# Tunable Mid-Infrared Graphene Plasmonic Cross-Shaped Resonator for Demultiplexing Application
## 1 Introduction  
Surface plasmon polaritons (SPPs) are evanescent electromagnetic surface waves, shorter in wavelength than the incident light wave, which travel along the metal-dielectric. The terms of'surface plasmon' and 'polariton' are respectively involved charge motion in highly conductive matter, and electromagnetic waves in the dielectric or vacuum. The materials which are frequently used in plasmonic structures are typically metals such as silver and gold, which are exploited in various applications such as filters [1; 2; 3], demultiplexers [4; 5; 6], sensors [7; 8; 9], and switches [10; 11; 12].  
The parameters of the dielectric constants of metals are challengeable to be adjusted and controlled in different wavelengths [13; 14; 15]. In comparison, graphene is a two-dimensional (2D) sheet which dielectric constant can be modulated dynamically by alternation of its applied bias voltage enabling unique features to be utilized in mid-infrared (MIR) region [16; 17; 18; 19; 20]. In practice, graphene has strong confinement of lightwaves, long propagation length, and low loss making it superior to metals [21; 22; 23]. Because of the significant advantages of graphene, many graphene based structures--such as filters [24; 25], demultiplexers [26; 27], modulators [28; 29], couplers [30; 31], absorbers [32; 33], and solar cells [34]--are designed and analyzed. Fabrication of graphene-based devices in MIR region was recently reported in [35; 36]. The graphene/SiO2 MIR resonators are compatible with CMOS filters and resonators [37; 38] making them attractive.  
Previously published works [4; 5; 24; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48] have reported transmission ratios up to 99% and FWHM values between 2-650 nm. In the design of demultiplexers, it is important to minimizethe cross talk, thus the aim of this study was to find a design for demultiplexer which presents a better cross talk comparing to [4; 5; 26; 39; 44; 45; 46]. Moreover, a demultiplexer design should be conducted so that it maintains a desired single mode resonance in a wider wavelength range than previously reported structures [4; 5; 24; 26; 39; 40; 42; 43; 44; 45; 46; 47; 48].  
Plasmonic metal-based cross-shaped resonator and its demultiplexing application are investigated previously in [4]. The proposed cross-shaped resonator in [4] is single mode in the near-infrared wavelength range of 400 nm to 2 \(\upmu\)m while the proposed single mode resonator is designed to work at the wider MIR wavelength range. In addition, the transmission spectra of our structures aimed to be tunable since the Fermi energy of graphene can be changed without needing to re-fabricate the structures. Moreover, the cross talk of the graphene-type demultiplexer is improved compared to the metal-based one. To the best of our knowledge, tunable graphene cross-shaped resonator side-coupled to another resonator with the function of wavelength selecting and demultiplexing has not been studied yet.  
In this manuscript, a new kind of plasmonic two-channel demultiplexer based on input/output graphene waveguides and cross-shaped resonator is proposed for (MIR) region. The resonator is investigated by coupled mode theory (CMT) and three-dimensional finite-difference time-domain (3D-FDTD) methods. By changing Fermi level of graphene, the length of the resonator, and the width of the resonator, the resonance wavelengths can be tuned. First, we study the transmission of the cross-shaped resonator. Then, two resonators are designed and integrated into one structure to achieve two-channel demultiplexer structure. The advantages of our designed structures are their nanometer dimensions which would be used in future MIR devices and photonic integrated circuits. The proposed concept provides an interesting and useful route for implementing photonic structures for MIR region.