Cavity-enhanced continuous graphene plasmonic resonator for infrared sensing

Optics Communications ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Cavity-enhanced continuous graphene plasmonic resonator for infrared sensing Wei Wei a,b,c,d,n, Jinpeng Nong a,b,c, Yong Zhu b,nn, Linlong Tang c, Guiwen Zhang b, Jun Yang c, Yu Huang c, Dapeng Wei c,d a

Key Laboratory of Optoelectronic Technology & Systems, Ministry of Education of China, Chongqing University, Chongqing 400044, China College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China c Chongqing institute of green and intelligent technology, Chinese Academy of Sciences, Chongqing 401122, China d Chongqing Engineering Research Center of Graphene Film Manufacturing, Chongqing 401329, China b

art ic l e i nf o

a b s t r a c t

Article history: Received 23 November 2015 Received in revised form 19 May 2016 Accepted 3 June 2016

We propose a cavity-enhanced resonator based on graphene surface plasmonics for infrared sensing. In such a resonator, a continuous and non-patterned monolayer graphene serves as the sensing medium by exciting surface plasmons on its surface, which can preserve the excellent electronic property of graphene and avoid the interaction between biomolecules and dielectric substrate. To improve its sensing performance, an optical cavity is employed to enhance the coupling of the incident light with the resonator. Simulation results demonstrate that the reflection spectra of the resonator can be modified to be narrower and deeper to improve the figure of merit (FOM) of the device significantly by adjusting the structure parameters of the cavity and the Fermi energy level. The FOM can achieve a high value of up to 20.15 RIU
1, which is about twice larger than that of the traditional structure without a cavity. Furthermore, the resonator can work in a wide angle range of the incident light. Such a plasmonic resonator with excellent features may provide a strategy to engineer graphene-based SPR sensor with high detection accuracy. & 2016 Elsevier B.V. All rights reserved.

Keywords: Cavity-enhanced Graphene Surface plasmonics Infrared sensor

1. Introduction Surface plasmon resonance (SPR) [1,2] is well known as one of the most outstanding optical sensing technology for allowing fastspeed, label-free and non-destructive detection with high sensitivity. Extensive efforts have been devoted to engineering metalbased SPR biosensors at visible and near-infrared frequencies [3–5]. However, the intrinsic shortcomings of traditional noble metals, such as the high surface inertness, the high intrinsic hydrophobicity and the large electronic density of states [6–8], become the major obstacles on the way of developing infrared SPR sensors. Graphene [9] that emerged as a revolutionary two-dimensional (2D) material, offers an unique opportunity to address this situation. It supports the propagation of surface plasmonics waves at infrared frequencies [10–12] with lower loss and higher confinement compared to the metals. And it can also adsorb the n Corresponding author at: Key Laboratory of Optoelectronic Technology & Systems, Ministry of Education of China, Chongqing University, Chongqing 400044, China. nn Corresponding author at: College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China. E-mail addresses: [email protected] (W. Wei), [email protected] (Y. Zhu).

biomolecules efficiently attributed to its high surface-to-volume ratio and the π-stacking interactions between graphene and biomolecules. In addition, the frequency of surface plasmonics can be widely modulated within a wide range of infrared waveband via external gate voltage [13]. The combination of these distinctive features renders graphene a promising plasmonics material for infrared SPR sensing. Recently, the excitations of localized surface plasmons in patterned graphene (nano-ribbons [14], nano-rings [15], nano-disks [16] and anti-dot arrays [17]) have been theoretically investigated for SPR sensing [7,18,19]. Though the performance of sensors are improved by optimizing the structure parameters and the properties of graphene layers, the preparation process of patterned graphene destroys its integrity. This severely decreases the contact area between graphene and biomolecules, and also dramatically reduces its electron mobility, which restricts the further improvement of the performance. Therefore, it is highly desirable to excite the surface plasmons in continuous graphene sheet. Apart from preserving the integrity and the high mobility of graphene, continuous graphene sheet can also provide brand-new advantages for sensing applications, including (1) excellent antifouling ability, (2) negligible interference from the interaction between biomolecules and dielectric substrate due to the high

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electron density of hexagonal rings that can be impermeable to the atoms and molecules, and more importantly, (3) offering a homogenous and complete 2D surface that is responsible for the highly uniform and effective surface loading of the biomolecules [20,21]. Recent studies theoretically and experimentally demonstrated the excitations of the surface plasmons in continuous graphene sheet with various sub-wavelength grating to compensate the mismatch of wavevector [22–25]. In such schemes, the rough sub-wavelength structures may degenerate the performance of the devices due to the deterioration of mobility caused by the increase of the interface scattering compared to the flat substrate. To resolve these problems, a hybrid grating structure is proposed by adding a low-permittivity buffer layer underneath the graphene sheet, which exhibits an improvement of 45.13% in sensitivity [26]. However, the improvement of the sensitivity of such transmission configuration is always accompanied with the dramatical red-shift of the resonance wavelength. This results in the increase of the real part of surface conductivity, and consequently the broadening of the spectral line, which decreases the figure of merit (FOM) of the devices. Though the FOM for a specific resonant wavelength can be theoretically improved by increasing the quality (carrier mobility) of graphene, it cannot be tuned in practice since the carrier mobility is the intrinsic property of

graphene. Further improvement of the FOM remains challenge. Herein, we propose a cavity-enhanced infrared SPR sensor based on surface plasmons in continuous graphene sheet to improve the FOM of the sensor while maintaining the quality of graphene. A thick gold film is introduced to form a resonance cavity to enhance the interaction between the graphene and the incident wave. Thus the spectral lines can be reshaped (to be narrower and deeper) without changing the resonance wavelength to achieve the maximum FOM. The temporal coupled mode theory is employed to reveal the reshaping of the spectral line with varying F–P cavity length. Finally, we further investigate the actively tuning of FOM by adjusting the Fermi energy level and the dependence of the performance on the incident angle. Understanding of these mechanisms will greatly facilitate the design of graphene-based SPR sensors with high detection accuracy.

2. Structure and method A schematic view of the considering cavity-enhanced continuous graphene plasmonic resonator is illustrated in Fig. 1(a). A continuous doped graphene sheet is resting on an insulator-covered sub-wavelength silicon grating (ICSWSG). The graphene

Fig. 1. (a) Schematic of the ICSWSG resonator with deposited reflective layer. (b) Calculated GSP mode pattern when Tbuf ¼ 10 nm, Λ ¼200 nm, W ¼ 100 nm, Hgra ¼200 nm, Tspa ¼200 nm and D ¼100 nm. The while lines in (b) depict the profile of the ICSWSG. (c) The evolution of the reflection spectra with increasing refractive index of the sensing medium.

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surface plasmonic (GSP) mode is excited in graphene with subwavelength grating to compensate the mismatch of wavevector. The proposed structure can be fabricated in practice, and one feasible strategy can be done by the following steps: First, a silicon wafer is patterned into a periodic array of gratings using standard optical lithography or focused ion beam. Then, a common used derivative of poly-hydroxystyrene (NFC) is spin-coated onto the surface to form a buffer layer. The thickness and uniformity of the buffer layer can be controlled by adjusting the spin speed. Afterwards, a CVD-grown graphene film is transferred onto the top of the buffer layer. Finally, the Au electrodes on the graphene surface and the Au reflective layer can be deposited by thermal evaporation. Therefore, we believe the present structure can be fabricated by current micro/nanofabrication technology. In such configuration, a cavity can be formed between the graphene and the reflective layer, which can enhance the interaction between incident light and graphene. To obtain the resonance characteristics of the cavity-enhanced infrared resonator, a physical model is built using COMSOL multiphysics employing finite element method. Graphene is modeled as a monolayer with thickness of 0.34 nm [19,27]. The thickness of the buffer layer is Tbuf ¼10 nm. The period, width and height of grating are fixed as Λ ¼200 nm, W ¼100 nm and Hgra ¼500 nm, respectively. The dielectric constant of the spacer (Si) and the NFC are εSi ¼11.7 and εNFC ¼ 2.4 [26]. The permittivity of the metallic reflective layer (gold) is given by the Drude model [28]. Variable mesh sizes are chosen to ensure a sufficient number of mesh cells are present in each layer of the structure. As a transverse magnetic (TM) polarization plane wave impinges on the top of the structure, the dispersion relationship of surface plasmonics wave in the continuous graphene sheet can be given by [29]

q (ω) = iε0

(na2

+ εeff ) 2πc σ (ω) λ0

(1)

where q is the wavevector of graphene plasmonic wave, ω is the angle frequency of the incident light, c is the speed of light in vacuum, ε0 is the vacuum permittivity, na is the refractive index of the sensing medium above the graphene and λ0 is the incident wavelength. In the considering infrared frequencies, s(ω) is the surface conductivity accounting only for intraband transitions that is described by Drude model

σ (ω) =

2π ω + sin θ Λ c

(4)

where θ is the incident angle. In this paper, we mainly focus on the GSP mode excited by the first diffraction order (m ¼ 1) due to the relatively low excitation efficiency of high diffraction orders [23]. The GSP mode profile is illustrated in Fig. 1(b). One can see that, the excitation of GSP exhibits strong ability to capture light from free space and concentrate optical energy into sub-wavelength spots on the graphene surface, resulting in the dramatical enhancement of the near-field |Ex| peak intensity up to  1.62  106 V/m. Meanwhile, due to the Ohmic loss, the optical energy of the GSP wave is dissipated while it propagates along the graphene sheet, yielding a notch in the reflection spectra. The corresponding resonant wavelength λ0 for a normal-incidence wave (θ ¼0) is expressed as

λ0 =

π ℏc 2ε0 (na2 + εeff ) Λ e Ef

(5)

Clearly, the resonance wavelength is very sensitive to the refractive index change around local dielectric environment. This feature makes it possible for the SPR sensing applications. The change in refractive index leads to the shift of the resonance dip, as illustrated in Fig. 1(c).The overall performance of the sensor can be evaluated by figure of merit (FOM) [31,32] defined as Eq. (6).

FOM =

S ΔR FWHM

(6)

Here, ΔR ¼1
R0 is the resonance depth, S is the sensitivity defined as the shift in resonant wavelength (δλ0) in responds to the changes (δna) in refractive index of the analyte

S=

δλ 0 π ℏc = e δn a

2ε 0 Λ Ef

na na2 + εeff

(7)

and FWHM is of the full width at half maximum. Therefore, to achieve a large FOM, the resonance dip should have a large wavelength shift with the same refractive index change, a narrow line width and a large resonance depth, respectively [7]. For a specific sensitivity, the key to improve the FOM is reshaping the spectral line to be narrower (smaller FWHM) and deeper (larger ΔR).

3. Results and discussion

e2Ef i π ℏ2 ω + iτ −1

(2)

where e is the elementary charge, τ ¼ μ is the electron relaxation time of charge carriers, μ is the carrier mobility of graphene, vF is the fermi velocity, Ef is the Fermi energy level of graphene, ħ is the reduced Planck's constant. Since the period of the sub-wavelength grating is much smaller than the incident wavelength, the grating can be approximated as an uniform medium with permittivity of εgra ¼ (1
f)*εNFC þf*εSi, where εSi and εNFC are the dielectric constant of the silicon grating and NFC, f ¼W/Λ is the occupation ratio of grating. For simplicity, the effective permittivity εeff of the buffer layer and grating when they are taken as an effective uniform medium can be further written as [30] Ef/evF2

εeff ≡ εNFC

Re (q) = m

3

( εgra + εNFC )⋅exp ( 2qTbuf ) + ( εgra − εNFC ) ( εgra + εNFC )⋅exp ( 2qTbuf ) − ( εgra − εNFC )

(3)

The plasmons in continuous graphene sheet can be excited by external incident TM light once the period of the sub-wavelength grating and the dispersion relationship (Eq. (1)) satisfy the following phase matching condition

We first compare the performance of the sensors before and after adding a reflective layer. The transmission spectrum of the traditional transmission-type sensor before adding a thick reflective layer is shown in Fig. 2(a). An asymmetric Fano-like spectral line shape can be observed due to the interference between the non-resonance transmitted light (the part of the light that directly pass the device) and the resonance transmitted light (the part of the light that first absorbed and then re-emitted by the graphene plasmon resonant mode) [33]. It possesses bandwidth of 123 nm and resonance depth of only 0.64. After adding a reflective layer, the transmission light is suppressed and the reflection spectrum is detected and presented in Fig. 2(b). It shows that the resonance wavelength slightly redshifts from 8.345 μm to 8.372 μm after a reflective layer is added. Meanwhile, the spectral line becomes narrower (FWHM ¼85 nm) and deeper (ΔR¼0.79). It can be attributed to the fact that an asymmetric Fabry–Perot (F– P) cavity [34,35] is formed between graphene and reflective layer, which allows the incident light make two passes (forward and reflected) through the graphene sheet. This leads to the reshaping of the spectral line and consequently, an improvement of 86.6% in FOM from 9.78 RIU
1 to 18.25 RIU
1, indicating that the FOM can

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Fig. 2. (a) The transmission spectrum when carrier mobility μ¼10,000 cm2 (V
1 s
1) for Fermi energy level Ef ¼ 0.6 eV. (b) The reflection spectrum after adding a reflective layer when μ¼10,000 cm2 (V
1 s
1). Insets are the cross section of the hybrid structures.

be dramatically improved by adding a reflective layer. In such a resonance cavity, the intensity of the interaction between graphene and the incident light is determined by three parameters, i.e. the reflectance of the top graphene layer, the reflectance of the bottom metal mirror and the F–P cavity length. Among these parameters, the reflectance of the bottom metal mirror is determined by the thickness D of the reflective layer, and the F–P cavity length is related to the spacer thickness Tspa. While the reflectance of graphene is an intrinsic property of graphene that determined by the material properties, and it can hardly be tuned once the Fermi level is fixed. Hence, we first focus on modulating the graphene-light interaction to improve the performance of the sensor by tuning D and Tspa for a fixed Fermi level, and then investigate the active tuning of Fermi level on the performance of the sensor. The effect of the reflectance of the bottom metal mirror (thickness D of the reflective layer) on the reflection spectral line and the performance of the sensor is first investigated. Simulations are performed fixing Tspa ¼200 nm and μ ¼10,000 cm2 (V
1 s
1). One can see from the reflection spectra in Fig. 3(a) that the spectral line exhibits an obvious reshaping behavior with decreasing D from 50 nm to 5 nm, resulting in the variation of the FOM, as plotted in the solid sphere red line in Fig. 3(b). The figure illustrates that the FWHM maintains at 133 nm and the FOM is nearly unchanged when D is larger than 15 nm (typically the skin depth

of gold [36]). Nevertheless, when D is smaller than 15 nm, the GSP wave can penetrate through the thin metal layer and leak out of the F–P cavity. This reduces the coupling strength between the incident light and the resonator, which leads to the broadening of the spectral line from 133 nm to 261 nm, as shown in the open sphere black line in Fig. 3(b). Consequently, the FOM falls sharply by 52.9% from 14.98 RIU
1 to merely 7.22 RIU
1 (D¼ 5 nm). Therefore, the minimum thickness of the reflective layer should be larger than the skin depth of the metal to suppress the transmission light totally to ensure the coupling strength of the F–P cavity with GSP mode. We then explore the modulation of F–P cavity length (spacer thickness Tspa) on the spectral line and the performance of the sensor. The reflection spectra with several sets of spacer thickness Tspa are displayed in Fig. 4(a). It shows that the notch broadens and becomes deeper as Tspa increases from 900 nm to 1400 nm. The reflectance as function of the spacer thickness Tspa and the wavelength λ is further mapping in Fig. 4(b). The strong coupling between the F–P cavity and the GSP mode leads to an avoided crossing. Clearly, the resonance wavelength slightly changes with varying spacer thickness and periodically floats at 8.34–8.37 μm. To quantitatively reveal the reshaping of the spectral line and its impact on the FOM, the Ra and FWHM are extracted from Fig. 4(b) and plotted in Fig. 4(c). One can see that Ra and FWHM vary periodically with Tspa, and this results in the periodical

Fig. 3. (a) The reflection spectra with varying thickness of reflective layer from 5 nm to 50 nm when Tspa ¼ 200 nm, Ef ¼0.6 eV and μ¼ 10,000 cm2 (V
1 s
1). (b) The extracted FWHM and the calculated FOM as a function of the thickness D of reflective layer.

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Fig. 4. (a) The reflection spectra with varying spacer thickness Tspa when Ef ¼ 0.6 eV and μ¼ 10,000 cm2(V
1 s
1). (b) Reflectance as a function of spacer thickness and wavelength. (c) The extracted Ra and FWHM from the reflection spectra with varying spacer thickness. (d) The calculated FOM with varying spacer thickness.

variation of FOM with the same period, as plotted in Fig. 4(d). The FOM reaches its maximum value of 20.15 RIU
1 with an interval of 1250 nm in a period, which is 22.4 times larger than the minimum value (0.9 RIU
1). According to the F–P physical model, the predicting variation period of the FOM is determined by the resonant wavelength λ0 and refractive index n of the spacer through T0 ¼ λ0 /2n, which is in good agreement with the simulation results in Fig. 4(d). Therefore, the spectral lines can be modulated periodically to achieve the maximum FOM by fabricating the suitable length of the F-P cavity in the initial design. To further quantitatively acquire the condition to obtain the maximum FOM of the sensor, a temporal coupled mode [37] physical model is built. The device is modeled as a resonator with intrinsic loss rate of γ0 and resonant frequency of ω0. The resonator couples with the incident TM wave with leakage rate of γ1 that can be characterized using the temporal coupled mode equations. Thus when the reflective layer is thick enough, the transmission light is totally suppressed and the reflectance of the resonator at ω is

R=

(ω − ω 0 )2 + (γ0 − γ1)2 (ω − ω 0 )2 + (γ0 + γ1)2

(8)

This gives us two key parameters (R0 and FWHM) of the spectral lines. The resonant reflectance R0 at ω ¼ ω0

R0 =

(γ0 − γ1)2 (γ0 + γ1)2

(9)

and the corresponding FWHM as

FWHM = 2 (γ0 + γ1)

(10)

Eqs. (9) and (10) indicate that the intrinsic loss rate γ0 and the leakage rate γ1 are the essential physical parameters that dominate the spectral line of sensor. In the physical model, the intrinsic loss rate γ0 is determined by the relaxation time τ of graphene through γ0 E1/(2τ) in the considering infrared region, while the leakage rate γ1 is decided by the spacer thickness T. By substituting Eqs. (9) and (10) into Eq. (6), and assuming ΔR¼(1
Ra), the FOM is further written as

FOM = 2S

γ0 γ1 (γ0 + γ1)3

(11)

According to its first order derivative, there exists a solution to obtain the maximum FOM, i.e. γ1 ¼ 2γ0 for a fixed γ0. By substituting this condition into Ra ¼(γ0
γ1)2/(γ0 þ γ1)2, we arrive at a constant reflectance of Ra ¼1/9. It is surprising that the FOM does not achieve the maximum value when the resonance curves have the smallest bandwidth or the largest resonance depth. Moreover, this predicting theoretical value is coincident with the simulation results in Fig. 4(c) and (d). Hence, the FOM can acquire a maximum value by adjusting the F–P cavity length to satisfy the condition of Ra E 11% in the initial design.

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Fig. 5. (a) Reflection spectra with varying Fermi energy level Ef of graphene from 0.4 eV to 0.8 eV when Tspa ¼1250 nm, D¼ 200 nm and μ¼ 10,000 cm2 (V
1 s
1). (b) The calculated FOM as a function of Fermi energy level of graphene for sensor with and without reflective layer. (c) Reflectance as a function of incident angles and wavelength when μ¼10,000 cm2 (V
1 s
1), D ¼200 nm, Ef ¼ 0.6 eV and Tspa ¼ 1250 nm. (d) The calculated FOM as a function of incident angle θ from
90 deg to 90° for structure with (red solid sphere) and without (blue open sphere) reflective layer. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Since the F–P cavity length is the geometrical parameter that can be adjusted only during fabrication, it cannot be actively controlled after the fabrication of the F–P cavity. Therefore, we further consider active tuning of FOM by changing the Fermi energy level Ef of graphene. The evolution of the reflection spectra with varying Fermi energy level when Tspa ¼ 1250 nm are illustrated in Fig. 5(a). The figure indicates that the sensor can operate within a wide range of infrared waveband (from 11.16 μm to 7.32 μm) by applying an external gate voltage. The blue shift of the resonance wavelength leads to the degradation of the sensitivity from 2418 nm/RIU to 1590 nm/ RIU as Ef increases from 0.4 eV to 0.8 eV. Meanwhile, the FWHM decreases from 160 nm to 74 nm and the resonance depth ΔR increases from 0.36 to 0.98 monotonously. However, the FOM does not exhibit a monotonous variation tendency as depicted in solid sphere red line in Fig. 5(b). Instead, it initially increases and then decreases after reaching a maximum value of 20.15/RIU when Ef ¼0.6 eV, which shows an obvious improvement compared to that of the sensor without (open sphere blue line) the reflective layer. Such nonmonotonic behavior of FOM can be explained that the condition γ1 ¼ γ0/2 is no longer satisfied due to the variation of λ0 induced by the change of Ef for a fixed F–P cavity length. Therefore, the Fermi energy level of graphene should be adjusted to match the maximum condition in order to achieve the maximum FOM after the fabrication of the device. Finally, we found that the sensor exhibits excellent angle-independence property. The simulated reflectance is mapping in Fig. 5(c) as a function of incident angles and wavelength when D¼ 200 nm and Tspa ¼1250 nm. One noticeable feature is that the narrow bandwidth and large resonance depth of the reflection spectrum are maintained until the incident angle is larger than

85°, indicating that the proposed sensor possesses the ability to work in a wide angle range of incident light. This excellent angleinsensitive property is attributed to the deep sub-wavelength nature of graphene plasmons and effects of Bragg scattering at the Brillouin zone center [22]. Moreover, the FOM of the structure with reflective layer maintains at a high level of 20.15 RIU
1 over a wide range of incident angle from
85° to 85°, which is about twice larger than that (9.78 RIU
1) of the structure without reflective layer, as shown in Fig. 5(d). These excellent features declare that the structure with the reflective layer shows an obvious advantage over that without reflective layer in practical implementations.

4. Conclusions As a summary, a cavity-enhanced infrared sensor based on continuous graphene surface plasmonic is proposed. The asymmetric Fabry–Perot cavity formed by the graphene and the reflective layer enhances the interaction between the graphene and incident light, which consequently improves the performance of the sensor. A temporal coupled mode physical model is built to reveal the parameters that dominate the spectral line shape. It shows that by tuning the length of F–P cavity to satisfy the condition of Ra ¼1/9, a high FOM of 20.15 RIU
1 can be obtained, which outperforms the device without the reflective layer by two times. Moreover, the proposed sensor can operate in a wide range of incident angle. Our study offers a feasible approach to develop graphene-based SPR sensing devices with high detection accuracy at infrared frequencies.

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Acknowledgments This work is supported by National High Technology Research and Development Program of China (2015AA034801), National Natural Science Foundation of China (No.61405021), Specialized Research Fund for the Doctoral Program of Higher Education (20120191120021), Natural Science Foundation of Chongqing, China (cstc2014jcyjA40045) and the Fundamental Research Funds for the Central Universities (CDJZR12120004, 106112013CDJZR120006).

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Please cite this article as: W. Wei, et al., Optics Communications (2016), http://dx.doi.org/10.1016/j.optcom.2016.06.007i