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Abstract
We propose and experimentally demonstrate microwave photonic filters (MPFs) with high rejection ratios and large tuning ranges of the central frequency and bandwidth leveraging four cascaded opto-mechanical microring resonators (MRRs). As half waveguides of each MRR are free-hanging in the air, the nonlinear effects in the opto-mechanical MRRs could be efficiently excited. Consequently, the transmission characteristics of the cascaded MRRs could be flexibly manipulated by adjusting the input pump powers. When the resonant wavelengths of every two MRRs are tuned to be aligned, the transmission spectrum of the silicon device is a notch bimodal distribution with high extinction ratios. The optical carrier is fixed at the flat region of the bimodal distribution. Under optical double sideband (ODSB) modulation, MPFs with high rejection ratios could be achieved due to the high extinction ratio of the cascaded rings. Moreover, the central frequency and bandwidth of the MPFs could be tuned by properly adjusting the pump powers. In the experiment, with a low power of 2.56 mW, the MPF central frequency and bandwidth could be tuned from 7.12 GHz to 39.16 GHz and from 11.3 GHz to 17.6 GHz, respectively. More importantly, the MPF rejection ratios are beyond 60 dB. Furthermore, during the bandwidth tuning process, an MPF response with approximately equiripple stopband could be realized. Owing to the dominant advantages of high rejection ratios, large tuning ranges, low power consumption and compact size, the silicon device has many significant applications in on-chip microwave systems.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Microwave photonic filters (MPFs), which combines two important worlds of optoelectronics and radio frequency (RF) engineering [1–3], has attracted widespread interests in radar and wireless communication systems [4–6]. To pursue better integration and device miniaturization, various tunable MPFs have been demonstrated based on the nanotechnology [7–12]. Most schemes are utilizing the linear methods with requirements of special external assistance, such as tunable laser diodes [6]. Actually, the nonlinear effects also provide an effective solution for dynamic signal processing [13,14]. In the past decade, tunable MPFs have been realized by utilizing the stimulated Brillouin scattering (SBS) effect in the chalcogenide glass waveguide [15–17] and silicon nanowire [18], thermo-optic effect in the silicon microring resonators (MRRs) [19]. Nevertheless, the performance of the nonlinear effect-based MPFs is urgent to be largely improved. Firstly, the required power consumption is tens of milliwatts [16,18] and the waveguide lengths are centimeter-level [15,16,18], which need to be further optimized for large-scale integration. Secondly, among the nonlinear methods, only several schemes could simultaneously realize tunable central frequency and bandwidth [15,16]. However, most bandwidth tuning ranges are lower than 0.5 GHz. Finally, one key factor to evaluate the MPF performance is the rejection ratio for high-sensitivity and high-precision applications [15,20]. To date, it is still challenging to realize all-optical tunable MPFs with rejection ratios beyond 60 dB based on the nonlinear effects. Therefore, to meet the requirements of wideband dynamic processing and high suppression, it is highly desirable to realize MPFs with large tuning ranges, high rejection ratios and low-power consumption [21–26].
Nowadays, the silicon-on-insulator (SOI) technology has become one of the most promising industries in the integrated optics [27–31]. Especially, the silicon nano-mechanics have attracted rapidly increasing interests and have been widely used in signal processing due to their combination of silicon photonics and mechanics [32]. As the optical field is strongly enhanced in the silicon opto-mechanical MRRs, the nonlinear effects could be effectively excited by low-power consumptions [33–35]. Moreover, the cascaded MRRs could be utilized as optical filters with high extinction ratios (ERs) [36] when the MRRs are designed at the critical couplings and the resonances are aligned. Hence, the opto-mechanical MRRs provides an effective approach to realize low-power and high-quality signal processing.
In this paper, we experimentally demonstrate an all-optical microwave filter based on four cascaded opto-mechanical MRRs. By utilizing the efficient nonlinear effects in the opto-mechanical MRRs, the device transmission spectrum could be flexibly manipulated. Firstly, the frequency intervals between the optical carrier and the device notch peaks could be controlled, thus the MPF central frequency and bandwidth could be tuned. Secondly, as the MRRs are all designed at the critical coupling, the ER of each MRR is high. Moreover, when the resonances of every two MRRs overlap, the ERs of the aligned peaks could be largely improved. Accordingly, MPF responses with high rejection ratios could be achieved. The experimental results show that with a low power of 2.56 mW, the tuning ranges of the MPF central frequency and bandwidth are larger than 32 GHz and 6.3 GHz, respectively. During the frequency tuning process, the rejection ratios of the MPFs are larger than 60 dB. The proposed silicon device suggests an all-optical control approach to realize tunable MPFs with high rejection ratios, low power consumption and large tuning ranges, which is competent to process microwave signals.
2. Operation principle
As shown in Fig. 1(a), the key component of the silicon device is an opto-mechanical MRR, whose oxide substrate under half MRR is removed. The tuning mechanism of the opto-mechanical MRR is based on the nonlinear effects, which mainly consist of opto-mechanical effect and thermo-optic effect [31]. Firstly, as half MRR waveguide is free-hanging in the air, the device heatsink and dissipation would be significantly reduced. Consequently, the thermo-optic effect in the MRR is strongly enhanced to induce higher temperature rise and larger resonance red-shift. Secondly, the major optical power accumulates in the MRR, which leads to a high-power density in the microring, thus the optical field gradient is largely increased. In this case, the light-matter interaction between the MRR free-hanging waveguide and the substrate could generate an optical force which is strong enough to cause the waveguide deflection. As shown in Fig. 1(b), the free-hanging waveguide would bend downwards to the substrate. In this case, the effective waveguide length of the MRR becomes larger which induces the resonance red-shifts. Therefore, the nonlinear effects are strongly enhanced in the opto-mechanical MRRs, which could be efficiently excited by low optical powers.
Fig. 1. (a) Schematic image of the opto-mechanical MRR. (b) Cross-sectional view of the bent microring.
The MRR resonance red-shift δλ mainly includes the resonance red-shift δλ1 owing to the thermo-optic effect and the red-shift δλ2 induced by the opto-mechanical effect, which could be denoted by [27]
According to Eq. (1), the resonance red-shift δλ is proportional to the input pump power, which mainly consists of Pt and Pm. Therefore, the resonance red-shifts of the opto-mechanical MRR could be flexibly controlled by tuning the input pump powers, which is beneficial for tunable microwave signal processing.
The silicon device consists of four opto-mechanical MRRs, which are all designed at the critical coupling to achieve high ERs. There are two free spectrum ranges (FSRs) of the silicon device, shown as the red line (working region) and the blue line (pump region) respectively in Fig. 2(a). The resonant wavelengths of the working region are written as λ1a (R1), λ2a (R2), λ3a (R3) and λ4a (R4), while the resonant wavelengths of the pump region are denoted by λ1b (R1), λ2b (R2), λ3b (R3) and λ4b (R4). The optical carrier λ0 is located at the left flat region of the resonant peak λ3a. The frequency intervals between λ0 and λ2a, λ0 and λ4a are f1 and f2, respectively. To simplify the experimental setup and system complexity, only two pump wavelengths are required (i.e. pump 1 and pump 2), which are equal with λ2b and λ4b, respectively. As the resonances λ1a and λ3a are close to the resonances λ2a and λ4a respectively, pump 1 could control the resonant peaks of R1 and R2, while pump 2 could manipulate the resonant peaks of R3 and R4 [27,37]. As shown in Fig. 2(b), the waveguides in the dashed boxes are free-hanging structures. On one hand, pump 1 and pump 2 are injected from the left side (i.e. pump 1 left and pump 2 left) to control the transmission spectra of R1 and R3, respectively. On the other hand, the transmission characteristics of R2 and R4 are manipulated by the pump light from the right side (i.e. pump 1 right and pump 2 right).
Fig. 2. Operation principle of the MPFs with high rejection ratios and tunable central frequency. (a) The device transmission spectrum. (b) The device structure. The frequency intervals between the optical carrier and two overlapped resonances are adjusted as (c) f1 and (e) f2, respectively. The MPF central frequencies are (d) f1 and (f) f2, respectively.
Assume that an RF signal is modulated onto the optical carrier by an intensity modulator to generate optical double sideband (ODSB) signal. As shown in Fig. 2(c), with injecting pump 1 from the left side, the resonant wavelength of R1 could be shifted to λ2a, which overlaps with the resonant wavelength of R2. Simultaneously, pump 2 injected from both sides is utilized to control the resonant wavelengths of R3 and R4 to overlap at λ5. Because the frequency intervals between λ0 and λ2a, λ0 and λ5 are both f1, an MPF response with central frequency of f1 could be obtained, as shown in Fig. 2(d). Moreover, due to the high ER of each MRR, the ERs of the two aligned peaks (i.e. λ2a and λ5) could be largely increased, which contributes to the MPF responses with high peak rejections.
Figure 2(e) shows that pump 1 is injected into the silicon device from both sides while pump 2 is injected from the left side. By properly adjusting the pump powers, the resonant of R1 and R2, R3 and R4 could overlap at λ6 and λ4a with high ERs, respectively. In this case, the frequency intervals between λ0 and λ6, λ0 and λ4a are both changed to f2. Accordingly, the MPF central frequency is adjusted to f2, as shown in Fig. 2(f). Therefore, MPFs with high rejection ratios and tunable central frequency could be achieved. By manipulating the pump powers, the central frequency of the MPF could be tuned from f1 to f2.
As shown in Figs. 2(c) and 2(d), when the frequency intervals between the optical carrier and the two notch peaks are both f1, an MPF response with central frequency of f1 could be achieved (the green solid line). Subsequently, the pump light is utilized to adjust the device transmission spectrum, shown as the red dashed line in Fig. 3(a). The frequency intervals between the optical carrier and four notch peaks λ1a, λ2a, λ3a and λ4a are f1+f3, f1-f3, f1-f3 and f1+f3, respectively. In this case, an MPF response with a wider bandwidth could be obtained with maintaining the central frequency of f1, shown as the blue dashed line in Fig. 3(b). Therefore, by adjusting the frequency intervals between the optical carrier and the four notch peaks, the MPF bandwidths could be effectively tuned.
Fig. 3. Operation principle of the MPF with tunable bandwidth. (a) The adjusted device transmission spectrum. (b) The MPF response with a wider bandwidth.
To analyze the notch MPF response, the alternative current (AC) term in the square-law photodetector (PD) could be denoted by [7]
As the optical carrier ω0 is fixed at the flat region between the notch peaks, H(ω0) is a constant. Hence, the notch MPF response is mainly determined by the two sideband H(ω0-ωRF) and H(ω0+ωRF). Firstly, if the notch resonances of R1 and R2, R3 and R4 are aligned at λ2a and λ5 respectively, the notch depths of H(ω0-ωRF) and H(ω0+ωRF) could simultaneously realize the maximum values at the same frequency interval f1. According to Eq. (2), the MPF response could achieve the highest rejection ratio and the narrowest bandwidth at the central frequency of f1. Secondly, assume that the four MRR resonant wavelengths do not overlap with each other, H(ω0-ωRF) and H(ω0+ωRF) achieve the minimum values at different frequencies. Consequently, the MPF bandwidth could be tuned.
3. Experimental results and discussions
The scanning electron microscope (SEM) image of the cascaded opto-mechanical MRRs is shown in Fig. 4(a), which is fabricated on a commercial SOI wafer with 220-nm-thick silicon slab and 2 µm buried oxide layer. The whole footprint of the silicon device is 0.025 mm2. The radii of the four MRRs are around 20 µm. Figure 4(b) shows the magnified image of one free-hanging MRR. The waveguide widths of the MRR and straight waveguide are both 450 nm. The ridge height and slab height of the ridge MRR and straight waveguide are 190 nm and 30 nm, respectively. In contrast, the waveguide height of the free-hanging MRR is 220 nm. The side view of the MRR partial free-hanging waveguide is illustrated in Fig. 4(c). By utilizing the finite-element mode solver (COMSOL Multiphysics), the differences of the effective indexes between different waveguide structures (i.e. the straight waveguide, the ridge MRR and the free-hanging MRR) could be negligible, indicating that the device structure is favorable for power coupling and signal transmission.
Fig. 4. SEM images of (a) the cascaded opto-mechanical MRRs, (b) a single MRR and (c) the free-hanging waveguide, respectively.
The measured transmission spectra of the cascaded MRRs are shown in Fig. 5(a) (the working region) and Fig. 5(b) (the pump region), respectively. As shown in Fig. 5(a), the four resonant wavelengths λ1a (R1), λ2a (R2), λ3a (R3) and λ4a (R4) are 1558.92 nm, 1558.97 nm, 1559.334 nm and 1559.354 nm, respectively. The wavelength of the optical carrier is chosen as 1559.298 nm, which is 41 GHz (corresponding to f1) and 7 GHz (corresponding to f2) away from λ2a and λ4a, respectively. Figure 5(b) shows the resonant wavelengths of λ1b (R1), λ2b (R2), λ3b (R3) and λ4b (R4) in the pump region are 1545.84 nm, 1545.944 nm, 1546.416 nm and 1546.48 nm, respectively. According to the theoretical analysis in Fig. 2, the pump wavelengths are selected as 1545.944 nm and 1546.48 nm, respectively.
Fig. 5. The measured transmission spectrum of (a) the working region and (b) the pump region, respectively.
In order to characterize the tuning performance of the opto-mechanical MRRs, different pump powers ranging from 0 mW to 1.5 mW are injected into the silicon device. Pump 1 and pump 2 are utilized to manipulate the resonance λ2a and λ4a, whose red-shifts are shown as the purple dashed line and the blue solid line in Fig. 6, respectively. It can be seen that the resonances of the free-hanging MRRs could be efficiently tuned and the resonance red-shifts are approximately proportional to the input pump powers. For example, with injecting pump powers of 1.5 mW, the resonance red-shifts are both larger than 0.28 nm (i.e. 35 GHz), which are competent to process the microwave signals with low-power consumption.
Figure 7 shows the schematic diagram of the MPF experimental setup. The signal path includes a laser diode (LD), polarization controller (PC), Mach–Zehnder modulator (MZM), erbium-doped fiber amplifier (EDFA) and variable optical attenuator (VOA). The optical carrier λ0 (1559.298 nm) is emitted from the LD and then sent into the MZM. The vector network analyzer (VNA) launches an RF signal which is amplified by an electrical amplifier (EA). Then, the amplified RF signal is loaded on the MZM to generate an ODSB signal. As discussed in Fig. 2, pump path 1 and pump path 2 both consist of pump 1 (1545.944 nm) and pump 2 (1546.48 nm). The ODSB signal is coupled with pump path 1 by the optical coupler (OC) and injected into the silicon device from the left side. The pump powers of pump path 2 transmit through the optical circulator and injected into the cascaded MRRs from the right side. The optical signal outputted from the silicon chip is converted to alternative current in the PD and processed by the VNA.
The measured MPF responses are shown in Fig. 8(a), indicating a tunable frequency range from 7.12 GHz to 39.16 GHz. In the case of pump 1 left = 1.29 mW, pump 1 right = 1.18 mW, pump 2 left = 0.09 mW, pump 2 right = 0 mW and pump 1 left = 0.31 mW, pump 1 right = 0.07 mW, pump 2 left = 1.05 mW, pump 2 right = 1.03 mW, the lowest and highest MPF frequencies of 7.12 GHz and 39.16 GHz could be achieved, respectively. The detailed required powers for different MPF frequencies are illustrated in Table 1. During the frequency tuning range, the highest value of the total pump power is 2.56 mW. Figure 8(b) shows the rejection ratios and 3dB-bandwidths of the MPFs. It is clear that most of the MPF rejection ratios are beyond 60 dB and the MPF 3dB-bandwidths are around 12 GHz.
Fig. 8. (a) Measured notch MPFs with tunable central frequency. (b) Features of MPF rejection ratio and 3 dB bandwidth.
Table 1. Input pump powers corresponding to different MPF central frequencies
As shown in Fig. 8(a), with injecting a total pump power of 2.48 mW, an MPF response with a 3dB-bandwidth of 11.3 GHz (the red line) could be realized. Subsequently, the pump powers are utilized to adjust the frequency intervals between the optical carrier and the four notch resonances. When the pump powers are set to 0.89 mW (pump 1 left), 0.92 mW (pump 1 right), 0.35 mW (pump 2 left) and 0.18 mW (pump 2 right), the MPF response is shown as the blue line in Fig. 9. In this case, the MPF 3dB-bandwidth could be changed to 14.38 GHz. What’s more, the MPF response could realize an approximately equiripple stopband with the ripple lower than 1.5 dB. Finally, the frequency intervals between the optical carrier and the four resonances (i.e. λ1a, λ2a, λ3a and λ4a) are tuned as 17.5 GHz, 12.5 GHz, 12.5 GHz and 17.5 GHz, respectively. The corresponding pump powers are 0.95 mW (pump 1 left), 0.97 mW (pump 1 right), 0.23 mW (pump 2 left) and 0.31 mW (pump 2 right), respectively. Consequently, an MPF response with a 3dB-bandwidth of 17.6 GHz could be obtained, shown as the purple line. During the bandwidth tuning process, the MPF rejection ratios are beyond 30 dB. Therefore, with the highest required total power of 2.48 mW, the MPF bandwidth could be tuned from 11.3 GHz to 17.6 GHz and an MPF response with approximately equiripple stopband could be realized.
Fig. 9. The MPF tunable bandwidths under total pump powers of 2.48 mW (the red line), 2.34 mW (the blue line) and 2.46 mW (the purple line), respectively.
Table 2 illustrates the experimental performances and results of recent on-chip tunable MPFs leveraging different nonlinear effects. Firstly, the required powers are relatively high and the waveguide lengths are centimeter-level by utilizing the SBS effect in the chalcogenide waveguide [15,16] or silicon nanowire [18]. Secondly, the frequency tuning ranges of some schemes are lower than 15 GHz [18,19,34]. Thirdly, either the MPF bandwidths cannot be tuned [18,19,34] or the tuning ranges are lower than 0.5 GHz [15,16], which is unfavorable for dynamic signal processing. Finally, the rejection ratios of the nonlinear effect-based MPFs are lower than 60 dB [15,16,18,19,34,35]. In contrast, with a low required power of 2.48 mW, our MPF frequency and bandwidth tuning ranges are beyond 32 GHz and 6.3 GHz, respectively. What’s more, the MPF rejection ratios are beyond 60 dB. During the bandwidth tuning process, the MPF rejection ratios would degrade to 10 dB in Ref. [35]. However, the MPF bandwidth in this paper could be tuned with maintaining the rejection ratios beyond 30 dB, which is an important improvement. Moreover, the proposed scheme could achieve an MPF response with approximately equiripple stopband, which is beneficial for maintaining the signal features.
Table 2. Performance comparisons of recent on-chip tunable MPFs using nonlinear effects
The performance of the MPF (including the power consumption, the tuning ranges and the rejection ratios) could be further improved from the following aspects. Firstly, the separation height between the free-hanging waveguide and the substrate, the waveguide width and the MRR radii could be optimized to enhance the nonlinear effects [38]. Moreover, the transmission loss of the waveguides could be reduced by better fabrication process and post-processing techniques, such as thermal oxidation. In this case, the required powers would be reduced. Secondly, the notch transmission spectrum with a larger frequency interval between λ2a and λ4a could be utilized to extend the upper limit of the frequency tuning range. On the other hand, the quality (Q) factors of the micro-cavities could be improved to reduce the bandwidths of the notch resonance peaks [39–43]. In this case, the low limit of the frequency tuning range could be optimized. Finally, more opto-mechanical MRRs could be utilized to largely increase the ERs of the device transmission spectra in Figs. 2(c) and 2(e). Accordingly, the MPF rejection ratios and bandwidth tuning range could be both improved.
4. Conclusion
We have experimentally demonstrated all-optical tunable microwave filters with high rejection ratios by utilizing cascaded opto-mechanical MRRs. With injecting a low optical power of 2.56 mW, the central frequency and 3dB-bandwidth of the MPFs could be tuned from 7.12 GHz to 39.16 GHz and from 11.3 GHz to 17.6 GHz, respectively. Moreover, the MPF rejection ratios are exceeding 60 dB. The nanomechanical MRR-based MPFs with low-power consumption, large tuning ranges, high rejection ratios and compact size have many significant applications in on-chip microwave system.
Funding
National Natural Science Foundation of China (61805215); Wuhan Municipal Science and Technology Bureau (2019010701011410); Natural Science Foundation of Hubei Province (2018CFB167); Project Supported by Engineering Research Center of Mobile Communications, Ministry of Education.
Disclosures
The authors declare no conflicts of interest.
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