Journal of Optics J. Opt. 17 (2015) 125801 (5pp)
doi:10.1088/2040-8978/17/12/125801
Graphene-based hybrid plasmonic modulator Jin-Soo Shin1, Jin-Soo Kim2 and Jin Tae Kim2 1
Department of Electrical Engineering, KAIST, Daejeon 34141, Korea Creative Future Research Laboratory, Electronics and Telecommunications Research Institute (ETRI), Daejeon 34129, Korea
2
E-mail:
[email protected] Received 13 May 2015, revised 6 July 2015 Accepted for publication 28 July 2015 Published 8 October 2015 Abstract
A graphene-based hybrid plasmonic modulator is designed based on an asymmetric doubleelectrode plasmonic waveguide structure. The photonic device consists of a monolayer graphene, a thin metal strip, and a thin dielectric layer that is inserted between the grapheme and the metal strip. By electrically tuning the graphene’s refractive index, the propagation loss of the hybrid long-range surface plasmon polariton strip mode in the proposed graphene-based hybrid plasmonic waveguide is switchable, and hence the intensity of the guided modes is modulated. The highest modulation depth is observed at the graphene’s epsilon-near-zero region. The device characteristics are characterized over the entire C-band (1.530–1.565 μm). Keywords: grapheme, modulator, plasmonics 1. Introduction
electrically tuning the graphene’s refractive index. As a result, the intensity of the guided mode is modulated. In this study, we propose a simple graphene-based hybrid plasmonic modulator as an extended application of graphene plasmonics in optoelectronic systems for data communications. The proposed device configures an asymmetric doubleelectrode structure that consists of a graphene film and a thin metal strip. They are separated by a thin dielectric layer. The optical characteristics of the proposed device are numerically investigated on the entire C-band (1.530–1.565 μm) by electrically tuning the graphene’s refractive index. We found that the highest modulation depth is observed at the graphene’s epsilon-near-zero region.
In optics, graphene, one-atom-thick two-dimensional material of carbon atoms densely packed in a honeycomb, has attracted a great attention because of its exceptional photonic and opto-electronic properties [1, 2]. Interestingly, graphene is an excellent lightwave guiding medium for surface plasmon polarition. Numerous theoretical investigations on lighwave guiding along graphene have been performed [3–7]. Based on the capability, a variety of graphene-based plasmonic devices have been experimentally demonstrated to date, including a waveguide, a thermo-optic modulator, and a photodetector [8–10]. The concepts of graphene-plasmonics-based optoelectronic systems recently proposed [11]. The recent advances in the basic study on the graphene plasmonics and practical engineering applications to the opto-electronic devices have been discussed in recent reviews [12–15]. Compared to the conventional novel metal, graphene’s unique linear band structure allows its complex permittivity to be tuned by adjusting its Fermi level. The optical properties of graphene could be modulated by electrical gating or chemical doping. Based on the graphene’s refractive index tunability, numerous optical modulators have been investigated [16–18]. The propagation characteristics of the hybrid guided mode in the graphene-integrated dielectric waveguide are switched by 2040-8978/15/125801+05$33.00
2. Architectural concept and characterization Figure 1(a) exhibits the schematic view of the proposed graphene plasmonic modulator. A monolayer graphene sheet is placed on a dielectric substrate (e.g. acrylate-based UVcurable polymer materials that are used in [8–10]) with a refractive index of n1. The width and length of the graphene are L and W, respectively. A thin second dielectric layer with thickness d and refractive index of n2 is placed on the graphene sheet. It serves as a core layer. A thin Au strip with width wm and thickness tm is placed on the core layer, which 1
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J-S Shin et al
J. Opt. 17 (2015) 125801
from graphene’s dynamic conductivity that is derived from the Kubo formalism [22], s = sintra + sinter =
⎛ mc ⎞⎞ ⎛ -m c - ie 2 ⎜ e k B T + 1 ⎟⎟ 2 ln + ⎜ 2 ⎝ ⎠⎠ p (w + i2G) ⎝ k B T ⎤ - ie2 (w + i2G) ⎡ ¥ ¶fd ( - e) - ¶fd (e) ⎥, ⎢ e + d ⎣ 0 (w + i2G)2 - 4 (e / )2 ⎦ p2 (1 )
ò
where fd (e) = (e(e- mc ) / kB T + 1)-1 is the Fermi–Dirac distribution, is the reduced Plank’s constant, ω is the angular frequency, μc is the chemical potential, Γ=1/τ is the charged particle scattering rate, kB is the Boltzmann constant, and T is the temperature. The chemical potential can be defined as where mc = v F (p a 0 (Vg - VDirac ) )1/2 , 16 1 1 a 0 » 4.3 ´ 10 m V , VDirac is the voltage offset, and v F is the Fermi velocity of Dirac fermions in graphene [18]. Vg - VDirac is the biased voltage to modify the chemical potential. The surface permittivity of graphene is derived by eg = 1 + is (w, mc ) /we0 D, where Δ is the thickness of graphene assumed to be 1 nm [5]. An electrical gating through the Au strip changes the graphene’s carrier density (conductivity) and hence its refractive index is switchable. Accordingly the optical properties of the hybrid LR-SPP mode could be modulated by electrical gating. Graphene plasmons can interact with a substrate as a form of a coupled (hybridized) plasmon–phonon mode [23]. Previous experimental investigations on graphene ribbons 50–250 nm wide on a dielectric substrate reveals that when the plasmon frequency exceeds the intrinsic graphene optical phonon frequency of 1,580 cm–1, plasmons in graphene can decay through simultaneous emission of optical phonons and electron–hole pairs [24, 25]. If graphene nanoribbons are placed on a SiO2 substrate, the plasmon lifetime of the hybrid plasmon–phonon mode is about 20 fs, which corresponds to a propagation length of 200 nm [25]. The mid-infrared damping mechanisms for plasmons in graphene nanoribbons of subwavelength mode confinement may be non-negligible loss factors to consider while we investigate the proposed graphene-integrated asymmetric double-electrode structure. However, it is uncertain that these plasmonic damping mechanisms are applicable to the micro-wide graphene stripe plasmonic waveguide studied in this study. Similar to the metal stripe embedded in a dielectric [19], the field of the guided mode in the proposed graphene-integrated hybrid plasmonic waveguide modulator is confined more in a dielectric [8]. Thus, it is hardly easy to find out a complete quantitative solution to the phonon-coupled plasmon damping of the proposed photonic device. This is beyond the scope of the present study and will be the subject of a further work. We assume that the plasmon damping in the proposed plasmonic waveguide is mainly attributed to the surface plasmonic absorption by an ultra-thin tunable lossy guiding medium of graphene as used in [17, 18]. Based on the calculated graphene’s refractive index [18], we investigate the optical properties of the guided mode in the proposed graphene-integrated asymmetric double-electrode
Figure 1. (a) Schematic diagram of the graphene-based plasmonic
modulator and (b) cross-section view. (c) Contour plot of the hybrid LR-SPP strip mode at a 1.55 μm wavelength.
Figure 2. Propagation loss of the hybrid LR-SPP mode in the
graphene plasmonic modulator as a function of graphene’s chemical potential (μc), where wm=10 μm, tm=20 nm, d=300 nm, n1=1.47, and n2=1.45. The inset shows the effective refractive indices (Neff) of the hybrid LR-SPP modes.
is used as an input and output waveguide. Finally, the same material used as the substrate covers whole device structure. Figure 1(b) shows the cross-section view of the device, indicating that this waveguide structure is like an asymmetric double-electrode structure. The graphene-integrated asymmetric double-electrode structure supports so called hybrid long-range surface plasmon polarition (LR-SPP) strip mode at a 1.55 μm wavelength [19, 20]. This is clearly shown in figure 1(c), where wm=10 μm, tm=20 nm, d=300 nm, W=∞, n1=1.47, and n2=1.45. The refractive index of Au is 0.52+i10.74 [21]. The complex refractive index of graphene is calculated 2
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J. Opt. 17 (2015) 125801
loss, PLoff. On the contrary, the propagation loss is at the highest value at μc=0.525 eV. Hence we define this as the on-state propagation loss, PLon. The optical characteristics of the asymmetric doubleelectrode graphene plasmonic modulator can be tuned by adjusting the width or thickness of the metal strip, or the thickness or refractive index of the dielectric core layer [27, 28]. Figure 3 exhibits PLoff and PLon of the guided modes as a function of core index n2, core layer thickness d, graphene width W, and metal strip width wm, respectively, where n1=1.47 and wm=10 μm. Considering the minimum metal thickness that eliminates the possibility of an island structure forming during film fabrication, we fixed tm=20 nm. The refractive index of the core layer (n2) has a great effect on the vertical confinement of the hybrid LR-SPP mode. As n2 increases, the vertical size of the guided mode decreases, shown as the insets of figure 3(a). It means that the field of the hybrid guided mode is confined more at the metal– core dielectric interface and at the graphene–core dielectric interface. The loss from the lossy plasmonic modes increases. Accordingly, PLoff and PLon increase gradually as n2 increases. The rate of PLon increase is higher than that of PLoff increase. The difference between PLoff and PLon is high for large n2. We may expect the highest on/off extinction ratio with a device having a high index core. The dependence of PLoff and PLon on the core layer thickness d is shown in figure 3(b). The numerical calculation shows that PLoff and PLon are slightly dependent on d for the device with a high index core, n2=1.50. The rate of PLoff increase is very low and that of PLon increase is subtle with an increasing d. On the contrary, for the device with a low index core (n2=1.47), PLon decreases significantly with an increasing d. PLoff is nearly invariant. PL of the guided mode is affected from the graphene width W. The numerical investigations on this issue are shown in figure 3(c). It exhibits PLoff and PLon as a function of graphene width W, where wm=10 μm. For Wwm, the graphene width included in the guided mode is nearly the same because the metal strip width that determines the mode field diameter is fixed. The loss from graphene is nearly the same regardless of W. Variations of PLoff and PLon are not significant when W is larger than wm. The metal with wm has an effect on the lateral confinement of the guided modes [27]. As wm increases the propagation loss of the guided mode also increases because the field is confined more into a wider metal strip. Figure 3(d) exhibits PLoff and PLon as function of wm, where d=300 nm and W=∞. PLoff exhibits stable behavior with an increasing wm. However, PLon first increases and then reaches a saturated value. The loss from the Au strip and graphene increases as wm increases because wide wm confines more field of the guided mode. Based on the aforementioned theoretical investigations, we determined the optimized refractive index
Figure 3. Propagation loss of the hybrid guided modes in the
proposed graphene-based hybrid plasmonic modulator as a function of (a) core index n2, (b) core layer thickness d, (c) graphene width W, and (d) metal strip width wm.
plasmonic waveguide using a finite element method. Figure 2 shows the propagation loss of the guided modes as a function of graphene’s chemical potential μc. We set wm=10 μm, tm=20 nm, d=300 nm, and W=∞. Experimentally graphene’s chemical potential is highly susceptible to the substrate where it is transferred [26]. However, we considered an ideal case that graphene is not doped at the initial state. The inset of figure 2 represents the real part of the effective refractive index (Neff) of the guided modes. The dynamic behavior of Neff indicates that the phase modulation of the graphene from a dielectric material to a metallic material occurs. Presumably, the optical characteristics of the guided mode are switchable by tuning the refractive index of graphene by changing its chemical potential with electrical gating. For μc
