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We propose and experimentally demonstrate a continuously tunable all-optical microwave filter using a silicon opto-mechanical microring resonator (MRR). By finely adjusting the pump light with submilliwatt power level, transmission spectrum of the MRR could be continuously shifted based on the nonlinear effects, including the opto-mechanical effect and thermo-optic effect. Therefore, in the case of optical single sideband (OSSB) modulation, the frequency intervals between the optical carrier (near one MRR resonance) and the corresponding resonance could be flexibly manipulated, which is the critical factor to achieve continuously tunable microwave photonic filter (MPF). In the experiment, the central frequency of the MPF could be continuously tuned from 6 GHz to 19 GHz with the pump power lower than −2.5 dBm. The proposed opto-mechanical device is competent to process microwave signals with dominant advantages, such as compact footprint, all-optical control and low power consumption. In the future, using light to control light, the opto-mechanical structure on silicon platforms might have many other potential applications in microwave systems, such as microwave switch.
© 2017 Optical Society of America
1. Introduction
Compared with conventional electrical filters, microwave photonic filters (MPFs) have attracted great interest for their dominant advantages, such as high bandwidth, tunability, reconfigurability and immunity to electromagnetic interference [1–3]. To process unpredictable and random microwave signals in wireless communication systems, various tunable MPFs have been proposed, such as using fiber optical technology [4–7]. In recent years, due to the advantages of high index contrast and compatible with complementary metal-oxide semiconductor (CMOS), silicon-on-insulator (SOI) technology has become the mainstay of silicon photonics [8–10]. In order to pursue better integration and reliability, some tunable MPFs based on silicon devices have been presented [11–14]. However, most schemes are based on linear effects and require some special assistance, such as tunable lasers [15,16], which increases the complication and cost of the systems. Actually, nonlinear effects could also offer effective approaches for tunable microwave processing [17,18]. To date, only several works have experimentally demonstrated to realize tunable MPFs based on silicon nonlinear effects, such as thermo-optic effect [19] and stimulated Brillouin scattering (SBS) [20]. However, their relatively high power consumptions or long waveguide lengths limit the progress of developing their practical applications in optical communication systems [21–25]. In order to break these limitations, an effective solution for all-optical tunable MPFs is highly desired with compact size, low power consumption and compatible with silicon photonic integration.
In the past decade, opto-mechanical structures have attracted increasing interest in integrated chips [26–29]. Especially in free-hanging microring resonators (MRRs), the nonlinear effects could be excited with lower pump powers, such as the opto-mechanical effect and thermo-optic effect. The opto-mechanical effect is induced by the opto-mechanical interaction between the pump light and free-hanging MRR [28,29]. As the gradient of the optical field is significantly enhanced in the MRRs, the optical force could be amplified by several orders of magnitude [30,31]. With injecting resonant pump light with milliwatt power level, the generated optical gradient force between the MRR and the underneath substrate could effectively cause nanometer or even micrometer deformation of the free-hanging ring [32,33], which would change the effective optical path of the MRR [34]. And the size of waveguide deformation is determined by the level of input pump power. Moreover, the thermo-optic effect also plays an important role to induce resonance red-shifts of opto-mechanical MRRs for reducing the pump power [35]. Because the removal of the oxide substrate can significantly reduce the ring heatsink, the free-hanging MRRs would experience much higher temperature rises than the devices without the free-hanging parts. As a result, the opto-mechanical device is more efficient to induce spectrum shift [30] and their transmission responses could be flexibly manipulated for signal processing. To pursue lower input pump power and higher response speed, the opto-mechanical devices provide an alternative solution enabling all-optical control in silicon photonic devices to effectively process microwave signals [31].
In this paper, using light to control light, we experimentally demonstrate a tunable MPF on silicon platform utilizing an opto-mechanical MRR as an all-optical control, highly efficient and low power consumption approach. The operation principle of the tunable MPF is based on the nonlinear effects in a free-hanging MRR, mainly including the opto-mechanical effect and thermo-optic effect. As the critical device, transmission spectrum of the free-hanging MRR could be modulated by low pump power, in order to achieve continuously tunable frequency intervals between the optical carrier and resonant wavelength. With injecting pump power lower than −2.5 dBm, the central frequency of the notch MPF could be continuously tuned from 6 GHz to 19 GHz. The proposed scheme suggests an all-optical control approach using silicon photonic devices to realize continuously tunable MPF with low power consumption and compact footprint, which is significant in the microwave systems.
2. Operation principle
The all-optical tunable MPF is based on a silicon opto-mechanical structure which consists of a single bus waveguide and a lateral MRR. As shown in Fig. 1(a), half of the substrate (SiO2) underneath the MRR is removed, leaving half arc of the MRR to be free-hanging. The pump light λp is accurately aligned at one resonant wavelength of the MRR. When the pump light λp is coupled into the MRR, the nonlinear effects including the opto-mechanical effect and thermo-optic effect would result red-shifts of the MRR spectrum.
Fig. 1 (a) Schematic diagram of the opto-mechanical MRR. (b) Cross-sectional illustration of the deflected MRR influenced by the optical gradient force.
The opto-mechanical effect and optical gradient force in integrated devices have been widely investigated [30–38]. The optical gradient force between the free-hanging MRR and the underneath substrate is caused by the evanescent fields of the resonant pump light, which induces a mechanical optical nonlinearity into the device [37, 38]. Thus, the opto-mechanical devices could be driven by the optical force through the inelastic interaction between the photons and the nanostructures. In this case, as shown in Fig. 1(b), the free-hanging arc of the MRR is bent downwards to the substrate by the optical forces. Because of the bending deformation, the effective length of optical path becomes larger which results in a red-shift of the MRR resonant wavelength.
The optically induced force can be expressed as [36]
where L is the length of the free-hanging arc, Pm is the circulating pump power on the ring for opto-mechanical effect, c is the vacuum speed of light, neff is the effective index of the free-hanging MRR and g represents the waveguide separation between the free-hanging arc and the substrate.The resonant wavelength shift δλ1 owing to the opto-mechanical effect can be determined by [31]
where is the opto-mechanical tuning efficiency, Pm is the circulating pump power on the ring for opto-mechanical effect, and k is the beam stiffness.On the other hand, the resonant wavelength shift δλ2 induced by the thermo-optic effect can be expressed as [39]
where λ0 is the resonant wavelength, ng is the group index, and δnTO is the silicon refractive index variation induced by the thermo-optic effect.The index change δnTO can be written as [40, 41]
where Γth is the effective confinement factor corresponding to the thermo-optic effect, kth is silicon thermo-optic coefficient, Rth is the thermal resistance of the silicon ring resonator, and Pt is the optical pump power for the thermal effect.Therefore, the total resonant wavelength shift δλ can be described by
Equation (5) reveals that the MRR red-shift δλ is proportional to the input pump power Ppump (mainly including Pm and Pt). Because coupling efficiencies of the MRR resonant wavelengths are higher, the pump light aligned at the resonances could induce stronger opto-mechanical interaction and thermal effect which would cause the larger resonance red-shifts.
Figures 2(a)-2(d) illustrate the operation principle of the proposed all-optical tuning process of the MPF. A random radio frequency (RF) is modulated onto an optical carrier by optical single sideband (OSSB) modulation, and the wavelengths of the optical carrier and the sideband are defined as λs and λs + λ1 respectively. As shown in Fig. 2(a), the optical carrier (λs) is located at the left flat edge of one notch resonance of the MRR. Then the OSSB signal (λs and λs + λ1) is injected into the free-hanging MRR without any pump light (pump off). When the sideband λs + λ1 just scans at the resonant notch peak of the resonator, the final RF response reaches the minimum, otherwise the output RF response should be the maximum. The frequency corresponding to wavelength of λ1 is defined as f1. Therefore, a notch MPF with central frequency of f1 is obtained, as shown in Fig. 2(b). Then, a pump light λp aligned with another resonant peak and the OSSB signal are simultaneously injected into the MRR (pump on). The transmission spectrum of the MRR would experience a wavelength red-shift (defined as λ2 - λ1), shown as the black dotted line in Fig. 2(c). The frequency corresponding to wavelength of λ2 is defined as f2. Thus the frequency interval between the optical carrier and the resonant wavelength becomes larger, leading to a notch MPF with a higher central frequency of f2, as shown in Fig. 2(d). In this way, the central frequency of the MPF could be tuned from f1 to f2. Therefore, by adjusting the input power of pump light, an all-optical tunable MPF has been achieved.
Fig. 2 Operation principle of the tunable MPF. (a)(b) Pump off: central frequency of the MPF is f1. (c)(d) pump on: central frequency of the MPF is f2.
In order to experimentally demonstrate the all-optical tunable MPF, we design and fabricate the free-hanging MRR on a commercial SOI wafer with 220-nm-thick silicon slab and 2 μm buried oxide layer. The free-hanging part of the MRR was released by selective etching process of three steps. At first, the layout of MRR and bus waveguide was transferred to ZEP520A photoresist by high resolution E-beam lithography (EBL) and etched downward for 195 nm to form a ridge waveguide through inductively coupled plasma (ICP) etching. Then, only half of the MRR which is away from the bus waveguide was patterned by the second EBL and etched downward for another 25 nm. In this case, the other half of the MRR and whole bus waveguide have 25 nm silicon slab layer to protect those fixed structure from later hydrofluoric (HF) acid. Finally, HF acid wet-etch was used to selectively undercut the buried oxide layer so as to release the free-hanging MRR, followed by critical point drying to avoid stiction. The scanning electron microscope (SEM) image of the free-hanging MRR is shown in Fig. 3(a). The bus waveguide, fixed arc and free-hanging arc of MRR have been marked with pink dotted line, blue dotted line and red dotted line, respectively. The radius and waveguide width of the MRR are 20 μm and 450 nm, respectively. The gap between the MRR and the bus waveguide is 210 nm. The vertical grating coupler is used to couple the optical signals from the fibers to silicon devices. As shown in Fig. 3(b), the etched depth, period and duty cycle of the coupler are 70 nm, 630 nm and 56%, respectively. The inset shows part of the zoom in grating coupler.
Figure 4(a) shows the measured transmission spectrum of the free-hanging MRR. The resonant wavelengths are 1547.49 nm, 1552.05 nm and 1556.61 nm respectively, indicating a free spectral range (FSR) of 4.56 nm. The extinction ratios (ERs) of the three resonant wavelengths are 22 dB (1547.49 nm), 20 dB (1552.05 nm) and 17 dB (1556.61 nm), respectively. Thus the resonance of 1547.49 nm with the maximum ER is chosen as the working region to realize the tunable MPF and pump light is accurately aligned at another resonance of 1552.05 nm. The zoom in spectrum of the working region around 1547.49 nm is shown as Fig. 4(b). To achieve better performance of beat frequency, the wavelength of 1547.442 nm in the left flat edge of the working region is selected as the optical carrier, which is 6 GHz away from the resonant wavelength of 1547.49 nm.
Fig. 4 (a) Measured transmission spectrum of the opto-mechanical MRR. (b) Zoom in resonant peak of 1547.49 nm.
In order to investigate the red-shifts of the free-hanging device, different pump powers are injected into the MRR respectively. With enhancing the pump power in the order of −18.5 dBm, −9.0 dBm, −5.5 dBm and −4.0 dBm, the MRR transmission spectra with red-shifts of 0.002 nm (blue solid line), 0.019 nm (red dotted line), 0.058 nm (green dashed line) and 0.079 nm (pink dash-dotted line) are shown in Fig. 5(a), respectively. Furthermore, we have also measured the resonance red-shifts as a function of the pump power ranging from −30 dBm to 0 dBm in steps of 3 dBm, as shown in Fig. 5(b).
Fig. 5 (a) Measured transmission spectra of the MRR under different pump powers. (b) The red-shifts of the MRR resonance under different input pump powers.
The frequency response of the notch MPF is deduced as follows. Assume that the RF signal (angular frequency of ωr) is modulated onto the optical carrier (angular frequency of ωo) by a phase modulator (PM). Thus the output optical field after phase modulation can be expressed as
where Eo is amplitude of the input optical field and γ is the phase modulation depth.Under a small signal model and neglecting the high order sidebands, optical double sideband (ODSB) signal of phase modulation can be expressed as
where Jn is the nth-order Bessel function of the first kind.By using a rectangular bandpass filter to remove the sideband of ωo - ωr, an OSSB signal (ωo and ωo + ωr) could be achieved. Then the OSSB signal is transmitted into the silicon MRR, the output optical field after the device can be expressed as
where H(ω) is the amplitude transmission function of the MRR.Neglecting the J12 term, the alternative current (AC) in the square-law photo-detector (PD) can be expressed as
Therefore, according to Eq. (9), when the sideband component ωo + ωr is aligned at the notch resonant peak, the MPF response reaches the minimum, otherwise it is a constant. Thus a notch MPF with central frequency of ωr could be realized. What is more, the pump light could cause different resonance red-shifts which means the intervals (i.e. ωr) between the optical carrier and the corresponding notch resonance are controllable. In this case, central frequency of the notch MPF is tunable by injecting different pump powers.
In order to simulate the frequency response of the notch tunable MPF, we substitute the measured resonance in Fig. 4(b) (i.e. 1547.49 nm) into Eq. (9). The optical carrier is fixed at 1547.442 nm. Thus in the case of no input pump light, a notch MPF with central frequency of 6 GHz could be obtained, shown as the blue solid line in Fig. 6. To further illustrate tunability of the MPF central frequency, three pump powers of −7.5 dBm, −4.5 dBm and −3.0 dBm have been chosen to shift the MRR resonance with 0.032 nm, 0.072 nm and 0.096 nm respectively. In these cases, the frequency intervals between the optical carrier and resonance could be tuned as 10 GHz, 15 GHz and 18 GHz, respectively. Therefore, a notch tunable MPF with the central frequencies of 6 GHz (blue solid line), 10 GHz (red dotted line), 15 GHz (green dashed line) and 18 GHz (pink dash-dotted line) could be achieved, as shown in Fig. 6.
3. Experimental results and discussions
In order to demonstrate the all-optical tunable MPF, we carry out experiments with the configuration as shown in Fig. 7. The blue solid lines and red dotted lines represent optical path and electrical path, respectively. The RF signal (for example, 19.5 GHz) from the vector network analyzer (VNA) (sweeping frequency, 20 GHz) is amplified by an electrical amplifier (EA) to drive the PM. The continuous-wave (CW) beam (1547.442 nm, 6 dBm) emitted from the laser diode (LD1) is modulated by the PM to generate an ODSB signal, shown as the green dashed line in Fig. 8. Subsequently, the ODSB signal is amplified by a forward erbium doped fiber amplifier (EDFA1). One sideband of the ODSB signal is eliminated by an optical bandpass filter to generate an OSSB signal. The transmission responses of the optical filter (bandwidth of 40 GHz) and the OSSB signal are shown as the blue dotted line and red solid line in Fig. 8, respectively. It should be noted that the optical carrier is located at the rising edge while the sideband is on the flat top of the optical filter. Thus the output powers of the optical carrier and sideband are almost same in order to get better beat performance. And then the OSSB signal with power of −5 dBm is injected into the silicon free-hanging MRR. The pump path consists of LD2, EDFA2, and a variable optical attenuator (VOA) to provide different pump powers. The wavelength of pump light emitted from LD2 is fixed at the MRR initial resonance of 1552.05 nm. Subsequently, the pump light is transmitted into the silicon chip through the optical circulator to induce red-shift of the MRR spectrum. After compensating the power attenuation by EDFA3, the output optical signal of the MRR is converted to alternative current by the PD and finally analyzed in the VNA.
Fig. 7 Schematic illustration of the experimental setup. The blue solid lines: optical path, The red dotted lines: the electrical path. LD: laser diode, PC: polarization controller, PM: phase modulator, EDFA: erbium-doped fiber amplifier, VOA: variable optical attenuator, PD: photodetector, EA: electrical amplifier, VNA: vector network analyzer.
It should be noted that as the pump power could be adjusted with high resolution (at least with steps of 0.01 dBm), frequency intervals between the optical carrier and the corresponding MRR resonance could be continuously manipulated so as to achieve continuously tunable MPF. The experimental frequency responses of the all-optical tunable MPF are shown in Fig. 9(a). With finely increasing the pump power from −30 dBm to −2.5 dBm, the central frequency of the notch MPF could be continuously tuned from 6 GHz to 19 GHz. Moreover, the highest operation frequency of the MPF is limited by the bandwidth of VNA. Thus the notch MPF could be tuned to higher frequency by using a VNA of larger measurement range. The 3dB bandwidth (the green line) and highest rejection ratio (the blue line) are 6 GHz and 49 dB respectively, as shown in Fig. 9(b). In the experiment, the rejection ratios of the MPF could be partly increased by the residual lower sideband due to the imperfect stability and filtering characteristics of the tunable bandpass filter, namely incomplete suppression to the lower sideband [42]. When the upper sideband scans at the MRR notch resonance, the amplitude of the attenuated upper sideband might be close to the residual lower sideband. Due to the approximately equal amplitude and π phase difference of the two sidebands, the signal power at the modulated RF frequency would be dramatically cancelled after detection by the PD [42, 43].
Fig. 9 (a) Measured notch MPFs with tunability of central frequency. (b) Features of rejection ratio and 3dB bandwidth.
Table 1 presents the performance comparisons of recent experimental demonstrations of on-chip tunable MPFs using nonlinear effects. In most works, high rejection ratios also come with high pump powers. Moreover, the waveguide lengths to motivate SBS effect are relatively long for on-chip integration. Therefore, the opto-mechanical MRR in this work is significant in on-chip tunable microwave systems, for reducing the input pump power while maintaining both the high MPF rejection ratio and compact device size.
Table 1. Performance comparisons of recent on-chip tunable MPFs using nonlinear effects
The performance of the tunable MPF is mainly determined by the free-hanging MRR, including transmission loss, ER and quality (Q) factor. Therefore, in the future the proposed scheme has many potential improvements. First, the transmission loss of the waveguides could be reduced by better fabrication process [44] and post-processing techniques [45], such as thermal oxidation [46]. For example, by employing the optical waveguides of 0.026 dB/cm loss [47] and MRR of 2 dB/cm transmission loss [48], the required pump power could be largely decreased. Second, by designing the MRR at the critical coupling to achieve maximum ER, the rejection ratio of the MPF could be significantly increased. Furthermore, the photonic crystals have smaller mode volumes compared with MRRs, which requires lower pump power to be activated [49]. Thus the pump power might be further reduced by using the photonic crystals instead of the MRR-based systems.
The tuning speed of current ring-based MPFs limits the progress of developing their practical applications in high-speed optical processing systems [50, 51]. The response speed of thermal tuning is about several hundred microseconds [42, 52] and the response speeds in the technology of tunable laser [16] or optical filter [53] are much lower. Fortunately, the opto-mechanical devices could realize a higher response speed (tens of nanoseconds) [31], which have significant applications for high-speed signal processing. In the future, some waveguide parameters of the MRR could be optimized to get better response performance. By optimizing the coupling gap and waveguide width, both higher coupling pump power and a smaller separation gap contribute to induce stronger optical nonlinear effects. Therefore, larger frequency shifts and faster responses could be realized. Besides the application of all-optical tunable MPF, the proposed mechanism in compact silicon devices might have other significant applications in microwave systems of all-optical control, such as microwave modulation and switch.
4. Conclusion
We have experimentally demonstrated an all-optical tunable MPF based on an opto-mechanical MRR. The experimental performances show that the central frequency of the MPF could be continuously tuned ranging from 6 GHz to 19 GHz, by injecting pump power lower than −2.5 dBm. Our experiment provides a tunable notch MPF scheme of compact footprint and low power consumption to remove certain undesired RF signals, which is useful in on-chip microwave photonic systems. Additionally, using light to control light, the compact opto-mechanical devices might have other significant applications to process microwave signals, such as microwave switch.
Funding
National Key Scientific Instrument & Equipment Development Program of China (2012YQ09016701); National Natural Science Foundation of China (NSFC) (61503350); Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan).
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