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Abstract
The mode-division multiplexing (MDM) is an effective technology with huge development potential to improve the transmission capacity of optical communication system by transmitting multiple modes simultaneously in a few-mode fiber. In traditional MDM technology, the fundamental modes of multiple channels are usually modulated by external individual arranged electro-optic modulators, and then multiplexed into the few-mode fiber or waveguide by a mode multiplexer. However, this is usually limited by large device footprint and high power consumption. Here, we report a mode-selective modulator and switch to individually modulate or switch the TE11, TE12 and TE21 modes in a few-mode waveguide (FMW) to overcome this limitation. Our method is based on the graphene-polymer hybrid platform with four graphene capacitors buried in different locations of the polymer FMW by utilizing the coplanar interaction between the capacitors and spatial modes. The TE11, TE12 and TE21 modes in the FMW can be modulated and switched separately or simultaneously by applying independent gate voltage to different graphene capacitor of the device. Our study is expected to make the selective management of the spatial modes in MDM transmission systems more flexible.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The rapid growth of Internet traffic is leading to the capacity of the single-mode fiber is gradually approaching its nonlinear Shannon limit [1,2]. To further enhance the capacity of data transmission, different multiplexing techniques have been employed, such as polarization division multiplexing (PDM), wavelength division multiplexing (WDM), and mode division multiplexing (MDM) [3–5]. Among them, MDM technology has attracted increasing attention since it can expand the capacity in a single wavelength channel by employing high-order modes, which is helpful to reduce the power consumption compared with other multiplexing methods [6,7]. In a typical MDM system, the fundamental modes generated by the signal sources are usually loaded into different channels by external individual arranged electro-optic (EO) modulators and then converted to high-order modes through mode converters and multiplexed into the few-mode fiber or waveguide [8]. In the transmission link, in order to load information into different spatial modes, these modes still need to be converted into fundamental modes, which are then modulated by the individual arranged EO modulators and then multiplexed into the few-mode fiber [9]. As the key element, many kinds of mode (de) multiplexer have been proposed and developed [10–13]. However, this scheme is complicated and suffers from some limitations, including high insertion loss, large device footprint, and high cost [14]. In this paper, we report a mode-selective modulator and switch based on the polymer-graphene hybrid platform to individually modulate or switch the spatial modes in a few-mode waveguide (FMW).
Graphene-on-waveguide photonics have shown great potential for photonic integrated circuits applications and attracted extensive attention in recent years, such as mode-locked lasers [15], optical modulators [16], optical polarizers [17], photodetectors [18], and mode-selective devices [19–21], etc. Especially, due to the excellent optical and electrical properties, graphene has been proved to be an ideal material for realizing novel optical modulators with high performances [22,23]. On the other hand, polymer waveguides have the advantages of various materials, simple and flexible fabricating technology with low processing temperature, which is helpful to bury the graphene layer anywhere inside the waveguide. This platform has been explored for achieving mode filters [24,25], thermo-optical switches [26,27], and all-optical switches [28]. Moreover, in our previous work, we also explored the application the graphene-polymer hybrid waveguides for the optical switch and modulators [27,29,30].
In this paper, we explored a method to realize the mode-selective modulator and switch, which is based on the graphene-polymer hybrid platform with four graphene capacitors buried in different locations of a polymer FMW by utilizing the coplanar interaction between the capacitors and spatial modes. By optimizing the width and buried location of each graphene capacitor, the TE11, TE12 and TE21 modes in the polymer FMW can interact with the corresponding graphene capacitor, respectively, and then be modulated or switched separately or simultaneously by applying independent gate voltage to different graphene capacitor of the device. Compared with the current MDM system with a number of external individual arranged modulators, the designed device can be directly coupled with few-mode fibers or waveguides without additional components that can reduce the insertion loss, device footprint and cost, and make the selective management of the spatial modes in MDM transmission systems more flexible.
2. Principle and design of the device
Figure 1(a) shows the schematic of designed mode-selective modulator and switch based on graphene-polymer hybrid waveguides, which consists of a polymer FMW and four graphene capacitors buried inside different locations of the polymer waveguide. The polymer FMW is a conventional strip waveguide with sandwich structure formed on the silicon substrate, and designed to support TE11, TE12 and TE21 modes simultaneously. The polymer SU-8 2002 and EpoClad were employed as the core and cladding material, respectively. In the FMW, the electric field of different spatial modes has different distribution, therefore, can be selectively controlled by designing and optimizing the located position and width of the each graphene capacitor. Figures 1(b-d) show the cross-sectional views of the four graphene capacitors at each position. Each graphene capacitor consists of two monolayer graphene layers insulated by a 20-nm-thick Al2O3 layer. The thickness of the monolayer graphene is 0.35 nm. The Au electrodes are deposited on the extend graphene strips as the contacts to apply gate voltages. The graphene capacitor buried in the center of core is used to modulate the TE11 mode. The graphene capacitor on upper side of the core and buried inside the upper cladding is used to modulate the TE12 mode. The graphene capacitors on both sides of the core and buried inside the side cladding are used to modulate the TE21 mode. These four graphene capacitors buried in different positions of the FMW can be used to separately or simultaneously modulate and switch the TE11, TE12 and TE21 modes by flexibly applying gate voltage on the contact. The refractive indices of the used silicon, SU-8 2002, EpoClad and Al2O3 are 3.450, 1.572, 1.559, and 1.732, respectively, under 1550 nm wavelength.
Fig. 1. Illustration of the mode-selective modulator and switch configuration. (a) 3D view of the device. The cross-sectional views of the four graphene capacitors at each position of (b) graphene capacitor 1, (c) graphene capacitor 2 and (d) graphene capacitor 3 and 4.
In order to enable the designed waveguide support TE11, TE12 and TE21 modes, the dimension of the strip waveguide is firstly optimized before developing the device. Figure 2(a) shows the effective index of the waveguide without graphene capacitors versus the width of the waveguide core (wcore). In order to avoid the degenerate modes in the few mode waveguide, the height of waveguide core (hcore) is designed to be 0.5 µm larger than the core width. The dispersion curves of the TE11, TE12, TE21 and TE22 modes of the few mode waveguide were calculated at 1550 nm wavelength, as shown in Fig. 2(a). For our designed device that supports TE11, TE12 and TE21 modes, the wcore should be chosen in the range of 5.0∼7.0 µm. Specifically, considering the coupling loss between the waveguide and optical fiber and the mode-selective modulating function, the wcore and hcore were selected with 6.0 µm and 6.5 µm, respectively. Figure 2(b) shows the optical field distribution of TE11, TE12 and TE21 modes simulated by the finite element method. Therefore, the graphene capacitor at each position can interact and overlap with the specific optical mode. In order to realize mode-selective modulation or switching, i.e. one of the modes is modulated and others are not affected, it is necessary to further optimize the located position and width of each graphene capacitor. Figures 2(c) and 2(d) show the normalized electric field intensity of the TE11, TE12 and TE21 modes. From the electric intensity of TE11 mode in the horizontal and vertical direction, the strong interaction between graphene capacitor 1 and TE11 mode can be obtained when the graphene capacitor 1 is buried in the center of core. Meanwhile, to avoid the influence of graphene capacitor 1 on the other two modes, the width of capacitor 1 (w1) is designed to be 1.0 µm, which can be understood from the optical field distribution and the normalized electric field intensity of the three modes shown in Figs. 2(b-d). The graphene capacitor 1 has almost no interaction with TE12 and TE21 modes. Figure 2(c) shows the normalized electric field intensity of capacitor 1 and capacitor 2 in the vertical direction. The graphene capacitor 2 should be buried above the waveguide core to modulate the TE12 mode and avoid the influence of capacitor 2 on TE11 mode. As shown in Fig. 2(d), the normalized electric field intensity of TE21 mode reaches the maximum value on both sides of the waveguide core, so the graphene capacitor 3 and 4 should be buried on the left and right sides of the core, respectively, to modulate the TE21 mode. Moreover, the capacitor 3 and 4 should be buried in the center next the core with little overlap with TE12 mode to avoid the influence of them on TE11 mode.
Fig. 2. (a) The effective index of the waveguide without graphene capacitors versus the width of the waveguide core (wcore). (b) Optical field distribution of TE11, TE12 and TE21 modes. (c) Normalized electric field intensity of the TE11 and TE12 modes. (d) Normalized electric field intensity of the TE11 and TE21 modes.
Based on the above analysis, we further optimize the located positions and widths of other three graphene capacitors to realize the mode-selective modulation or switching. Figure 3 shows the optimization results of graphene capacitor 2 and 3, and 4. In the simulation, there is no graphene capacitor at other positions when one graphene capacitor at certain position is modulated separately. For the TE11, TE12 and TE21 modes, we calculated the imaginary part of effective mode index (Im(Neff)) of each mode, and then obtained the mode power attenuation (MPA) as a function of the graphene capacitor 2 width (w2) with different distance from the surface of core to the graphene capacitor 2 (d2), as shown in Figs. 3(a-c). The MPA increases with the increase of w2 for three modes with different d2. This means that wider w2 can enhance the interaction between graphene capacitor 2 and TE12 mode, while the influence on other modes also increases simultaneously. However, when the distance d2 increases from 0 µm to 2.5 µm, the MPA shows the opposite trend and gradually decreases for the three modes, which is mainly due to the gradual decrease of the overlap between the graphene capacitor 2 and the electric field of the three modes. Therefore, we choose w2 and d2 as 4.0 µm and 2.0 µm, respectively, to selectively modulate the TE12 mode. Based on the same considerations, we further calculated the MPA as a function of the graphene capacitor 3 width (w3) with different distance from the side surface of core to the graphene capacitor 3 (d3), as shown in Figs. 3(d-f). These simulated results can be also applied to the optimization of graphene capacitor 4, because the graphene capacitor 4 has the same size and located position with that of graphene capacitor 3. The MPA changes of graphene capacitor 3 and 4 for the three modes have the similar trend with that of graphene capacitor 2. Therefore, in order to selectively modulate the TE21 mode without affecting other modes (TE11 and TE12), we choose w3 (w4) and d3 (d4) as 3.0 µm and 2.0 µm, respectively.
Fig. 3. Optimization results of graphene capacitor 2, and 3 and 4. (a-c) The MPA as a function of the graphene capacitor 2 width with different distance from the surface of core to the graphene capacitor 2. (d-e) The MPA as a function of the graphene capacitor 3 and 4 width with different distance from the side surface of core to the graphene capacitor 3 and 4.
We also designed the fabrication process for our proposed device, as shown in Fig. 4. Firstly, an EpoClad film was spin-coated onto the silicon substrate and fully cured to form the under-cladding, and the half of core layer SU-8 2002 was fabricated on the under-cladding via spin-coating, lithography and wet-etching processes. The EpoClad was then spin-coated onto the sample to cover the core, and the upper-cladding layer on top of the core layer was etched away by using the inductively coupled plasma (ICP) method to expose the core surface. Secondly, the monolayer graphene film was transferred to the surface of waveguide core via the wet-transfer technique [31]. Then, a 20-nm thick Al2O3 film was deposited onto the bottom graphene layer by using the atomic layer deposition (ALD) method [32]. The top graphene film was then wet-transferred onto the Al2O3 layer to form the desired capacitor structure. Next, the graphene capacitors 1, 3 and 4 can be patterned by using the lithography and ICP etching processes at the same time. Thirdly, the other half of waveguide core and upper-cladding were fabricated via spin-coating, lithography and wet-etching processes. The graphene capacitor 2 in the upper-cladding was fabricated by using the same processes as above. Then, the final upper-cladding was fabricated by using the spin-coating, lithography and wet-etching processes. The connection between the graphene nanoribbons and electrodes was also fabricated in these processes. Finally, the contact electrodes can be fabricated by using the lithography, electron beam evaporation and lift-off processes. The last two steps show the contact electrode structure of graphene capacitors at different positions.
3. Performance analysis and discussion
After optimizing the parameters of the device, we further characterized the performance of the proposed device. First, we characterized the electro-absorption properties of the device. The MPA of the waveguide plays an important role in analyzing the working states of the device, which can be calculated from the Im(Neff) determined by the chemical potential of graphene. Figure 5 shows the MPA of three modes as a function of chemical potential when each graphene capacitor is modulated separately. In the simulation process, when one of the graphene capacitor at specific position is selectively modulated, the chemical potential of graphene in other capacitors is always maintained at 0.6 eV. Figure 5(a) shows the MPA of three modes versus the chemical potential of graphene in capacitor 1. It can be seen that the MPA of TE11 mode decreased sharply when the chemical potential of graphene µ > 0.3 eV and then keeps at a low level, which indicates that the waveguide absorbs a large amount of optical signal when µ = 0.3 eV and then, when µ = 0.6 eV, the optical signal can pass through waveguide with very low loss. Therefore, the chemical potential of graphene µ = 0.3 eV and 0.6 eV can be defined as “OFF” state and “ON” state, respectively. Under “OFF” state, the maximum MPA of TE11 mode reaches to ∼59 dB/cm and the MPA of other modes remains stable throughout. This means that graphene capacitor 1 can be selectively modulated with less influence on other modes. Similarly, Figs. 5(b) and 5(c) show the selectively modulated results when regulating graphene capacitor 2 and graphene capacitor 3 and 4, respectively. Under “OFF” state, the maximum MPA of TE12 and TE21 modes is ∼23 dB/cm and ∼24 dB/cm, respectively. The chemical potential of graphene can be adjusted by the applied gate voltage, as shown in Fig. 5(d). With the device switched from OFF-state to ON-state, the required applied voltage ΔU is about 0.79 V. The insertion loss of the device mainly comes from the MPA induced by graphene and the coupling loss between the waveguide and few-mode fiber. Under “OFF” state, the insertion losses induced by graphene are higher than ∼23 dB/cm, while under “ON” state, the insertion losses induced by graphene are lower than ∼2.5 dB/cm. The calculated coupling losses for TE11, TE12 and TE21 modes are about 1.4 dB, 1.9 dB and 2.0 dB, respectively.
Fig. 5. The MPA of three modes as a function of chemical potential when (a) graphene capacitor 1, (b) graphene capacitor 2, and (c) graphene capacitor 3 and 4 is modulated separately. (d) The applied gate voltage as function of the chemical potential of graphene.
Figure 6(a) shows the extinction ratios of the device as a function of the graphene capacitor length (L) for TE11, TE12, and TE21 modes, respectively. The extinction ratio for the modulated mode can reach 23 dB, when the length of each graphene capacitor is selected as 0.4 cm, 1.0 cm, 1.0 cm and 1.0 cm, respectively. Finally, we simulated the varied wavelength influence on MPA of TE11, TE12, and TE21 modes by sweeping the wavelength from 1525 nm to 1565 nm when µ=0.3 eV, as shown in Fig. 6(b). It can be seen that the MPA of three modes are higher than ∼20 dB/cm and relatively stable level within the C-band, which illustrates that the proposed device can work stably in a broad band.
Fig. 6. (a) The extinction ratios of the device as function of the length of graphene capacitor for TE11, TE12, and TE21 modes. (b) The varied wavelength influence on MPA of TE11, TE12, and TE21 modes.
We also investigated the dynamic response of the presented device by using an equivalent electrical circuit model [16,29]. The 3-dB modulation bandwidth can be defined and expressed as f3-dB = 1/2πRC, where R and C is the total series resistance and the capacitance of the device, respectively. The R includes the sheet resistance of graphene Rs and metal-graphene contact resistance Rc, which has been carefully discussed in our previous work [29,30]. In the calculation, Rs = 100 Ω/□ is the sheet resistance, Rc = 100 Ω-µm is the contact resistance. The C = ɛrɛ0S/d is the parallel-plate capacitor formed by the structure of graphene capacitor and can be estimated from a simple parallel capacitor mode, where d represents the thickness of the Al2O3, ɛr is dielectric constant of Al2O3, S = Wg × L stands for the overlap area of two graphene layers. Based on the above analysis, the calculated 3-dB bandwidth of graphene capacitor 1, 2 and 3(4) are 31.5 GHz, 2.8 GHz and 4 GHz, and the power consumption (Ebit = C(ΔU)2/4) for modulating TE11, TE12 and TE21 modes are about 12.6 pJ/bit. 126.0 pJ/bit and 94.5 pJ/bit, respectively. This device can also be used as a mode-selective switch with the corresponding switching time of 31 ps, 357 ps and 250 ps for TE11, TE12 and TE21 modes, respectively.
Fig. 7. The Re(Neff) of three modes as a function of chemical potential when (a) graphene capacitor 1, (b) graphene capacitor 2, and (c) graphene capacitor 3 and 4 is modulated separately.
Fig. 8. The quasi-linear phase changes of (a) TE11 mode, (b) TE12 mode, and (c) TE21 mode versus the chemical potential under different modulation lengths.
The proposed device can be also used as an electro-refraction optical modulator. Since the phase of the optical mode is determined by the real part of effective mode index of the hybrid waveguide (Re(Neff)), the electro-refraction phase modulation can be achieved by reasonably tuning the chemical potential of graphene. The phase changes as a function of the Re(Neff) variation can be evaluated and expressed as Δϕ=2πΔRe(Neff)L/λ, where λ is the operating wavelength, L is the modulation length (i.e. the effective length of the graphene capacitor). In order to analyze the phase variation of each mode, we calculate the Re(Neff) of three modes of the proposed device with the change of the chemical potential of graphene, as shown in Fig. 7. Figure 7(a) shows the Re(Neff) of three mode versus the chemical potential of graphene in capacitor 1. It can be seen that the Re(Neff) of TE11 mode decreases quasi-linearly with the increment of µ increases from 0.46 to 1.0 eV, and the maximum variation of Re(Neff) for TE11 mode is 0.000235. While the Re(Neff) of other two modes remains stable throughout. Similarly, Figs. 7(b) and 7(c) show the selectively modulated results when regulating graphene capacitor 2 and graphene capacitor 3 and 4, respectively. The maximum Re(Neff) variation of TE12 and TE21 modes are 0.000085 and 0.000083, respectively, when µ changes from 0.46 to 1.0 eV. Moreover, the MPA of each modes stays at a low level when µ increases from 0.46 to 1.0 eV, as shown in Figs. 5(a-c). Hence, the electro-refraction phase modulation can be designed with this characteristic. In the simulation, the phase shift at µ = 0.46 eV is assumed be zero. The phase change varies with chemical potential of graphene under different modulation lengths is shown in the Fig. 8. As shown in Fig. 8(a), the phase shift of TE11 mode can be quasi-linearly tuned from 0 to π with the modulation length of L = 3.3 mm when the µ changes from 0.46 to 1.0 eV. Similarly, as shown in Figs. 8(a) and 8(c), the modulation length required to reach the π-phase shift for TE12 and TE21 modes are 9.1 mm and 9.3 mm, respectively.
4. Conclusion
In conclusion, we have theoretically designed and demonstrated a mode-selective modulator and switch to individually modulate or switch the TE11, TE12 and TE21 mode, which is based on the graphene-polymer hybrid platform with four graphene capacitors buried in different locations of the polymer FMW by utilizing the coplanar interaction between the capacitors and spatial modes. By regulating chemical potential of graphene capacitor located in different position, the TE11, TE12 and TE21 modes can be individually and simultaneously modulated in the single modulator. With the applied voltage of 0.79 V, the extinction ratio of the device for the modulated mode can reach 23 dB, when the length of each graphene capacitor is selected as 0.4 cm, 1.0 cm, 1.0 cm and 1.0 cm, respectively. The calculated 3-dB bandwidth of graphene capacitor 1, 2 and 3(4) are 31.5 GHz, 2.8 GHz and 4.0 GHz, and the corresponding power consumption for modulating TE11, TE12 and TE21 modes are about 12.6 pJ/bit. 126.0 pJ/bit and 94.5 pJ/bit. The presented device can be also used as an electro-refraction optical modulator. Compared with the current MDM system, the designed device could reduce optical insertion losses induced by fan-in and fan-out devices. Moreover, the system footprint and costs could also be scaled down by decrease the number of external individual arranged modulators and freed from mode (de)multiplexers. The proposed device with the function of selective modulation could be also used as the mode-selective variable optical attenuator for the minimization of differential-mode gain [33], which has important applications in the MDM systems.
Funding
National Key Research and Development Program of China (2019YFB2203002); National Natural Science Foundation of China (61875069); Fundamental Research Funds for the Central Universities.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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