, Volume 14, Issue 2, pp 313–320 | Cite as

Enhanced Air Microcavity of Channel SPP Waveguide HALby Graphene Material

  • Ge Wang
  • Jun ZhuEmail author
  • Duqu Wei
  • Frank Jiang
  • Yuanmin HuangEmail author


The two-dimensional material, represented by graphene, is an immediate research focus of interdisciplinary fields, such as nanophotonics and life sciences. The unique advantages of surface plasmon polaritons, such as enhanced transmission and sub-wavelength structure, bring opportunities for achieving all optical circuits. In this paper, based on graphene, silicon dioxide, air cavity, and so on, a novel channel surface plasma waveguide was developed. By contrasting the waveguide characteristics of graphene and gold, it is found that the mode field could be restricted in air cavity region using graphene, and the deep sub-wavelength of light field was restrained. Besides, through finite element simulation, it is investigated that propagation losses could be as low as 0.019 dB/μm, the area of normalized mode field could be as low as 0.014 λ2, and the limiting factor is 0.5. Compared with the current waveguide, the above result shows that the propagation losses is an order of magnitude lower; 20.52% of limiting factor is promoted, besides; better waveguide characteristics could be obtained with realization of sub-wavelength optical field limit. Meanwhile, the production process of waveguide structure is simple, and it is an important way to solve the high speed and miniaturization and integration of optoelectronic integrated technology in the future.


Graphene Air microcavity Surface plasmon polaritons 


Surface plasmon polaritons (SPPs) have the characteristics of highly localized and near-field enhancement, which can break the diffraction limit of light. Because of the unique nature of SPPs, researchers have conducted extensive research on this issue and proposed various devices and mechanisms. In 2006, JA Dionne of the California Institute of Technology studied the two-dimensional Ag/SiO2/Ag waveguide structure, exhibiting both long-range propagation and spatial confinement of light with lateral dimensions of less than 10% of the free-space wavelength [1]. The Holmgaard team proposed a dielectric-loaded surface plasmon polariton waveguide structure, which further improved the propagation length [2]. Three years later, a long-range dielectric-loaded surface plasmon polariton waveguide structure was proposed. This structure not only can achieve the confinement of the optical field and its propagation length reach the order of millimeters, but also, the loss of this structure is still larger [3]. In 2008, Oulton proposed a hybrid nano-optical waveguide based on circular dielectric nanowires [4]. Then, Liu showed a waveguide structure capable of achieving a low threshold (1104 cm−1) and sub-wavelength laser [5]. G Magno successfully applied waveguide structures to the sensing field [6]. The J Mu research team proposed a waveguide structure used in active devices and nano-sensor fields [7]. Babak Olyaeefar proposed inverse rib deep sub-wavelength surface hybrid plasmonic waveguide [8]. Ma Renmin and his collaborators for the first time reduced the threshold to the laser threshold level of commercially available lasers by systematically optimizing the gain materials, metal materials, and resonant cavities [9].

Graphene [10] is a nano-material with a single atomic layer thickness commonly used in the infrared and terahertz bands, supporting the propagation of surface electromagnetic waves. When graphene has a very low chemical potential, the monolayer graphene shows the semiconductor properties and can support the transverse electric (TE) wave; when graphene is highly doped, its properties are similar to that of metal films, which can support the polarization of transverse magnetic SPPs [11]. Compared with noble metals, the advantage of graphene is that it has a very small loss and can satisfy the constraint of the mode field [10, 12, 13]. Yu Sun presented a novel graphene plasmonic waveguide based on a high-index ridge; simulation results and theoretical analyses revealed that the proposed waveguide is capable of extending the propagation length 16% than the conventional ribbon waveguide [14].

In summary, a channel surface plasma waveguide was designed by combining the excellent optical properties of graphene with the waveguide. Firstly, by contrasting normalized electric field and propagation loss in the presence and absence of graphene, the results revealed that the waveguide performance was significantly improved with the presence of graphene. Secondly, the performance of waveguide was further quantified and analyzed by changing structural parameters, air gap, and the height of graphene. In this paper, based on mode effective index, normalized mode field area, propagation length, propagation loss, confinement factor, and gain threshold, the performance of the waveguide is analyzed. Finally, compared with the same type of waveguide structure, it is found that the performance of the above waveguide device has a significant improvement. It is indicated that this structure is potentially used in ultra-compact high-density plasma devices and photonic integrated circuits.

Waveguide Structure and Method Analysis

Structure Analysis

Figure 1 shows the geometrical model of the channel surface plasma waveguide proposed in this paper (Fig. 1a is the three-dimensional structure of waveguide; Fig. 1b is the two-dimensional profile of the waveguide). As shown in Fig. 1, the structure is composed of silicon dioxide with low refractive index dielectric as the buffer layer, graphene and air cavity with little loss as the middle part, and rectangle silver as the bottom. Compared with other metal, lower loss in the communication range could be obtained when using silver as the metal part. The horizontal width of all layers is w, r and h are the width and thickness of air cavity respectively, h also is the thickness of graphene, and t is the height of silicon dioxide and silver. Compared with other waveguides, the waveguide proposed in this paper reduces the propagation loss and could limit the sub-wavelength optical field.
Fig. 1

Structure of a three-dimensional and b two-dimensional profile waveguides

Methods Analysis of Finite Element Simulation

Figure 2 shows the results of the finite element simulation. As shown in Fig. 2a, c, the normalized electric field distribution and propagation loss of the fundamental mode are obtained as a function of the model size. It can be seen from the figure that the waveguide formed by the gold film can realize the restriction of the electric field, but the propagation loss is large. We improved the structure, replacing gold with a single layer of graphene with the same width and thickness, while keeping other parameters unchanged. The results obtained are shown in Fig. 2b, d; compared with Fig. 2a, c, it can be clearly seen that after using graphene, the electric field strength and restraining ability are greatly improved, and the propagation loss is drastically reduced. This is because the graphene’s physical properties are closer to the metal, but at the same time, it has the characteristics of a semiconductor, and the mode field can be well confined to the air cavity region, achieving a deep sub-wavelength confinement of the optical field.
Fig. 2

Normalized electric field and propagation loss of the fundamental mode of the proposed waveguide at w = 2000 nm, h = 1 nm, r = 10 nm (propagation loss varies with the width r). Au: a normalized electric field distribution and c propagation loss. Graphene: b normalized electric field distribution and d propagation loss

The Theory of Mode Parameters

Analyzing the mode parameters of the waveguide is one of the important steps in the study of optical devices, and we will quantitatively analyze these parameters. We used the finite element method to analyze the characteristic parameters of the waveguide to measure the performance of the proposed structure. This paper mainly studies the waveguide characteristics of the designed structure from the following aspects: mode effective index (neff), normalized mode field area (SF), confinement factor (Γ), gain threshold (gth), and propagation loss (Loss).

Mode Effective Index

The mode effective index is an important indicator of the optical waveguide. The calculation of effective refractive index is of great significance for the design of surface plasma waveguides. The effective refractive index is defined as the ratio of the propagation constant to the wave vector in the vacuum and can be expressed as:

$$ {n}_{\mathrm{eff}}=\frac{\beta }{{\mathrm{k}}_0} $$
where β is the propagation constant and k0 is the wave vector in vacuum, which can be expressed as:
$$ {k}_0=\frac{2\pi }{\lambda } $$

Normalized Mode Field Area

The normalized mode area represents the ability of a waveguide structure to restrain the mode field. The smaller the value, the stronger the constraint of the waveguide structure on the optical field is; the expression [15] is:

$$ {A}_m=\frac{{\left[\iint {\left|E\right|}^2 dA\right]}^2}{\iint {\left|E\right|}^4 dA} $$
$$ {A}_0=\frac{\lambda^2}{4} $$
$$ \mathrm{SF}=\frac{A_m}{{\mathrm{A}}_0} $$
A0 is the diffraction-limited area of free space, Am represents the effective mode field area, and λ is the wavelength in vacuum.

Energy Confinement Factor

Surface plasmon waveguides usually consist of many parts. The materials of each part are different, and the ability to limit energy naturally varies. The energy confinement factor is the measure of the energy distribution in the waveguide and is defined as the ratio of the energy Ws of a specific region of the waveguide to the total energy W of the mode field. The expression [16] is:

$$ \Gamma =\frac{W_s}{W}=\frac{\iint_sW\left(x,y\right) dA}{\iint_{\mathrm{all}}W\left(x,y\right) dA} $$

Gain Threshold

The gain threshold refers to the minimum gain at which the laser satisfies the lasing conditions. The smaller the gain threshold, the smaller the gain required for laser lasing and the better the laser performance, expressed as [5]:

$$ {g}_{\mathrm{th}}=\left({k}_0\times {n}_{\mathrm{im}}+\ln \left(1/\mathrm{R}\right)/\mathrm{L}\right)/\varGamma \cdotp \left({n}_{\mathrm{eff}}/{n}_{\mathrm{wire}}\right) $$
where, k0 is the wave vector in vacuum, as shown in formula (2); nim is the imaginary part of the effective refractive index of the pattern; neff is the effective refractive index of the pattern; nwire is the refractive index of the gain medium; L is the length of the gain medium waveguide; R is the facet reflectivity, expressed as:
$$ R=\left({n}_{\mathrm{eff}}-1\right)/\left({n}_{\mathrm{eff}}+1\right) $$

Propagation Loss

The propagation loss represents the energy loss of light transmitted in the waveguide structure and is one of the most direct parameters of the performance of the waveguide structure.

Its calculation formula is:

$$ \mathrm{Loss}=-20\lg \left(\mathrm{e}\right){n}_{\mathrm{im}}{k}_0\approx 2\times 4.34\times {k}_0\times {n}_{\mathrm{im}} $$
where nim is the imaginary part of the mode effective refractive index.

Results of Waveguide Characteristics

We study the influence of geometric parameters on the proposed channel type surface plasmon waveguide characteristics. When the horizontal width w and the height t are constant, the mode parameters of the waveguide structure with different graphene thicknesses are affected by the variation of the air gap width, as shown in Figs. 3 and 4. When the horizontal width w and the width r of the air cavity are constant, the mode parameters of the waveguide structure that analyzed the heights of different SiO2 and Ag are affected by the change in the height of the graphene, as shown in Figs. 5 and 6. The method for calculating the mode parameters is shown in the “Waveguide structure and method analysis” section.
Fig. 3

a Mode effective index. b Propagation loss. c Confinement factor. d Normalized mode area

Fig. 4

Gain threshold

Fig. 5

a Mode effective index. b Propagation loss. c Confinement factor. d Normalized mode area

Fig. 6

Gain threshold

Effect of Air Gap Width r on Waveguide Characteristics

From Fig. 3a, b, it can be seen that the coupling effect of graphene and air gradually decreases with the increase of air gap width r; effective refractive index and propagation loss with the increase of air gap width all showed a trend of decrease. When the air gap width is fixed, the height h is smaller, and the larger the effective refractive index is. This is because as the air gap area increases, the metal generates a larger ohmic effect, resulting in energy diffusion. Because of the propagation loss we define the propagation loss of light in the waveguide structure, so we want to get a smaller value. At this point, the maximum value of propagation loss is no more than 0.065 dB/μm, which is an order of magnitude less than the maximum 0.1 in the paper mentioned in [6], and it reaches a very low propagation loss. The energy confinement factor is a measure of the distribution of energy in a waveguide and is defined as the ratio of energy in a specific region of the waveguide to the total energy in the mode field. Figure 3c shows that as the air gap width and height increase, the coupling effect decreases, causing the energy diffusion to increase the confinement factor. The maximum value is 0.51, and in [16], the maximum value is 0.35 and the minimum value is 0.15. Compared with the waveguide structure proposed in this paper, the efficiency is increased by 20.52%. It is shown that more energy is distributed around graphene, thus verifying that graphene has good optical field limitation. Figure 3d shows that the designed structure has a smaller mode field area, which is always less than 0.048, thus validating that the proposed waveguide has strong mode field confinement capability and can limit the energy to a very small range. The maximum value is not more than 0.048; the maximum value of the [16] proposed is 0.4. Compared with the waveguide structure proposed in this paper, the energy constraint is increased by about 87.5%, and it has a very strong energy constraint capability.

Next, we integrated the parameters of the waveguide characteristics, selected the waveguide length L = 30 μm, and calculated the gain threshold, as shown in Fig. 4.

From the above figure, we can see that when the height h is fixed, the gain threshold decreases with the increase of width r. Conversely, when the width r remains constant, the gain threshold decreases with the increase of height h. This is because as the coupling effect diminishes, so does the energy. The energy required to supplement the low energy also reduced, i.e., the lower gain threshold is 8.1×104 cm−1.

Influence of Height h on Waveguide Characteristics

In Fig. 5a, b, it can be seen that when the fixed height t is constant, the effective refractive index and propagation loss of the model decrease with the increase of h. As can be seen from Fig. 5b, propagation loss is as low as 0.02 dB/μm. Figure 5c, d shows that the energy confinement factor and the normalized mode field area increase as the height h increases; the confinement factor increases rapidly with height at t = 20 nm; the normalized mode field area increases slowly with increasing heights t and h; when the height t = 20 nm, and h = 1 nm, the normalized mode field area is as low as 0.014 λ2, showing lower propagation loss and stronger mode field limiting ability.

As shown in Fig. 6, when the height t is fixed, the gain threshold decreases sharply with increasing height h when the air gap width r is less than 4 nm and decreases slowly when r is greater than 4 nm. However, when the graphene height h is constant, the gain threshold changes little with increasing t. The comparison of these data is clearly shown in Table 1.
Table 1

Gain threshold value with the change of t and h (unit: 106 cm−1)

Unit, nm

t = 20

t = 50

t = 80

t = 110

t = 140

t = 170

h = 1







h = 2







h = 3







h = 4







h = 5







h = 6







h = 7







h = 8







h = 9







In summary, by changing the geometric parameters of the structure, such as the height h and the width r of the air gap, the height t of SiO2 and Ag can adjust the characteristics of the waveguide structure. Therefore, we choose the optimal parameters, t = 20 nm, h = 1 nm, and r = 20 nm, the propagation loss, the normalized mode field area, and the limiting factor to obtain the best value.

Conclusion and Discussion

In this paper, a novel channel surface plasma waveguide was developed; the characteristics of different structure sizes and parameters have been studied and analyzed. The structure adopts a multi-layer mixed structure, which has a good optical field limiting ability and a low propagation loss.

By adjusting the geometric parameters of the waveguide, we get a working wavelength of λ = 1.55 μm, a propagation loss as low as 0.019 dB/μm, a normalized mode field area as low as 0.014 λ2, and a limiting factor of 0.5 orders. Compared with the current waveguide, the propagation losses of the proposed waveguide is an order of magnitude lower; 20.52% of limiting factor is promoted. Therefore, better waveguide characteristics could be obtained with the realization of sub-wavelength optical field limit.

In addition, the waveguide structure uses Ag and SiO2 structures to act as metal and buffer layers and has a simple manufacturing process and a realizable type. It is an important approach to solve the problems of high speed, miniaturization, and integration of photoelectric integration technologies in the future.


Funding Sources

This work was supported by Guangxi Natural Science Foundation (2017GXNSFAA198261), National Natural Science Foundation of China (Grant No. 61762018), Guangxi Youth Talent Program (F-KA16016), Innovation Project of Guangxi Graduate Education(XJGY201807, XJGY201811), Guangxi Scholarship Fund of Guangxi Education Department, and Youth Backbone Teacher Growth Support Plan of Guangxi Normal University (Shi Zheng Personnel (2012) 136).


  1. 1.
    Dionne JA, Sweatlock LA, Atwater HA, Polman A (2006) Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization. Phys Rev B 73(3):035407CrossRefGoogle Scholar
  2. 2.
    Holmgaard T, Bozhevolnyi SI (2007) Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides. Phys Rev B 75:245405CrossRefGoogle Scholar
  3. 3.
    Holmgaard T, Gosciniakand J, Bozhevolnyi SI (2010) Long-range dielectric-loaded surface plasmon-polariton waveguides. Opt Express 18(22):23009–23015CrossRefGoogle Scholar
  4. 4.
    Oulton RF, Sorger VJ, Genov DA, Pile DFP, Zhang X (2008) A hybrid plasmonic waveguide for subwavelength confinement and long range propagation. Nat Photonics 2(8):496–500CrossRefGoogle Scholar
  5. 5.
    Liu JT, Xu BZ, Zhang J (2012) Gain-assisted indented plasmonic waveguide for low-threshold nanolaser applications. Chinese. Phys B 21(10):424–428Google Scholar
  6. 6.
    Magno G, Grande M, Petruzzelli V et al (2013) Asymmetric hybrid double dielectric loaded plasmonic waveguides for sensing applications. Sensors Actuators B Chem 186(186):148–155CrossRefGoogle Scholar
  7. 7.
    J M, Chen L, Li X, Huang WP (2013) Hybrid nano ridge plasmonic polaritons waveguides. Appl Phys Lett 103(13):131107–131107–4Google Scholar
  8. 8.
    Olyaeefar B, Khoshsima H, Khorram S (2015) Inverse-rib hybrid plasmonic waveguide for low-loss deep sub-wavelength surface plasmon polariton propagation. Opt Quant Electron 47(7):1791–1800CrossRefGoogle Scholar
  9. 9.
    S Wang XY, Wang B, Li et al (2017) Unusual scaling laws for plasmonic nanolasers beyond the diffraction limit. Nat Commun 8(1):1889CrossRefGoogle Scholar
  10. 10.
    Jablan M, Buljan H, Soljacic M (2009) Plasmonics in graphene at infra-red frequencies. Phys Rev B 80(24):245435CrossRefGoogle Scholar
  11. 11.
    Ooi KJA, Chu HS, LK Ang PB (2013) Mid-infrared active graphene nanoribbon plasmonic waveguide devices. J Opt Soc Am B 30(12):3111–3116CrossRefGoogle Scholar
  12. 12.
    Mikhailov SA, Ziegler K (2007) New electromagnetic mode in graphene. Phys Rev Lett 99(1):016803CrossRefGoogle Scholar
  13. 13.
    Sun Y, Bian Y, Zhao X, Zheng Z et al (2013) Low-loss graphene plasmonic waveguide based on a high-index dielectric wedge for tight optical confinement. Lasers Electro-opt 14381182Google Scholar
  14. 14.
    Lv HB, Liu YM, ZY Y et al (2014) Hybrid plasmonic waveguides for low-threshold nanolaser applications. Chin Opt Lett 12(11):112401CrossRefGoogle Scholar
  15. 15.
    YS Bian Z, Zheng X, Zhao L, Liu J et al (2013) Nanowire based hybrid plasmonic structures for low-threshold lasing at the subwavelength scale. Opt Commun 287:245–249CrossRefGoogle Scholar
  16. 16.
    Sun Y, Zheng Z, Cheng J, Liu J (2014) Graphene surface plasmon waveguides incorporating high-index dielectric ridges for single mode transmission. Opt Commun 328(10):124–128CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Electronic EngineeringGuangxi Normal UniversityGuilinChina
  2. 2.College of Mathematics and StatisticGuangxi Normal UniversityGuilinChina

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