- Email: [email protected]
A fabrication-friendly graphene-based polarization insensitive optical modulator
Optik - International Journal for Light and Electron Optics 182 (2019) 1093–1098
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
A fabrication-friendly graphene-based polarization insensitive optical modulator
T
⁎
Zhonghua Yang, Rongguo Lu , Yujiao Wang, Songwei Cai, Yujia Zhang, Xiaoju Wang, Yong Liu State Key Laboratory of Electronic Thin Films and Integrated Devices, School of Optoelectronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 China
A R T IC LE I N F O
ABS TRA CT
Keywords: Mode conversion Optical-modulator Polarization-insensitive Graphene
Graphene is a suitable material for high efficient optical modulator. However, graphene-based modulators are of strong polarization dependence. Here a fabrication-friendly structure for graphene-based polarization insensitive electro-absorption modulator (EAM) is reported. The modulator consists of two adiabatic tapers (ATs), two asymmetric directional couplers (ADCs) and an active region. The ATs and ADCs are used to realize mode conversion and mode coupling. The theoretical analysis of the modulator was performed. The device can operate at the spectrum of 1.5 μm–1.6 μm. The extinction ratio (ER) is of > 24dB and the insertion loss is of < 6dB for both modes. The 3dB modulation bandwidth is about 80GHz based on theoretical calculation at the cost of 300μm device length.
1. Introduction In recent years, 2D functional electro-optic materials, such as grapheme [1], dichalcogenides [2] and black phosphorus [3], have been discovered, which promotes the development of Integrated optoelectronic devices and brakes the traditional performance limitation. Among these materials, graphene is considered as an ideal material to realize high efficient optical modulator because of some attractive advantages [4], such as constant absorption over a wide spectrum [5], ultra high carrier mobility under room temperature [6], electrically controllable conductivity and compatibility with CMOS processing. Graphene as electro-optic material, the characteristics of anisotropic dielectric [7,8] needs to be considered. The permittivity in plane is tunable. However, The perpendicular permittivity of graphene is a constant of 1 or 2.5. Therefore, graphene can only strongly interact with the in-plane electric field [9], which is the reason why previously reported graphene-based modulators are strong polarization dependence [9–12]. Generally, the polarization state of light in waveguide or fiber is random. In order to realize the wide commercial application of graphene-based modulator, the problem of polarization dependence needs to be solved. Some graphene-based polarization insensitive modulation (PIM) devices have been reported before, but they are complicated [13,14]. In this letter, we demonstrate a PIM structure that is comprised of two mode conversion structures ATs/ADCs and two symmetric waveguide arms (Fig. 1(a)). There is a cascaded taper structure can support the mode conversion of TM0 mode into TE1 mode at the input port. The cascaded taper consists of three shorter tapers to reduce the total length of the device [15]. Then, a ADC couples TE1 to TE0 from the wide waveguide to the narrow waveguide. In contrast, the TE0 mode that does not have mode conversion passes through the wide straight waveguide. At the end of the ADC the width of wide straight waveguide is tapered to be the same width of
⁎
Corresponding author. E-mail address: [email protected] (R. Lu).
https://doi.org/10.1016/j.ijleo.2019.02.024 Received 11 September 2018; Received in revised form 11 January 2019; Accepted 11 February 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 182 (2019) 1093–1098
Z. Yang, et al.
Fig. 1. Modulator configuration. (a) Three-dimensional schematic representation. (b) Cross-section of the graphene active region. (c) Top-view of the left part of the device.
the narrow waveguide. Since two arms strip1 and strip2 have the same structures, the same overlaps between the graphene layer and the optical mode profile modes are the same (Fig. 1(c)). The both launched TM0 and TE0 modes are greatly tuned by the strip1 and the strip2 respectively. At the output port, TE0 mode in strip1 waveguide can be reverted back to its original TM0 mode by the right AT/ADC. The tilted [13] and vertical [14] graphene sheets are difficult for CMOS technology. Compared with the previous structures, the vertical and tilted graphene sheets are not used in this work. The cross section diagram of the graphene active region is presented in Fig. 1(b). Two Si waveguides with the same widths W4 = 0.4 μm are semi-embedded in the SiO2 substrate to ensure the graphene sheets to be smoothly paved in the waveguide center where light-graphene interaction reaches the highest. Two graphene sheets are separated by a hexagonal boron nitride (hBN) layer with thickness of 40 nm. The electrode structure is Au-Pd-graphene, for the contact resistance between graphene and Pd is less than 100(Ωμm) [16]. The width between electrode and waveguide is about 0.8 μm to avoid the perturbed optical modes [9]. As a result, a PIM device with the total length of ˜300 μm is realized. The extinction ratio (ER) is of > 24 dB and the insertion loss is of < 6 dB for both TE0 and TM0 modes. The operating spectrum is of 1.5 μm to 1.6 μm. The 3 dB modulation bandwidth is about 80 GHz based on theoretical calculation at the cost of 100 μm active region length (Lgra) (Fig. 1(c)).
2. Principle and structure Graphene’s chemical potential μc can be dynamically tuned by the applied drive voltage. In this model, graphene is treated as an anisotropic material. The perpendicular permittivity ε⊥ of graphene does not vary with the μc and it always stays as a constant of 2.5, whereas the in-plane permittivity of the grapheme ε|| can be tuned (Fig. 2(a)). In order to realize graphene-based PIM, the approach of mode conversion is taken, which both TE0 and TM0 modes can be converted to TE0 and tuned almost identically by the drive voltage. To realize the mode conversion, the effective indexes (Neff) of different modes are analyzed with the change of waveguide core width Wco. Here, A strip waveguide with fixed thickness of hco = 0.26 μm is used on a SOI wafer (Fig. 2(b) insert). It can be seen that there is a mode hybridization region around Wco = 0.72 μm, which can achieve a mode conversion when light propagates along an AT whose ports widths Win and Wout are chosen as Win < Wco < Wout [17]. To be compact, the AT is designed to be three segments (Fig. 1(c)) as the following parameters: Win = 0.6 μm, W1 = 0.7 μm, W2 = 0.74 μm, and W3 = 0.8 μm. Fig. 3(a–c) shows the calculated mode conversion efficiency η as the segment length Li (i = 1,2,3) varies when the TM0 and TE0 modes are launched at the left input port (Fig. 3(d)). Firstly, it is clear that TE0 mode does not change at any value of Li (i = 1,2,3), which is important to ensure TE0 to pass through straight waveguide without interference. It can be seen that the η always keeps a high value of more than 92% when L1 or L3 varies from 1 μm to 100 μm. The contribution of L1 and L3 to the η is very small, because
Fig. 2. (a) Calculated permittivity of graphene sheet(real part, imaginary part and magnitude) as a function of chemical potential for λ = 1550 nm. (b) The effective indexes (Neff) of the eigenmodes of an SOI nanowire with an air upper-cladding as a function of waveguide width Wco. 1094
Optik - International Journal for Light and Electron Optics 182 (2019) 1093–1098
Z. Yang, et al.
Fig. 3. Mode conversion efficiency η of the launched TM0 and TE0 modes as a function of L1(a), L2(b) and L3(c) respectively. It is worthy of note that when Li is analysed, other parameters of Lj (j ≠ i) keep long enough (eg.200 μm). The parameters are λ = 1550 nm, hco = 0.26 μm, Win = 0.6 μm, W1 = 0.7 μm, W2 = 0.74 μm, W3 = 0.8 μm. (d) electric and magnetic field distributions of the launched TM0 mode under the condition of L1 = 10 μm, L2 = 50 μm, L3 = 10 μm.
the sizes of W1 and W3 are far from the hybridization region around Wco = 0.72 μm. Therefore, the length of L1 and L3 is chosen as 10 μm. L2 that has a waveguide width around 0.72 μm has a strong effect on η. When the L2 varies from 1 μm to 200 μm, the η can change from 0 to 1. It can be seen that the mode conversion efficiency η is even close to 100% when L2 = 50 μm. Consequently, the segment lengths are chosen as L1 = 10 μm, L2 = 50 μm and L3 = 10 μm. Then, a TM0 mode transmission is simulated by using eigenmode expansion (EME) method and the electric and magnetic field distributions are presented in Fig. 3(d), where the phenomenon of the mode conversion can be clearly observed. Since the TE1 mode in narrow waveguide needs to convert to TE0 mode, an ADC is used. Fig. 4(a) shows the fluctuation of the couple efficiency γ of TE1 mode to TE0 mode, when a TE1 mode is launched at the left input port (Fig. 4(b)). The length of direction coupler Ldc = 7 μm is chosen as an optimal value.
Fig. 4. (a) The illustration of the couple efficiency γ of the TE1 to TM0 as the function of couple length Ldc under the condition of Wgap = 40 nm. (b) The magnetic field distribution under the condition of Ldc = 7 μm. 1095
Optik - International Journal for Light and Electron Optics 182 (2019) 1093–1098
Z. Yang, et al.
Fig. 5. (a) The absorption coefficient the graphene embedded waveguide as a function of chemical potential μc. (b) the different insert losses (left) and graphene coefficient α (right) as a function of wavelength at different μc. (c) The transmissivity T and its difference ΔT as a function wavelength at different μc. (d) The modulation depth of the two modes as a function of wavelength.
3. Modulator performance The insert loss consists of the mode conversion loss (MCL), the couple loss between the narrow waveguide and the wide waveguide (CL1), the couple loss between the passive Si waveguide section and the graphene modulator section (CL2), and graphene absorption loss (GAL), where the GAL should be considered as the insert loss at the "ON" state while it should be considered as the modulation absorption at the "OFF" state. The MCL and the CL are only meaningful for the launched TM0 mode, but they are meaningless for the launched TE0 mode, because there is almost no mode conversion and the mode coupling for the launched TE0 mode. Fig. 5(a) shows the fluctuation of the absorption of the graphene waveguide as a function of chemical potential (μc). It can be seen that the highest and the lowest values can be obtained at μc = 0.1 eV and μc = 0.8 eV respectively. So the points μc = 0.1 eV and μc = 0.8 eV are set as the “OFF” state point and the “ON” state point respectively. Fig. 5(b) shows the fluctuations of all the insert losses as a function of wavelength. The MCL is the total loss of two ATs and the CL1 is the total loss of two ADCs. The couple loss between waveguide and graphene modulator section is also considered twice as CL2. It can be seen that the MCL is wavelength dependent. The MCL is very low around center wavelength, but it has a high value when the wavelength is far from the center wavelength. The value of MCL ranges from 0.004 dB to 1.01 dB. The CL1 is also wavelength dependent and it is twice higher than MCL, because the size of narrow waveguide is not the best one but it's acceptable for the mode coupling. If the coupler structure is further researched, a higher performance coupler can be realized. Since the effective index of the graphene embedded waveguide is chemical potential dependent, the CL2 is also chemical potential dependent. Here, we just consider the CL2 at the states μc = 0.1 eV and μc = 0.8 eV and the fluctuation of the CL2 as a function of wavelength is presented in Fig. 5(b). The CL2 is very low at the level of < 0.4 dB for both states. CL1, CL2 and MCL exist, no matter which state the device is in. However, the GAL should be considered when the modulator is at the “ON” state. The fluctuations of graphene absorption coefficient(α) as a function of wavelength at different states are shown in Fig. 5(b). The α is of > 0.26 dB/μm at 0.1 eV and is of < 0.027 dB/μm at 0.8 eV. The graphene length is Lgra = 100 μm. Then the GAL can be obtained by GAL=α∙Lgra that is of < 2.7 dB at μc = 0.8 eV. Therefore, the insert loss of the launched TM0 mode at the “ON” state is Lon(TM0)=MCL + CL1+CL2on+GALon and the transmissivity Ton(TM0)=eLon(TM0). The insert loss of the launched TE0 mode at the “ON” state is Lon(TE0)=CL2on +GALon and the transmissivity Ton(TE0)=eLon(TE0). For the “OFF” state, the transmissivity is Toff(TM0)=eLoff(TM0) and Toff(TE0)=eLoff(TE0). Fig. 5(c) shows the fluctuations of the transmissivity at the different states as a function of wavelength. The Ton(TM0) is of > e6 dB that means the insert loss of TM0 mode at the “ON” state is Lon(TM0) < 6 dB. The Ton(TE0) is of > e3.1 dB and Lon(TE0) is of < 3.1 dB. The Toff(TE0) is of > e28.8 dB and the Toff(TM0) is of > e31.4 dB. The differences of transmissivity ΔT are also presented in Fig. 5(c). It can be seen that the ΔT is 1096
Optik - International Journal for Light and Electron Optics 182 (2019) 1093–1098
Z. Yang, et al.
wavelength dependent and has the same fluctuations for both states. The ΔT is of > -3 dB. The ER is a very important index for EAM and it can be defined as:
ER = Ton (dB ) − Toff (dB ) For the TM0 state,
ERTM = (MCLon + CL1on + CL2on + GALon ) − (MCLoff + CL1off + CL2off + GALoff ) Since the MCLon= MCLoff, CL1on= CL1off, the ERTE can be simplified as:
ERTM = (CL2on + GALon ) − (CL2off + GALoff ) For the TE0 state, ′ ′ ERTE = (CL2′on + GALon ) − (CL2′on + GALon )
Since the strip1 and strip2 are the same structures, the equations of CL2′ = CL2 , GAL′ = GAL are true for both “ON” and “OFF” states. Then
ERTE = ERTM The difference of ER for both modes is zero and the fluctuation of ER as a function of wavelength is presented in Fig. 5(d). The ER ranges from 24.5 dB to 25.5 dB when the wavelength ranges from 1.5 μm to 1.6 μm. The different performance indexes between two polarization modes are the output power that can be characterized by the normalized output intensity. The normalized output intensity is equal to T and the difference of normalized output intensity is ΔT. The ΔT has been analyzed before (Fig. 5(c)). It can be seen that the fluctuation of ΔT for both states are same, because the ΔT only depends MCL and CL1 that is chemical independent. Consequently, the difference of ER for both polarization modes is zero and a graphene-based PIM device is realized, with a modulation depth of > 24 dB and a insert loss of < 6 dB. For an optical modulator, the 3 dB modulation bandwidth f3dB that is always the one of the most important parameters needs to be considered. Since graphene has ultrahigh carrier mobility at room temperature, a graphene-based modulator’s operation speed is no longer limited by minority carrier lifetime like traditional semiconductor modulators. The f3dB of a graphene-based modulator is mainly impeded by RC delay, which can be expressed as:
f3dB =
1 2πRC
Where R is the device’s total resistance, including graphene sheet resistance Rs and metal-graphene contact resistance Rc, which has been carefully discussed in the previous works [11,18,19], C is the capacitance of modulator, which mainly consists of the capacitor that is formed by the two graphene sheets. Although this capacitor is not an ideal parallel plate capacitor model, the parallel plate capacitor model is still used to calculate the C, to preliminarily estimate the f3dB. In our calculations, Rc = 100Ωμm [16] and Rs = 200Ω/□ [20] are used, and the distance between electrode and active region is about 0.8 μm. The estimated f3dB is about 80 GHz. In the structure, the length of graphene sheets is so long between two electrodes that the graphene sheet resistance is pretty high. For a further study, another electrode can be added between two waveguide arms to reduce the graphene sheet resistance then a higher f3dB bandwidth can be obtained. Moreover, lower values of both Rs and Rc are possible in the future, which means higher f3dB can be obtained. 4. Conclusions In conclusion, we propose a structure of a broadband polarization insensitive graphene-based electro-absorption optical modulator. In the structure, two ATs and two ADCs were used to realize polarization insensitive modulator. The device performance parameters insert loss, modulation depth, operating spectrum width, 3 dB bandwidth and polarization sensitivity were studied. The results show that both TE0 and TM0 modes have almost high modulation depth of > 24 dB at the cost of 300 μm device length. The operating wavelength ranges from 1.5 μm to 1.6 μm. The insert loss for both modes are less than 6 dB. The theoretical modulation bandwidth of the device is about 80 GHz. It is worthy of note that the structure parameters of the mode converter and mode coupler are not optimal. If the parameters of the structure are properly chosen, the values of MCL and CL1 will close to zero. Then the insert losses are only determined by GAL and CL2 that are less than 2.7 dB and 0.4 dB. What’s more, the ΔT will also close to zero and the graphene based PIM device will be more polarization insensitive. So the device fulfills the requirement of polarization independent modulation. We believe that the device structure will simplify the fabrication steps and promote the commercialization of the graphene-based electro-optic modulator and this structure can also be used to study other 2D materials based PIM modulator. 5. Method The proposed modulator geometry was investigated using two dimensional finite element method (FEM) simulations using software COMSOL. The ATs and ADCs were investigated using three dimensional eigenmode expansion (EME) method simulations using software Lumerical FDTD. In the calculations, the refractive indexes of the Si ribs, the SiO2 substrate and the hBN spacer are n1 = 3.485, n2 = 1.444 and n3 = 1.98 respectively. 1097
Optik - International Journal for Light and Electron Optics 182 (2019) 1093–1098
Z. Yang, et al.
To evaluate the mode effective index and mode power attenuation of the considered structure the gate- dependent complex dielectric constant of graphene has to be calculated. The complex dielectric function ε|| (ω) can be obtained from the complex optical conductivity of graphene, consisting of interband and intraband contributions [21], ′ ′′ σtotal = σintra + σinter + iσinter
σintra = σ0
4μ π ℏ(τ1 − iω)
ℏω − 2μ ℏω + 2μ ⎞ 1 1 ′ σinter = σ0 ⎛1 + arctan − arctan π ℏτ2 π ℏτ2 ⎠ ⎝ ⎜
′′ σinter = σ0
⎟
1 (2μ + ℏω)2 + ℏ2τ22 ln 2π (2μ − ℏω)2 + ℏ2τ22
Where σ0 = e 2/4 ℏ= 60.8μS is the universal optical conductance, by using
ε∥ (ω) = 2.5 +
iσ (ω) ωε0 hg
where, hg = 0.7 nm is a thickness of the grapheme layer. As the complex conductivity σ(ω, μ, Γ, T) depends on the angular frequency ω, the charge particle scattering rate Γ = 1/τ with τ being the relaxation time, the chemical potential μ and temperature T [22], the dielectric constant of the graphene layer was calculated as a function of chemical potential for λ = 1550 nm, T = 296 K (room temperature) and τ1 = 1.2 ps for interband conductivity and τ2 = 10fs for intraband conductivity. Acknowledgements This work was funded by National Nature Science Foundation of China (No. 61435010, 61307070, 61421002, 61704021) and the Fundamental Research Funds for the Central Universities (ZYGX2016J070). References [1] A.C. Ferrari, F. Bonaccorso, V. Fal’Ko, et al., Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, Nanoscale 7 (11) (2015) 4598–4810. [2] W. Choi, N. Choudhary, G.H. Han, et al., Recent development of two-dimensional transition metal dichalcogenides and their applications, Mater. Today (3) (2017) 20. [3] X. Ling, H. Wang, S. Huang, et al., The renaissance of black phosphorus, Proc. Natl. Acad. Sci. U. S. A. 112 (15) (2015) 4523. [4] S. Yu, X. Wu, Y. Wang, et al., 2D materials for optical modulation: challenges and opportunities, Adv. Mater. 29 (14) (2017) 201606128. [5] R.R. Nair, P. Blake, A.N. Grigorenko, et al., Fine structure constant defines visual transparency of graphene, Science 320 (5881) (2008) 1308. [6] K.I. Bolotin, K.J. Sikes, Z. Jiang, et al., Ultrahigh electron mobility in suspended graphene, Solid State Commun. 146 (9) (2008) 351–355. [7] R. Hao, W. Du, E.P. Li, et al., Graphene assisted TE/TM-independent polarizer based on mach–zehnder interferometer, Ieee Photonics Technol. Lett. 27 (10) (2015) 1112–1115. [8] Z. Chang, K.S. Chiang, Experimental verification of optical models of graphene with multimode slab waveguides, Opt. Lett. 41 (9) (2016) 2129–2132. [9] M. Liu, X. Yin, E. Ulinavila, et al., A graphene-based broadband optical modulator, Nature 474 (7349) (2011) 64–67. [10] M. Liu, X. Yin, X. Zhang, Double-layer graphene optical modulator, Nano Lett. 12 (3) (2012) 1482–1485. [11] S.J. Koester, M. Li, High-speed waveguide-coupled graphene-on-graphene optical modulators, Appl. Phys. Lett. 100 (17) (2012) 611. [12] C.T. Phare, Y.H.D. Lee, J. Cardenas, et al., Graphene electro-optic modulator with 30 GHz bandwidth, Nat. Photonics 9 (8) (2015). [13] S.W. Ye, D. Liang, R.G. Lu, et al., Polarization independent modulator by partly tilted graphene induced electro-absorption effect, Ieee Photonics Technol. Lett. PP (99) (2017) 1. [14] X. Hu, C. Gui, J. Wang, A graphene-based polarization-insensitive optical modulator[C]// integrated photonics research, Silicon Nanophotonics (2014) JT3A.25. [15] D. Dai, H. Wu, Realization of a compact polarization splitter-rotator on silicon, Opt. Lett. 41.10 (2016) 2346. [16] H. Zhong, et al., Realization of low contact resistance close to theoretical limit in graphene transistors, Nano Res. 8 (5) (2015) 1669–1679. [17] D. Dai, J.E. Bowers, Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires, Opt. Express 19.11 (2011) 10940–10949. [18] S.W. Ye, Z.S. Wang, L.F. Tang, Y. Zhang, R.G. Lu, Y. Liu, Electro-absorption optical modulator using dual-graphene-on-graphene configuration, Opt. Express 22 (October(21)) (2014) 26173–26180. [19] F. Bonaccorso, Z. Sun, T. Hasan, A.C. Ferrari, Graphene photonics and optoelectronics, Nature Photon. 4 (September (9)) (2010) 611–622. [20] W.W. Cai, Y.W. Zhu, X.S. Li, R.D. Piner, R.S. Ruoff, Large area few-layer graphene/graphite films as transparent thin conducting electrodes, Appl. Phys. Lett. 95 (September (12)) (2009) 123115. [21] J. Gosciniak, D.T. Tan, Theoretical investigation of graphene-based photonic modulators, Sci. Rep. 3 (7451) (2013) 1897. [22] Q. Bao, K.P. Loh, Graphene photonics, plasmonics, and broadband optoelectronic devices, ACS Nano 6 (2012) 3677–3694.
1098
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
A fabrication-friendly graphene-based polarization insensitive optical modulator
T
⁎
Zhonghua Yang, Rongguo Lu , Yujiao Wang, Songwei Cai, Yujia Zhang, Xiaoju Wang, Yong Liu State Key Laboratory of Electronic Thin Films and Integrated Devices, School of Optoelectronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 China
A R T IC LE I N F O
ABS TRA CT
Keywords: Mode conversion Optical-modulator Polarization-insensitive Graphene
Graphene is a suitable material for high efficient optical modulator. However, graphene-based modulators are of strong polarization dependence. Here a fabrication-friendly structure for graphene-based polarization insensitive electro-absorption modulator (EAM) is reported. The modulator consists of two adiabatic tapers (ATs), two asymmetric directional couplers (ADCs) and an active region. The ATs and ADCs are used to realize mode conversion and mode coupling. The theoretical analysis of the modulator was performed. The device can operate at the spectrum of 1.5 μm–1.6 μm. The extinction ratio (ER) is of > 24dB and the insertion loss is of < 6dB for both modes. The 3dB modulation bandwidth is about 80GHz based on theoretical calculation at the cost of 300μm device length.
1. Introduction In recent years, 2D functional electro-optic materials, such as grapheme [1], dichalcogenides [2] and black phosphorus [3], have been discovered, which promotes the development of Integrated optoelectronic devices and brakes the traditional performance limitation. Among these materials, graphene is considered as an ideal material to realize high efficient optical modulator because of some attractive advantages [4], such as constant absorption over a wide spectrum [5], ultra high carrier mobility under room temperature [6], electrically controllable conductivity and compatibility with CMOS processing. Graphene as electro-optic material, the characteristics of anisotropic dielectric [7,8] needs to be considered. The permittivity in plane is tunable. However, The perpendicular permittivity of graphene is a constant of 1 or 2.5. Therefore, graphene can only strongly interact with the in-plane electric field [9], which is the reason why previously reported graphene-based modulators are strong polarization dependence [9–12]. Generally, the polarization state of light in waveguide or fiber is random. In order to realize the wide commercial application of graphene-based modulator, the problem of polarization dependence needs to be solved. Some graphene-based polarization insensitive modulation (PIM) devices have been reported before, but they are complicated [13,14]. In this letter, we demonstrate a PIM structure that is comprised of two mode conversion structures ATs/ADCs and two symmetric waveguide arms (Fig. 1(a)). There is a cascaded taper structure can support the mode conversion of TM0 mode into TE1 mode at the input port. The cascaded taper consists of three shorter tapers to reduce the total length of the device [15]. Then, a ADC couples TE1 to TE0 from the wide waveguide to the narrow waveguide. In contrast, the TE0 mode that does not have mode conversion passes through the wide straight waveguide. At the end of the ADC the width of wide straight waveguide is tapered to be the same width of
⁎
Corresponding author. E-mail address: [email protected] (R. Lu).
https://doi.org/10.1016/j.ijleo.2019.02.024 Received 11 September 2018; Received in revised form 11 January 2019; Accepted 11 February 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 182 (2019) 1093–1098
Z. Yang, et al.
Fig. 1. Modulator configuration. (a) Three-dimensional schematic representation. (b) Cross-section of the graphene active region. (c) Top-view of the left part of the device.
the narrow waveguide. Since two arms strip1 and strip2 have the same structures, the same overlaps between the graphene layer and the optical mode profile modes are the same (Fig. 1(c)). The both launched TM0 and TE0 modes are greatly tuned by the strip1 and the strip2 respectively. At the output port, TE0 mode in strip1 waveguide can be reverted back to its original TM0 mode by the right AT/ADC. The tilted [13] and vertical [14] graphene sheets are difficult for CMOS technology. Compared with the previous structures, the vertical and tilted graphene sheets are not used in this work. The cross section diagram of the graphene active region is presented in Fig. 1(b). Two Si waveguides with the same widths W4 = 0.4 μm are semi-embedded in the SiO2 substrate to ensure the graphene sheets to be smoothly paved in the waveguide center where light-graphene interaction reaches the highest. Two graphene sheets are separated by a hexagonal boron nitride (hBN) layer with thickness of 40 nm. The electrode structure is Au-Pd-graphene, for the contact resistance between graphene and Pd is less than 100(Ωμm) [16]. The width between electrode and waveguide is about 0.8 μm to avoid the perturbed optical modes [9]. As a result, a PIM device with the total length of ˜300 μm is realized. The extinction ratio (ER) is of > 24 dB and the insertion loss is of < 6 dB for both TE0 and TM0 modes. The operating spectrum is of 1.5 μm to 1.6 μm. The 3 dB modulation bandwidth is about 80 GHz based on theoretical calculation at the cost of 100 μm active region length (Lgra) (Fig. 1(c)).
2. Principle and structure Graphene’s chemical potential μc can be dynamically tuned by the applied drive voltage. In this model, graphene is treated as an anisotropic material. The perpendicular permittivity ε⊥ of graphene does not vary with the μc and it always stays as a constant of 2.5, whereas the in-plane permittivity of the grapheme ε|| can be tuned (Fig. 2(a)). In order to realize graphene-based PIM, the approach of mode conversion is taken, which both TE0 and TM0 modes can be converted to TE0 and tuned almost identically by the drive voltage. To realize the mode conversion, the effective indexes (Neff) of different modes are analyzed with the change of waveguide core width Wco. Here, A strip waveguide with fixed thickness of hco = 0.26 μm is used on a SOI wafer (Fig. 2(b) insert). It can be seen that there is a mode hybridization region around Wco = 0.72 μm, which can achieve a mode conversion when light propagates along an AT whose ports widths Win and Wout are chosen as Win < Wco < Wout [17]. To be compact, the AT is designed to be three segments (Fig. 1(c)) as the following parameters: Win = 0.6 μm, W1 = 0.7 μm, W2 = 0.74 μm, and W3 = 0.8 μm. Fig. 3(a–c) shows the calculated mode conversion efficiency η as the segment length Li (i = 1,2,3) varies when the TM0 and TE0 modes are launched at the left input port (Fig. 3(d)). Firstly, it is clear that TE0 mode does not change at any value of Li (i = 1,2,3), which is important to ensure TE0 to pass through straight waveguide without interference. It can be seen that the η always keeps a high value of more than 92% when L1 or L3 varies from 1 μm to 100 μm. The contribution of L1 and L3 to the η is very small, because
Fig. 2. (a) Calculated permittivity of graphene sheet(real part, imaginary part and magnitude) as a function of chemical potential for λ = 1550 nm. (b) The effective indexes (Neff) of the eigenmodes of an SOI nanowire with an air upper-cladding as a function of waveguide width Wco. 1094
Optik - International Journal for Light and Electron Optics 182 (2019) 1093–1098
Z. Yang, et al.
Fig. 3. Mode conversion efficiency η of the launched TM0 and TE0 modes as a function of L1(a), L2(b) and L3(c) respectively. It is worthy of note that when Li is analysed, other parameters of Lj (j ≠ i) keep long enough (eg.200 μm). The parameters are λ = 1550 nm, hco = 0.26 μm, Win = 0.6 μm, W1 = 0.7 μm, W2 = 0.74 μm, W3 = 0.8 μm. (d) electric and magnetic field distributions of the launched TM0 mode under the condition of L1 = 10 μm, L2 = 50 μm, L3 = 10 μm.
the sizes of W1 and W3 are far from the hybridization region around Wco = 0.72 μm. Therefore, the length of L1 and L3 is chosen as 10 μm. L2 that has a waveguide width around 0.72 μm has a strong effect on η. When the L2 varies from 1 μm to 200 μm, the η can change from 0 to 1. It can be seen that the mode conversion efficiency η is even close to 100% when L2 = 50 μm. Consequently, the segment lengths are chosen as L1 = 10 μm, L2 = 50 μm and L3 = 10 μm. Then, a TM0 mode transmission is simulated by using eigenmode expansion (EME) method and the electric and magnetic field distributions are presented in Fig. 3(d), where the phenomenon of the mode conversion can be clearly observed. Since the TE1 mode in narrow waveguide needs to convert to TE0 mode, an ADC is used. Fig. 4(a) shows the fluctuation of the couple efficiency γ of TE1 mode to TE0 mode, when a TE1 mode is launched at the left input port (Fig. 4(b)). The length of direction coupler Ldc = 7 μm is chosen as an optimal value.
Fig. 4. (a) The illustration of the couple efficiency γ of the TE1 to TM0 as the function of couple length Ldc under the condition of Wgap = 40 nm. (b) The magnetic field distribution under the condition of Ldc = 7 μm. 1095
Optik - International Journal for Light and Electron Optics 182 (2019) 1093–1098
Z. Yang, et al.
Fig. 5. (a) The absorption coefficient the graphene embedded waveguide as a function of chemical potential μc. (b) the different insert losses (left) and graphene coefficient α (right) as a function of wavelength at different μc. (c) The transmissivity T and its difference ΔT as a function wavelength at different μc. (d) The modulation depth of the two modes as a function of wavelength.
3. Modulator performance The insert loss consists of the mode conversion loss (MCL), the couple loss between the narrow waveguide and the wide waveguide (CL1), the couple loss between the passive Si waveguide section and the graphene modulator section (CL2), and graphene absorption loss (GAL), where the GAL should be considered as the insert loss at the "ON" state while it should be considered as the modulation absorption at the "OFF" state. The MCL and the CL are only meaningful for the launched TM0 mode, but they are meaningless for the launched TE0 mode, because there is almost no mode conversion and the mode coupling for the launched TE0 mode. Fig. 5(a) shows the fluctuation of the absorption of the graphene waveguide as a function of chemical potential (μc). It can be seen that the highest and the lowest values can be obtained at μc = 0.1 eV and μc = 0.8 eV respectively. So the points μc = 0.1 eV and μc = 0.8 eV are set as the “OFF” state point and the “ON” state point respectively. Fig. 5(b) shows the fluctuations of all the insert losses as a function of wavelength. The MCL is the total loss of two ATs and the CL1 is the total loss of two ADCs. The couple loss between waveguide and graphene modulator section is also considered twice as CL2. It can be seen that the MCL is wavelength dependent. The MCL is very low around center wavelength, but it has a high value when the wavelength is far from the center wavelength. The value of MCL ranges from 0.004 dB to 1.01 dB. The CL1 is also wavelength dependent and it is twice higher than MCL, because the size of narrow waveguide is not the best one but it's acceptable for the mode coupling. If the coupler structure is further researched, a higher performance coupler can be realized. Since the effective index of the graphene embedded waveguide is chemical potential dependent, the CL2 is also chemical potential dependent. Here, we just consider the CL2 at the states μc = 0.1 eV and μc = 0.8 eV and the fluctuation of the CL2 as a function of wavelength is presented in Fig. 5(b). The CL2 is very low at the level of < 0.4 dB for both states. CL1, CL2 and MCL exist, no matter which state the device is in. However, the GAL should be considered when the modulator is at the “ON” state. The fluctuations of graphene absorption coefficient(α) as a function of wavelength at different states are shown in Fig. 5(b). The α is of > 0.26 dB/μm at 0.1 eV and is of < 0.027 dB/μm at 0.8 eV. The graphene length is Lgra = 100 μm. Then the GAL can be obtained by GAL=α∙Lgra that is of < 2.7 dB at μc = 0.8 eV. Therefore, the insert loss of the launched TM0 mode at the “ON” state is Lon(TM0)=MCL + CL1+CL2on+GALon and the transmissivity Ton(TM0)=eLon(TM0). The insert loss of the launched TE0 mode at the “ON” state is Lon(TE0)=CL2on +GALon and the transmissivity Ton(TE0)=eLon(TE0). For the “OFF” state, the transmissivity is Toff(TM0)=eLoff(TM0) and Toff(TE0)=eLoff(TE0). Fig. 5(c) shows the fluctuations of the transmissivity at the different states as a function of wavelength. The Ton(TM0) is of > e6 dB that means the insert loss of TM0 mode at the “ON” state is Lon(TM0) < 6 dB. The Ton(TE0) is of > e3.1 dB and Lon(TE0) is of < 3.1 dB. The Toff(TE0) is of > e28.8 dB and the Toff(TM0) is of > e31.4 dB. The differences of transmissivity ΔT are also presented in Fig. 5(c). It can be seen that the ΔT is 1096
Optik - International Journal for Light and Electron Optics 182 (2019) 1093–1098
Z. Yang, et al.
wavelength dependent and has the same fluctuations for both states. The ΔT is of > -3 dB. The ER is a very important index for EAM and it can be defined as:
ER = Ton (dB ) − Toff (dB ) For the TM0 state,
ERTM = (MCLon + CL1on + CL2on + GALon ) − (MCLoff + CL1off + CL2off + GALoff ) Since the MCLon= MCLoff, CL1on= CL1off, the ERTE can be simplified as:
ERTM = (CL2on + GALon ) − (CL2off + GALoff ) For the TE0 state, ′ ′ ERTE = (CL2′on + GALon ) − (CL2′on + GALon )
Since the strip1 and strip2 are the same structures, the equations of CL2′ = CL2 , GAL′ = GAL are true for both “ON” and “OFF” states. Then
ERTE = ERTM The difference of ER for both modes is zero and the fluctuation of ER as a function of wavelength is presented in Fig. 5(d). The ER ranges from 24.5 dB to 25.5 dB when the wavelength ranges from 1.5 μm to 1.6 μm. The different performance indexes between two polarization modes are the output power that can be characterized by the normalized output intensity. The normalized output intensity is equal to T and the difference of normalized output intensity is ΔT. The ΔT has been analyzed before (Fig. 5(c)). It can be seen that the fluctuation of ΔT for both states are same, because the ΔT only depends MCL and CL1 that is chemical independent. Consequently, the difference of ER for both polarization modes is zero and a graphene-based PIM device is realized, with a modulation depth of > 24 dB and a insert loss of < 6 dB. For an optical modulator, the 3 dB modulation bandwidth f3dB that is always the one of the most important parameters needs to be considered. Since graphene has ultrahigh carrier mobility at room temperature, a graphene-based modulator’s operation speed is no longer limited by minority carrier lifetime like traditional semiconductor modulators. The f3dB of a graphene-based modulator is mainly impeded by RC delay, which can be expressed as:
f3dB =
1 2πRC
Where R is the device’s total resistance, including graphene sheet resistance Rs and metal-graphene contact resistance Rc, which has been carefully discussed in the previous works [11,18,19], C is the capacitance of modulator, which mainly consists of the capacitor that is formed by the two graphene sheets. Although this capacitor is not an ideal parallel plate capacitor model, the parallel plate capacitor model is still used to calculate the C, to preliminarily estimate the f3dB. In our calculations, Rc = 100Ωμm [16] and Rs = 200Ω/□ [20] are used, and the distance between electrode and active region is about 0.8 μm. The estimated f3dB is about 80 GHz. In the structure, the length of graphene sheets is so long between two electrodes that the graphene sheet resistance is pretty high. For a further study, another electrode can be added between two waveguide arms to reduce the graphene sheet resistance then a higher f3dB bandwidth can be obtained. Moreover, lower values of both Rs and Rc are possible in the future, which means higher f3dB can be obtained. 4. Conclusions In conclusion, we propose a structure of a broadband polarization insensitive graphene-based electro-absorption optical modulator. In the structure, two ATs and two ADCs were used to realize polarization insensitive modulator. The device performance parameters insert loss, modulation depth, operating spectrum width, 3 dB bandwidth and polarization sensitivity were studied. The results show that both TE0 and TM0 modes have almost high modulation depth of > 24 dB at the cost of 300 μm device length. The operating wavelength ranges from 1.5 μm to 1.6 μm. The insert loss for both modes are less than 6 dB. The theoretical modulation bandwidth of the device is about 80 GHz. It is worthy of note that the structure parameters of the mode converter and mode coupler are not optimal. If the parameters of the structure are properly chosen, the values of MCL and CL1 will close to zero. Then the insert losses are only determined by GAL and CL2 that are less than 2.7 dB and 0.4 dB. What’s more, the ΔT will also close to zero and the graphene based PIM device will be more polarization insensitive. So the device fulfills the requirement of polarization independent modulation. We believe that the device structure will simplify the fabrication steps and promote the commercialization of the graphene-based electro-optic modulator and this structure can also be used to study other 2D materials based PIM modulator. 5. Method The proposed modulator geometry was investigated using two dimensional finite element method (FEM) simulations using software COMSOL. The ATs and ADCs were investigated using three dimensional eigenmode expansion (EME) method simulations using software Lumerical FDTD. In the calculations, the refractive indexes of the Si ribs, the SiO2 substrate and the hBN spacer are n1 = 3.485, n2 = 1.444 and n3 = 1.98 respectively. 1097
Optik - International Journal for Light and Electron Optics 182 (2019) 1093–1098
Z. Yang, et al.
To evaluate the mode effective index and mode power attenuation of the considered structure the gate- dependent complex dielectric constant of graphene has to be calculated. The complex dielectric function ε|| (ω) can be obtained from the complex optical conductivity of graphene, consisting of interband and intraband contributions [21], ′ ′′ σtotal = σintra + σinter + iσinter
σintra = σ0
4μ π ℏ(τ1 − iω)
ℏω − 2μ ℏω + 2μ ⎞ 1 1 ′ σinter = σ0 ⎛1 + arctan − arctan π ℏτ2 π ℏτ2 ⎠ ⎝ ⎜
′′ σinter = σ0
⎟
1 (2μ + ℏω)2 + ℏ2τ22 ln 2π (2μ − ℏω)2 + ℏ2τ22
Where σ0 = e 2/4 ℏ= 60.8μS is the universal optical conductance, by using
ε∥ (ω) = 2.5 +
iσ (ω) ωε0 hg
where, hg = 0.7 nm is a thickness of the grapheme layer. As the complex conductivity σ(ω, μ, Γ, T) depends on the angular frequency ω, the charge particle scattering rate Γ = 1/τ with τ being the relaxation time, the chemical potential μ and temperature T [22], the dielectric constant of the graphene layer was calculated as a function of chemical potential for λ = 1550 nm, T = 296 K (room temperature) and τ1 = 1.2 ps for interband conductivity and τ2 = 10fs for intraband conductivity. Acknowledgements This work was funded by National Nature Science Foundation of China (No. 61435010, 61307070, 61421002, 61704021) and the Fundamental Research Funds for the Central Universities (ZYGX2016J070). References [1] A.C. Ferrari, F. Bonaccorso, V. Fal’Ko, et al., Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, Nanoscale 7 (11) (2015) 4598–4810. [2] W. Choi, N. Choudhary, G.H. Han, et al., Recent development of two-dimensional transition metal dichalcogenides and their applications, Mater. Today (3) (2017) 20. [3] X. Ling, H. Wang, S. Huang, et al., The renaissance of black phosphorus, Proc. Natl. Acad. Sci. U. S. A. 112 (15) (2015) 4523. [4] S. Yu, X. Wu, Y. Wang, et al., 2D materials for optical modulation: challenges and opportunities, Adv. Mater. 29 (14) (2017) 201606128. [5] R.R. Nair, P. Blake, A.N. Grigorenko, et al., Fine structure constant defines visual transparency of graphene, Science 320 (5881) (2008) 1308. [6] K.I. Bolotin, K.J. Sikes, Z. Jiang, et al., Ultrahigh electron mobility in suspended graphene, Solid State Commun. 146 (9) (2008) 351–355. [7] R. Hao, W. Du, E.P. Li, et al., Graphene assisted TE/TM-independent polarizer based on mach–zehnder interferometer, Ieee Photonics Technol. Lett. 27 (10) (2015) 1112–1115. [8] Z. Chang, K.S. Chiang, Experimental verification of optical models of graphene with multimode slab waveguides, Opt. Lett. 41 (9) (2016) 2129–2132. [9] M. Liu, X. Yin, E. Ulinavila, et al., A graphene-based broadband optical modulator, Nature 474 (7349) (2011) 64–67. [10] M. Liu, X. Yin, X. Zhang, Double-layer graphene optical modulator, Nano Lett. 12 (3) (2012) 1482–1485. [11] S.J. Koester, M. Li, High-speed waveguide-coupled graphene-on-graphene optical modulators, Appl. Phys. Lett. 100 (17) (2012) 611. [12] C.T. Phare, Y.H.D. Lee, J. Cardenas, et al., Graphene electro-optic modulator with 30 GHz bandwidth, Nat. Photonics 9 (8) (2015). [13] S.W. Ye, D. Liang, R.G. Lu, et al., Polarization independent modulator by partly tilted graphene induced electro-absorption effect, Ieee Photonics Technol. Lett. PP (99) (2017) 1. [14] X. Hu, C. Gui, J. Wang, A graphene-based polarization-insensitive optical modulator[C]// integrated photonics research, Silicon Nanophotonics (2014) JT3A.25. [15] D. Dai, H. Wu, Realization of a compact polarization splitter-rotator on silicon, Opt. Lett. 41.10 (2016) 2346. [16] H. Zhong, et al., Realization of low contact resistance close to theoretical limit in graphene transistors, Nano Res. 8 (5) (2015) 1669–1679. [17] D. Dai, J.E. Bowers, Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires, Opt. Express 19.11 (2011) 10940–10949. [18] S.W. Ye, Z.S. Wang, L.F. Tang, Y. Zhang, R.G. Lu, Y. Liu, Electro-absorption optical modulator using dual-graphene-on-graphene configuration, Opt. Express 22 (October(21)) (2014) 26173–26180. [19] F. Bonaccorso, Z. Sun, T. Hasan, A.C. Ferrari, Graphene photonics and optoelectronics, Nature Photon. 4 (September (9)) (2010) 611–622. [20] W.W. Cai, Y.W. Zhu, X.S. Li, R.D. Piner, R.S. Ruoff, Large area few-layer graphene/graphite films as transparent thin conducting electrodes, Appl. Phys. Lett. 95 (September (12)) (2009) 123115. [21] J. Gosciniak, D.T. Tan, Theoretical investigation of graphene-based photonic modulators, Sci. Rep. 3 (7451) (2013) 1897. [22] Q. Bao, K.P. Loh, Graphene photonics, plasmonics, and broadband optoelectronic devices, ACS Nano 6 (2012) 3677–3694.
1098