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传统的多重等离子体诱导透明效应(plasmon induced transparency, PIT)的产生依赖于多个明暗模之间的耦合. 然而, 为了打破明暗模这一传统机制, 探索一种新的产生方式迫在眉睫. 本文提出一种由纵向石墨烯带和3个横向石墨烯条组成单层石墨烯超表面, 它能够通过两个单PIT之间的协同效应激发出三重PIT. 深入研究发现, 该三重PIT的物理本质源于两个单PIT之间的非相干耦合. 通过调整石墨烯的费米能级和载流子迁移率, 成功实现五频异步光开关向六频异步光开关的动态转换, 其中六频异步光开关的性能非常优异: 当频率点为3.77 THz和6.41 THz时, 调制深度和插入损耗分别达到99.31%和0.12 dB; 当频率点为4.58 THz时, 退相时间和消光比分别为3.16 ps和21.53 dB. 此外, 当调控范围集中在2.8—3.1 THz波段时, 该三重PIT体系能够展现出高达1212的群折射率. 基于以上结果, 说明该石墨烯结构有望为性能优异的慢光设备、光开关等光学器件设计提供新的理论指导.Surface plasmons (SPs) are generated by the interaction of conduction electrons on the surface of a metallic medium with photons in light wave, and they have an important phenomenon called plasmon-induced transparency (PIT). The PIT effect is crucial for improving the performance of nano-optical devices by strengthening the interaction between light and matter, thereby enhancing coupling efficiency. As is well known, traditional PIT is mainly achieved through two main ways: either through destructive interference between bright and dark modes, or through weak coupling between two bright modes. Therefore, it is crucial to find a new excitation method to break away from these traditional approaches. In this work, we propose a single-layer graphene metasurface composed of longitudinal graphene bands and three transverse graphene strips , which can excite a tripe PIT through the synergistic effect between two single-PITs. We then leverage the synergistic effect between these two single-PITs to realize a triple-PIT. This approach breaks away from the traditional method of generating PIT through the coupling of bright and dark modes. The numerical simulation results are also obtained using the finite-difference time-domain, which are highly consistent with the results of the coupled-mode theory, thereby validating the accuracy of the results. In addition, by adjusting the Fermi level and carrier mobility of graphene, the dynamic transition from a five-frequency asynchronous optical switch to a six-frequency asynchronous optical switch is successfully achieved. The six-frequency asynchronous optical switch demonstrates exceptional performance: at frequency points of 3.77 THz and 6.41 THz, the modulation depth and insertion loss reach 99.31% and 0.12 dB, respectively, while at the frequency point of 4.58 THz, the dephasing time and extinction ratio are 3.16 ps and 21.53 dB, respectively. Additionally, when the tuning range is from 2.8 THz to 3.1 THz band, the triple-PIT system exhibits a remarkably high group index of up to 1212. These performance metrics exceed those of most traditional slow-light devices. Based on these results, the structure is expected to provide new theoretical ideas for designing high-performance devices, such as optical switches and slow-light devices.
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Keywords:
- plasmon-induced transparency /
- synergistic effect /
- optical switch /
- slow-light
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图 1 (a)石墨烯超材料模型结构的全视图; (b)石墨烯结构侧视图; (c)石墨烯结构俯视图, Lx = Ly = 4 μm, m1 = 2.2 μm, m2 = 2.3 μm, m3 = 0.6 μm, s1 = 0.4 μm, s2 = 0.25 μm, w1 = 0.8 μm, w2 = 0.6 μm; (d)石墨烯结构的制备流程图
Fig. 1. (a) Full view of the graphene metamaterial model structure; (b) side view of graphene structure; (c) top view of graphene structure, Lx = Ly = 4 μm, m1 = 2.2 μm, m2 = 2.3 μm, m3 = 0.6 μm, s1 = 0.4 μm, s2 = 0.25 μm, w1 = 0.8 μm, w2 = 0.6 μm; (d) flow chart for the preparation of graphene structures.
图 3 (a), (b)不同石墨烯阵列的透射光谱; (c)整体结构形成的三重PIT透射谱(Ef = 1 eV, μ = 1.0 m2$ / $(V·s)); (d)dip1, dip2, dip3, dip4对应共振频率下的电场分布图
Fig. 3. (a), (b) Transmission spectra of the different arrays; (c) triple-PIT transmission spectra formed by the overall structure (Ef = 1 eV, μ = 1.0 m2/(V·s)); (d) plot of the electric field distribution at the corresponding resonance frequencies for dip1, dip2, dip3, and dip4.
图 4 (a)三重PIT对应的透射光谱与石墨烯费米能级的关系; (b)不同费米能级下三维透射谱的演化
Fig. 4. (a) Transmission spectra corresponding to the triple PIT versus graphene Fermi energy levels; (b) evolution of 3 D transmission at different Fermi energy levels.
图 5 (a)费米能级处于0.8 eV, 1.2 eV时, 载流子迁移率μ = 1.0 m2/(V·s)情况下五频异步光开关的调制, 其中“ON”表示“打开”, “OFF”表示“关闭”; (b)费米能级处于0.8 eV, 1.2 eV, 迁移率μ = 3.0 m2、(V·s)情况下的六频光开关调制
Fig. 5. (a) Modulation of a five-frequency asynchronous optical switch with carrier mobility μ = 1.0 m2/(V·s) at Fermi energy levels of 0.8 eV, 1.2 eV, where “ON” means “open”, “OFF means “close”; (b) six-frequency asynchronous optical switch modulation with Fermi energy levels at 0.8 eV, 1.2 eV and mobility μ = 3.0 m2/(V·s).
图 6 (a)透射谱与载流子迁移率之间的关系(EF = 1.0 eV); (b)不同载流子迁移率下透射谱的演化; (c)不同载流子迁移率下Re(neff)的演化
Fig. 6. (a) Relationship between transmission spectrum and carrier mobility ( EF = 1.0 eV); (b) the evolution of the transmission spectrum with carrier mobility; (c) the evolution of Re(neff) with carrier mobility.
图 7 (a)—(d)费米能级EF = 0.9, 1.0, 1.1, 1.2 eV的情况下群折射率和相移随频率的变化(μ = 3.0 m2$ / $(V·s))
Fig. 7. (a)–(d) Variation of group refractive index and phase shift with frequency for the Fermi energy levels EF = 0.9, 1.0, 1.1, 1.2 eV, respectively (μ = 3.0 m2$ / $(V·s)).
表 1 不同频率下DM, TD, LI, RE参数
Table 1. DM, TD, LI, RE parameters at different frequencies.
μ = 1.0 m2/(V·s) μ = 3.0 m2/(V·s) Frequency/THz DM/% LI/dB TD/ps RE/dB Frequency/THz DM/% LI/dB TD/ps RE/dB 3.12 85.46 0.14 3.57 8.02 2.56 94.53 0.70 7.12 9.89 3.77 86.01 0.31 4.75 8.12 3.12 95.96 0.29 5.34 13.77 4.58 96.02 0.11 4.08 13.15 3.77 99.31 0.17 4.56 17.26 5.32 84.60 0.18 3.19 7.75 4.58 98.21 0.21 3.16 21.53 6.41 95.12 0.26 3.70 12.03 5.32 98.65 0.18 5.97 18.24 6.41 96.45 0. 12 3.73 16.11 
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表 2 不同图案化石墨烯的性能比较
Table 2. Comparison of the properties of different patterned grapheme.
Reference
/yearModulation mode Material structure Group
indexDM/
%LI/
dBTD/
psRE/
dB[58]/2020 Dual-frequency Single-layer patterned graphene 358 93.0 0.32 — — [59]/2020 Multiple-frequency Single-layer patterned graphene — 77.7 — — 12.5 [60]/2021 Multiple-frequency Single-layer patterned graphene 321 92.0 — 3.2 — [61]/2022 Multiple-frequency Single-layer patterned graphene — 99.9 0.33 0.848 — [62]/2022 Multiple-frequency Single-layer patterned graphene 1100 97.1 0.04 — — [63]/2023 Multiple-frequency Single-layer patterned graphene — 97.7 5.4 3.86 16.41 [64]/2023 Multiple-frequency Monolayer patterned black
phosphorus219 — — 0.22 — [65]/2024 Multiple-frequency Single-layer patterned graphene 1000 87.5 — — — [30]/2024 Multiple-frequency Single-layer patterned graphene 781 98.0 0.51 — — This work Multiple-frequency Single-layer patterned graphene 1212 99.3 0.120 3.16 21.53
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