sensors Article

Molecular Spectrum Capture by Tuning the Chemical Potential of Graphene Yue Cheng 1 , Jingjing Yang 1, *, Qiannan Lu 1 , Hao Tang 2 and Ming Huang 1, * 1 2

*

Wireless Innovation Lab of Yunnan University, School of Information Science and Engineering, Kunming 650091, Yunnan, China; [email protected] (Y.C.); [email protected] (Q.L.) Radio Monitoring Center of Yunnan Province, Kunming 650228, Yunnan, China; [email protected] Correspondence: [email protected] (J.Y.); [email protected] (M.H.); Tel./Fax: +86-871-503-3743 (J.Y. & M.H.)

Academic Editor: Galina Nemova Received: 2 April 2016; Accepted: 18 May 2016; Published: 27 May 2016

Abstract: Due to its adjustable electronic properties and effective excitation of surface plasmons in the infrared and terahertz frequency range, research on graphene has attracted a great deal of attention. Here, we demonstrate that plasmon modes in graphene-coated dielectric nanowire (GNW) waveguides can be excited by a monolayer graphene ribbon. What is more the transverse resonant frequency spectrum of the GNW can be flexibly tuned by adjusting the chemical potential of graphene, and amplitude of the resonance peak varies linearly with the imaginary part of the analyte permittivity. As a consequence, the GNW works as a probe for capturing the molecular spectrum. Broadband sensing of toluene, ethanol and sulfurous anhydride thin layers is demonstrated by calculating the changes in spectral intensity of the propagating mode and the results show that the intensity spectra correspond exactly to the infrared spectra of these molecules. This may open an effective avenue to design sensors for detecting nanometric-size molecules in the terahertz and infrared regimes. Keywords: graphene; surface plasmons; sensors; molecules

1. Introduction Surface plasmon polaritons (SPPs), which are electromagnetic excitations propagating along the interface between a dielectric and a metal [1], offer a promising solution to control electromagnetic waves at subwavelength scale. These electromagnetic surface waves arise via the coupling of the electromagnetic fields to oscillations of the conductor’s electron plasma [2]. Owing to their advantages of novel optical properties, such as selective absorption and scattering of light, subwavelength electromagnetic confinement and local optical field enhancement, SPPs have attracted a great deal of attention and have been widely used in integrated optics, chemosensing, biosensing, etc. [3–9]. Among the available plasmonic materials, the frequency range of which lies in the visible to near-infrared, noble metals are usually chosen to support SPPs for their relatively low losses [10]. However, in the mid-infrared to terahertz frequency, due to the difficulty in controlling and varying the permittivity functions of noble metals and the existence of material losses, only loosely bound surface waves can be supported by noble metals. Recently, experiments confirmed that doped graphene supports surface plasmons as well [11]. Graphene, a newly two-dimensional material with a thickness of only one atom, is considered a novel plasmonic material for the terahertz to infrared spectral region [12–14]. Graphene surface plasmons (GSPs) exhibit exceptional electrical tunability, low intrinsic loss, highly confined optical field and other fascinating properties due to the fact graphene has special electronic energy band structures [11,15–18]. Various graphene nanostructures were proposed to support GSPs modes. Currently, the design of optical devices using graphene has become a hot Sensors 2016, 16, 773; doi:10.3390/s16060773

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research topic. A variety of devices such as nanoribbons [19,20], nano-discs [21], graphene-metal plasmonic antennas [22] and graphene resonance sensors [23] have been proposed. Moreover, several experiments [10,24–27] have also indicated that a graphene layer can tightly coat a dielectric nanowire due to van der Waals force. Graphene-microfiber/nanowire combined system has been proposed for various applications [24–29]. Detection and sensing at the molecular level have attracted much attention and some graphene-based schemes were presented [23,30]. Graphene-based platforms for the detection of individual gas molecules [31], protein monolayers [32] and DNA [33] open exciting prospects for chemo- and bio-sensing. In addition, an ultra-compact tunable plasmon ring resonator which is composed of a monolayer of graphene and a graphene ring was proposed and analyzed numerically by Huang et al. [34]. The characteristics of the plasmon ring resonator, such as resonance frequency tenability and high quality factor were analyzed numerically. However, the application of the resonator as a sensor has not been explored yet. In this study, we investigate the sensing characteristic of a tunable graphene-coated dielectric nanowire (GNW) waveguide, which could be used to detect molecules. The transverse resonant modes are simulated numerically in detail using the finite element method, and validated by theoretical analysis. It is found that a small change in the chemical potential can induce the resonant mode to shift by a large frequency range. We also show that the mode behavior of the GNW can be influenced by the relative permittivity of a thin layer dielectric which is supposed to be the analyte attached to the outer side of GNW waveguide. Remarkably, the GNW is proven to play a pivotal role as a highly sensitive platform for broadband molecular sensing. 2. Physical Model and Principles The GNW is a graphene-coated dielectric nanowire which is excited by a graphene ribbon. The geometry of the GNW is shown in Figure 1. A dielectric nanowire core of relative permittivity ε1 = 2.1ε0 is surrounded by a graphene layer with a conductivity σg expressed by the Kubo formula [35,36], which represents a finite temperature as σg = σintra + σinter with the intraband and interband contributions being: σintra “

σinter

e2 “ 2 4}

«

” ´ µ ¯ı 2ie2 T c ln 2 cosh 2T }2 π pω ` iΓq

1 1 ` arctan 2 π

ˆ

}ω ´ 2µc 2T

˙

p}ω ` 2µc q2 i ´ ln 2π p}ω ´ 2µc q2 ` p2Tq2

(1) ff (2)

where ε0 is the permittivity of vacuum, T = 300 ˆ kB is the temperature energy, kB is the Boltzmann constant, µc is the chemical potential, Γ represents the carrier scattering rate and h¯ denotes the reduced Planck constant. The radius of the dielectric nanowire is R1, the thickness of the graphene is 0.5 nm as an anisotropic layer. The permittivity of the graphene is approximated by ε = 1 + iσg /ε0 ωt as proposed in [37], where t is the effective thickness. The longitudinal component of electric p1q

field Ez and magnetic field Hz could be represented as Ez p1q Hz p2q Hz

“ Bm Im pµ1 ρq exp pjmφq exp pjβzq , for ρ < R, and

p2q Ezb

“ Am Im pµ1 ρq exp pjmφq exp pjβzq , “ Cm Km pµ2 ρq exp pjmφq b exp pjβzq ,

“ Dm Km pµ2 ρq exp pjmφq exp pjβzq , for ρ > R, where µ1 “ β2 ´ ω2 ε1 µ0 and µ2 “ β2 ´ ω2 ε2 µ0 . Im (µ1 ρ) and Km (µ2 ρ) are the modified Bessel functions of the first and second kind (m = 0, 1, 2 . . . ). Am , Bm , Cm and Dm are arbitrary constants which are determined by the boundary conditions. The terms µ0 , k0 and ω are the magnetic permittivity, wavenumber in free space and radian frequency, respectively, µ1 and µ2 are related to the mode field confinement. By applying the relation between the longitudinal and transverse EM field components, and boundary condition, the eigen-equation for the m-th order mode [10] is:

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ˇ ˇ ˇ ˇ ˇ ˇ ˇ ˇ ˇ ˇ ˇ

I((m pµ1))Rq jmβ ( I( pµ))Rq ´µ 2 R m 1

00 0 ωµ0 (´ ( )) µ1 Im pµ1 Rq

ˇ ˇ ´K((m pµ)2)Rq 0 0 − ˇ 0 −jmβ ωµ0 ´ ˇ ( ) − pµ pµ K Rq ´ K Rq m m 2 2 )) ) ˇˇ − µ2 ( µ22 R (( 1 =0 ˇ “ 0(3) (3) jωε 1 ´ mβ jωε mβ − (3) (( pµ1))Rq − ´ µ2 2 K(´m pµ2)Rq ((m pµ)2)Rq=0ˇ − ´ µ2 R I((m pµ1))Rq 2R K µ1 Im −´ σg I((m pµ1))Rq µ − ˇ 2 1 ( ) − ˇ mβ jωµ (I(m pµ)1)Rq σg ´µ2 R I(m pµ1)Rq ´ σg µ 0 I((´m pµ1))Rq 0 − − 0 − −´K((m pµ2))Rq ˇ 1 ( ) 0 1

By get the propagation constant ββ of order mode and By solvingEquation Equation(3), (3),we wecould could get the propagation constant βthe of m-th the order mode By solving solving Equation (3), we could get the propagation constant of the m-thm-th order mode and SPs = the corresponding EM field. The real part of β relates to the surface plasmons’ wavelength λ and the corresponding EM field. The real part of β relates to the surface plasmons’ wavelength the corresponding EM field. The real part of β relates to the surface plasmons’ wavelength λSPs = 2π/Re(β), and effective mode as 0. The imaginary part ββ relates to λ2π/Re(β), the effective mode index is defined as Re(β)/k of β relates SPs = 2π/Re(β), 0 . The imaginary and the theand effective mode index index is is defined defined as Re(β)/k Re(β)/k 0. The imaginary part of ofpart relates to the the propagation loss of surface plasmons, and propagation length can be defined as 1/2Im(β), which to the propagation loss of surface plasmons, and propagation length can be defined as 1/2Im(β), which propagation loss of surface plasmons, and propagation length can be defined as 1/2Im(β), which means of its original power after travelling such aa distance. A means surface plasmons’mode modedecays decaysto to1/e 1/e original power after travelling such a distance. means surface surface plasmons’ plasmons’ mode decays to 1/e ofof itsits original power after travelling such distance. A larger μ 1 (μ 2 ) leads to I m (μ 1 ρ) [K m (μ 2 ρ)] increasing (decreasing) more quickly, which means the field is A larger Im1(µ ρ)m[K (µ2increasing ρ)] increasing (decreasing) more quickly, which means field 1 (µ 2 ) leads larger μ1µ(μ 2) leads to to Im(μ ρ)1[K (μm2ρ)] (decreasing) more quickly, which means thethe field is better confined near the graphene [10]. is better confined near the graphene [10]. better confined near the graphene [10].

Figure 1. 1. Schematic illustration illustration of the the graphene-coated dielectric dielectric nanowire waveguide. waveguide. Figure Figure 1.Schematic Schematic illustrationof of thegraphene-coated graphene-coated dielectricnanowire nanowire waveguide.

Figure Figure shows the theoretical and simulation results for the dispersion relations of GSPs modes Figure222shows showsthe thetheoretical theoreticaland andsimulation simulationresults resultsfor forthe thedispersion dispersionrelations relationsof ofGSPs GSPsmodes in The solid lines represent the simulation results while the dotted lines in GNW GNW of of the the first first five five orders. orders. The solid lines represent the simulation results while the dotted lines orders. results while correspond results. We notice that m = 0 mode is cutoff-free and the effective mode correspond to to the the theoretical theoretical results. We notice that m = 0 mode is cutoff-free and the effective mode theoretical results. We notice that m = indexes indexes of of all all modes decrease monotonically with decreasing decreasing frequency. also indicates indicates aa larger larger all modes modes decrease decrease monotonically monotonically with decreasing frequency. frequency. ItIt also proportion of the mode energy resides inside the GNW near the graphene-nanowire at proportion of the mode energy resides inside the GNW near the graphene-nanowire at high frequencies, proportion of the mode energy resides inside the GNW near the graphene-nanowire at high high frequencies, at they are localized outside while at low while frequencies, they are mainly localized outside the GNW. frequencies, while at low low frequencies, frequencies, they are mainly mainly localized outside the the GNW. GNW.

Figure Figure 2. Theoretical (dotted lines) and simulation (solid lines) results for the dispersion relations of Figure 2. 2. Theoretical Theoretical (dotted (dotted lines) lines) and and simulation simulation (solid (solid lines) lines) results results for for the the dispersion dispersion relations relations of of GSPs modes in the GNW. GSPs modes in the GNW. GSPs modes in the GNW.

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Sensors 2016, 16, 773 Analysis 3. Simulation and

3. Simulation and Analysis 3. Simulation and Analysis 3.1. Resonance Mode Analysis 3.1. Resonance Mode Analysis TheResonance 3D geometrical structure of the GNW waveguide excited by a graphene ribbon is exhibited 3.1. Mode Analysis geometrical of cross-section the GNW waveguide excited by aThe graphene exhibited in FigureThe 3a. 3D Figure 3b is a structure schematic of the structure. GNWribbon couldisbe regarded as The 3D of the GNW waveguide excited by graphene ribbon is exhibited in Figure 3a. geometrical Figure 3b is structure a schematic cross-section of the structure. Thea GNW could be regarded as a a graphene ribbon rolled around a dielectric nanowire, which can be silicon and GaN. In this apaper in Figure 3a. Figure 3b isaround a schematic cross-section of the structure. The GNW regarded graphene ribbon rolled a dielectric nanowire, which can be silicon andcould GaN. be In this paperas we we choose a dielectric nanowire a relative permittivity ε1 silicon = 2.1ε0and and magnetic conductivity graphene ribbon rolled around awith dielectric which GaN. In this paper we choose a dielectric nanowire with a relativenanowire, permittivity ε1 =can 2.1εbe 0 and magnetic conductivity μ0. The µ0 . The studied structure is embedded in complex air. Theconductivity complex conductivity of the thin layer choose astructure dielectric with a relative permittivity ε1 = 2.1ε 0 and magnetic conductivity μ0.graphene The studied isnanowire embedded in air. The of the thin layer graphene colored in colored isby given by the Kubo formula In this paper, we ambient studied structure is embedded in air. The complex conductivity of theambient thinchoose layer graphene colored grayinisgray given the Kubo formula [35,36]. In [35,36]. this paper, we choose temperature Ttemperature = 300 in k, gray given by potential theμKubo formula In the this paper, we choose ambient T =carrier 300 k, the T = 300 k,ischemical 0.5[35,36]. eV, carrier scattering rate Γ =temperature 1.32 meV the represents c = and chemical potential c = 0.5µeV, the and carrier scattering rate Γ = 1.32 meV represents chemical potential carrier scattering scattering rate.rate. μc = 0.5 eV, and the carrier scattering rate Γ = 1.32 meV represents the carrier scattering rate.

(a) (a)

(b) (b)

Figure 3. (a) Schematic diagram of the sensor model based on the cylindrical dielectric loaded with a

Figure 3. (a)3. Schematic diagram ofofthe sensor modelbased based cylindrical dielectric Figure (a) Schematic sensor model onon thethe cylindrical loadedloaded with a with thin layer graphene anddiagram monolayerthe graphene waveguide; (b) Cross-section ofdielectric the structure. a thinthin layer graphene graphenewaveguide; waveguide; Cross-section the structure. layer grapheneand andmonolayer monolayer graphene (b)(b) Cross-section of theofstructure.

Figure 4. Simulation results of magnetic-field (Hz) distribution at the resonant state of mode 1–8 for Figure 4. Simulation results magnetic-field (H (Hz))distribution at the resonant state of mode 1–8 for the4.GNW. Figure Simulation results ofofmagnetic-field z distribution at the resonant state of mode 1–8 for the GNW. the GNW.

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The Thetransverse transverseresonance resonancecharacteristics characteristicsof ofthe theGNW GNWare arestudied studiedbased based on on the the commercial commercial finite finite element method (FEM) software COMSOL Multiphysics. In the simulation, the radius of the dielectric element method (FEM) software COMSOL Multiphysics. In the simulation, the radius of the dielectric core core isisset setto tobe beRR11== 190 190 nm, nm, the the thickness thickness of ofthe thegraphene graphene hh== 0.5 0.5 nm, nm,while whilethe thecoupling couplingdistance distance between the graphene ribbon and the outer surface of the GNW is set to be g = 10 nm. The excitation between the graphene ribbon and the outer surface of the GNW is set to be g = 10 nm. The excitation source source of of unit unit amplitude, amplitude, with with magnetic magnetic vector vector parallel parallel to to the the z-axis z-axis is is set set at at port1 port1 of of the thegraphene graphene ribbon. ribbon. A A radiation radiation boundary boundary condition condition is is used used to totruncate truncatethe thecomputational computationaldomain. domain. The The whole whole space is meshed by triangle grids except for the graphene ribbon and the graphene layer of the GNW, space is meshed by triangle grids except for the graphene ribbon where wheresmooth smoothmapped mappedmesh meshgrids gridsare areadopted adoptedto toensure ensurethe the simulation simulation accuracy. accuracy.The Themagnetic magneticfield field distribution Figure 4. 4. Transverse resonant modes with orders of distributionin inthe thevicinity vicinityofofthe theGNW GNWisisshown showninin Figure Transverse resonant modes with orders m = 1, 2, 3, 4, 5, 6, 7, 8 can be observed in the frequency range of 7.13 THz to 49.36 THz. It is seen that of m = 1, 2, 3, 4, 5, 6, 7, 8 can be observed in the frequency range of 7.13 THz to 49.36 THz. It is seen the fieldsfields are tightly confined to thetosurface of theof GNW. Therefore, this area quite thatmagnetic the magnetic are tightly confined the surface the GNW. Therefore, thiswill areabewill be sensitive to the dielectric environment. quite sensitive to the dielectric environment. In resonant spectrum spectrumof ofthe theGNW GNWininthe thefrequency frequencyofof7.0 7.0THz–33.0 THz–33.0 THz. In Figure Figure 5, 5, we plot the resonant THz. It Itis issimulated simulatedbybyfrequency frequencysweep. sweep.AAprobe probeisis located located at at the the point that possesses possesses the the maximum maximum magnetic the resonant resonantstate statetotorecord recordthe the variation of |H frequency. to z | with magnetic field in the variation of |H z| with frequency. FromFrom left toleft right, right, the spectral correspond to modes 2, 43, and 4 and Theresonant resonantfrequency frequencyof of the GNW isis the spectral lines lines correspond to modes 1, 2,1,3, 5.5.The calculated calculatedand andcompared comparedwith withthe thetheoretical theoreticalresults, results,as asshown shownin inTable Table1.1.A A good good agreement agreementbetween between the eigenfrequency (f ) and the resonant frequency (f ) confirms the effectiveness of the GNW. the eigenfrequency (fee) and the resonant frequency (frr) confirms the effectiveness of the GNW.

Figure 5. The resonant frequency spectrum. Figure 5. The resonant frequency spectrum. Table 1. Comparison of the eigenfrequency (fe) and the simulated resonant frequency (fr) for modes 1 Table 1. Comparison of the eigenfrequency (f e ) and the simulated resonant frequency (f r ) for modes 1 to 8 of the GNW. to 8 of the GNW.

Mode 1 Mode fe(THz) 7.133 fr(THz) f e (THz) 7.131 f r (THz)

2

3

4 4 25.907 12.46912.47319.189 7.133 19.198 25.893 25.907

7 8 42.717 32.590 36.103 36.093 32.605 42.717 42.712 49.361

7.131

32.590

112.473 2 19.1983 12.469

19.189

25.893

5

6

5 32.605

6 36.1037

36.093

42.712

8 49.361 49.357

49.357

3.2. The Dependence of the Resonant Spectrum on the Chemical Potential 3.2. The Dependence of the Resonant Spectrum on the Chemical Potential In order to investigate the tunability of the resonant frequency of the GNW, frequency spectra withIn respect change ofthe thetunability chemical potential of graphene are simulated. The frequency chemical potential orderto tothe investigate of the resonant frequency of the GNW, spectra in graphene can be controlled with potentially fast speed using a FET structure [11], where the with respect to the change of the chemical potential of graphene are simulated. The chemical potential 1/2 approximate relationship is μc with  (Vpotentially g) and Vgfast is the gateusing voltage [38]. structure It has been shown that in graphene can be controlled speed a FET [11], where thea 1/2 chemical potential changeisofµ0.1 eV can be obtained with a gate voltage of a few volts [11,39], so we approximate relationship 9 (V ) and V is the gate voltage [38]. It has been shown that c g g a varied gatechange voltageofto0.1 control thebechemical of the graphene. We suppose that the aapplied chemical potential eV can obtainedpotential with a gate voltage of a few volts [11,39], so chemical graphene fromthe 0.5chemical eV to 0.55 eV withofintervals of 0.1 We eV,suppose and thenthat we we appliedpotential a variedof gate voltagevaries to control potential the graphene. extract the variation field amplitude frequency. Taking modes 4, eV, 5 asand an example, the chemical potentialofofmagnetic graphene varies from 0.5with eV to 0.55 eV with intervals of3,0.1 then we the simulation results are shown in Figure 6a–c. It is seen that the spectra are red shifted as the chemical potential of graphene increases. It is clear that the response to an increase of 0.1 eV in the

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extract the variation of magnetic field amplitude with frequency. Taking modes 3, 4, 5 as an example, the simulation results are shown in Figure 6a–c. It is seen that the spectra are red shifted as the Sensors 2016, 16, 773 of 11 chemical potential of graphene increases. It is clear that the response to an increase of 0.1 6eV in the chemical potential of graphene is a frequency shift of 707.2, 562.0, and 707.2 GHz on average. The chemical potential of graphene is a frequency shift of 707.2, 562.0, and 707.2 GHz on average. The inset portrays amplification of the resonant peakspeaks in the range ofof20.54–20.58 when the insetthe portrays the amplification of the resonant in frequency the frequency range 20.54–20.58 THz THz when chemical potentialpotential is 0.52 eV. TheeV. resonant frequency variesvaries linearly withwith chemical potential, as as shown the chemical is 0.52 The resonant frequency linearly chemical potential, in Figure 6b.in Figure 6b. shown

(a)

(b)

(c)

(d)

Figure 6. (a–c) Resonant frequency spectrum of modes 3, 4, 5 for a variation of chemical potential; (d)

Figure 6. (a–c) Resonant frequency spectrum of modes 3, 4, 5 for a variation of chemical potential; The relation between resonant frequency and the chemical potential. (d) The relation between resonant frequency and the chemical potential.

4. Sensing Application

4. Sensing Application

4.1. Sensing Characteristics

4.1. Sensing Characteristics

To explore the sensing properties of the GNW, we suppose that a layer of analyte with thickness

To the sensingtoproperties GNW, weas suppose that a layer of analyte with thickness (k) explore of 8 nm is attached the surface of of the the graphene, shown in Figure 7. Relative permittivity of attached analytetoisthe denoted as εof 2, and surrounding medium air. In 7. order to investigate the of (k) of the 8 nm is attached surface the the graphene, as shown in isFigure Relative permittivity sensing performance of the GNW, spectra with respect change of analyte the the attached analyte is denoted as ε2 ,resonant and thefrequency surrounding medium is air. to Inthe order to investigate permittivity were simulated. Firstly, we suppose that the analyte is lossless and the real part sensing performance of the GNW, resonant frequency spectra with respect to the change of of the analyte relative permittivity varies from 1.0 to 1.5 with an interval of 0.1. Taking mode 4 as an example, permittivity were simulated. Firstly, we suppose that the analyte is lossless and the real part of the simulation results are shown in Figure 8a. The inset denotes the magnetic-field (Hz) distribution at relative permittivity varies from 1.0 to 1.5 with an interval of 0.1. Taking mode 4 as an example, the resonant state of mode 4 when the analyte is absorbed to the surface of the GNW. It is seen that simulation results are shown in Figure 8a. The inset denotes the magnetic-field (Hz) distribution at the spectra are red shifted with increasing permittivity. The relative frequency shift in response to an the resonant when the analyte is absorbed to the surface of the GNW. is seen increase state of 0.1 of in mode analyte4permittivity is a significant resonant frequency downshift of 27.4ItGHz on that the spectra are red shifted with increasing permittivity. The relative frequency shift in response average. Then, we investigate the impact of the imaginary part of the analyte on the resonant spectra. to an increase of 0.1 inofanalyte permittivity is a significant frequency downshift of depicted 27.4 GHz on For a variation imaginary part, simulation results of resonant the resonant frequency spectra are in Figure It is clear the imaginary partofofthe theimaginary analyte permittivity mainly influences amplitude average. Then,8b.we investigate the impact part of the analyte on thethe resonant spectra. the spectra. For a of variation of imaginary part, simulation results of the resonant frequency spectra are depicted in Figure 8b. It is clear the imaginary part of the analyte permittivity mainly influences the amplitude of the spectra.

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ε2

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ε1

ε1 ε2

k

k

Analyte Analyte

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Analyte

ε1 R1 R1

k port1 port1

h

h

R1 g

g

port2 port2

Figure 7. A schematic illustration of the GNW sensor model with a layer of analyte absorbed to the

port1 of port2 Figure 7. 7. AA schematic ofhthe theGNW GNW sensor model a layer of analyte absorbed gmodel Figure schematicillustration illustration sensor withwith a layer of analyte absorbed to the to the surface of graphene. surface of of graphene. surface graphene.

Figure 7. A schematic illustration of the GNW sensor model with a layer of analyte absorbed to the surface of graphene.

(a) (b) (a) (b) Figure 8. The resonant frequency spectra of mode 4 for a variation of the real part (a) and imaginary Figure 8. The resonant frequency spectra of mode 4 for a variation of the real part (a) and imaginary distribution resonant part ofresonant analyte permittivity. The insetof denotes magnetic-field Figure 8. (b) The frequency spectra modethe 4 for a variation (H ofz)the real partat (a)the and imaginary (a) The inset denotes the magnetic-field (Hz) distribution (b) at the resonant part (b) of analyte permittivity. state ε2 = permittivity. 1.2. part (b) ofwhen analyte The inset denotes the magnetic-field (Hz ) distribution at the resonant state when8.εThe 2 = 1.2. resonant frequency spectra of mode 4 for a variation of the real part (a) and imaginary state Figure when ε2 = 1.2. part (b) ofSensing analyte permittivity. The inset denotes the magnetic-field (Hz) distribution at the resonant 4.2. Molecular 4.2. Molecular Sensing state when ε2 = 1.2.

It is known 4.2. Molecular Sensingthat unambiguous identification of low concentration chemical mixtures can be

It is known that unambiguous identification of low concentration chemical mixtures can be performed by Sensing broadband enhanced infrared absorption (BEIRA) [30], due to the infrared spectrum 4.2. Molecular performed by broadband enhanced infrared absorption (BEIRA) [30], due to the infraredmixtures spectrum can be It that unambiguous identification low concentration chemical of is theknown molecule which acts as a unique fingerprint. Inofthe mid-infrared to terahertz regime, graphene of the molecule which acts as a unique fingerprint. In the mid-infrared to terahertz regime, graphene isanknown that unambiguous identification low concentration chemical mixtures can be of performed broadband enhanced absorption (BEIRA) [30],Besides, due to the spectrum sheetItisby ideal carrier of highlyinfrared confined surfaceofplasmon modes. frominfrared the preceeding sheet is an ideal carrier of highly confined surface plasmon modes. Besides, from the preceeding performed by broadband enhanced infrared absorption (BEIRA) [30], due to the infrared spectrum the molecule which acts as a unique fingerprint. In of thethe mid-infrared terahertz regime, graphene analysis we obtained that the resonant frequency GNW sensortocan be flexibly tuned by analysis we obtained that the frequency of the mid-infrared GNW sensortocan be flexibly tuned by ofisthe which acts as aresonant unique fingerprint. the terahertz regime, graphene the carrier chemical potential of graphene, and In amplitude of the resonance peak varies linearly sheetadjusting anmolecule ideal of highly confined surface plasmon modes. Besides, from the preceeding adjusting the chemical potential of graphene, and amplitude ofmodes. the resonance peak linearly sheetthe an ideal carrier ofthe highly confined surface plasmon Besides, fromvaries thepeak preceeding with imaginary part of analyte permittivity, so we predicted that the resonance canadjusting act analysis weisobtained that the resonant frequency ofso the GNW sensor can beresonance flexibly tuned by with the imaginary part of thethe analyte permittivity, we predicted that the can peak tuned can actby analysis we obtained that resonant frequency of the GNW sensor be flexibly as a probe for capturing the molecular spectrum which may be reflected in the change of resonance theaschemical potential ofthe graphene, and amplitude of theberesonance variesoflinearly with the a probe for molecular spectrum which may reflected inpeak the change resonance adjusting thecapturing chemical potential of graphene, and amplitude of the resonance peak varies linearly peak amplitude, as shown in Figure 9. imaginary part of the analyte permittivity, so we predicted that the resonance peak can act as a probe peak amplitude, as shown 9. permittivity, so we predicted that the resonance peak can act for with the imaginary part in of Figure the analyte

capturing the molecular spectrum which spectrum may be reflected in the change in of the resonance peak amplitude, as a probe for capturing the molecular which may be reflected change of resonance as shown Figure 9.as shown in Figure 9. peak in amplitude,

Figure 9. A schematic illustration of molecular spectrum capture. Figure 9. A schematic illustration of molecular spectrum capture. Figure 9. A schematic illustration of molecular spectrum capture.

Figure 9. A schematic illustration of molecular spectrum capture.

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In what follows, we perform mode analysis to demonstrate the capture of molecular spectrum with the GNW. The absorption spectrum of the analyte used in the simulation is obtained from the National Institute of Standards and Technology (NIST, Gaithersburg, MD, USA) [40]. The intensity of Sensors 2016, 16, 773 8 of 11 the surface plasmon along the z direction is I = e´z/L . Here, z denotes the length of the GNW which is put along the z axis as shown in Figure 7. L is the propagation length of the mode, which is defined as In what follows, we perform mode analysis to demonstrate the capture of molecular spectrum L/λ0 = 1/Im(neff ). λ0 is the free space wavelength, neff is the effective mode index. We set Imol and I0 to with the GNW. The absorption spectrum of the analyte used in the simulation is obtained from the indicate the intensities with and without molecules deposited on the graphene surface. National Institute of Standards and Technology (NIST, Gaithersburg, MD, USA) [40]. The intensity Taking the liquid ethanol molecule as an example, the normalized intensity spectra (I /I0 ) of the surface plasmon along the z direction is I = e−z/L. Here, z denotes the length of the GNWmol which are illustrated in Figure 10a. It is seen that the variation of the signal directly maps the strong is put along the z axis as shown in Figure 7. L is the propagation length of the mode, which is defined characteristic features of the molecule infrared absorption spectrum shown in the insect of Figure 10a. as L/λ0 = 1/Im(neff). λ0 is the free space wavelength, neff is the effective mode index. We set Imol and I0 to More importantly, a sample only 2.0 µm long can produce a gigantic 3 dB (50%) drop in intensity with indicate the intensities with and without molecules deposited on the graphene surface. the proposed sensor, which indicates exceptional sensitivity.

(a)

(c)

(b)

(d)

Figure10. 10.Intensity Intensitychange changecaused causedby bypresence presenceofofanalyte. analyte.(a) (a)Ethanol; Ethanol;(b) (b)Toluene; Toluene;(c) (c)Sulfurous Sulfurous Figure anhydride;(d) (d)Ethanol Ethanolinindifferent differentthickness. thickness.InInpanels panels“a–c”, “a–c”,the theinsets insetsshow showthe theabsorption absorptionspectrum spectrum anhydride; of the analyte in the same frequency region as the main axis. of the analyte in the same frequency region as the main axis.

Taking the liquid ethanol molecule as an example, the normalized intensity spectra (Imol/I0) are To achieve such a wide band detection, the surface plasmon modes should have two features, i.e., illustrated in Figure 10a. It is seen that the variation of the signal directly maps the strong confinement to the surface of plasmonic materials and existing in an extended frequency band, within characteristic features of the molecule infrared absorption spectrum shown in the insect of Figure 10a. which the molecular vibrational modes appear. To demonstrate the tunability features of the SPP mode, More importantly, a sample only 2.0 μm long can produce a gigantic 3 dB (50%) drop in intensity liquid toluene molecules of which the characteristic absorption spectrum is localized in the frequency with the proposed sensor, which indicates exceptional sensitivity. range of 18–24 THz is adopted in the simulation. Similarly, an intensity change which directly maps To achieve such a wide band detection, the surface plasmon modes should have two features, the fingerprint of the molecule is obtained, as shown in Figure 10b. But since the absorption loss of i.e., confinement to the surface of plasmonic materials and existing in an extended frequency band, toluene molecule is smaller than that of ethanol, it needs a 20 µm long sample along the z direction within which the molecular vibrational modes appear. To demonstrate the tunability features of the to induced a 3 dB change in mode intensity. Figure 10c shows the simulation results of the gaseous SPP mode, liquid toluene molecules of which the characteristic absorption spectrum is localized in sulfurous anhydride molecule, of which the characteristic absorption spectrum is localized in the the frequency range of 18–24 THz is adopted in the simulation. Similarly, an intensity change which directly maps the fingerprint of the molecule is obtained, as shown in Figure 10b. But since the absorption loss of toluene molecule is smaller than that of ethanol, it needs a 20 μm long sample along the z direction to induced a 3 dB change in mode intensity. Figure 10c shows the simulation results of the gaseous sulfurous anhydride molecule, of which the characteristic absorption spectrum is localized in the frequency of 38–43 THz. As before, a transmission spectrum of the GNW sensor which

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frequency of 38–43 THz. As before, a transmission spectrum of the GNW sensor which maps well with the fingerprint of the molecule can also be obtained. Owing to the fact the absorption loss of a gas molecule is less than that of a liquid molecule, the sulfurous anhydride molecule needs a 600 µm long sample along z direction to induced 3 dB change in mode intensity. Taking again ethanol as an example, the variation of intensity spectra with respect to analyte thickness is shown in Figure 10d. It is clear that with the increase of the analyte thickness, the drop in intensity becomes deeper. Last but not least, the sensitivity can be improved considerably by changing the parameters of the GNW sensor, such as the radius, and the permittivity of the dielectric, which means that smaller scale samples can be detected. Therefore, it is possible to identify different chemical substances using the proposed sensor and it may provide an effective way for detecting nanometric-size molecules. 5. Conclusions In summary, we demonstrate that plasmon modes of the GNW waveguide can be excited when coupled to a graphene ribbon. The GNW works as a probe for capturing a molecular spectrum. This is due to the factor that the resonant spectra of the GNW sensor can be flexibly tuned by adjusting the chemical potential of graphene, and the peak values of the spectra decrease linearly with the increase of analyte loss. Mode analysis reveals that intensity spectra of the GNW maps well with the absorption spectra of the molecules deposited on the surface of the graphene ring, which further verifies the broadband molecular sensing capabilities. Acknowledgments: This work was supported by the National Natural Science Foundation of China (Grant Nos. 61161007, 61261002, 61461052, 11564044), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20135301110003, 20125301120009), China Postdoctoral Science Foundation (Grant No. 2013M531989, 2014T70890), and the Key Program of Natural Science of Yunnan Province (Grant Nos. 2013FA006, 2015FA015). Author Contributions: Yue Cheng performed the simulation and wrote the paper. Jingjing Yang and Ming Huang conceived the methodology and analyzed the data. Qiannan Lu and Hao Tang analyzed the data and revised the paper. Conflicts of Interest: The authors declare no conflicts of interest.

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