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Abstract
We propose and experimentally demonstrate a continuously tunable all-optical microwave filter based on a photonic crystal (PC) L3 cavity. Due to the small cavity mode volume and prominent optical properties, the required power to arouse the cavity nonlinear effects is low as microwatt level. Moreover, the cavity resonance could be continuously shifted by finely adjusting the input powers. Therefore, under optical single sideband modulation, the frequency interval between the optical carrier and cavity resonance could be controllable. In this case, the central frequency of the microwave photonic filter (MPF) could be continuously tuned with low power consumption. To the best of our knowledge, the experimental tuning efficiency of 101.45 GHz/mW is a record for on-chip tunable all-optical microwave filters. With dominant features of all-optical control, ultra-high tuning efficiency (101.45 GHz/mW), large rejection ratios (48 dB) and compact footprint (100 µm2), the proposed silicon nanocavity is competent to process microwave signals, which has many useful applications in on-chip energy-efficient microwave photonic systems.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
With dominant advantages of flexible tunability and reconfigurability, wide bandwidth and immunity to electromagnetic interference, microwave photonic filters (MPFs) have attracted widespread attentions in wireless communication and radar systems [1–5]. In order to process random radio frequency (RF) signals, numerous tunable MPFs have been demonstrated by utilizing fiber technology [6–9]. In the past decade, owing to the features of compatible with complementary metal-oxide semiconductor (CMOS) [10], compact silicon-on-insulator (SOI) devices are used to realize tunable MPFs in order to pursue better reliability, stability and integration [11–13]. Most schemes require special assistants, such as tunable laser diodes or optical filters, which increase the system complication. To date, only several nonlinear effects are utilized to achieve on-chip all-optical tunable MPFs, such as thermo-optic effect [14] or opto-mechanical effect [15,16] in microring resonators (MRRs), and stimulated Brillouin scattering (SBS) in chalcogenide waveguide [17] or silicon waveguides [18]. However, their relatively low tuning efficiencies or long waveguide lengths (centimeter level) are not beneficial to realize low-power and large-scale integrations. To break the above limitations, it is urgent to realize an effective solution for tunable MPFs with high tuning efficiencies so as to promote the applications of microwave photonic chips [19–22].
In the last decade, photonic crystal (PC) nanocavity has attracted increasing interests due to its small mode volume and strong light-matter interactions [23–28]. The nonlinear effects in the nanocavity are largely enhanced and could be excited by ultra-low powers [29–32], which has been used to realize mangy applications, including high-sensitive sensors [33–35], light emitting diodes [36–38] and nonreciprocal transmission [39–41]. Therefore, the nanocavities especially the PC cavity provide efficient and all-optical control solutions to process optical signals with low power consumption [42–45]. However, there is limited efforts to realize tunable all-optical microwave filters by using silicon PC cavities.
In this paper, we experimentally demonstrate a tunable all-optical microwave filter based on an on-chip silicon PC L3 cavity. By injecting optical powers lower than 0.069 mW, the central frequency of the all-optical microwave filter could be continuously tuned from 13 GHz to 20 GHz. Namely, the MPF tuning efficiency could realize up to 101.45 GHz/mW. To our knowledge, this is the highest tuning efficiency for all-optical microwave filters, which has important applications in on-chip microwave photonic systems with low-power consumption.
2. Operation principle
The key device to realize all-optical tunable MPF is an on-chip PC L3 cavity, which consists of a PC membrane with a line of three holes missing. As shown in Fig. 1, the device consists of a cavity and a waveguide. The amplitudes of the input light from port 1 and reflected light to port 1 are expresses as S+1 and S−1, respectively. The amplitudes of the PC cavity mode and output light to port 2 are described by u and S−2, respectively. The lattice constant and the radius of air holes are denoted by a and r, respectively. The propagation distance of the light wave is written as 2d. The decay rates from the nanocavity into the free space and into the waveguide are expressed as 1/τv and 1/τin, respectively.
The relationships between the cavity modes in time domain, input and output light wave can be described as follows
Based on Fourier transformation, transmittance of the cavity can be denoted by
The tuning mechanism of the all-optical microwave filter is based on the strong nonlinear effects in the PC cavity. Due to the small mode volume and long resonant photon lifetimes, stored electromagnetic energy density of the PC cavity would be extremely high. Thus the required powers to manipulate the PC cavities are much lower than the microring-based systems. When optical powers are injected into the cavity, nonlinear effects would be aroused, including thermo-optic effect, plasma dispersion effect and Kerr effect. The thermo-optic effect resulting from two-photon absorption, free-carrier absorption and linear absorption would increase the material refractive index and induce cavity resonance red-shift, whose response time is microsecond level. On the contrary, the generated free carriers would cause the dispersion effect and induce a resonance blue-shift with a faster response time of nanosecond level. Moreover, the Kerr effect in the silicon device is not strong due to the material characteristics, and its response time is picosecond level.
Under the nonlinear effects, the resonant angular frequency of the nanocavity would be shifted to
Total energy decay rate could be described as
Figure 2 shows the simulated transmission spectra of the PC cavity based on Eq. (4), when τv and the cavity resonant wavelength are set as 0.6 ns and 1550 nm, respectively. The wavelength of the input pump light is chosen as 1550 nm (i.e. the initial resonant wavelength). By utilizing the nonlinear coupled mode model of PC cavity [50,51], the transmission spectra of the PC L3 cavity at different input powers are calculated, shown as the black solid line (no input power), red dotted line (0.008 mW), green dash-dotted line (0.013 mW), pink dashed line (0.017 mW) and blue solid line (0.02 mW) in Fig. 2(a). The extinction ratios are about 29 dB. It can be seen that with injecting optical powers low as microwatt levels, the nanocavity resonance could be continuously shifted with high tuning efficiencies. The zoom-in image of the cavity transmission spectra is shown in Fig. 2(b). It can be seen that the corresponding resonance red-shifts are 0.004 nm (red dotted line), 0.008 nm (green dash-dotted line), 0.012 nm (pink dashed line) and 0.016 nm (blue solid line), respectively.
Fig. 2. (a) Simulated transmission spectra of the PC cavity at different input powers. (b) Zoom-in image of the PC transmission spectra.
The frequency response of the all-optical microwave filter is discussed as follows [15]. The wavelength of optical carrier is denoted by λc (corresponding to frequency fc) which is located in the flat edge of the cavity notch resonance. An input RF signal Vr cos(2πfrt) with an amplitude of Vr and a frequency of fr is utilized to modulate the optical carrier fc. The generated optical single sideband (OSSB) signal by phase modulation can be expressed as
Then the OSSB signal is injected into the PC cavity and finally processed in the square-law photo-detector (PD). The alternative current (AC) in the PD can be described by
On the basis of Eq. (8), the key factor to realize tunable all-optical microwave filter is to manipulate the frequency intervals (i.e. ωr) between the optical carrier ωc and the corresponding notch resonance. The operation principle is to tune the cavity resonant wavelength in all-optical domain. As shown in Fig. 3(a), the black curve represents the original transmission spectrum of the PC cavity. The optical carrier λc is located in the left flat edge of the black notch peak, and the wavelength interval between λc and the resonant wavelength is λ1 (corresponding to frequency of f1). Then the OSSB signal is sent into the PC cavity without any pump light. When the sideband λc + λ1 exactly aligns at the cavity resonant wavelength, the output microwave response reaches the minimum value, otherwise the final microwave response would be a maximum constant. Therefore, a notch MPF with central frequency of f1 is obtained, shown as the pink solid curve in Fig. 3(b). Subsequently, a pump power is injected into the device in order to cause the nonlinear effects in the PC cavity. Thus the device transmission spectrum would be shifted to the red dashed curve in Fig. 3(a). In this case, the wavelength interval between λc and red-shift resonant peak increases to λ2 (corresponding to a larger frequency of f2), which leads to a larger MPF central frequency of f2, shown as the green dashed curve in Fig. 3(b). Through utilizing the nonlinear effects in the PC cavity, the central frequency of the MPF could be tuned from f1 to f2 in all-optical domain. Therefore, tunable all-optical microwave filter could be realized by manipulating the input pump powers.
Fig. 3. Operation principle of the tunable all-optical microwave filter. (a) Red-shift transmission spectrum of the cavity. (b) The all-optical microwave filter with tunable central frequency.
In order to experimentally demonstrate the all-optical tunable MPF, we design and fabricate the PC L3 nanocavity on a commercial SOI wafer with 220-nm-thick silicon slab and 3 µm buried oxide layer. By E-beam lithography (EBL), the PC cavity structure was transferred to ZEP520A photoresist. Subsequently, through inductively coupled plasma (ICP) etching, the device pattern was defined on the top silicon layer which was etched downward for 220 nm. Figure 4(a) shows the scanning electron microscope (SEM) image of the silicon device whose footprint is about 10 µm ×10 µm. The lattice constant a and air hole radius r are 420 nm and 120 nm, respectively. As shown in Fig. 4(b), the finite difference time domain (FDTD) method is utilized to simulate the electric field (Ey) profiles of the cavity resonant mode. The field intensity of the compact nanocavity is largely enhanced.
Fig. 4. (a) SEM image of the silicon PC L3 cavity, respectively. (b) The simulated electric field (Ey) profiles of the cavity resonant mode.
Figure 5(a) shows the measured transmission spectrum of the fabricated PC nanocavity under different input pump powers. Without input powers, the device original spectrum is shown as the green solid line. The initial resonant wavelength and extinction ratio (ER) of the PC cavity are 1552.72 nm and 27 dB, respectively. When the input power of the initial resonant wavelength (i.e. 1552.72 nm) is set to 0.018 mW, the resonance of the PC cavity would shift to 1552.73 nm due to the nonlinear effects, shown as the red dotted curve. Subsequently, we continue to enhance the input power to 0.025 mW. In this case, the cavity spectrum could experience a larger red-shift of 0.02 nm, shown as the blue dashed curve. Furthermore, in order to investigate the relationships between the input powers and red-shifts of the resonant wavelength, different powers are injected into the nanocavity. As shown in Fig. 5(b), when the input power is tuned as 0.06 mW, the red-shift of cavity resonant wavelength is larger than 0.048 nm (i.e. 6 GHz). Therefore, the silicon PC nanocavity could be efficiently tuned.
Fig. 5. (a) Measured transmission spectrum of the PC cavity under different input powers. (b) The resonant red-shifts under different input powers.
To simulate the frequency response of the tunable all-optical microwave filters, we combine the measured cavity transmission spectrum in Fig. 5 and Eqs. (4)–(8). The wavelength of the optical carrier is fixed at 1552.6 nm which is 15 GHz away from the cavity resonance 1552.72 nm. In the case of no pump power, a notch MPF with central frequency of 15 GHz could be achieved, shown as the blue solid line in Fig. 6. To further investigate the tunability of the MPFs, different pump powers of 0.016 mW, 0.022 mW and 0.027 mW are selected to shift the cavity resonances with 0.008 nm, 0.016 nm and 0.024 nm, respectively. Therefore, the corresponding MPFs with central frequencies of 16 GHz, 17 GHz and 18 GHz could be realized, shown as the pink dash-dotted line, red dotted line and green dashed line respectively.
3. Experimental results and discussions
3.1 Experimental results
The experimental configuration to demonstrate the tunable all-optical microwave filter is shown in Fig. 7. The electrical path and optical path are expressed by the red dotted line and green solid line, respectively. There are two major optical paths, including signal path (the blue box) and pump path (the red box). The signal path is to realize OSSB modulation. The RF signals emitted from the vector network analyzer (VNA) are amplified by the electrical amplifier (EA) to drive the phase modulator (PM). The optical carrier is launched from the laser diode 1 (LD1) whose wavelength is fixed at 1552.616 nm. Namely, the frequency interval between the optical carrier and cavity resonant wavelength is 13 GHz. The output signals from the PM is optical double sideband (ODSB) signal and then sent into the optical filter to remove one sideband. Thus OSSB signals could be generated and injected into the PC cavity. The output light from the silicon chip is transmitted into the PD through the optical circulator and the converted AC is finally analyzed by the VNA. On the other hand, the pump path including LD2, erbium-doped fiber amplifier (EDFA2) and variable optical attenuator (VOA2) could provide different optical powers. The wavelength of the pump light is aligned at the initial resonant wavelength of the nanocavity, namely 1552.72 nm. Through the optical circulator and the grating coupler, the variable powers are sent into the PC cavity to induce the required resonance red-shifts. In this case, continuously tunable all-optical MPFs could be experimentally achieved.
Fig. 7. Schematic illustration of the experimental setup. The green 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 the optical powers provided by the pump path could be adjusted with high resolution so as to continuously control the frequency interval between the optical carrier and cavity resonance. In this case, the central frequency of the all-optical microwave filter could be continuously tuned by precisely manipulating the pump powers. As shown in Fig. 8(a), with finely increasing the pump powers from none to 0.069 mW, the corresponding MPF frequencies could be continuously tuned from 13 GHz to 20 GHz. As the highest required power is 0.069 mW to realize a frequency tuning range of 7 GHz, the MPF tuning efficiency is 101.45 GHz/mW. Figure 8(b) shows the rejection ratios of the MPF, which are around 45 dB.
Table 1 illustrates recent experimental performances of on-chip tunable MPFs based on different nonlinear effects. Firstly, we have realized an ultra-high tuning efficiency up to 101.45 GHz/mW. The tuning efficiencies of previous schemes are lower than 25 GHz/mW. Secondly, compared with other devices, the size of our cavity (100 µm2) has decreased for several orders of magnitudes. Especially, the waveguide lengths to arouse the SBS effect in chalcogenide or silicon waveguides are centimeter magnitude which are not beneficial for large-scale integration. Therefore, the proposed PC cavity with a compact footprint of 100 µm2 is significant to largely reduce the power consumptions and footprints of the on-chip all-optical systems.
Table 1. Performances of recent on-chip tunable MPFs using nonlinear effects
3.2 Discussions
The influence of the sideband power on the MPF central frequency is investigated. According to Eq. (7), the power of the optical sideband is related with the input optical field and the Bessel function. Although the input RF powers have an impact on the Bessel function, one key factor to determine the power of the optical sideband is the input optical field. Consequently, with high or low input RF powers, the power change of the optical sideband and its influence on the MPF frequency could be controlled by adjusting the power of the input light (e.g. −10 dBm). With tuning the input RF powers from −90 dBm to 10 dBm, the measured maximum frequency shift of the MPF is lower than 0.03 GHz and the filter shape almost remains unchanged. Therefore, the cavity-based MPF could handle a large dynamic input range.
By calculating the device characteristics (including the refractive index changes), the contributions of the various nonlinear effects to the cavity resonance shifts are also explored. Firstly, the index change δnTO induced by the thermal effect can be written as
Secondly, the normalized modal index change due to the dispersion effect could be denoted by
Finally, the normalized modal index change induced by the Kerr effect could be expressed as
By utilizing the above equations and adopting the parameters in Ref. [51], the resonance shifts induced by the thermal effect (green dashed line), the Kerr effect (blue dotted line), the dispersion effect (orange dot-dashed line) and the total effects (the red solid line) are calculated respectively, as shown in Fig. 9. It can be seen that the thermal effect dominates the resonance shifts of the nanocavity.
From the perspective of Q factor, two major parameters of the all-optical microwave filters could be improved by using a high-Q cavity. Firstly, the required input powers could be reduced [52], thus the tuning efficiency could be accordingly enhanced. The Q factor indicates the ability to store energy in the PC cavity. A higher Q factor represents a lower rate of energy loss and the oscillations die out more slowly. Because of the cavity small mode volume and the high Q factor, stored electromagnetic energy and energy density would be extremely high. Thus the optical nonlinear effects could be significantly enhanced which leads to lower required powers [53]. Secondly, the minimum of the MPF central frequency could realize a lower value. With a high-Q cavity, the frequency interval between the optical carrier and the cavity resonance could be much closer. Namely, the MPF could be tuned from lower than 1 GHz (e.g. Q = 2×105). And theoretically, there is approximately no restriction of the maximum central frequency in our scheme. In this case, the tuning range of the proposed MPF could be tuned from several hundred MHz to tens of GHz, which is competent to process microwave signals in wireless communication systems. On the other hand, by designing the cavity at critical coupling, the rejection ratios of the MPF could be optimized due to the larger cavity extinction ratios. Furthermore, the device transmission loss could be decreased by utilizing post-processing technology and better fabrication technology [54–56], which is also beneficial to improve the MPF tuning efficiencies [57].
4. Conclusion
We have experimentally demonstrated the realization of an all-optical tunable MPF based on a PC L3 nanocavity. With precisely adjusting the input optical powers to induce the cavity nonlinear effects, the central frequency of the all-optical microwave filter could be continuously tuned from 13 GHz to 20 GHz. The highest required power is as low as 0.069 mW indicating an ultra-high tuning efficiency of 101.45 GHz/mW. The MPF rejection ratios could realize 48 dB. Moreover, the compact footprint of the silicon device is only 100 µm2. The experimental results show that the proposed silicon nanocavity is an efficient solution to realize on-chip tunable MPFs with dominant advantages of ultra-high tuning efficiency, all-optical control and compact footprint, which has useful applications in on-chip microwave photonic systems.
Funding
National Natural Science Foundation of China (61805215, 61801063); 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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