Transmission properties and molecular sensing application of CGPW

Jianfeng Yang; Jingjing Yang; Wei Deng; Fuchun Mao; Ming Huang

doi:10.1364/OE.23.032289

1 Introduction

Surface plasmon polaritons (SPPs) are electromagnetic excitations propagating at the interface between a dielectric and a conductor, evanescently confined in the perpendicular direction. These electromagnetic surface waves arise via the coupling of the electromagnetic fields to oscillations of the conductor’s electron plasma [1]. Due to novel optical properties, such as selective absorption and scattering of light, subwavelength electromagnetic confinement and local optical field enhancement, SPPs are widely used in integrated optics, chemosensing, biosensing, etc [2–7 ]. The emergence of graphene makes it possible to reshape the landscape of photonics and optoelectronics. Since graphene has special electronic energy band structures, graphene surface plasmons (GSPs) exhibit exceptional electrical tunability, low intrinsic loss, highly confined optical field and other fascinating properties in the midinfrared and terahertz regime [8–10 ], various graphene nanostructures were proposed to support GSPs modes. Graphene nano-ribbon waveguides with small mode area and ultra-high effective refractive indices could be used for future very-large-scale integration (VLSI) [11]. A compact modal size and typically long propagation lengths were realized by graphene-based hybrid plasmonic waveguide [12]. Graphene-coated nanospheres, graphene-coated nanowire and dielectric loaded graphene plasmon waveguide provided new freedoms to manipulate GSPs modes [13–16 ]. Moreover, sensing applications based on graphene have become the subject of intense research in recent years. Detection and sensing at the molecule level have attracted much attention from researchers and some graphene-based schemes were presented [17, 18 ]. Graphene-based platforms for detections of individual gas molecule [19], protein monolayers [20] and DNA [21] opened exciting prospects for chemo- and bio-sensing. In addition, theoretical study also predicted that GSPs may be exploited for many potential applications, such as complete optical absorption [22], graphene cloak [23, 24 ], plasmonic rainbow trapping by a graphene monolayer [25], optical antennas [26], optical waveguide [27] and electro-optical logic gates [28]. However, to the best of our knowledge, the coupled GSPs modes in cylindrical graphene plasmon waveguide has not been characterized yet.

In this work, we investigate the GSPs modes of cylindrical graphene plasmon waveguide (CGPW), which could be regarded as a bent vertically offset graphene ribbon pairs waveguide [27]. First of all, an analytical model is presented and guided GSPs eigen modes are obtained by solving Maxwell’s equations in cylindrical coordinate. In the second stage, dispersion relations are derived by numerical solutions of the dispersion equation. Influencing factors of the mode behavior of CGPW, such as the Fermi level of graphene and the geometric parameters of the waveguide are analyzed in detail. We also introduce a figure of merit (FOM) to measure the performance of CGPWs. Finally, a new CGPW-based scheme for broadband and high sensitivity molecular sensing is proposed. We show that spectral intensity profile of the GSPs mode extracted at a fixed point in the mode propagation direction of the CPPW directly maps the absorption spectrum of the deposited molecular layer, giving rise to broadband molecular sensing capabilities.

2. Analytical model

Let us begin with the schematic plot in Fig. 1 . CGPW which consists of two rolled graphene ribbons, a dielectric core and a dielectric interlayer could be regarded as a bent vertically offset graphene ribbon pairs waveguide. The permittivity of the dielectric core and interlayer is $ε_{1}$ and $ε_{2}$ , respectively. The whole structure is embedded in a medium with permittivity $ε_{3}$ . The radius of the inner graphene layer is $r_{1}$ and that of the outer is $r_{2}$ . Graphene is modeled as a 0.5 nm-thick anisotropic layer [29].

Fig. 1 Schematic of the cylindrical graphene plasmon waveguide (a) Cross section; (b) Perspective view.

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The properties of CGPW will be first explored by considering its dispersion relation. We start by solving Maxwell’s equations in cylindrical coordinate with the origin setting at the center of the waveguide and express the field in each region for the eigen GSPs mode. The longitudinal components of the electric-magnetic (EM) fields inside region 1 can be written as

{\begin{cases} E_{1 z} = A_{m} I_{m} (k_{t 1} ρ) e^{i m φ} e^{i β z} \\ H_{1 z} = A_{m}^{'} I_{m} (k_{t 1} ρ) e^{i m φ} e^{i β z} \end{cases} (ρ < r_{1}),

those in region 2 are

{\begin{cases} E_{2 z} = [B_{m} I_{m} (k_{t 2} ρ) + B_{m}^{'} K_{m} (k_{t 2} ρ)] e^{i m φ} e^{i β z} \\ H_{2 z} = [C_{m} I_{m} (k_{t 2} ρ) + C_{m}^{'} K_{m} (k_{t 2} ρ)] e^{i m φ} e^{i β z} \end{cases} (r_{1} < ρ < r_{2}),

and in region 3 we have

{\begin{cases} E_{3 z} = D_{m} K_{m} (k_{t 3} ρ) e^{i m φ} e^{i β z} \\ H_{3 z} = D_{m}^{'} K_{m} (k_{t 3} ρ) e^{i m φ} e^{i β z} \end{cases} (ρ > r_{2}),

where

β

is the propagating constant along

z

direction and

k_{t i} = \sqrt{β^{2} - ω^{2} ε_{i} μ_{0}} (i = 1, 2, 3)

are the transverse wavevectors.

A_{m}, A_{m}^{'}, B_{m}, B_{m}^{'}, C_{m}, C_{m}^{'}, D_{m}, D_{m}^{'}

are chosen here to weight the field but they are interdependent.

I_{m} (k_{t i} ρ)

and

K_{m} (k_{t i} ρ) (i = 1, 2, 3)

are modified Bessel functions of the first and second kind (

m = 0, 1, 2, 3...

). The transverse EM fields in each region could be obtained as

{\begin{cases} E_{ρ} = - \frac{1}{k_{t}^{2}} (j β \frac{\partial E_{z}}{\partial ρ} + \frac{j ω μ}{ρ} \frac{\partial H_{z}}{\partial φ}) \\ E_{φ} = - \frac{1}{k_{t}^{2}} (\frac{j β}{ρ} \frac{\partial E_{z}}{\partial φ} - j ω μ \frac{\partial H_{z}}{\partial ρ}) \\ H_{ρ} = - \frac{1}{k_{t}^{2}} (j β \frac{\partial H_{z}}{\partial ρ} - \frac{j ω ε}{ρ} \frac{\partial E_{z}}{\partial φ}) \\ H_{φ} = - \frac{1}{k_{t}^{2}} (\frac{j β}{ρ} \frac{\partial H_{z}}{\partial φ} + j ω ε \frac{\partial E_{z}}{\partial ρ}) \end{cases} .

For the structure composed of a dielectric core, a dielectric interlayer, two graphene sheets and the surrounding air medium, field-matching equations at the boundary surface

ρ = r_{1}

and

ρ = r_{2}

are expressed as follows:

E_{1 z} = E_{2 z}, E_{1 φ} = E_{2 φ}, H_{2 z} - H_{1 z} = - σ_{g} E_{1 φ}, H_{2 φ} - H_{1 φ} = σ_{g} E_{1 z},

E_{2 z} = E_{3 z}, E_{2 φ} = E_{3 φ}, H_{3 z} - H_{2 z} = - σ_{g} E_{2 φ}, H_{3 φ} - H_{2 φ} = σ_{g} E_{2 z} .

Satisfying the above continuity conditions gives

[M] {[A_{m}, A_{m}^{'}, B_{m}, B_{m}^{'}, C_{m}, C_{m}^{'}, D_{m}, D_{m}^{'}]}^{T} = 0,

here M is an

8 \times 8

matrix as follows:

[M] = [\begin{matrix} I_{m} (k_{t 1} r_{1}) & 0 & - I_{m} (k_{t 2} r_{1}) & - K_{m} (k_{t 2} r_{1}) & 0 & 0 & 0 & 0 \\ \frac{m β}{k_{t 1}^{2} r_{1}} I_{m} (k_{t 1} r_{1}) & \frac{j ω μ_{0}}{k_{t 1}} I_{m}^{'} (k_{t 1} r_{1}) & \frac{- m β}{k_{t 2}^{2} r_{1}} I_{m} (k_{t 2} r_{1}) & \frac{- m β}{k_{t 2}^{2} r_{1}} K_{m} (k_{t 2} r_{1}) & \frac{- j ω μ_{0}}{k_{t 2}} I_{m}^{'} (k_{t 2} r_{1}) & \frac{- j ω μ_{0}}{k_{t 2}} K_{m}^{'} (k_{t 2} r_{1}) & 0 & 0 \\ \frac{m β}{k_{t 1}^{2} r_{1}} σ_{g} I_{m} (k_{t 1} r_{1}) & \begin{array}{l} \frac{j ω μ_{0}}{k_{t 1}} σ_{g} I_{m}^{'} (k_{t 1} r_{1}) \\ - I_{m} (k_{t 1} r_{1}) \end{array} & 0 & 0 & I_{m} (k_{t 2} r_{1}) & K_{m} (k_{t 2} r_{1}) & 0 & 0 \\ \begin{array}{l} \frac{j ω ε_{1}}{k_{t 1}} I_{m}^{'} (k_{t 1} r_{1}) \\ - σ_{g} I_{m} (k_{t 1} r_{1}) \end{array} & \frac{- m β}{k_{t 2}^{2} r_{1}} I_{m} (k_{t 1} r_{1}) & \frac{j ω ε_{2}}{k_{t 2}} I_{m}^{'} (k_{t 2} r_{1}) & \frac{j ω ε_{2}}{k_{t 2}} K_{m}^{'} (k_{t 2} r_{1}) & \frac{m β}{k_{t 2}^{2} r_{1}} I_{m} (k_{t 2} r_{1}) & \frac{m β}{k_{t 2}^{2} r_{1}} K_{m} (k_{t 2} r_{1}) & 0 & 0 \\ 0 & 0 & I_{m} (k_{t 2} r_{2}) & K_{m} (k_{t 2} r_{2}) & 0 & 0 & - K_{m} (k_{t 3} r_{2}) & 0 \\ 0 & 0 & \frac{- m β}{k_{t 2}^{2} r_{2}} I_{m} (k_{t 2} r_{2}) & \frac{- m β}{k_{t 2}^{2} r_{2}} K_{m} (k_{t 2} r_{2}) & \frac{- j ω μ_{0}}{k_{t 2}} I_{m}^{'} (k_{t 2} r_{2}) & \frac{- j ω μ_{0}}{k_{t 2}} K_{m}^{'} (k_{t 2} r_{2}) & \frac{m β}{k_{t 3}^{2} r_{2}} K_{m} (k_{t 3} r_{2}) & \frac{j ω μ_{0}}{k_{t 3}} K_{m}^{'} (k_{t 3} r_{2}) \\ 0 & 0 & \frac{m β}{k_{t 2}^{2} r_{2}} σ_{g} I_{m} (k_{t 2} r_{2}) & \frac{m β}{k_{t 2}^{2} r_{2}} σ_{g} K_{m} (k_{t 2} r_{2}) & \begin{array}{l} \frac{j ω μ_{0}}{k_{t 2}} σ_{g} I_{m}^{'} (k_{t 2} r_{2}) \\ - I_{m} (k_{t 2} r_{2}) \end{array} & \begin{array}{l} \frac{j ω μ_{0}}{k_{t 2}} σ_{g} K_{m}^{'} (k_{t 2} r_{2}) \\ - K_{m} (k_{t 2} r_{2}) \end{array} & 0 & K_{m} (k_{t 3} r_{2}) \\ 0 & 0 & \begin{array}{l} \frac{j ω ε_{2}}{k_{t 2}} I_{m}^{'} (k_{t 2} r_{2}) \\ - δ_{g} I_{m} (k_{t 2} r_{2}) \end{array} & \begin{array}{l} \frac{j ω ε_{2}}{k_{t 2}} K_{m}^{'} (k_{t 2} r_{2}) \\ - δ_{g} K_{m} (k_{t 2} r_{2}) \end{array} & \frac{- m β}{k_{t 2}^{2} r_{2}} I_{m} (k_{t 2} r_{2}) & \frac{- m β}{k_{t 2}^{2} r_{2}} K_{m} (k_{t 2} r_{2}) & \frac{j ω ε_{3}}{k_{t 3}} K_{m}^{'} (k_{t 3} r_{2}) & \frac{m β}{k_{t 3}^{2} r_{2}} K_{m} (k_{t 3} r_{2}) \end{matrix}],

where

I_{m}^{'} (k_{t i} ρ) = I_{m + 1} (k_{t i} ρ) + \frac{m}{k_{t i} ρ} I_{m} (k_{t i} ρ)

and

K_{m}^{'} (k_{t i} ρ) = - K_{m + 1} (k_{t i} ρ) + \frac{m}{k_{t i} ρ} K_{m} (k_{t i} ρ)

.

| M | = 0

is the dispersion equation for the m-th eigen GSPs mode of CGPW. Solving the equation we can get the dispersion relations and corresponding EM fields. The transmission properties of different modes are determined by the effective mode index

n_{e f f}

, which is complex and defined as

β / k_{0}

,where

k_{0}

is free space wavevector . The confinement near the graphene surface of the mode is characterized by the real part of the effective mode index [

Re (n_{e f f})

], and the propagation loss is characterized by the imaginary part [

Im (n_{e f f})

]. The plasmon mode have a wavelength

λ_{s p p} = λ_{0} / Re (n_{e f f})

and an evanescent decay away from the graphene

δ \approx 1 / 2 Re (n_{e f f})

, where

λ_{0}

is the wavelength in free space. The propagation length is defined as

L = λ_{0} / 4 π Im (n_{e f f})

, which means

1 / e \approx 37 %

intensity decay length of the guided plasmon along the propagation direction.

3. Results and discussion

3.1 transmission properties

Numerical simulations based on the finite-element method (FEM) software COMSOL are performed to investigate the transmission properties of CGPW, then we numerically solve the dispersion equation to get the dispersion relations. In this paper, we choose $r_{1} = 200 nm$ and $r_{2} = 207 nm$ . Since higher permittivity value of dielectric trends to drag the EM field to the interface between the graphene and dielectric, we set $ε_{1} = ε_{2} = 6.25$ . The permittivity of the graphene is approximated by $ε = 1 + i σ_{g} / ε_{0} ω t$ as proposed in [29], where $t$ is the effective thickness. The conductivity is described according to the local random phase approximation of the Kubo formula [30], which reads for finite temperature as $σ_{g} = σ_{int r a} + σ_{int e r}$ with the intraband and interband contributions being

σ_{int r a} = \frac{2 i e^{2} T}{ℏ^{2} π (ω + i Γ)} \ln [2 \cos h (\frac{E_{F}}{2 T})] = \frac{i e^{2} E_{F}}{ℏ^{2} π (ω + i Γ)} (E_{F} ≫ T),

σ_{int e r} = \frac{e^{2}}{4 ℏ} [\frac{1}{2} + \frac{1}{π} arc \tan (\frac{ℏ ω - 2 μ_{c}}{2 T}) - \frac{i}{2 π} \ln \frac{{(ℏ ω + 2 E_{F})}^{2}}{{(ℏ ω - 2 E_{F})}^{2} + {(2 T)}^{2}}] (E_{F} ≫ T),

where

T = 300 \times k_{B}

is the temperature energy,

k_{B}

is the Boltzmann constant,

E_{F}

is the Fermi level,

Γ

represents the carrier scattering rate and

ℏ

denotes the reduced Planck constant. In this paper, we set

E_{F} = 0.5 eV

and

Γ = 1.32 meV

, unless otherwise stated.

The dispersion relations and propagation lengths are depicted in Fig. 2(a) and 2(b) . Unlike top-bottom graphene pairs waveguide [11], the dispersion relations of GSPs modes of CGPW won’t split into symmetric or anti-symmetric branches due to asymmetric configuration. FEM simulation results and numerical solutions of the analytical mode show good agreement with each other, especially when the frequency is away from the cutoff frequency. However, when the frequency is approaching the cutoff, slight deviation can be observed. We believe the reason is that when cutoff is approaching, $Re (n_{e f f})$ decreases, which means that the confinement of GSPs mode becomes weak, leading to the EM field in the central region can’t be negligible any longer. The insets of Fig. 2(b) shows the 1-th order mode patterns at different frequencies. It’s seen that the field distribution of the mode at $17 THz$ has poor confinement, indeed $n_{e f f}$ can’t account for the EM field in the central region of CGPW yet in this condition. Low order modes are often located at high wavevectors and long propagation lengths which both decrease as the mode order increases. However, for CGPW, in the frequency range of A-B[see Fig. 2(a)], fundamental mode have smaller $Re (n_{e f f})$ than 1-th order mode, which means that the 1-th order mode shows a tighter confinement at these frequencies. Moreover, the fundamental mode is cutoff-free and the confinements of all the modes become weak as the frequency decreases. Figure 2(c) illustrates the mode patterns of the first 4 order modes (the inset shows an amplified view of the electric field distribution of fundamental mode). The field is tightly confined near the interface between the graphene and dielectric. We find that a kind of gap mode with high propagation loss in the dielectric interlayer similar to that of ref [31]. are also supported by this structure, but it is not discussed here for brevity.

Fig. 2 (a) Dispersion relations of the first 6 order GSPs modes in CGPW. (b) Propagation lengths of GSPs modes in CGPW. In both (a) and (b), solid lines are obtained by FEM and green dashed curves are numerical solutions of the dispersion equation. (c) Mode patterns (the amplitudes of E) of the first 4 order modes at the frequency of $40 THz$ .

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The Fermi level which can be tuned by the doping level and gate voltage has a strong impact on the modal behavior. The relationship between the Fermi level and the carrier density on the monolayer graphene is $E_{F} = \sqrt{{(ℏ v_{F})}^{2} - {(π T)}^{2} / 3} \approx ℏ v_{F} \sqrt{n_{c} π}$ , where $v_{F} = 10^{6} m/s$ is the Fermi velocity and $n_{c}$ is the carrier density. Since carrier density has reached as high as $10^{14} {cm}^{-2}$ in recent experiments [32, 33 ], we set the range of Fermi level to $0.2 eV \sim 1.2 eV$ . Figure 3 shows the characteristics of GSPs modes at different Fermi levels. A higher Fermi level decreases the confinement, which can be understood because the graphene becomes more like a perfect conductor with increased conductivity [see Eq. 8(a)] and supports surface plasmon modes whose fields extend more into the dielectric media. The propagation losses of the modes decrease as the Fermi level increases and some high order modes (m = 4, 5) cut off at high doping level.

Fig. 3 The real part of effective mode index and propagation length as a function of the Fermi level at the frequency of $40 THz$ . $d = 7 nm$ .

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To investigate the influence of coupling distance $d$ on the modal behavior, two probes $P$ and $Q$ are set at the points near the two graphene sheets along the blue line (see the inset of Fig. 4 ) to record the variation of maximum electric field intensity with the coupling distance. Simulation is performed at the frequency of 40THz, and the radius of the inner graphene layer is fixed at $r_{1} = 200 nm$ . Figure 4 shows the dependence of $Re (n_{e f f})$ of the fundamental mode and the ratio $| E (Q) | / | E (P) |$ on the coupling distance. Here, $| E (P) |$ and $| E (Q) |$ are the amplitudes of electric field intensities at points $P$ and $Q$ . It's seen that $Re (n_{e f f})$ increases nearly linearly with the coupling distance, and it gradually becomes saturated (see the red dashed line in Fig. 4), which indicates that increasing the distance to a certain value will have little effect on the confinement of the mode. Meanwhile, the slope of $| E (Q) | / | E (P) |$ curve increases gradually with the coupling distance, which implies that more mode energy is concentrated to the outer graphene layer. In other words, with the increase of the coupling distance, the two-layer structure will be degraded into monolayer CGPW since the coupling effect between the graphene layers becomes weaker.

Fig. 4 $Re (n_{e f f})$ of the fundamental mode (blue line) and the ratio $| E (Q) | / | E (P) |$ (scarlet line) as a function of the coupling distance at the frequency of $40 THz$ . $E_{F} = 0.5 eV .$

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Due to multi-mode propagation may lead to signal fading and unwanted mode conversion, single-mode operation is highly preferred for many applications. It is feasible to get single mode operation region by tuning the radius of CGPW. Figure 5(a) shows mode number as a function of CGPW radius and frequency. The single-mode region lies in the left of the figure. Numbers of the guided modes increase with the radius at a fixed frequency. $Re (n_{e f f})$ of the fundamental mode as a function of the frequency and radius is plotted in Fig. 5(b). As can be seen, $Re (n_{e f f})$ of fundamental mode increases with the frequency at a fixed radius. Meanwhile, increasing the radius will give rise to an increase of $Re (n_{e f f})$ when the frequency is greater than 20THz. As a result, the best confinement phenomenon can be found at $50THz$ when the radius is 220 nm. Theoretically, within a certain range, a larger radius may lead to $I_{m} (k_{t} ρ)$ and $K_{m} (k_{t} ρ)$ increasing or decreasing more quickly, giving rise to a better confined field near the graphene sheet, which is in good agreement with the simulation.

Fig. 5 (a) Single-mode and multi-mode operation regions as a function of the radius and frequency. (b) $Re (n_{e f f})$ of fundamental mode as a function of frequency and radius. The blue region on the bottom shows the single-mode region.

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There is a well-known tradeoff between propagation loss and confinement in surface plasmon (SP) mode, i.e., propagation length increases at the expense of weakened confinement. As such the FOM [which is defined as the ratio of $Re (n_{e f f})$ to $Im (n_{e f f})$ [34]] offers us an intuition to the performance of the plasmon waveguide. Figure 6(a) shows the frequency-dependent FOM curves of the first 6 order modes. FOM decreases as the mode order increases and a cross phenomenon between the fundamental mode and 1-th mode can be observed. The FOM of high order modes increase rapidly with the frequency, then it gradually decreases as the frequency increases. A maximum and minimum value exist in the FOM curve of fundamental mode and FOM varies from 30 to 40 in the single mode region. Figure 6(b) presents the coupling distance dependent FOM at the frequency of $40 THz$ . FOM fluctuates as the coupling distance increases and a trough appears. We believe this is due to the factor that when $d < 20 nm$ , larger distance leads to larger propagation loss (see the inset of Fig. 6(b)); when $d > 20 nm$ , the propagation loss decreases as the distance increases due to the poor coupling effect (the value of $| E (Q) | / | E (P) |$ in Fig. 4 becomes greater, which implies that CGPW more resembles a monolayer structure). Figure 6(c) illustrates the Fermi level dependent FOM curves of different modes. It's seen that each mode has its optimum Fermi level. Besides, 1-th mode has better FOM than the fundamental mode at high doping level ( $E_{F} > 0.9 eV$ ).

Fig. 6 FOM as a function of frequency (a) ( $d = 7 nm, E_{F} = 0.5 eV$ ), coupling distance (b) ( $f = 40 THz, E_{F} = 0.5 eV$ ) and the Fermi level (c) ( $f = 40 THz, d = 7 nm$ ). The inset of Fig. 6(b) is $Im (n_{e f f})$ as a function of the coupling distance.

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3.2 sensing characteristics

It is known to us all that unambiguous identification of low concentration chemical mixtures can be performed by broadband enhanced infrared absorption (BEIRA) [18], due to infrared spectrum of the molecule which acts as a unique fingerprint. Graphene sheet is an ideal carrier of highly confined SP modes in the midinfrared and terahertz regime. In this section, a new molecular sensor based on CGPW is proposed, as depicted in Fig. 7(a) . Related parameters are the same as the settings in section 3.1. The analyte is deposited on the graphene surface with a thickness of 3 nm. We choose here ethanol molecule as an example, for which the transmittance spectrum is obtained from the National Institute of Standards and Technology (NIST) [35]. Since molecules exhibit a strong absorption lines in the infrared, the propagation losses will be greater at those frequencies. The intensity of surface plasmon along the propagation direction is $I = e^{- z / L}$ , where $z$ is the propagation distance. Therefore, at a fixed position along z direction, the intensity can be calculated by the propagation length $L$ . We set $I_{m o l}$ and $I_{0}$ to indicate the intensities with and without molecules deposited on the graphene surface. The obtained normalized signal $I_{m o l} / I_{0}$ is illustrated in Fig. 7(b) at three different positions. The variation of the signal directly maps the strong characteristic features of the molecule infrared absorption spectrum shown in the inset of Fig. 7(b). More importantly, only $1 μm - long$ sample can produce a gigantic, 3 $dB$ (50%) drop in intensity with the proposed sensor, which means exceptional sensitivity.

Fig. 7 (a) Cross-section of the sensor based on CGPW. (b) Intensity change caused by the presence of ethanol molecule as analyte in dB. (c) Intensity change caused by the presence of toluene molecule as analyte in dB. In both (b) and (c), the insets show the absorption spectrum of the analyte in the same frequency region as the main axis.

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To achieve such a wide band detection, the SP modes should have two features, i.e., confining to the surface of plasmonic materials and existing in an extended frequency band, within which the molecular vibrational modes appear. In order to demonstrate the broadband sensing characteristics, toluene molecule of which the characteristic absorption spectrum is localized in the frequency range of 18-25THz is adopted in the simulation. Similarly, an intensity change which directly maps the fingerprint of the molecule is obtained, as shown in Fig. 7(c). But since the absorption loss of toluene molecule is less than that of ethanol, it needs a $5 μm-long$ sample along the propagation direction to induce a 3 $dB$ change in mode intensity. Last but not least, the sensitivity can be improved considerably by tuning the parameters of the sensor, such as the radius, the permittivity of the dielectric and the Fermi level, which means that smaller scale sample can be detected. Therefore, it is possible to identify different chemical substances using the proposed method and may provide an effective way for detecting nanometric-size molecules.

4. Conclusion

In summary, a cylindrical graphene plasmon waveguide model has been proposed and its dispersion equation is derived. The dispersion relation of the CGPW model is investigated both numerically and analytically, and a good agreement is achieved. Results show that the mode behavior of CGPW can be influenced by the Fermi level of graphene, the coupling distance between two graphene sheets and the radius of the fiber. Figures of merit which depend on frequencies, the Fermi level and the coupling distance are illustrated to measure the performance of CGPW. Remarkably, CGPW is proven to be a highly sensitive platform for broadband molecular sensing.

Acknowledgement

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).

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Transmission properties and molecular sensing application of CGPW

Abstract

1 Introduction

2. Analytical model

3. Results and discussion

3.1 transmission properties

3.2 sensing characteristics

4. Conclusion

Acknowledgement

References and links

Cited By

Figures (7)

Equations (10)

Optics Express