Tunable Fano resonance based on grating- coupled ... - OSA Publishing

Vol. 25, No. 20 | 2 Oct 2017 | OPTICS EXPRESS 23880

Tunable Fano resonance based on gratingcoupled and graphene-based Otto configuration JICHENG WANG,1,2,3,* CI SONG,1 JING HANG,1 ZHENG-DA HU,1 AND FENG ZHANG3 1

School of Science, Jiangsu Provincial Research Center of Light Industrial Optoelectronic Engineering and Technology, Jiangnan University, 214122 Wuxi, China 2 School of IoT Engineering, Jiangnan University, 214122 Wuxi, China 3 Key Laboratory of Semiconductor Materials Science, Institute of Semiconductors, Chinese Academy of Sciences, PO Box 912, Beijing 100083, China *[email protected]

Abstract: A grating-coupled Otto configuration consisting of multilayer films including a few layers of graphene and a germanium prism is proposed. A sharp and sensitive Fano resonance appears when a graphene surface plasmon polaritons (GSPPs) mode from the graphene-dielectric interface couple with the planar waveguide (PWG) mode. We utilize the classical harmonic oscillator (CHO) to explain Fano resonance and study the influence of various parameters of the configuration on the reflection spectra. The highly sensitive sensor can be achieved by introducing detected materials into Otto structure. In addition, we investigated the effects from material loss arising in our designs. All of the simulations are performed by a finite element method (FEM). © 2017 Optical Society of America OCIS codes: (050.0050) Diffraction and gratings; (130.3120) Integrated optics devices; (310.2785) Guided wave applications; (310.4165) Multilayer design.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

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#303575 Journal © 2017

https://doi.org/10.1364/OE.25.023880 Received 28 Jul 2017; revised 12 Sep 2017; accepted 15 Sep 2017; published 20 Sep 2017


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1. Introduction Surface plasmon polaritons (SPPs), a kind of surface wave, propagate along the interface between the metallic and dielectric materials with exponentially decaying fields in both sides [1]. The plasmonic nanostructures, owing to their unique properties, are able to break through the diffraction limit and thus allow light to propagate in the sub-wavelength structure [2]. For instance, plasmonic has been mainly studied in metal-insulator-metal (MIM) waveguides [3, 4], photonic crystals [5, 6], metasurfaces [7, 8], etc., enabling the design of various micronano optical devices such as integrated photonic circuits [9], filters [10], sensors [11], etc. However, these devices are difficult to tune actively and have huge ohmic losses at visible wavelength, since they are usually made of noble metals. Graphene, a novel two-dimensional material which consists of a single layer of carbon atoms densely arranged in a honeycomb lattice [12, 13], has been widely applied as a novel plasmonic material in the infrared frequency regime [14]. Graphene exhibits excellent mechanical [15], electronic [16], and optical properties [17]. In particular, the carrier density and corresponding Fermi energy level of graphene can be actively modulated by external bias voltages or chemical doping, which lead to drastic variations in its optical properties [18]. In recent years, graphene structures have attracted great attention for Fano resonance and plasmonic waveguides [19, 20]. Fano resonances(FRs) [21] were first discovered in a quantum mechanical study of the autoionzation spectra of He atom, and they arise from the interaction of a narrow discrete resonance with a broad spectral line or continuum [22]. Fano resonances generate a sharp asymmetry of spectral absorption lines and an abrupt variation in amplitude and phase, when a broad resonance and a narrow resonance are coupled. Recently, a variety of Fano resonances have been explored [23–25]. Zheng et al. [26] have designed a modified multilayer thin film coupled Otto configuration to produce FRs in the mid-IR range, but it is hard to control due to its broad resonance caused by the SPhP mode. Guo et al. [27] proposed a tunable Fano resonance based on the interference between graphene surface plasmon polaritons (GSPPs) and a dielectric waveguide mode. However, the adjustment of sensitivity is still not achievable. In this paper, we propose an improved grating-coupled Otto configuration consisting of multilayer thin films, including a few graphene layers and a germanium prism, followed by a numerical study of the dependence of its reflection spectra on geometrical parameters. The surface conductivity of the graphene layer can be dramatically tuned by the Fermi level EF. We utilize the finite element method (FEM) [28] to perform the simulation works. The results are simulated by using the MUMPS solver in COMSOL multiphysics. The waveguide mode shows a narrow resonance excited by the planar waveguide (PWG), while the graphenedielectric interface excites a GSPP mode, bringing a broad resonance. The sharp Fano resonance appears when these two modes coupled. We use the classical harmonic oscillator (CHO) to explain Fano resonance and propose several modulation schemes to adjust the characteristics of the reflection spectra. Furthermore, we introduce a detecting layer in the Otto configuration and then achieve a sensitive sensor with high FOM, which can be used to design an environment-sensitive sensor.


2. Theoretical model and experimental scheme As illustrated in Fig. 1(a), the grating-coupled Otto configuration presented in this paper is composed of multilayer thin films and a germanium prism, with a few layers of graphene inserted between the grating and detected materials. The structural materials and geometrical parameters are indicated in Fig. 1(a), and the thickness of each layer is assumed to be d1 = d2 = d3 = 2μm, and d4 = 0.5μm. In the following study, it was assumed that refractive indices np of the germanium prime, ns of the substrate and n2 of the PWG core were all set as 4. Refractive indices n1 of the cladding layer and n3 of the grating layer, made of CaF2, are both set to be 1.3. The detecting layer with refractive index nd was designed to place the materials waiting to be detected. The incident field in the mid-infrared regime was considered to be transverse magnetic (TM), exciting graphene and waveguide SPP modes. According to the Kubo formula [29, 30], the optical properties of graphene monolayer are related to its complex surface conductivity σ, which is the sum of two sections: interband and intraband. These can be written as  2 EF − (ω + iτ −1 )   e2 , ln  =i 4π   2 EF + (ω + iτ −1 )   

(1)

E − F  EF  e 2 k BT kBT =i 2 + 2 ln(e + 1)  , -1  π  (ω + iτ )  k BT 

(2)

σ int er

σ int ra

where e, ћ and kB are elementary charge, reduced Planck's constant, and Boltzmann constant, respectively. In the graphene layer, the momentum relaxation time denoted by τ and the temperature of the environment denoted by T were set to 0.2 ps [31, 32] and 300 K, respectively. Moreover, the incident wavelength λ was set to be 10.6 μm throughout this work. The surface conductivity of graphene is controlled by its Fermi level EF, which can be dramatically modulated by the electrical gating. The EF is able to reach 1 eV in experiment by using top-gate electrical doping in extended graphene [33]. Figure 1(b) is based on Eq. (1) and Eq. (2) and the permittivity of the monolayer graphene, which can be described as εg = 1 + iσ/(ωε0dg). In the numerical simulation, the thickness dg of the monolayer graphene was set to 0.34nm.


Fig. 1. (a) 3D schematic illustration of grating-coupled and graphene-based Otto configuration. (b) The real part (black) and imaginary part (red) of relative permittivity of the monolayer graphene in relation to the Fermi level EF. (c)The effective refractive index NGSPP of different number of graphene layers in relation to the Fermi level EF. (d) Schematic illustration of the fabrication procedures of the grating-coupled and graphene-based Otto configuration.

One of the significant parameters of graphene is the GSPP effective refractive index NGSPP = kGSPP/k0, where kGSPP is the wave vector of SPP on graphene. The prism is able to excite SPPs only if its refractive index is larger than that of the GSPP. Realistically it is impossible to find a prism to overcome the huge momentum mismatch, as the monolayer graphene only can excite GSPP owning to its very large refractive index, especially in the infrared frequency regime. In this paper, in order to reduce NGSPP, a few layers of graphene were used to increase σ. It is reasonable to consider each graphene film as non-interacting monolayer when the number of its layers N is less than 6 (N