Chen, “Dual-band infrared perfect absorber based on asymmetric T-shaped plasmonic array,” Opt. Express 22(5), A335–A343 (2014). [CrossRef] [PubMed]
21. R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008). [CrossRef] [PubMed]
22. H. G. Yan, F. N. Xia, W. J. Zhu, M. Freitag, C. Dimitrakopoulos, A. A. Bol, G. Tulevski, and P. Avouris, “Infrared spectroscopy of wafer-scale graphene,” ACS Nano 5(12), 9854–9860 (2011). [CrossRef] [PubMed]
23. P. B. Catrysse and S. H. Fan, “Nanopatterned metallic films for use as transparent conductive electrodes in optoelectronic devices,” Nano Lett. 10(8), 2944–2949 (2010). [CrossRef] [PubMed]
24. H. Y. Jang, S. K. Lee, S. H. Cho, J. H. Ahn, and S. Park, “Fabrication of metallic nanomesh: Pt nano-mesh as a proof of concept for stretchable and transparent electrodes,” Chem. Mater. 25(17), 3535–3538 (2013). [CrossRef]
25. M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009). [CrossRef]
26. A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84(16), 161407 (2011). [CrossRef]
27. Y. Francescato, V. Giannini, and S. A. Maier, “Strongly confined gap plasmon modes in graphene sandwiches and graphene-on-silicon,” New J. Phys. 15(06), 063020 (2013). [CrossRef]
28. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011). [CrossRef] [PubMed]
29. E. H. Hwang, S. Adam, and S. Das Sarma, “Carrier transport in two-dimensional graphene layers,” Phys. Rev. Lett. 98(18), 186806 (2007). [CrossRef] [PubMed]
30. N. K. Emani, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Graphene: A dynamic platform for electrical control of plasmonic resonance,” Nanophotonics 4(1), 214–223 (2015). [CrossRef]
31. N. K. Emani, D. Wang, T. F. Chung, L. J. Prokopeva, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Plasmon resonance in multilayer graphene nanoribbons,” Laser Photonics Rev. 9(6), 650–655 (2015). [CrossRef]
32. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
33. L. L. Tang, J. L. Du, C. L. Du, P. Zhu, and H. F. Shi, “Scaling phenomenon of graphene surface plasmon modes in grating-spacer-graphene hybrid systems,” Opt. Express 22(17), 20214–20222 (2014). [CrossRef] [PubMed]
34. Y. Zhao and Y. Zhu, “Graphene-based hybrid films for plasmonic sensing,” Nanoscale 7(35), 14561–14576 (2015). [CrossRef] [PubMed]
35. B. Vasić, G. Isić, and R. Gajić, “Localized surface plasmon resonances in graphene ribbon arrays for sensing of dielectric environment at infrared frequencies,” J. Appl. Phys. 113(1), 013110 (2013). [CrossRef]
