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Abstract
Metasurfaces have attracted extraordinary interest in achieving novel, ultrathin and compact photonic devices. To date, however, the realization of electrically tunable high-speed metasurfaces remains a great challenge. In this work, we present an electro-optic (EO) polymer/silicon hybrid metasurface modulator with an estimated 3dB modulation bandwidth up to 118 GHz. The specially designed metasurface utilizes a broken in-plane inversion symmetry structure to generate a high-Q resonance. The high-Q property enhances the EO modulation effect, so that a 16 dB extinction ratio is theoretically verified under a driving voltage Vp-p of 4V. The pulse modulation results in an ultra-fast single-lane data rates up to 300 Gbps driven by a low RF power. The presented modulator should be applicable for high-speed and low-energy intelligent tunable metasurface, space optical communication and so on.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces are artificially designed arrays of metallic or dielectric sub-wavelength optical structures on planar substrates [1]. Extending competencies in controlling the phase, amplitude, or polarization of light on nano-scale, thereby stimulate the development of engineering novel flat and ultrathin optical devices [2–5]. Due to the inherent merits of compact footprint, flexible design and high-performance, the optical devices based on metasurfaces are creating burgeoning interest in photonic integration.
Recently, the development of active metasurfaces attraction has grown exponentially, because they would enable promising applications in dynamic beam steering, reconfigurable metalenses, high-speed imaging and space large-bandwidth communications [6–10]. Prior research has explored micro-electromechanical system (MEMS) to realize tunable metasurfaces [11,12]. However, the modulation speed is at kHz and the design/manufacturing process is relatively complex [13]. Compared with MEMS, achieving metasurfaces directly by engaging active material could substantially simplify the design and facilitate the fabrication. For example, phase-transition materials, such as GST [14] and VO2 [15], have been incorporated as the fundamental metasurface elements to obtain tunable optical response. The refractive index of these phase-transition materials can be controlled via loaded heat in tailoring the phases of reflected or transmitted light of individual element. The accumulated phase change of all the elements can provide a control of the propagated light (intensity, polarization and so on). Unfortunately, the performance for phase-transition materials based devices are also limited by the modulation speed in the order of kHz [16].
For breaking high speed limitation, all optical and electrical modulations have been demonstrated [17]. In contrast to optical pumping, electrical modulation has been proven to be a robust, high speed, energy-efficient and reversible scheme for optical communication, information coding, data communication link and so on [18]. Organic electro-optic (EO) polymers have demonstrated its potential in recent years owing to its high EO coefficient (r33) >100 pm/V, ultrafast EO response time (less than 10 femtoseconds), compatibility concerning other substrates and straightforward spin-coating fabrication process [19,20]. These attractive features of EO polymers have empowered diverse and outstanding performances in organic or organic-inorganic hybrid waveguide modulators [21,22]. Previously, we have demonstrated various EO polymer waveguide modulators with high EO coefficients, low driving voltages and high-speeds up to 200 Gbps [23–26]. If EO polymer could be combined with metasurfaces, it may promote a GHz modulation, a convenient electrical-control and a relatively simple fabrication.
In this work, we have designed and characterized an EO polymer/silicon (Si) hybrid metasurface modulator (HMM) operating in the near-infrared wavelength. The designed HMM utilizes Si nano-arrays covered by the EO polymer to form a resonator. The broken in-plane inversion symmetry structure of the Si nano-arrays contributes to a high Q-factor of 1910 in the resonator. Meanwhile, the EO polymer in HMM can provide a linear EO (Pockels) effect with an EO coefficient of 200 pm/V [27]. As a result, the presented device displays an extinction ratio of 16 dB under a driving voltage Vp-p of 4V, and a 3 dB bandwidth up to 118 GHz.
2. EO polymer / Si HMM design
In an EO polymer modulator, the phase change Δφ of the propagated light is described by the following equation [28]:
where Δn is the change of refractive index induced by the EO effect, L represents the length of the modulation path, n denotes the effective refractive index, r33 denotes the EO coefficient of the EO polymer, and Γ is overlap factor between the optical field and the electrical field E. Here, E is equal to V/d, where V is the applied voltage and d is the inter-distance of the electrodes. For a conventional Mach-Zehnder waveguide modulator [29], L is from several millimeters to centimeters, so an enough Δφ can be obtained even with a low V of several volts. However, a metasurface usually has a thickness in the order of the operation wavelength. If a top-bottom electrode structure is utilized as shown in Fig. 1(a), the light may penetrate the device with a L of just several micrometers. This will force the metasurface modulator to be driven with a high V of several hundred volts. To induce an obvious modulation within such a thin film under a low V, one approach is to construct a high Q-factor resonator in the metasurface to enhance the light experiencing the refractive index change.In order to realize a high Q-factor, we designed a HMM with the configuration as depicted in Fig. 1(a). Introducing 600 nm thick EO polymer layer sandwiched between the top and bottom ITO electrodes (thickness is 100 nm). The specially designed Si metasurface consists of periodic lattices of Si bars resting on the bottom ITO as shown in Fig. 1(b). All the Si bars have the same height h of 160 nm and length l of 700 nm. One unit of the periodic lattice is composed of a pair of Si rectangular bars having different widths, denoted as ${b_1}$ and ${b_{2{\; }}}$for the Q-factor optimization. The units are arranged in a square array with lattice constants of${\; }{p_{x{\; }}}$ = 740 nm,${\; }{p_y}$ = 790 nm and g = 235 nm. The lattice constants are chosen such that the Fano resonances of the HMM occur in the O-band of the optical communication and the grating diffraction is prevented [1].
Fig. 1. (a) Schematic of the designed EO polymer/Si hybrid metasurface modulator (HMM) and (b) enlarged diagram of one unit cell: one period is${\; }{p_x} \times {p_y}$, where${\; }{p_{x{\; }}}\textrm{and}\; {p_y}$ is 740 nm and 790 nm, respectively. Other geometric parameters are $h$=160 nm,${\; }l$=700 nm and g=235 nm. The widths of the Si rectangular bars are set as b1 and b2 for the Q-factor optimization.
The designed HMM was simulated by using finite-difference time-domain (FDTD) method. We used the commercial software Lumerical to perform the numerical simulations. In the simulations, the refractive index of Si is given according to the fitting Palik experimental data [30], and the refractive index of the EO polymer is set as 1.65 based on our previous experiment [31]. The index of the ITO is set as 1.63, which has been measured by the spectroscopic ellipsometry. Due to the periodic lattices, the periodic boundary conditions (PBCs) have been employed in both x and y directions and perfect matched layers (PMLs) for the z direction.
As a plane-wave light with the polarization along tshe x-axis is normally incident to the device, it will excite Fano resonances in the HMM [32]. For the Fano resonances, breaking the geometrical symmetry enables the nano-structured metasurfaces to exhibit a quadrupolar mode, which weakly couples to the incident wave [33,34]. With the coupling between the new-emergent narrow quadrupole and the original dipole continuum, Fano resonances accompanied by a high Q-factor may be produced [35]. To gain a deeper insight into the effect of the broken symmetry, we further study the asymmetry of the HMM to obtain the highest Q-factor. In the designed HMM as shown in Figs. 1(a) and 1(b), the asymmetry of the unit period is controlled by the difference in bar widths, which could be expressed by the asymmetry factor c =$\frac{{{b_1} - {b_2}}}{{{b_1}}}$. Figure 2(a) and (b) shows the resonance wavelength and Q-factor as functions of the asymmetry factor c, respectively. Due to the specially designed lattice constants, the resonance peak locates in the wavelength range from 1.32 um to 1.36 um and has a blue shift as c increases. As can be noticed in Fig. 2(b), Q-factor grows from 990 to 1910 as the asymmetry factor increases from 0.25 to 0.85. A maximum Q-factor of ∼1910 is obtained when c is 0.85 corresponding to the ${b_{2{\; }}}$is 30 nm. The simulated reflective spectrum as c=0.85 is shown in Fig. 2(c). A Si-bar with a width < 30 nm is usually difficult for the practical nano-fabrication [36], so we only take account of the situation that c is ≤ 0.85. As a result, the optimal c to obtain the largest Q-factor is 0.85, indicating ${b_{1{\; }}}$=200 nm and ${b_{2{\; }}}$=30 nm.
Fig. 2. Asymmetry factor dependent (a) resonance wavelength and (b) Q-factor of the modulator in the absence of applied electric-field (c) Reflective spectrum of the modulator when the asymmetry factor is 0.85.
The electric-field dependent refractive index change Δn/E is a key parameter, because it determines the resonance tunability [37]. Based on Eq. (1), we can derive
In our design, E is along z direction due to the vertical electrode structure, so Γ can be considered as the portion of the optical mode confined in the EO polymer. To achieve a high electric-field dependent refractive index change Δn/E, majority of optical mode would need to reside within the EO polymer layer. We have simulated the optical field distribution in the HMM at the resonance wavelength of 1327 nm (c=0.85) as shown in Fig. 3. It can be observed that there is a discontinuous distribution at the boundary between the Si and the EO polymer and that more of the optical mode extends deep into the EO polymer layer. This is caused by the discontinuity of the electric field at high-low refractive index contrast interfaces [38]. According to our calculations, Γ is approximately 55% and independent of the asymmetry factors. This value is larger than that of the state-of-art EO polymer slot waveguide modulators (approximately 30%) [39], which will contribute to obtain a high Δn/E.3. Results and discussions
To examine the EO modulation effect in the HMM, we have simulated the change in reflected spectra with the applied voltage. In simulation, the EO coefficient of the EO polymer is set as 200pm/V [25] and Δn is calculated by using Eq. (2). In our designed device, the resistivity of the EO polymer is 106 ∼108 Ωm [40]. The resistivity of Si is around 2.3*103 Ωm [41], so that all the driving voltage will be loaded on the EO polymer layer. The reflected spectral shift at DC voltages of ±2 V is shown in Fig. 4(a). As can be observed, the waveform has little change under different applied DC voltages and the modulation extinction ratio is 16 dB at ±2 V.A linear regression of the resonance wavelength under different voltage provides a resonance tunability of 0.32 nm/V is shown in Fig. 4(b).
Fig. 4. (a) Reflective spectra under the applied DC voltage ±2V and (b) linear fitting of the resonance wavelength under different applied DC voltages.
In the HMM, the EO effect origins from the EO polymer, so the influence of the EO polymer thickness on the tunability and modulation extinction ratio has been calculated. As the thickness increased from 0.5 to 0.75 um, we find that there is a tradeoff. The tunability decreases from 0.36nm/V to 0.26nm/V, which is caused by that the electric-field becomes weaker with the thicker polymer under the same DC voltage. Meanwhile, the calculated modulation extinction ratio increases from 10 dB (0.5 um-thick polymer) to 16 dB (0.6 um) and then decreases to 11 dB (0.75 um) with the DC voltages of ±2V. Considering these factors, we select the 0.6 um-thick EO polymer in this work to realize a tunability of 0.32 nm/V and a modulation extinction ratio of 16 dB.
In a resonator modulator, several factors limit the modulation bandwidth, including materials, photon lifetime, walk-off between electrical and optical signals and RF (radio frequency) electrodes [35]. In our case, the EO polymer has an ultrafast EO response time (< 10fs) and a velocity matching between the optical and RF signals up to at least 250 GHz [42] .Therefore, the device 3 dB modulation bandwidth (f3dB) is determined by the RC (Resistor-Capacitance) time and the photon lifetime, as expressed by
The 118 GHz bandwidth of the HMM promises the high-speed digital transmission, because the speed under non-return-to-zero (NRZ) modulation can be estimated empirically to be 1.3f3dB [43]. In order to characterize the response to the digital signals, we applied pseudo random NRZ sequence to the HMM and investigated the eye diagram. The simulated configuration is shown in Fig. 5(a). The pulse train consists of a 223 -1 pseudo random bit sequence (PRBS) signal with a peak-to-peak voltage of 1.14 V, both rising and falling time assumed to be 3.33 ps. The tunable laser is adjusted to work at the HMM resonance wavelength of 1327 nm. A high-bandwidth photodetector (PD) was assumed as a receiver. The dark current and thermal noise caused by the 50 Ω resistance of the PD were assumed to be 10 nA and 18pA/(Hz)0.5 [44]. Figure 5(b) shows the obtained eye diagram, which is clearly opened with an extinction ratio of 3.8 dB at 300 Gbps NRZ driving signal. Though the calculation is theoretically based on the ideal condition, the obtained result indicates the potentially available ultra-high speed applications of the HMM.
Fig. 5. (a) Block diagram of the eye diagram evaluation and (b) 300 Gbps eye diagram of the HMM with a driving voltage of 1.14 V and an extinction ratio of 3.8 dB.
4. Conclusion
In conclusion, we have investigated EO polymer/Si HMM operating at O-band of the optical communication. Enhanced modulation efficiency was achieved by exploiting asymmetrical Si nano-arrays, which generated a high-Q resonance at the optimized asymmetry factor. The device demonstrated a modulation extinction ratio of 16 dB at DC voltages of ±2 V when the EO coefficient of the EO polymer is 200 pm/V. The designed HMM performed a 3dB-bandwidth of 118 GHz and a 300 Gbps NRZ digital modulation. Such a device may initiate high-speed free-space optical commination with the function as traditional waveguide modulators in fiber-communication. Recently, we noticed that 2D material-based EO modulators also exhibited high speeds of gigahertz [45,46], so the proposed HMM scheme may also be broadened to 2D material. In addition, a single HMM occupies a quite small area, so that it can be readily extended to a large modular array. If each modulator is controlled independently, the modulator array should also find its applications in high-speed imaging, beam shaping, LiDAR and so on.
Appendix
In the following table, we compare the performance of our HMM with prior works, all of which have recently demonstrated electrically tunable properties. In the table, the HMM is the theoretical result and others are the experimental results. From Table 1, it can be seen that the HMM has the potential of not only offering a large tunability, but also a high RF modulation bandwidth and speed.
Table 1. Comparison with the prior works.
Funding
National Natural Science Foundation of China (62075184).
Acknowledgements
This work is supported by National Natural Science Foundation of China (62075184).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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