Plasmonic tuning in mid-infrared regime with a composite array of graphene ribbons and silver nanowires

Accepted Manuscript Plasmonic tuning in mid-infrared regime with a composite array of graphene ribbons and silver nanowires Cheng Sun, Xiaoqiu Wang, Yuxuan Zheng, Tianhui Yang, Mengjia Zeng PII:

S1386-9477(17)31642-9

DOI:

10.1016/j.physe.2017.12.002

Reference:

PHYSE 12973

To appear in:

Physica E: Low-dimensional Systems and Nanostructures

Received Date: 25 October 2017 Revised Date:

25 November 2017

Accepted Date: 1 December 2017

Please cite this article as: C. Sun, X. Wang, Y. Zheng, T. Yang, M. Zeng, Plasmonic tuning in midinfrared regime with a composite array of graphene ribbons and silver nanowires, Physica E: Lowdimensional Systems and Nanostructures (2018), doi: 10.1016/j.physe.2017.12.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Plasmonic tuning in mid-infrared regime with a composite array of graphene ribbons and silver nanowires Cheng Sun∗1, 2 and Xiaoqiu Wang, Yuxuan Zheng, Tianhui Yang, Mengjia Zeng1 1)

College of Physical Science and Technology, Dalian University, Dalian, 116622,

2)

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China

Liaoning Engineering Laboratory of Optoelectronic Information Technology,

Dalian, 116622, China

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This work reports on a study regarding the systematic tuning of plasmonic resonance wavelength in the mid-infrared regime, by using a composite array composed of graphene ribbons and silver nanowires. A composite array that consists of graphene

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ribbons and silver nanowires are proposed on top of a glass substrate. The light transmittance is numerically simulated in the mid-infrared wavelength range from 6 to 20µm with several parameters being varied, including the Fermi energy level and the layer number of the graphene ribbons, the radius of the silver nanowires, as well as the grating constant of the array. The results demonstrate that the plasmonic

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resonance wavelength associated with the composite array and the corresponding full width at half maximum can systematically be tuned in the mid-infrared range, by carefully adjusting the parameters of either the graphene ribbons or the silver nanowires, or both. Based on the tuning characteristics revealed by this study, we

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suggest that the structure of the composite array comprised of graphene ribbons and silver nanowires be implemented in further designs of plasmonic tuning devices at

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mid-infrared wavelengths.

Keywords: Plasmonic tuning; Mid-infrared; Graphene ribbon; Silver nanowire

1

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I.

INTRODUCTION

Recently, plasmonic devices and structures operating in the mid-infrared wavelength regime have been intensively investigated, since this wavelength range has been demon-

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strated to be essential in various potential applications such as chemical and molecular sensing, thermal imaging, remote explosive detecting, materials processing and optical spectroscopy, etc.1–4 Compared with the low performance of either slow response time or limited tunability associated with the existing plasmonic devices that are based on conven-

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tional semiconductors5–7 , graphene-a novel material that possesses many unique electronic properties-has been shown to have great potentials in the design of plasmonic devices with

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high speed and broad tunablility8 . So far, several graphene-based structures have been studied to achieve good-quality plasmonic devices, utilizing the plasmonic modes in graphene. For instance, the possibility of building graphene-based optoelectronic switches by electrically controlling the light intensity that was reflected inside a prism placed on top of graphene was studied9 ; the surface plasmon dispersion relation for monolayer graphene sheets and a separated parallel pair of graphene monolayers was analytically calculated, and the synthesis

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of highly confined surface plasmon modes with doped graphene sheets in the mid-infrared and terahertz range was also discussed10 ; several tunable infrared plasmonic devices by using graphene/insulator stacks was experimentally demonstrated11 ; recently, the graphene-ringbased structures for highly tunable optical antennas in teraherz range was also proposed12 .

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Apart from graphene, thanks to the great plasmonic characteristics of certain metals (e.g., silver or gold), there have been intensive studies relating to the graphene/metal based

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nano-structures, and the hybrid structures have also been demonstrated to have great potentials in making devices that posses a good plasmonic tuning ability in the mid-infrared wavelength range. For example, the enhanced and selective photodetection using graphenestabilized hybrid plasmonic silver nanoparticles was addressed13 ; the optical properties of silver nanoparticles integrated graphene oxide thin films on glass and silicon substrates were reported14 ; the spatial self-phase modulation effect was demonstrated in graphene oxide with silver and gold nanoparticles15 ; the metal/graphene coreshell nano-structure was investigated to enhance the surface plasmon resonance tunability16 ; recently, a sensitive silver nanorod/reduced graphene oxide SERS analytical platform was proposed and its application to the quantitative analysis of iodide in solution was also discussed17 . 2

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Nowadays, in the design of the plasmonic devices that operate with a plasmonic resonance wavelength in the mid-infrared regime, to systematically tune the plasmonic wavelength and the Full Width at Half Maximum (FWHM) in the graphene/metal based nano-structures becomes a key issue. In this work, we propose a composite array nano-structure composed

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of graphene ribbons and silver nanowires on top of a SiO2 substrate. This composite array demonstrates a systematic tuning ability for the plasmonic resonance wavelength and the FWHM, with varying the parameters of the graphene ribbons and the silver nanowires in

STRUCTURE AND METHOD

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II.

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the mid-infrared wavelength range from 6 to 20µm.

As shown in Fig.1, a composite array was designed on top of a substrate of SiO2 , which consisted of a set of graphene ribbons and a series of semi-circle silver nanowires. In the composite array, the individual graphene ribbon and the silver nanowire alternated in the x-axis, as indicated in ’G’ and ’Ag’ in Fig.1, respectively. Along the y-axis, the ribbons and nanowires were infinite. In this work, the width of the graphene ribbon was set to be

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half the grating constant of the array (labeled ’d’ in Fig.1), and the nanowire was always positioned in the middle of the other half, with a radius of R. The Fermi energy level and the layer number of the graphene were labeled µc and N , respectively. In order to keep the main feature of the results to always fit the wavelength window of 6 - 20µm studied in this

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work, the values of the grating constant were chosen differently, according to the different values of the other parameters of the composite array. Although the ratio of the width of

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the graphene ribbon to the period of the silver nanowire could be another parameter to vary, it was always kept to be 1 for simplicity in this work, that is, for any given value of the grating constant, d, the width of the graphene ribbon and the period of the silver nanowire were the same, and were both d/2 in this work. The Finite Difference Time Domain (FDTD) method was performed on all the simulations in this work18 . In the calculations, a plane-wave light in the mid-infrared wavelength range of 6 - 20µm was normally incident (i.e., along the z-axis shown in Fig.1a), and the electric field of the light was kept x-polarized. Perfect Match Layer (PML) boundary conditions were used in the z direction, and periodic boundary conditions were employed in the x − y plane where the graphene ribbons and silver nanowires were placed. The mesh size was 3

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Z

Light

G

Ag

G

(a)

Ag

G

Ag

R

SiO2

d/2

…

d/2

d G

y

G

Ag

d/2

d/2

μc N

2R

G

Ag

(b)

…

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…

Ag

x

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y

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…

d

z

x

FIG. 1. Schematic structure of the composite array consisting of graphene ribbons and semi-circle silver nanowires on top of a substrate of SiO2 : (a) side view and (b) top view. In (a) a plane-wave

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light was normally incident from air. A set of graphene ribbons (indicated in ’G’) and a set of semi-circle silver nanowires (indicated in ’Ag’) were placed in alternation along the x-axis, and the ribbons and nanowires were infinite in the y direction. The width of the ribbon was d/2, which

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was half the grating constant of the array, d. The semi-circle nanowires were always kept in the middle of the other half, and the radius of the semi-circle was R. In this work, 2R < d/2. The

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Fermi energy level and the layer number of the graphene were µc and N , respectively.

always kept smaller than 1/10 of the shortest wavelength studied in the simulation region of non plasmon-carrying media to avoid the artifacts that might be induced by the simulation method. In the simulations, a plane monitor that measured the light transmittance was placed beneath the composite array in the x − y plane (not shown in Fig.1 for clarity), and the distance between the monitor plane and the array plane was set to 0.625µm. The optical constants for silver were from Palik’s experimental data, which was given in Ref.19 . The optical constants for a single graphene layer was derived from the surface conductivity (labeled σ) as follows20 : 4

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σ = σintra + σinter

e2 kB T µc + 2ln(e−µc /kB T + 1)] [ 2 π¯ h (ω − i2Γ) kB T

(2)

e2 2µc − (ω − i2Γ)¯ h ln[ ] 4π¯ h 2µc + (ω − i2Γ)¯ h

(3)

σinter = −i

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σintra = −i

(1)

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where σintra and σinter are the intraband and interband terms, respectively. e is the charge of an electron, kB is Boltzmann’s constant, T is the temperature and was set to be 300K

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in this work. h ¯ is the reduced Plancks constant, ω is the angular frequency of the light, Γ is the scattering rate and µc is the Fermi energy level of the graphene. In this work, the phenomenological scattering rate was assumed to be Γ = 0.11meV; this number was based on the typical values of the carrier mobility21,22 , and a similar value was also used in literature23 . The value of N σ was used as the conductivity for multi-layer graphene where N is the layer number24 . Note that the interband term has no analytical solutions, and Eq.3

III.

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is a widely used approximation when kB T  µc , h ¯ ω 25 , which was held in this work.

RESULTS AND DISCUSSIONS

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It is known that varying the Fermi energy level and the layer number of graphene can change its surface conductivity, and it in turn affects the plasmonic resonance behavior in-

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duced by the graphene ribbons; this effect was also demonstrated in our previous work26 . In this work, the effects of the Fermi energy level and the layer number on the plasmonic characteristics of the composite array composed of graphene ribbons and silver nanowires were studied. The light transmittance of the composite array was simulated in the wavelength range of 6 - 20µm, first with varying the Fermi energy level, µc , from 0.2eV to 1.0eV. The corresponding results are presented in Fig.2. In Fig.2, the layer number was N =2, the radius of the silver nanowire was R=50nm, and the grating constant of the array was d=1400nm or 600nm. Note that for graphene, the linear dispersion, as indicated in the equations for the surface conductivity (Eqs.1-3), holds only within the low energy regime, which is generally µc ≤ 1.0eV. Meanwhile, from the experimental perspective, it is also possible to achieve 5

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(a)

1 0.9

µc = 0.95eV µc = 0.85eV

0.6 0.5

µc = 0.75eV

0.4

µc = 0.65eV

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µc = 0.55eV

0.2 0.1 0

(b)

µc = 0.45eV 8

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µc = 0.55eV µc = 0.45eV µc = 0.35eV µc = 0.25eV 18

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FIG. 2. Wavelength-dependent light transmittance at (a) d = 1400nm and (b) d = 600nm, determined from the structure of the composite array shown in Fig.1. In the simulation N = 2 and R

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= 50nm.

such Fermi energy levels through chemical or electrostatic doping methods. Therefore, the maximum value for the Fermi energy level studied in this work was set to 1.0eV. Regarding Fig.2, there appears a minimum in the light transmittance curve for each value

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of µc . As known to the community, plasmon resonances can be excited in a single graphene ribbon or a silver nanowire. Further, in an array of graphene ribbons or an array of silver

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nanowires, the plasmonic resonance effects can also occur. The appearance of the minimum in the transmittance curve shown in Fig.2 indicates that this may be a manifestation of the net result of the plasmon resonance associated with the array of graphene ribbons23,27 and that induced in the array of silver nanowires. The feature revealed in Fig.2 provides us with a promising scheme to systematically tune the plasmonic resonance wavelength by adjusting the optical properties of the composite array, as varying the parameters including the Fermi energy level and the layer number of graphene, the radius of silver and the grating constant of the composite array. It should be noted that although the plasmon resonance of silver nanowires in the visible-near infrared range is well known to the community and has already been extensively investigated, the results in this work reveal that the silver nanowires may 6

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25

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d = 1400nm d = 600nm

(a)

d = 1400nm d = 600nm

(b) 1.6

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1.2

FWHM [µ m]

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Resonance wavelength [ µ m]

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µ c [eV]

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FIG. 3. Fermi energy level dependent (a) resonance wavelength and (b) FWHM, determined from the transmittance curves shown in Fig.2. In the simulation N = 2 and R = 50nm. In both (a) and

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(b) the lines are intended to guide the eye and do not represent or intend to be a fit to the data.

also contribute to the overall plasmonic behaviors of the composite array in the mid-infrared range, and this argument will be further verified when the silver radius dependence of the transmittance curve is addressed later in this work. Based on this, the resonance minimum

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feature observed in Fig.2 may be attributed to both the plasmon resonance associated with the graphene ribbons and that induced in the silver nanowires.

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Referring again to Fig.2, it is observed for both values of d that the resonance wavelength blue-shifts as the Fermi energy level, µc , is raised. This blue-shift of the resonance wavelength is attributed to the increase in the surface conductivity of graphene, as its Fermi energy level is increased; a similar phenomenon was also observed in our previous work26 . Further, the detailed values for the resonance wavelength and the full width at half maximum of the resonance minimum were determined from Fig.2, and the corresponding results are given in Fig.3. It is clear from Fig.3a that for both d the resonance wavelength decreases with increasing µc ; this is a manifestation of the blue-shift trend observed in Fig.2. It is also observed from Fig.3a that for the same value of µc the bigger grating constant (i.e., d=1400nm) 7

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gives rise to a larger resonance wavelength, compared with the smaller one (i.e., d=600nm). Take µc =0.6eV for example, the resonance wavelength for d=1400nm is measured to be 16.1µm, which is larger than 11.2µm that is measured for d=600nm. Regarding Fig.3b, it is obvious that for both values of d the FWHM of the resonance minimum appears no

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significant change as µc is varied from 0.2eV to 1.0eV. The FWHM is approximately 1.25µm for d=1400nm while it is about 0.6µm for d=600nm. This result indicates that the FWHM of the resonance minimum for the composite array is weakly dependent on the Fermi energy level of the graphene ribbons.

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Further, in order to study the tuning effect of the composite array on the plasmonic resonance wavelength, a series of simulations were performed as the layer number of the

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graphene was varied from N = 1 to 10, and the resulting transmittance curves with the radius of the silver nanowire being R=150nm and R=50nm are plotted in Fig.4a and Fig.4b, respectively. In the simulations µc =1.0eV and d=1200nm. It should be noted that Eqs.1-3 are derived for the linear band structure, which is a unique property of single-layer graphene. For graphene with multiple layers, the band structure deviates from the linear behavior and becomes more complicated, since the weak inter-layer Var der Waals interaction would lead

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to the formation of other bands except for the linear component. Given that the Var der Waals interaction is weak and it may be neglected when the layer number is not large, an approximation was made in this simulation work for simplicity, so that the value of N σ was considered as the conductivity for multi-layer graphene where N is the corresponding

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layer number; similar treatments were also reported in literatures24 . Referring to Fig.4, for both radii studied the resonance wavelength blue-shifts as the layer number is increased. To

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quantify this feature, the wavelength and the FWHM of the resonance minimum is measured from Fig.4, and the results are shown in Fig.5a and Fig.5b, respectively. It is obvious from Fig.5a that the resonance wavelength decreases with raising the layer number from N = 1 to 10, and that for any given value of N both radii (i.e., R=150nm and 50nm) give rise to a similar resonance wavelength. In examining Fig.5b it is found that the FWHM also decreases as N increases. Besides, for a given value of N the FWHM appears larger for the larger R. Take N =5 for example, the FWHM is 1.1µm for R=150nm while it is 0.8µm for R=50nm. Based on the results indicated in Fig.5a and Fig.5b, it is concluded that although the resonance wavelength is weakly dependent on the radius of the silver, the FWHM is affected by the radius for a given value of N . 8

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N = 10 N=9 N=8 N=7 N=6 N=5 N=4 N=3 20 N=2 N=1

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Transmittance

(a)

FIG. 4. Wavelength-dependent light transmittance at (a) R = 150nm and (b) R = 50nm, determined from the structure of the composite array shown in Fig.1. In the simulation µc = 1.0eV and

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d = 1200nm.

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FIG. 5. Layer number dependent (a) resonance wavelength and (b) FWHM, determined from the transmittance curves shown in Fig.4. In the simulation µc = 1.0eV and d = 1200nm. In both (a) and (b) the lines are intended to guide the eye and do not represent or intend to be a fit to the data.

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Another parameter, which can also affect the plasmonic resonance behavior of the composite array, is the radius of the semi-circle silver nanowires. Below, with varying the radius from R=20nm to 450nm, a variety of simulations were also performed. The resulting transmittance curves are given in Fig.6, in the scenario of two different Fermi energy levels of the

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graphene, i.e., µc =0.4eV and 1.0eV. In the simulations N =7 and d=2000nm. By examining Fig.6, it is clear that as the radius is raised from 20nm to 450nm, a slight red-shift in the resonance wavelength is present; this feature is in good agreement with the above-mentioned results indicated in Fig.5a where the resonance wavelength determined from R=150nm and

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R=50nm are similar. Another feature revealed in Fig.6 is that there appears a pronounced broadening of the linewidth of the resonance minimum with increasing the radius. This

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broadening feature is a clear manifestation of the plasmonic characteristics of the silver nano-structures. This observation is accounted for by the fact that more plasmonic modes are involved in the formation of the minimum at resonance with increasing the radius of the silver, causing a more broadening linewidth of the minimum. The fact that varying the silver nanowire parameter can also affect the plasmonic properties of the composite array in the mid-infrared regime, which is revealed in Fig.6, clearly verifies the aforementioned statement

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that the appearance of the plasmon resonance minimum in the transmittance curve is the net result of the plasmonic resonance effect associated with the graphene ribbons and that induced in the silver nanowires.

To further quantify the features revealed in Fig.6, the resonance wavelength and the

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FWHM were determined from Fig.6, and the results are shown in Fig.7a and Fig.7b, respectively. It is observed from Fig.7a that it shows a slight increase in the resonance wavelength

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as the radius is increased. Additionally, for any given value of R, by comparing the results from two different µc , it is obvious that the smaller Fermi energy level (i.e., µc =0.4eV) gives rise to a larger resonance wavelength, which is consistent with the feature revealed in Fig.3a. Regarding Fig.7b, it is evident that with increasing the radius from R=20nm to 450nm the FWHM presents a substantial enhancement. For example, it is enhanced from 1.4µm to 5.5µm for µc =1.0eV. This enhancement of the FWHM is a manifestation of the linewidth broadening of the resonance minimum that is revealed in Fig.6. By comparing the FWHM from two different µc at a given R shown in Fig.7b, it shows a slight increase with decreasing the Fermi energy level from µc =1.0eV to 0.4eV. This is consistent with the trend observed from Fig.3b where the FWHM shows a weak dependence on µc . 10

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0.6 0.4 0.2 0

Transmittance

(b) 1

R= R= R= R= R= R= R= R= 8 R= R=

20nm 50nm 100nm 150nm 200nm 250nm 300nm 350nm 400nm 450nm

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FIG. 6. Wavelength-dependent light transmittance at (a) µc =0.4eV and (b) µc =1.0eV, determined from the structure of the composite array shown in Fig.1. In the simulation N = 7 and d = 2000nm.

The effect of the grating constant of the composite array on the resonance wavelength

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was also studied, and the simulated transmittance curves for various values of d are given in Fig.8. In the simulations µc =1.0eV, N =1, and R=100nm or 20nm. It is shown from Fig.8 that the resonance wavelength red-shifts as d is increased. It should be noted that in the design of this work, once the grating constant is changed both the width of the graphene

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ribbons and the period of the silver nanowires are changed. The features revealed in Fig.8 is the combined plasmonic effect characteristic of both the graphene and the silver.

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To further probe the features, the resonance wavelength and the FWHM were calculated from Fig.8 and the results are given in Fig.9a and Fig.9b, respectively. It is observed from Fig.9a that the resonance wavelength increases as d is raised. In addition, for different values of R with the same d the resonance wavelength appears similar, with the result from the larger R (i.e., 100nm) being slightly bigger; this is in good agreement with the feature indicated in Fig.7a where a slight increase in the resonance wavelength is observed as the radius is increased. Referring to Fig.9b, the FWHM also increases as the grating constant is increased. Besides, by comparing the results for two different radii at a given d, it is observed that the FWHM for the larger radius (i.e., R=100nm) is greater than that for the smaller one (i.e., R=20nm), and it is also found that as d is raised the difference between 11

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µc = 1.0eV

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FIG. 7. Radius dependent (a) resonance wavelength and (b) FWHM, determined from the transmittance curves shown in Fig.6. In the simulation N = 7 and d = 2000nm. In both (a) and (b) the lines are intended to guide the eye and do not represent or intend to be a fit to the data.

0.4 0.2 0 8

(b) 1 Transmittance

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0.8 0.6 0.4 0.2 0 8

d d d d d d

= 1600nm = 1400nm = 1200nm = 1000nm = 800nm = 600nm

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Transmittance

(a) 1

d d d d d d d

= 1600nm = 1400nm = 1200nm = 1000nm = 800nm = 600nm = 400nm

10

FIG. 8. Wavelength-dependent light transmittance at (a) R=100nm and (b) R=20nm, determined from the structure of the composite array shown in Fig.1. In the simulation µc =1.0eV and N = 1.

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FIG. 9. Grating constant dependent (a) resonance wavelength and (b) FWHM, determined from the transmittance curves shown in Fig.8. In the simulation µc =1.0eV and N = 1. In both (a) and

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(b) the lines are intended to guide the eye and do not represent or intend to be a fit to the data.

the two radii becomes less. For instance, the difference in the FWHM between the two radii is measured to be 0.4µm when d=600nm while it becomes only 0.1µm when d=1600nm. Interestingly, the ratio of the FWHM to the grating constant, FWHM/d, is estimated to be

CONCLUSIONS

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approximately 1 for larger d values, which is consistent with the result indicated in Fig.3b.

In this work, we have systematically investigated the plasmonic resonance wavelength of the composite array composed of graphene ribbons and silver semi-circle nanowires, at the mid-infrared range. By varying the parameters including the Fermi energy level and the layer number of the graphene, the radius of the silver nanowire, as well as the grating constant of the array, we have computed the transmittance curve for the composite array. Referring to the transmittance curve, we have then determined the resonance wavelength and the corresponding full width at half maximum. The results in this work indicate that the plasmonic resonance wavelength can be decreased in the wavelength range from 6 to 20 µm 13

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by increasing the Fermi energy level, increasing the layer number, or decreasing the grating constant, and that the full width at half maximum can be decreased by increasing the layer number, decreasing the radius, or decreasing the grating constant. Based on the findings presented in this work, we have illustrated that the proposed structure of the composite array

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consisting of graphene ribbons and silver nanowires provides an alternative scheme in the design of plasmonic tuning devices with dynamical tunability, in addition to the structure based on the array of graphene ribbons only.

ACKNOWLEDGEMENT

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V.

C. Sun acknowledges support by Grant Number Liao BaiQianWan [2017]5 from the

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Liaoning BaiQianWan Talents Program in China, and Grant Number 20170540044 from

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the Natural Science Foundation of Liaoning Province in China.

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2

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497. Grigorenko AN, Polini M, Novoselov KS (2012) Graphene plasmonics. Nature Photonics 6:749-758. 4

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Plasmonics of graphene/silver arrays are studied at mid-infrared regime

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Plasmonic resonance wavelength and full width at half maximum are tuned

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Resonance wavelength is decreased with increasing Fermi energy level of

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graphene FWHM is decreased with increasing graphene layer number and

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decreasing silver size