Project supported by the National Basic Key Research Program of China (Grant No. 2015CB932400), the National Key Research and Development Program of China (Grant No. 2016YFA0201600), the National Natural Science Foundation of China (Grant Nos. 51372045, 11504063, and 11674073), the Key Program of the Bureau of Frontier Sciences and Education, Chinese Academy of Sciences (Grant No. QYZDBSSW- SLH021), and the Science and Technology Projects of Beijing City, China (Grant No. Z161100002116016).
Project supported by the National Basic Key Research Program of China (Grant No. 2015CB932400), the National Key Research and Development Program of China (Grant No. 2016YFA0201600), the National Natural Science Foundation of China (Grant Nos. 51372045, 11504063, and 11674073), the Key Program of the Bureau of Frontier Sciences and Education, Chinese Academy of Sciences (Grant No. QYZDBSSW- SLH021), and the Science and Technology Projects of Beijing City, China (Grant No. Z161100002116016).
† Corresponding author. E-mail:
Project supported by the National Basic Key Research Program of China (Grant No. 2015CB932400), the National Key Research and Development Program of China (Grant No. 2016YFA0201600), the National Natural Science Foundation of China (Grant Nos. 51372045, 11504063, and 11674073), the Key Program of the Bureau of Frontier Sciences and Education, Chinese Academy of Sciences (Grant No. QYZDBSSW- SLH021), and the Science and Technology Projects of Beijing City, China (Grant No. Z161100002116016).
Graphene plasmons have become promising candidates for deep-subwavelength nanoscale optical devices due to their strong field confinement and low damping. Among these nanoscale optical devices, band-pass filter for wavelength selection and noise filtering are key devices in an integrated optical circuit. However, plasmonic filters are still oversized because large resonant cavities are needed to perform frequency selection. Here, an ultra-compact filter integrated in a graphene plasmonic waveguide was designed, where a rectangular resonant cavity is inside a graphene nanoribbon waveguide. The properties of the filter were studied using the finite-difference time-domain method and demonstrated using the analytical model. The results demonstrate the band-pass filter has a high quality factor (20.36) and electrically tunable frequency response. The working frequency of the filter could also be tuned by modifying the cavity size. Our work provides a feasible structure for a graphene plasmonic nano-filter for future use in integrated optical circuits.
Surface plasmons polaritons can break the diffraction limit, enabling nanoscale control of light and facilitating promising applications involving fabrication of highly integrated nanophotonic devices. Over past decades, a variety of devices based on metal plasmonics such as Mach-Zender interferometric modulators,[1,2] light amplifiers,[3] all-optical switches,[4,5] and even integrated photonic systems[6,7] have been successfully demonstrated both theoretically and experimentally. However, the large Ohmic losses in metal plasmons is a major obstacle limiting their use in nanophotonics applications.[8]
In the ongoing search for the next generation of plasmonic materials,[9] graphene is a very promising candidate. Due to its unique electronic band structure in which conical-shaped conduction and valence bands meet at the Dirac point,[10–13] graphene exhibits extraordinary optical properties such as strong and broadband light-graphene interactions. The easily tunable conductivity of graphene either via chemical doping or in situ electrostatic gating[14,15] has great potential in designing tunable optical functions or devices, such as engineered Bloch waves,[16] near-perfect light absorber[17] and the tunable optical bistability.[18,19] The Dirac Fermions features of carriers also result in the graphene plasmons (GPs) having very limited intrinsic loss[20] and ultra-high field confinement, where the wavelength has shrunk more than 100 times compared to light in free space.[21] Based on these advantages, a series of two-dimensional sub-wavelength graphene plasmonic devices, including light modulator,[22] plasmonic waveguides,[23] planar absorbers,[24] optical switches,[25] optical splitters,[26,27] and filters[28,29] have been studied. Waveguide filters for wavelength selectivity and noise filtering are key devices for signal processing. Recently, waveguide filters with different structures including teeth-shaped, band-disk-band and band-ring-band[30–32] have been studied. These filters always contain cavities approximately 2- to 3-fold larger than the width of the waveguide, which implies they have low spatial utilization and are inappropriate for largescale integration.
In this paper, we designed an ultra-compact plasmonic filter that was directly integrated in a graphene waveguide. A rectangular hole was introduced in the graphene nanoribbon waveguide to act as a resonant cavity (as shown in Fig.
A schematic of the designed graphene filter is presented in Fig.
We employed the FDTD method to simulate the transmission spectrum of the GP waveguide filter. Here, the graphene ribbon was modeled as a two-dimensional plane with the surface conductivity of σ(ω, Γ, μc, T). The surface conductivity contains the interband and intraband terms σ(ω, Γ, μc, T) = σintra + σinter. With an angular frequency ω, the intraband and interband terms are evaluated using the following formula:
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For confined plasmons supported on graphene ribbons, there are two plasmon waveguide modes:[35] one is the edge GP mode which is supported by a semi-infinite graphene ribbon (EGSP) and is well known to occur at the edge in graphene ribbon. The other one is the waveguide GP mode supported by infinite two-dimensional graphene sheets (2DGSP). When graphene sheets are modified into ribbon and the width decreases to tens of nanometers, the 2DGSP mode disappears, and only the edge mode remains. Compared with the 2DGSP, the EGSP has a higher effective refractive index,[36] which means we can achieve a higher concentration and transmission of electromagnetic field in an ultra-compact plasmonic device. Mode #1 and mode #2 shown in the inset of Fig.
According to previous mode analysis, we know that a 50 nm wide ribbon can support the EGSP mode #1, which is emitted from the source port (Port 1) and propagates along the x direction. Meanwhile, the transmission port (Port 2) was set to get the transmitted GPs on the right side of the cavity as depicted in Fig.
Figure
To further understand the feature of the filter, the CMT was adapted to analyze its behaviors. This cavity filter was considered a simplified band-ring-band (BRB) resonator as shown in Fig.
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![](cpb_27_9_094101/cpb_27_9_094101_ieqn1.gif)
![](cpb_27_9_094101/cpb_27_9_094101_ieqn2.gif)
![](cpb_27_9_094101/cpb_27_9_094101_ieqn3.gif)
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Combining Eqs. (
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We investigated the influence of the geometric parameters of the cavity on the resonant frequency. The calculated transmission spectra of the GP filter with varied l and d are displayed in Figs.
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![](cpb_27_9_094101/cpb_27_9_094101_ieqn4.gif)
![](cpb_27_9_094101/cpb_27_9_094101_ieqn5.gif)
The working frequency of this cavity filter could be electrically tuned in situ. Figure
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Next, we investigated the connection between the filter efficiency and basic parameters of the cavity filter. We defined the height difference (HD) between the resonance peak and dip as the filter efficiency as depicted in Fig.
In conclusion, we constructed an ultra-compact, tunable and highly efficient GPs waveguide filter using a simple rectangular cavity configuration. The filter exhibits a stable band-pass filtering effect with transmission reaching ∼ 80%. The working frequency of the filter could be tuned in a large frequency range based on cavity geometric design and in situ electrically gating. The efficiency of the filter is closely related to the graphene quality and performs very stably with different graphene Fermi levels and cavity geometries. These numerical results are corroborated by the CMT. The as-proposed cavity filter has promising applications in ultra-compact nanoscale optical circuits.
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