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Graphene Bragg gratings (GBGs) on microfiber are proposed and investigated in this paper. Numerical analysis and simulated results show that the mode distribution, transmission loss, and central wavelength of the GBG are controllable by changing the diameter of the microfiber or the refractive index of graphene. Such type of GBGs with tunability may find important applications in optical fiber communication and sensing as all-fiber in-line devices.
© 2014 Optical Society of America
1. Introduction
Graphene is attracting worldwide attention due to its unique electronic and photonic properties [1–3]. Many useful optical effects of graphene have been discovered, such as good transparency, strong nonlinearity, Fermi-level tunability, photovoltaic effects, Plasmon, etc [4–8], which have led to demonstrations of a number of graphene-based photonic devices, i.e. polarizers, saturation absorbers, modulators, switches, photo-detectors, LEDs, etc [9–14]. Recently, some theoretical studies on graphene Bragg gratings (GBGs) on silicon waveguides have been reported [15]. As the permittivity of graphene can be effectively modulated by controlling its chemical potential, the silicon waveguide based GBGs show great potential in many applications, for example, in integrated tunable filters, modulators, plasmonic transformers, and photonic reflectors [16]. Compared with the waveguide based Bragg grating, fiber Bragg grating (FBG) has been widely used in optical communication and sensing due to the outstanding advantages of the FBG such as all-fiber device, low cost, low insertion loss, and high flexibility [17, 18]. Thus, to study the optical features of the GBG on fiber is of significance for the designs and applications of GBG-based all-fiber devices, for example, tunable filters, sensors, fiber lasers and wavelength converters. In this paper, we propose GBGs on microfiber, as shown in Fig. 1 schematically, in which the monolayer graphene is wrapped along the microfiber periodically to form the grating cladding, with period of Λ. By numerically calculating the mode field distribution and propagation of the GBG, it is found that its mode distribution, transmission and reflection characteristics could be determined by the microfiber diameter, and modified by the refractive index of the graphene. First, by changing the diameter of the microfiber, the GBG with certain Bragg wavelength and reflectivity could be acquired. Secondly, by altering the refractive index of graphene, the reflection spectra of the GBG could be conveniently modified. These properties make GBGs promising for realization of various all-fiber-based photonic devices, such as lasers, modulators, tunable filters, and sensors.
2. Graphene based evanescent field enhancement
Graphene could be regarded as an ultrathin waveguide with complex permittivity [19]. Theoretically, it supports transverse electric (TE) polarized modes when its imaginary part of conductivity is positive (low chemical potential), while it supports transverse magnet (TM) polarized modes when its imaginary part of conductivity is negative (high chemical potential). The propagation constants β for TE and TM modes are shown in Eq. (1) [20–22]. Here k0 is the wave number in vacuum, σg is the conductivity of graphene, and η0 = (ε0/μ0)1/2 is the resistance. For pristine graphene with chemical potential less than 0.5eV, only TE mode should be taken into consideration. Using β = ng(ω/c), where ω is the light frequency and c is the light velocity. When light penetrating graphene vertically, the refractive index of graphene ng was measured to be ~2.6-i1.3 [23], however, when graphene works as a waveguide, the imaginary part of ng would be much larger [24]. The refractive index of the graphene waveguide for TE polarized mode was measured as ~3-i14 for 1550nm, with the thickness of graphene Δ = 0.5 nm [25]. Then, when the graphene is wrapped around the microfiber, it would influence the effective index and redistribute the mode field along the microfiber [26].
By using the finite element method (FEM) in COMSOL, the effective indexes of the graphene coated microfibers and their mode fields are simulated in Fig. 2.Here Fig. 2(a) and 2(b) show the cross-sectional views of the microfiber and the graphene coated microfiber (GCM), respectively. The radius of microfiber is R, the indexes of the microfiber, air and graphene are nMF = 1.45, nair = 1, and ng, respectively. Figure 2(c) shows correlation of the effective refractive index neff and the radius of the microfiber R, for the microfiber and GCM respectively. For the wavelength of 1000nm~2000nm, the effective indexes of the GCMs are smaller than the microfibers. Determined by the neff, the fractional power inside the core η is presented in Fig. 2(d) [27]. Accordingly, comparing with microfiber with the same radius, the GCM has more optical energy distributing out of the core. It indicates that the light transmitting along the microfiber would be spatially redistributed by the graphene cladding. Fixing the wavelength as 1550nm, specific examples are shown in Fig. 2(e)-2(j). Figure 2(e), 2(f) and 2(g) provide the electric field distributions of the fundamental mode of microfibers with radius of 0.2μm, 0.5um and 1um, respectively, corresponding to Fig. 2(a). likewise, Fig. 2(h), 2(i) and 2(j) provide the electric field distributions of the fundamental mode of GCMs with radius of 0.2μm, 0.5um and 1um, respectively, corresponding to Fig. 2(b). It is clear that the evanescent fields of microfiber could be effectively enhanced by coating a layer of graphene around it, for microfibers with R = 0.2μm, 0.5μm and 1μm, η ~0.15, 0.75 and 0.95, while for GCMs R = 0.2μm, 0.5um and 1um, η ~0, 0.67 and 0.9.
Fig. 2 (a) Cross sectional view of the microfiber. (b) Cross sectional view of the GCM. (c) Correlation of the microfiber radius and the effective index, for microfiber (solid curve) and GCM (dashed curve) respectively. (d) Correlation of the microfiber radius and the fractional power inside the core, for microfiber (solid curve) and GCM (dashed curve) respectively. (e), (f), and (g) are the mode fields for microfibers with radius of 0.2μm, 0.5μm and 1μm. (h), (i), and (j) are the mode fields for microfibers with radius of 0.2μm, 0.5μm and 1μm.
Considering that the coated graphene around the microfiber is unlikely to have a perfect cylindrical symmetry (with the coated angle φ = 360°), we also simulated the effects of asymmetries, adopting R = 0.5μm. When the coated angle φ varies from 180° to 360°, the effective index neff of the GCM decreases ~0.02 RIU, while the fractional power inside the core η decreases ~7%. For φ = 180°, 240° and 360°, the fundamental mode fields of the GCM are shown in Fig. 3(a).Moreover, the reflective spectra of them are simulated in Fig. 3(b), in which the incomplete coating makes reflectivity weaker dramatically. Figure 3(c) calculates the “φ-Loss” correlation on x polarization and y polarization, respectively. It demonstrates that along incompletely coated GCM, the loss of x polarized mode would higher than the y polarized mode [9, 28]. However, in practice, by using wet transferring method, the φ would be well controlled > 300° [26], so that the effect of asymmetry is negligible.
Fig. 3 (a) Typical mode field distributions and (b) reflection spectra for φ = 180°, 240°, and 360°. Here R is 0.5μm. (c)
3. Tunable reflection spectrum of the GBG on microfiber
Utilizing the transferring matrix method, we investigate the reflection spectrum of the GBG, and how to tune it, according to Eq. (2) and Eq. (3) [29]. Here, M is the transferring matrix, R is the reflectivity of the GBG, N is the period number, δj = (2π/λ)njdj, τj = η0nj, nj is the local effective index relating to graphene’s conductivity, and dj is local period length of the grating. The simulated optical properties of the GBG are shown in Fig. 4.Here, nMF = 1.45 is the index of fiber core ng = (εg)1/2 is the index of graphene [19, 25], Λ = 500nm is the period of the gratings. The number of grating periods is fixed as 2000. Figure 4(a) shows the R-reflectivity correlation of the GBG. Because the grating structure is formed by graphene deposited on the surface of microfiber, the larger R brings less light interacting with graphene, which leads to decreasing of the reflectivity. Figure 4(b) shows that by increasing the refractive index of the graphene cladding (ng), the GBG could be effectively modulated. Here the radius of all the microfibers is fixed to be 0.5μm. Such an increase of ng could be induced by voltage bias, chemical doping, or light exciting [16, 30–32]. When ng increases, because the effective index of the microfiber sections with graphene formed cladding decreases, the reflectivity and the reflection peak width of the GBG increases with its λB blue shifting. In this simulation, the side lobes were suppressed by apodization. Accordingly, for monolayer GBG with R = 0.5μm, the correlations of “Δng-reflectivity”, “Δng-ΔλB” and “Δng-Bragg peak width” are shown in Fig. 4(c)-4(e), respectively. The reflectivity and the Bragg peak bandwidth of the GBG increase with Δng, however, the ΔλB decreases with the Δng.
Fig. 4 Calculated results: (a) Reflectivity of the GBG with R of 0.2μm, 0.5μm and 1μm. Reflectivity of the GBG with R of 0.5μm varies with Δng = 0.01, 0.02 and 0.03. For the GBG, correlations of (c) Δng-reflectivity, (d) Δng-ΔλB and (e) Δng-Bragg peak width.
We also consider the reflectivity of the GBG utilizing bilayer graphene cladding. Compared to monolayer graphene with permittivity εg, bilayer graphene with a tunable band gap is more similar to a semiconductor with εg,2 = ~2εg [19, 33, 34]. Referring ε = n2 [9, 25], the refractive index of bilayer graphene ng,2 = (2ng2)1/2 approximately. Figure 5 presents the simulated results. Varying the radius of microfiber, the Bragg wavelength and the reflectivity of the GBG are shown in Fig. 5(a). Compared to the monolayer GBG with the same radius, bilayer GBG has smaller Bragg wavelengths and reflectivity. Varying the ng,2, the Bragg wavelength shift and the reflectivity of the bilayer GBG are shown in Fig. 5(b). In comparison with the monolayer GBG, the bilayer GBG has slightly higher modulation efficiency. In summary, the results of Fig. 5 present that both the monolayer and bilayer GBGs have the same tunable tendency. In practice, limited by the graphene deposition technology, there may be inhomogenities along the GBG, which would deteriorate the reflectivity of the GBG. Thus to ensure the periods of GBG homogeneous is essential in fabrication process, e.g. forming homogeneous Bragg gratings on monolayer graphene by highly accurate laser micromachining [35], and coating it around a microfiber via wet transferring [26].
Fig. 5 For the bilayer GBG: (a) “R-λB” (red solid curve) and “R-Reflectivity” (blue dashed curve) correlations. (b) “Δng-ΔλB” (red solid curve) and “Δng-Reflectivity” (blue dashed curve) correlations.
4. Conclusions
In this paper, Graphene Bragg Gratings (GBGs) on the microfiber are investigated. Simulated results illustrate that the graphene cladding would enhance the surface evanescent fields. By choosing a microfiber with proper diameter, GBGs with certain reflection spectra could be achieved. Moreover, by modulating the refractive index of the graphene via gating, doping or polarizing, the reflection spectra of the GBGs are tunable. Related to graphene based silicon waveguide Bragg gratings, such all-fiber based graphene Bragg gratings with low insertion loss and convenient tunability would pave a new way for the applications of graphene based devices, e.g. sensors, tunable filters, fiber lasers and wavelength converters [36–39]. The research also provides a good reference for designing novel fiber devices such as graphene based D-shape fiber gratings, tilted fiber gratings and photonic crystal fiber gratings, etc [40–42].
Acknowledgements
This work was supported by National Natural Science Foundation of China under Grant 61290312, 61107072, 61107073 and was also supported by Program for Changjiang Scholars and Innovative Research Team in Universities of China (PCSIRT) and the “111 Project” of China Education Ministry. Baicheng Yao and Yu Wu contributed equally to this work
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