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Abstract
We propose a hybrid plasmon polariton (HPP) Mach-Zehnder modulator (MZM) structure that combines the tight optical confinement of plasmonic waveguides and narrow slot waveguides with the low loss feature of photonic waveguides. Compared with conventional surface plasmon polariton (SPP) modulators, the HPP modulator exhibits lower propagation loss and better overall performance. Simulations based on the finite difference time-domain (FDTD) and finite element method (FEM) predict a half-wave voltage-length product of 0.078 V·mm for the HPP modulator. Meanwhile, the propagation loss is only 0.2 dB/μm, which is less than half of that for an SPP modulator. The modulation bandwidth of a 10-μm-long HHP modulator exceeds 650 GHz, while the total insertion loss of the device is estimated to be lower than 4 dB.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Mach-Zehnder modulators (MZMs) are of great importance in high-speed fiber communication systems, especially in high spectral efficiency networks utilizing advanced modulation formats [1]. Commonly used materials for electro-optical modulators include lithium niobate, III-V compound semiconductors, and organic materials with high nonlinear electro-optic (EO) coefficients. MZMs based on lithium niobate utilizing Pockels effect require footprints on the order of cm2 [2,3]. For III-V compound semiconductors, the available effects include the Pockels effect, Kerr effect, and quantum-confined Stark effect (QCSE) in multiple-quantum-wells (MQWs). The 3-dB modulation bandwidth of advanced InP based MZMs with an modulation length of 4 mm can exceed 60 GHz [4,5]. Due to the long modulation length, MZMs based on lithium niobate and III-V compound semiconductors usually require traveling-wave electrodes, and special schemes have to be adopted to realize velocity and impedance matching. Furthermore, the large footprint of such devices poses difficulty for improving the integration density. In order to simplify the electrode structure and increase the integration density, surface plasmon polariton (SPP) modulators incorporating materials with high EO coefficients are proposed. SPPs based on metal-insulator-metal (MIM) structure can be confined below the diffraction limit at the metal-dielectric interface [6], resulting in an effective mode area of just a few μm2. To further enhance the light-matter interaction, high EO coefficient materials can be combined with the MIM structure to implement optical modulation within a length of tens of microns. Both nonlinear organic materials, such as DLD164 (r33 = 180 pm/V) [7] or HD-BB-OH/YLD124 (r33 = 325 pm/V) [8], and inorganic materials with high EO coefficients, such as barium titanate (BTO) (r33 = 342 pm/V and r42 = 923 pm/V) [9], can be employed for this purpose. For example, SPP modulator based on DLD164 filled MIM structure has demonstrated a half-wave voltage-length product of 0.06 V·mm, together with a propagation loss of 0.4 dB/μm [10], while the SPP modulator based on HD-BB-OH/YLD124 exhibits a half-wave voltage-length product of 0.075 V·mm and a propagation loss of 0.5 dB/μm [11]. On the other hand, plasmonic structures based on BTO have also been demonstrated, with a propagation loss about 1.4 dB/μm [9].
Though SPP modulators exhibit enhanced modulation efficiency and reduced footprints, they suffer from pronounced propagation loss, which mainly originates from the ohmic loss of metals [12]. Two solutions have been proposed to improve the overall performance of SPP modulators. First, the device can be operated in the vicinity of the absorption resonances of the electro-optical material to enhance the modulation efficiency [13]. The enhanced EO coefficient around the material resonances helps reduce the device length, thus alleviating the influence of the absorption loss. However, this method results in severe constraint on the operating wavelength, making it difficult to achieve broadband operation. Secondly, plasmonic electro-optic ring modulators have been proposed to bypass the ohmic loss via “resonant switching” [14]. In addition to limited operation wavelength, such modulators cannot be adopted for advanced modulation formats.
In this work, we propose a novel hybrid plasmon polariton (HPP) Mach-Zehnder modulator (MZM) structure, which combines tight optical confinement of plasmonic waveguides and narrow slot waveguides with the low loss feature of photonic waveguides. As the HPP MZM does not rely on the absorption resonance of the EO material or resonant switching, broadband operation can be secured and advanced modulation formats can be implemented. Finite difference time-domain (FDTD) and finite element method (FEM) are used to evaluate the performance of the device. Simulation results reveal that a 10-μm-long HPP modulator exhibits a half-wave voltage of 7.8 Vpp and a bandwidth over 650 GHz. In addition, the propagation loss is only 0.2 dB/μm, which is more than half reduced compared with conventional SPP modulators. The total insertion loss of the device is less than 4 dB.
2. Design of the HPP modulator
The 3D schematic view as well as the cross-sectional and top view of the proposed HPP modulator are illustrated in Fig. 1. The MZM consists of two parallel HPP phase modulators separated by gold electrode. Two Y branches are used to split and combine the light entering and exiting the device, respectively. Each HPP phase modulator contains a silicon slot waveguide within two gold electrodes, and both the central and the side slots are filled with EO material. The EO coefficient is assumed to be r33 = 180 pm/V and does not vary with the slot width. The other properties of the EO material are the same as DLD164. At the wavelength of 1.55 μm, the real and imaginary parts of refractive index are 1.827 and 0.002, respectively. The dielectric constant for microwave signals at 40 GHz is 4.3964.
2.1 HPP waveguide
Though an SPP waveguide can provide tight optical confinement, the optical field is in direct contact with the metal electrodes, resulting in a high ohmic loss. Hybrid plasmonic-photonic-organic (PSOH) modulator has been proposed to reduce the ohmic loss by confining the optical field in the slots between the silicon waveguides and the metal electrodes [15]. However, the PSOH waveguide exhibits reduced optical confinement, as a considerable portion of the optical field resides in the wide silicon waveguides. Different from the above two waveguide structures, the proposed HPP waveguide contains a slot waveguide formed by two doped silicon cores. Thanks to the field-enhancement effect of the slot waveguide [16–18], the HPP waveguide sustains a high-power density in the central slot region, as shown in Fig. 2(a). Since the optical field is mainly confined in the central slot, the optical field in contact with the metal electrodes is significantly reduced. Thus the HHP waveguide is expected to exhibit a low ohmic loss. By introducing the n-doped silicon cores into the SPP waveguide to form a slot waveguide, not only is the optical field well confined, the RF field of the modulation signal is also confined within the slots and there is almost no voltage drop across the doped silicon cores, as shown in Fig. 2(b). This greatly enhances the modulation efficiency.
The modulation efficiency of the HHP modulator can be measured by the half-wave voltage-length product VπL, which is given by the following equation:
The doping of the silicon cores has a significant impact on the performance of the modulator. If intrinsic silicon cores are employed, a large portion of the modulation voltage will fall over the silicon cores, thus reducing the electric field loading efficiency of the EO material and leading to an increased half-wave voltage-length product. On the other hand, the voltage falling on the silicon cores is significantly reduced if doped silicon is used. As shown in Fig. 3, for n-type silicon cores with a doping of ND = 1019 cm-3, the value of the Vtotal/VEOM is close to 1, indicating that the doped silicon cores have negligible effect on the half-wave voltage-length product of the HPP modulator. The optical loss due to free carrier absorption in the doped silicon cores can be estimated by [20]:
Fig. 3. Vtotal/VEOM of the HPP modulator with the intrinsic silicon cores (blue line) and doped silicon cores (red line) (n-type doping of ND = 1019 cm-3).
The silicon core height hSi is chosen to be 400 nm to ensure excellent optical confinement in the HPP waveguide. The performance of the HPP modulator is mainly affected by three waveguide parameters: the central slot width Wc, side slots width Ws and silicon cores width WSi. The SPP modulator reported in Ref. [10] has a 90-nm-wide EO material filled slot. For comparison, the total width of the EO material filled slots in the HPP modulator is fixed to 90 nm, i.e. Wc + 2Ws = 90 nm. By optimizing the waveguide parameters, the HPP waveguide can exhibit excellent optical confinement while maintaining a much lower propagation loss than the all plasmonic counterparts, thereby obtaining the best overall performance.
First, we investigate the influence of Wc on the HPP modulator performance. Figure 4(a) shows the variation of nslow and Γ with Wc for a fixed WSi of 120 nm. As Wc increases, nslow first decreases and then increases, while Γ shows an opposite variation. The variation of α and VπL with Wc is plotted in Fig. 4(b). The propagation loss α increases monotonously with Wc, while VπL, which characterizes the modulation efficiency, assumes a minimum for Wc = 40 nm. As Wc increases, optical confinement of the silicon slot waveguide weakens, and more light resides in the side slots and comes in direct contact with the metal electrodes, thus increasing the propagation loss. The loss-half-wave voltage-length product αVπL given in Fig. 4(c) varies monotonously with Wc. Comparing Figs. 4(b) and 4(c), it is concluded that the overall performance of the HPP modulator, as characterized by αVπL, is mainly determined by the propagation loss α. Out of consideration for fabrication feasibility, Wc = 10 nm and Ws = 40 nm are adopted to ensure the best performance.
Fig. 4. (a) nslow (blue line) and Γ (red line), (b) α (blue line) and VπL (red line) and (c) αVπL of the HPP modulator when Wc varies from 10 nm to 70 nm. (d) nslow (blue line) and Γ (red line), (e) α (blue line) and VπL (red line) and (f) αVπL of the HPP modulator when WSi varies from 80 nm to 220 nm.
Next, we explore the impact of different WSi on the performance of the HPP modulator. Figure 4(d) plots the variation of nslow and Γ, while Fig. 4(e) shows α and VπL of the HPP modulator. It is seen that both α and Γ decrease with WSi, whereas nslow increases with WSi. As the width of silicon cores increases, the optical field becomes more confined within the central slot and the silicon cores. Therefore, the light in contact with the metal electrodes weakens, resulting in a reduced α. Meanwhile, as more light resides in the high refractive index silicon cores, Γ decreases and nslow increases. According to Eq. (1), VπL is determined by the product of nslow and Γ. As WSi increases, the increase in nslow is not enough to compensate for the decrease in Γ, resulting in an increase in VπL. The loss-half-wave voltage-length product αVπL are given in Fig. 4(f), which reaches a minimum around WSi = 170 nm. However, the difference between the maximum and the minimum of αVπL is only 1 dB·V, indicating that the overall performance of the HPP modulator remains roughly unvaried with WSi. It should be noted that although the overall performance of the modulator differs very little, the maximum values of α and VπL are more than doubled relative to their minimum. Therefore, the value of WSi should be appropriately chosen for devices with different modulation lengths, so as to ensure both low propagation loss and low half-wave voltage at the same time. When the modulation length is short, a smaller WSi should be adopted to obtain a low half-wave voltage. Although the propagation loss is large, a low total propagation loss can be obtained due to the short modulation length. On the other hand, a large WSi should be selected for devices with long modulation lengths. In our design, the modulation length is taken to be 10 μm, and WSi = 120 nm is selected, which can ensure a low half-wave voltage while maintaining a low propagation loss.
The optimized waveguide parameters are thus determined as: Wc = 10 nm, Ws = 40 nm, WSi = 120 nm and hSi = 400 nm. The propagation loss of this HPP waveguide structure is 0.2 dB/μm, while the half-wave voltage-length product of the HPP modulator is 78 V·μm.
2.2 Photonic-plasmonic converter
Silicon waveguide based Y branches are used to split and combine the light into and out of the HPP waveguides. The height and width of the silicon waveguide are designed to be 400 nm and 500 nm, respectively. To covert light from photonic mode in the silicon waveguide into the plasmonic mode in the HPP waveguide, photonic-plasmonic converter (PPC) are needed at the input and output of the modulation section [21].
In SPP modulators, the width of the slot between metal electrodes is narrower than that of the silicon waveguide, and a tapered coupling structure is employed to covert the optical mode in the silicon waveguide to the SPP mode in the metal slot. Generally, the coupling loss of the tapered coupling structure is greater than 1 dB/coupler. In addition, the PPC section increases the complexity and cost of device fabrication. Unlike the SPP modulator, the PPC section of the HPP modulator is formed by directly coupling the silicon waveguide to the modulator section, as shown in Fig. 5(a). As illustrated by Fig. 5(b), light can be efficiently coupled from the silicon waveguides into the HPP waveguides, by converting from the photonic mode (Fig. 5(c)) to the plasmonic mode (Fig. 5(d)). According to 3D FDTD simulations, the coupling loss of the HPP modulator is only 0.6 dB/coupler, lower than the coupling loss of the SPP modulators. In addition, this coupling structure does not require a tapered structure, which reduces the complexity and cost of device fabrication.
Fig. 5. (a) The PPC section schematic diagram of the HPP modulator, (b) optical power near the PPC section, (c) optical power in the silicon photonic waveguide and (d) optical power in the HPP waveguide.
2.3 Asymmetric structure
HPP modulator is designed to be asymmetric, i.e. the widths of the central slots of the two arms are different, so that the phase difference between the two arms differ by π/2, and the modulator can operate at the quadrature point under zero bias. Figure 6(a) plots the effective refractive index as a function of the central slot width, while Fig. 6(b) shows the required propagation length for a π/2 phase difference at a wavelength of 1.55 μm. For an HPP modulator with 10 μm modulation length, the quadrature operating condition can be satisfied with the two central slot widths chosen to be 10 nm and 16 nm, respectively.
Fig. 6. (a) Effective refractive index of the HPP waveguide as a function of the central slot width. (b) The propagation length required for π/2 phase difference, when the width of one central slot is fixed to 10 nm while that of the other varies from 11 nm to 20 nm.
The optimized parameters of the HPP modulator with the best overall performance are listed in Table 1.
Table 1. Parameters of asymmetric low loss HPP Mach-Zehnder modulator
3. Results and discussion
In order to compare the performance of the HPP modulator and the SPP modulator, we established an SPP modulator model similar to Ref. [10]. The cross-section and top view of the SPP modulator are illustrated in Figs. 7(a) and 7(b), respectively. The structural parameters of the SPP modulator are listed in Table 2. For a modulation length of 10 μm, the widths of the two slots are designed to be 90 nm and 100 nm, respectively, to achieve quadrature operation at zero bias voltage. The slots of the SPP modulator are filled with the same EO material as the HPP modulator. FEM is employed to evaluate the performance of the modulators. Triangular mesh is used in our simulation. The minimum unit is 1 nm, and the maximum unit is 60 nm. The resolution of the narrow region is set to 10 to ensure simulation accuracy. In our simulation, the device is surrounded by a 30 μm × 30 μm air box, which is much larger than the device (2.266 μm × 3.6 μm), and scatter boundary condition is adopted.
Table 2. Parameters of asymmetric SPP Mach-Zehnder modulator
3.1 Propagation loss
Figures 8(a) and 8(b) plot the slow-down factor and the propagation loss of the SPP modulator (blue line) and the HPP modulator (red line), respectively. The curves vary with WEOM, the total width of the EO material. For the SPP modulator, WEOM is simply the width of the slot between the gold electrodes. While for the HPP modulator, WEOM = 2Ws+Wc, i.e. the sum of the widths of the central and the side slots. In our simulations, the side slot width is fixed to 40 nm, while the central slot width varies from 10 nm to 100 nm, as WEOM varies from 90 nm to 180 nm. According to Fig. 8(a), the SPP modulator exhibits a slightly larger slow-down factor, since more light penetrates into the gold electrodes, leading to a more significant slow-down effect. However, the larger slow-down factor of the SPP modulator is accompanied by significantly higher propagation loss, as shown in Fig. 8(b). When the slot width of the SPP modulator is 90 nm, the propagation loss is as high as 0.43 dB/μm. For the HPP modulator, most of the light field is confined in the central slot, and there is little light field penetrating into the gold electrodes from the side slots. Therefore, the propagation loss is much lower, as shown in Fig. 8(b). When the central slot width of the HPP waveguide is 10 nm, the propagation loss is just 0.2 dB/μm. In addition, the high refractive index silicon cores help raise the effective refractive index of the HPP waveguide, thereby contributing to the slow-down effect. In general, the HPP modulator can achieve a slow-down effect similar to the SPP modulator, but with a much smaller propagation loss.
Fig. 8. (a) The slow-down factor, (b) propagation loss and (c) field energy interaction factor of the SPP modulator (blue line) and the HPP modulator (red line), respectively.
Figure 8(c) plots the field energy interaction factor of the SPP modulator (blue line) and the HPP modulator (red line). When the EO material width is not very large, the HPP modulator exhibits a lower field energy interaction factor, as part of the light field is confined to the silicon cores and does not contribute to the field energy interaction factor. As the EO material width increases, part of the light field in the SPP modulator would leak into the EO material above the slot region. Thus the field energy interaction factor decreases, and the propagation loss also decreases. On the other hand, the situation for the HPP modulator is different. When the central slot width of the HPP modulator increases, part of the light field in the silicon cores is transferred to the central and the side slots. This leads to an increase in both the field energy interaction factor and the propagation loss.
3.2 Modulation efficiency
When the intensity of the modulated RF field is constant, the modulation efficiency of modulators can be measured by the effective refractive index change Δneff, which is given by the following equation [21]:
where Δnmat/nmat is the relative refractive index change of the EO material.Figure 9(a) plots the effective refractive index variation in the SPP modulator (blue line) and the HPP modulator (red line) filled with the same EO material, assuming a modulation electric field of ERF = 1 MV/cm. Obviously, the relative index variation of the SPP modulator is greater than that of the HPP modulator when WEOM < 170 nm. The reduced modulation efficiency of the HPP modulator, which is caused by the reduction of the field energy interaction factor and the slow-down factor, leads to an increase in the half-wave voltage-length product, as shown in Fig. 9(b). When the EO material width is 90 nm, VπL of the SPP modulator and the HPP modulator is 53 V·μm and 78 V·μm, respectively.
Fig. 9. (a) The effective refractive index change and (b) the half-wave voltage-length product of the SPP modulator (blue line) and the HPP modulator (red line), respectively.
3.3 Overall performance
For the SPP modulator, high modulation efficiency and low propagation loss are incompatible. As WEOM increases, the optical confinement of the MIM structure weakens, resulting in a decrease in Γ. Meanwhile, the light field penetrating into the metal electrodes is reduced. Although the propagation loss α is reduced, the reverse energy flow contributing to nslow is also reduced, resulting in a smaller nslow. According to Eq. (3), the decrease of Γ and nslow leads to a reduced Δneff, i.e., a decrease in modulation efficiency. Thus, the overall performance of the SPP modulator is limited. Unlike the SPP modulator, the optical confinement in the HPP modulator relies on the silicon slot waveguides. Since Ws is kept unvaried, the increase of WEOM means that Wc increases. This leads to the weakening of the optical confinement of the silicon slot waveguide, and the light field in the side slots increases. The net result is an increase in Γ. Although α also increases, its change is only moderate. The slow-down factor nslow of the HPP modulator mainly comes from light in the high refractive index silicon cores. Therefore, the HPP modulator can obtain a nslow similar to that of the SPP modulator while ensuring much lower α. The increase of Γ compensates for the decrease of nslow, resulting in an increase of Δneff. Thus, the HPP modulator can achieve high modulation efficiency and low propagation loss at the same time.
Although the modulation efficiency of the HPP modulator is lower than that of the SPP modulator when WEOM <170 nm, the propagation loss of the HPP modulator is less than half that of the SPP modulator. To take both the modulation efficiency and propagation loss of the modulators into consideration, the loss-half-wave-voltage-length product αVπL is used to describe the overall performance of modulators. Figure 10 plots αVπL of the SPP modulator (blue line) and the HPP modulator (red line). When the EO material width is 90 nm, αVπL = 22.8 dB·V and 15.6 dB·V for the SPP modulator and the HPP modulator, respectively. And as the EO material width WEOM increases, the overall performance of the HPP modulator is always better than that of the SPP modulator. The reduction in the propagation loss of the HPP modulator compensates for the reduction in its modulation efficiency, resulting in a better overall performance. In other words, the HPP modulator exhibits lower propagation loss under the same half-wave voltage, or a lower half-wave voltage under the same propagation loss. For example, for the 5-μm-long SPP modulator reported in Ref. [10], the propagation loss is 2 dB and the half-wave voltage is 12 Vpp. On the other hand, for a 10-μm-long HPP modulator filled with the same EO material, the propagation loss is also 2 dB, but the half-wave voltage is only 7.8 Vpp. Considering that the coupling loss of the PPC section is 0.6 dB/coupler, the total insertion loss of the HPP modulator can be less than 4 dB. This is smaller than the typical insertion losses of 4-7 dB reported for well-engineered high-speed silicon modulators [22,23].
Fig. 10. The loss-half-wave voltage-length product of the SPP modulator (blue line) and the HPP modulator (red line), respectively.
3.4 Bandwidth and modulation depth
Since the electrode of the HPP modulator is very short, the device can be modeled as a lumped parameter circuit, so the modulation bandwidth is mainly limited by the RC constant. We estimate the bandwidth performance of the proposed HPP modulator by a single-port simulation through FEM. The resistance and capacitance of the device are extracted from the simulated S11 data by the following equations [24]:
with ZL = 50 Ω. For a modulation length of 10 μm, the resistance is ∼2.2 Ω and the capacitance is ∼4.7 fF. The theoretical bandwidth for the HPP modulator is estimated to be 650 GHz according to following equation:In Ref. [10], the theoretical bandwidth and measured bandwidth of a 5-μm-long SPP modulator are reported to be 1 THz and 70 GHz, respectively. The smaller theoretical bandwidth of our 10-μm-long HPP modulator is attributed to the increased capacitance due to longer device length. Nevertheless, our HPP modulator exhibits better overall performance.
In the above discussions, we assume an EO material with r33 = 180 pm/V, corresponding to monolithic polymer DLD164. Recent study shows that the EO coefficient of DLD164 is reduced to 110 pm/V for slot width less than 40 nm [25]. Assuming r33 = 110 pm/V for the EO material, the modulation depth of the HPP modulator is estimated to be 50% and 80% under a modulation voltage of 4 Vpp and 8 Vpp, respectively.
In addition to nonlinear organic materials like DLD164 and HD-BB-OH/YLD124, inorganic materials with high nonlinear coefficient, e.g. BTO (r33 = 342 pm/V and r42 = 923 pm/V), can also be used in the proposed HPP modulators. The EO coefficient of inorganic materials does not decrease with the slot width. If BTO (r33 = 342 pm/V) is used in the HPP modulator, it is estimated that αVπL is only 5.3 dB·V. The bandwidth of the BTO modulator is expected to exceed 40 GHz [26].
4. Conclusion
We have proposed a low loss HPP Mach-Zehnder modulator that combines tight optical confinement of plasmonic waveguides and narrow slot waveguides with the low loss feature of photonic waveguides. By adopting an asymmetric structure, the modulator can operate at the quadrature point at zero bias voltage. By optimizing the geometric parameters, a 10-μm-long HPP modulator is estimated to have a half-wave voltage of 7.8 Vpp, a total insertion loss lower than 4 dB, and a modulation bandwidth of 650 GHz. The proposed HPP modulator is found to exhibit better overall performance compared with the SPP modulator.
Funding
National Key Research and Development Program of China (2018YFB2201700); National Natural Science Foundation of China (51561145005, 51561165012, 61574082, 61621064, 61822404, 61875104, 61927811); Key Lab Program of BNRist (BNR2019ZS01005); Basic Research Priorities Program of Shenzhen (JCYJ20160608170030295); China Postdoctoral Science Foundation (2018M640129); Collaborative Innovation Centre of Solid-State.
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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