Enhanced Air Microcavity of Channel SPP Waveguide HALby Graphene Material
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Abstract
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 λ^{2}, 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.
Keywords
Graphene Air microcavity Surface plasmon polaritonsIntroduction
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
Methods Analysis of Finite Element Simulation
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 (n_{eff}), normalized mode field area (SF), confinement factor (Γ), gain threshold (g_{th}), 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:
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:
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 W_{s} of a specific region of the waveguide to the total energy W of the mode field. The expression [16] is:
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]:
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:
Results of Waveguide Characteristics
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 8.1×10^{4} 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 λ^{2}, showing lower propagation loss and stronger mode field limiting ability.
Gain threshold value with the change of t and h (unit: 10^{6} cm^{−1})
Unit, nm | t = 20 | t = 50 | t = 80 | t = 110 | t = 140 | t = 170 |
---|---|---|---|---|---|---|
h = 1 | 4.2777 | 4.3056 | 4.3141 | 4.34 | 4.3862 | 4.4497 |
h = 2 | 2.0899 | 2.1318 | 2.1441 | 2.1609 | 2.1864 | 2.2197 |
h = 3 | 1.3638 | 1.4079 | 1.421 | 1.4348 | 1.4532 | 1.4764 |
h = 4 | 1.0027 | 1.0464 | 1.0597 | 1.0718 | 1.0867 | 1.1048 |
h = 5 | 0.7874 | 0.8297 | 0.843 | 0.8541 | 0.8668 | 0.8879 |
h = 6 | 0.6449 | 0.6856 | 0.6987 | 0.709 | 0.7203 | 0.7333 |
h = 7 | 0.5438 | 0.5828 | 0.5957 | 0.6054 | 0.6157 | 0.6272 |
h = 8 | 0.4686 | 0.5059 | 0.5185 | 0.5277 | 0.5372 | 0.5476 |
h = 9 | 0.4105 | 0.4461 | 0.4585 | 0.4674 | 0.4762 | 0.4858 |
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 SiO_{2} 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 λ^{2}, 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 SiO_{2} 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.
Notes
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).
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