Positive link gain microwave photonic bandpass filter using Si3N4-ring-enabled sideband filtering and carrier suppression

Microwave photonic bandpass filters (MPBPFs) are important building blocks in radio-frequency (RF) signal processing systems. However, most of the reported MPBPFs fail to satisfy the stringent real-world performance metrics, particularly low RF insertion loss. In this paper we report a novel MPBPF scheme using two cascaded integrated silicon nitride (Si3N4) ring resonators, achieving a high link gain in the RF filter passband. In this scheme, one ring operates at an optimal over-coupling condition to enable a strong RF passband whilst an auxiliary ring is used to increase the detected RF signal power via tuning the optical carrier-to-sideband ratio. The unique combination of these two techniques enables compact size as well as high RF performance. Compared to previously reported ring-based MPBPFs, this work achieves a record-high RF gain of 1.8 dB in the passband, with a high spectral resolution of 260 MHz. Furthermore, a multi-band MPBPF with optimized RF gain, tunable central frequencies, and frequency spacing tunability is realized using additional ring resonators, highlighting the scalability and flexibility of this chip-based MPBPF scheme. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Microwave photonic filters (MPFs) eliminate unwanted interference and channelize the signal of interest, which play an important role in numerous applications such as RF receivers [1], as well as enabling optoelectronic oscillator (OEO) [2]. Compared with traditional electrical filter, MPFs exhibit advantages including high frequency, wide tunable range, and electromagnetic immunity [3]. Because of the improved stability and reduced system footprint enabled by compact integrated photonic devices, integrated microwave photonic filter (IMPF) has gained great interests [4].
Integrated microwave photonic bandpass filters (IMPBPFs) have been implemented using ring resonator based optical filter [5][6][7][8][9][10][11], on-chip Bragg gratings [12][13], multi-tap finite impulse response (FIR) [14][15], and stimulated Brillouin scattering (SBS) based selective sideband amplification [16][17]. Integrated ring resonators enable the implementation of IMPBPFs in a passive and potentially compact form, allowing multiple resonators to be cascaded on a single bus waveguide to expand the functionality [9,11]. In [5][6], the combined use of an intensity modulator and a ring resonator based on one-to-one spectrum mapping from the optical filter response to RF domain was demonstrated. However, it was difficult to achieve high extinction ratio using intensity-modulator-based scheme. In order to improve the extinction ratio, phase-modulator-based ring resonator approaches using RF interference cancellation was reported [7][8][9][10][11]. In [7][8][9][10], an MPBPF using a silicon-on-insulator (SOI) ring resonator as an optical notch filter to achieve phase modulation to intensity modulation conversion was proposed. Compared with the above-mentioned silicon ring resonators with a typical linewidth of tens of GHz or several GHz, the silicon nitride (Si 3 N 4 ) platform is able to offer narrower linewidth in sub-GHz level due to the lower waveguide loss [18]. In [11], a MPBPF with a 3 dB bandwidth of 0.673∼2.798 GHz based on a Si 3 N 4 ring resonator and phase modulation was demonstrated.
Although the above-mentioned ring-based bandpass filter demonstrations emphasize advanced functionality, the improvement of filter passband RF performance by optimizing the coupling configuration has not been studied. Furthermore, in contrast to the intensity modulation approach, the use of phase modulation does not offer the access to optical carrier-to-sideband ratio tuning for link performance optimization [18]. A chip-based approach that enables tunable carrier-tosideband ratio in a phase modulation configured link, would be very attractive as it would allow for increased system metrics, including RF gain, noise figure and spurious free dynamic range for practical RF applications [19][20].
In this paper, we report a positive link gain and versatile IMPBPF based on cascaded Si 3 N 4 ring resonators for optical sideband filtering and carrier suppression. We reveal that an over-coupled (OC) ring resonator with a π phase inversion enables high RF gain in the passband with narrow bandwidth. To further enhance the RF link gain, an auxiliary ring resonator operated in the under-coupled (UC) condition is used to optimize the optical carrier-to-sidebands ratio by suppressing the optical carrier of a phase-modulated signal. We experimentally achieved a chip-based MPBPF with a record-high RF gain of 1.8 dB, and a FWHM of 260 MHz. We also show that the number of passbands is scalable to achieve multichannel filter responses while sustaining optimized RF gain, by simply using additive ring resonators.

MPBPF with one ring resonator
The operating principle of the proposed MPBPF based on one ring resonator is shown in Fig. 1. In the optical domain, an optical carrier is phase modulated, generating two out-phase sidebands with an identical amplitude. A ring resonator is used to control the amplitude and phase of one sideband to achieve phase modulation to intensity modulation conversion. For a ring resonator operating at the OC status, a π-phase shift is introduced at the desired notch frequency in the upper sideband. After photodetection, the constructive interference between mixing products of carrier and two optical sidebands takes place at ω RF , forming a strong passband. Meanwhile, perfect destructive interference between mixing signals occurs outside the pass band frequency range, resulting in signal suppression. In contrast, for a ring resonator operating at the UC status, the amplitude of the optical signal at the desired notch frequency in the upper sideband is suppressed. After photodetection, partial destructive interference between mixing signals takes place at the pass band frequency. Similarly, perfect destructive interference between mixing signals occurs outside the pass band frequency range. Although both schemes can implement a passband response, the passband strength and bandwidth show distinct difference. In order to explain this, a theory model is established as follows.
According to the transfer function of the ring resonator, the extinction ratio E R of a ring resonator can be written as [21] Where a is the single-pass amplitude transmission, including both propagation loss in the ring and loss in the coupler, r is the self-coupling coefficient. Combined with the transfer function of the PM, the photocurrent at the output of the photodiode can be written as [9] Where I ave is the average photocurrent at the output of the PD, J n is the nth-order Bessel function of the first kind, m=πV RF /V π is the modulation index of the PM, V RF is the input RF signal voltage, V π is the RF half-wave voltage of the PM, φ=βL is the single-pass phase shift, with β the propagation constant of the circulating mode and L the round trip length, ω RF is the input RF signal frequency, which equals to the frequency difference between the optical carrier and the notch frequency of the ring resonator.
We considered a small signal approximation, i.e., m<<1, then J n (m)≈m n /(2 n n!). According to Eq. (2), when φ=2π, the gain of the proposed band-pass filter based on one ring resonator can be written as where Z in and Z out are the input and output impedance of the system. According to Eq. (2), the full width at half magnitude (FWHM) of the bandpass filter based on one ring resonator can be written as where FSR is the free spectrum range of the ring resonator, and A is the half peak power response of the band-pass filter, given by Based on Eqs. (1), (3), and (4), Fig. 2 shows the calculations of RF gain and FWHM a function of ring extinction ratio, which provides the theoretical basis of finding the desirable ring condition for optimal RF filtering performance (see Fig. 3). In this simulation, we use parameters of the actual devices used in the experiment as the following: FSR = 25.4 GHz, a = 0.986, ω RF =11 GHz, V π = 5 V, I ave =14 mA, and Z in =Z out =50 Ω. Note that the insertion loss of the input and output RF cables of the VNA is about 3 dB at 11 GHz frequency. It can be seen from Fig. 2(a) that the RF gain for the OC-ring-based MPBPF decreases as the ring extinction ration increases due to the decreased degree of constructive interference between the mixing signals at the notch frequency. On the contrary, the RF gain for UC-ring-based MPBPF increases as the increase in the ring extinction ration because of the reduced strength of partial destructive interference between the mixing signals at the notch frequency. Although the overall RF gain of the OC-ring-based MPBPF is higher than that of the UC one owing to the constructive interference between mixing products of optical carrier and two sidebands, the FWHM of OC-ring-based MPBPF is broader than in case of using an UC ring, as shown in Fig. 2(b). This is due to the fact that the self-coupling coefficient for OC ring is smaller than that for UC ring. In practical applications, a bandpss filter with higher RF gain and narrower bandwidth is preferred. In order to find out an optimal trade-off between gain and bandwidth, the ratio between RF gain and FWHM is introduced as the figure of merit to evaluate the performance of the ring-resonator-based MPBPF, as shown in Fig. 3. It can be seen from Fig. 3 that the ratio of RF gain to FWHM for OC-ring-based MPBPF is in general larger than that of UC one, indicating that the RF gain for OC-ring-based MPBPF shows a better overall performance than that of UC one with the same FWHM or the FWHM for OC-ring-based MPBPF is narrower than that of UC one with the same RF gain. From the curve, there exists an optimum spot that offers the peak ratio of RF gain to FWHM.

MPBPF with improved RF gain using an auxiliary ring resonator for carrier suppression
In an intensity-modulator-based microwave photonic link, the combined use of a low biasing Mach-Zehnder Modulator and an Erbium Doped Fiber Amplifier (EDFA) can improve the RF gain of the link [22][23]. One approach is to put the EDFA before the low biasing MZM [22]. In this case, extreme high input power to the MZM is required in order to ensure high power at the PD, which may damage the modulator. In order to solve this problem, another approach is to put the EDFA after the low biasing MZM and ensure that the input power to the PD are the same [23]. Thus, to investigate the gain optimization of the PM based MPBPF system, we use an additional ring resonator to suppress the optical carrier and place an EDFA after the PM to ensure the input power at the PD are the same. According to the above analysis, the first ring resonator works in the OC region to achieve phase modulation to intensity modulation conversion with high ratio of RF gain to FWHM. For the second ring resonator, it is operated in the UC regime to suppress the optical carrier, as shown in Fig. 4. The theoretical analysis is as follows. The output power of the first OC ring resonator can be written as Where P c and P s are the optical carrier and any one of optical sidebands power at the output of the PM, respectively. When another UC ring resonator is used to suppress the optical carrier, and a low noise-EDFA (LN-EDFA) is used to compensate the loss of the optical power, the output optical power of the LN-EDFA can be written as Where β is the optical carrier suppression ratio in dB. We can adjust the gain of the LN-EDFA to satisfy P 1r =P 2r . Thus, the required gain for LN-EDFA can be written as where is the power ratio between the optical carrier and sidebands of the first ring resonator. According to Eqs. (6), (7), and (8), the gain improvement of the band pass filter using two ring resonators is qualitatively represented by According to Eq. (10), the gain improvement can be plotted as a function of optical carrier suppression ratio at different input optical carrier-to-sidebands ratio, as shown in Fig. 5. This figure is important for guiding the subsequent experimental implementation. It can be seen from Fig. 5 that the amount of gain improvement increases and then decreases with the increase of optical carrier suppression ratio. The maximum gain improvement can be obtained when the power of the optical carrier equals to that of total sidebands. When the suppression of the optical carrier is less than 10 dB, the gain improvement is almost the same with different input optical carrier to sidebands ratio since ∆G≈1/β in this case, as shown in Eq. (10). When the suppression of the optical carrier is larger than 10 dB, the gain improvement for higher input optical carrier to sidebands ratio is larger than that for lower input optical carrier to sidebands ratio. This is due to the fact that the required gain of LN-EDFA to ensure the same optical power before the PD increases as the increase of input optical carrier to sidebands ratio. Furthermore, we should note that the noise of the system will be increased after reducing the input power of the LN-EDFA due to the noise dynamics of the optical amplifier [20]. Figure 6 depicts the experimental setup for demonstrating the proposed MPBPF. An optical carrier from a distributed feedback (DFB) laser was modulated by RF signals driven by a vector network analyzer (VNA), generating two equal-amplitude and out-phase optical sidebands via a phase modulator (PM) with a half-wave voltage of 5 V and an insertion loss of 3.4 dB. The modulated optical signal is then coupled into an integrated silicon nitride circuit fabricated using the low-loss TriPleX (Si 3 N 4 /SiO 2 ) technology [24]. The circuit consists of optical ring resonators coupled to one bus waveguide in series. The function of the first OC ring resonator is sideband filtering, the second UC ring resonator is used to suppress the optical carrier. In order to demonstrate the scalability of the proposed scheme, a third OC ring resonator is added to form the second passband. Each ring has an FSR of 25.4 GHz, and the coupling coefficient and resonance frequency are tunable through thermo-optic tuning. The chip has an optical insertion loss of 7.2 dB, with a low propagation loss of 0.2 dB/cm. Since the total intrinsic loss of the PM and Si 3 N 4 ring resonators circuit is 10.6 dB, a LN-EDFA is placed at an optimal location, i.e. after the chip to offset the optical insertion loss, after considering the power handling capability of modulators and chip. It also ensures that the optical power for one ring based MPBPF and two cascaded rings based MPBPF are the same. The amplified optical signal is detected by a photodetector (PD) and the converted RF signal is measured by the VNA. For all measurements, the photocurrent of the PD remained nearly constant around 14 mA.

Performance analysis and comparison
To demonstrate the MPBPF scheme with high RF gain, cascaded OC and UC ring resonators were used, based on the principle illustrated in Fig. 4. The extinction ratio of the OC ring resonator is 7 dB by adjusting the coupling coefficient to maximize the ratio of RF gain to FWHM as shown in the inset of Fig. 3. The optical carrier is suppressed by 6 dB by controlling the coupling coefficient of the UC ring resonator. The 20 dB extinction ratio of filter with tunable pass band frequencies can be achieved, as shown in Fig. 7. However, the shape is degraded when the central frequency is 3 GHz (see Fig. 7(b)). This is due to the extra phase shift of the optical carrier caused by the thermal drifting of the UC ring resonator, leading to imperfect destructive interference of the filter stopband. It can be also seen from Fig. 7 that high RF gain is achieved due to the optimized optical carrier to sidebands ratio. Positive RF gain can be obtained when the pass bands frequencies are 1 GHz and 3 GHz. The RF gain decreases with the increase in the passband frequency. This is owing to the fact that the RF half-wave voltage of the PM increases with the increase of the RF frequency, leading to a lower modulation efficiency. Furthermore, the loss of RF cable increases and the responsivity of the PD decreases with the increase of the RF frequency. It should be noted that the maximum frequency tuning range is ∼12 GHz, limited by half of the resonator's FSR (25.4 GHz). In order to show the advantage of two rings, we compare the performance of two cascaded ring resonators based MPBPF with the filter using only one OC ring, under the same received optical power at the PD. The measured RF gain, noise power spectral density (PSD), and noise figure of these two schemes over the entire tuning range of the filter (1-11 GHz) are shown in Fig. 8. It can be seen from Fig. 8(a) that the RF gain for two cascaded ring resonators based MPBPF is about 6 dB higher than that for OC ring resonator based filter. The experimental results are consistent with the theoretical analysis shown in Fig. 5. We can see from Fig. 8(b) that the noise figure for two cascaded ring resonators based MPBPF is a little lower than that for OC ring resonator based filter. This can be explained by noting that the increase of the noise power is smaller than the increase of the link gain, as shown in Fig. 8(a).
Another important performance metric in microwave photonic system is linearity which evaluates the signal distortion. In order to evaluate the linearity, two tone test with a tone spacing of 0.5 MHz is implemented. The measured third-order intermodulation (IMD3) signals powers as a function of input RF power at the two-tone center frequency of 11 GHz for both schemes are depicted in Figs. 9(a) and 9(b). It can be seen that the measured third-order SFDR for two cascaded ring resonators based MPBPF is 107.4 dB·Hz 2/3 with the noise power spectral density of −140.6 dBm/Hz, which is about 1 dB higher than that for OC ring resonator based MPBPF. This is due to the fact that the increase of noise floor and IMD3 are smaller than the increase of the fundamental signal. The performance comparison for SFDR over the entire tuning range is shown in Fig. 9(c). It can be seen from Fig. 9(c) that the variations of the SFDR for two cascaded ring resonators based MPBPF from 1 GHz to 11 GHz is 99.7-107.4 dB·Hz 2/3 . The SFDR for low frequency is smaller than that for high frequency since the relative intensity noise at low frequency is higher than that at high frequency.

Scalable passbands using multiple ring resonators
Multiband MPBPF is important for RF applications where RF signals of interest are accommodated in different frequency channels and crosstalk needs to be isolated. The number of passbands with optimized RF gain can be increased by activating more ring resonators. As shown in Fig. 10, a second independently tunable pass band is subsequently added by activating a third OC ring resonator. The center frequency and frequency interval of the two passbands MPBPF can be tuned independently. It is noted that the RF gain for both passbands are high, and the gain difference between two pass bands is owing to the frequency-dependent power response of electro-optical devices, including RF cables, the modulator, and the photodetector. In order to simultaneously demonstrate the negligible RF loss and high suppression of the proposed MPBPF, a signal-filtering experiment was performed, emulating the practical application scenario where the strong unwanted interference needs to be suppressed while maintain the quality of the signal of interest. In the experiment, a relatively weak RF signal of interest is input to our filter, in the presence of a strong interference signal. After passing through a bandpass filter with a central frequency of 4.97 GHz, a FWHM of 260 MHz, and a gain of −0.6 dB, the output RF spectral is measured, as shown in Fig. 11. The input power of RF signal of interest is −60.3 dBm and the frequency is 4.97 GHz which locates at the pass band, while the power of interference signal is −49.6 dBm and the frequency is 5.9 GHz which locates outside the passband. It can be seen from Fig. 11 that after filtering, the RF signal of interest is just attenuated by 0.6 dB while the interference signal is suppressed by 28 dB. The result shows the capacity to select the desired signal, while blocking strong jamming signals in the adjacent channel in practical applications.

Discussion
We compared the performance of our proposed IMPBPF to previously reported techniques in terms of RF gain, FWHM, and gain to FWHM ratio, as shown in Table 1. In terms of the RF gain, our MPBPF shows a significant advantage over other reported work, increasing to 1.8 dB from −54.5 dB [5,[7][8][9][10][11]25]. In contrast to SOI-based MPBPFs [5,7,8], the resolution of our filter exhibits an improvement of at least one order of magnitude. The comparison of G/FWHM indicates that our filter exhibits distinct overall advantages over the reported work. For the proposed MPBPF, the maximum RF gain can be obtained when the power of the optical carrier equals to that of total sidebands, as shown in Fig. 5. It should be noted that, the zero phase point of an UC ring resonator is unstable due to the resonance drifting caused by thermal effects. To minimize this effect in experiments, we used an UC ring resonator with a low rejection ratio for carrier suppression. Temperature feedback control can also be used to reduce the thermal drifting of the ring resonator for practical applications [26][27]. To further suppress the optical carrier to improve the RF gain, one possible approach is to use a phase modulation configuration and hybrid photonic circuits consisting SBS waveguides and ring resonators [28]. Furthermore, integrated phase modulator with a lower RF half-wave voltage of 3.5 V at 10 GHz [29] and on-chip photodetector with a higher responsivity of 1.04 A/W [30] are available on the shelf, which can be used to improve the RF gain, according to Eq. (3).
Since cascaded ring resonators are employed, it is necessary to analyze the thermal crosstalk of our system, which is measured by fixing one ring resonator and changing the coupling coefficient and phase of the other ring resonator through thermo-optic tuning. By tuning a large voltage range from 0 to ∼27 V, the measured maximum frequency shift of the un-tuned ring is 13.5 MHz which is < 4% of the ring's FWHM. Such insignificant frequency drifts can be corrected or compensated using the 12-bit voltage control subsystem used in our silicon nitride ring circuit [31].
In order to optimize the performance of the proposed MPBPF, the position of the LN-EDFA that is required in our current implementation is important. If the LN-EDFA is placed before the PM, additional optical loss should be introduced before the optical signal injected to the LN-EDFA since the optical power before the PM is far beyond the normal input power range of the LN-EDFA. Besides, the output power of the LN-EDFA must be high enough to compensate the insertion loss of the PM and the ring resonators chip, which may damage the modulator [21]. If the LN-EDFA is placed before the ring resonators chip, in-cavity optical intensity will be much stronger to cause significant thermal drifting of the ring resonance. Thus, considering the optical power after the ring resonators chip is still high (6 mW) enough to avoid introducing large noise, we placed the LN-EDFA after the ring resonators chip to offset the loss caused by carrier suppression, so that the RF gain, noise figure and SFDR of the proposed filter are optimum.
It is possible to integrate all components of the proposed ring resonator based MPBPF on a chip, reducing the overall footprint of the system, since the low-loss heterogeneous III-V/silicon laser [32], low half-wave voltage electro-optical modulator [33], and high-speed photodetectors are available on chip [30,34]. Moreover, the demonstrated RF bandpass filter has great potential in other applications, such as OEO [2,35] and microwave frequency measurement [36] compared with bandstop filters, due to the high passband gain and high spectral resolution.

Conclusion
We have demonstrated a MPBPF based on cascaded silicon nitride ring resonators, exhibiting key features of high gain, low noise figure, and large SFDR. First, the comprehensive theoretical model for ring-resonator-based MPBPF was established, and the RF gain to FWHM ratio of the filter is for the first time introduced and optimized. We have revealed that the OC ring resonator based MPBPF has larger RF gain to FWHM ratio compared with UC-ring-resonator-based filter. Based on an OC ring resonator, to further improve the RF gain in the filter passband, another auxiliary UC ring resonator was used to optimize the optical carrier-to-sidebands ratio by suppressing the optical carrier. Experimental results show that a record-high passband gain of 1.8 dB, a noise figure of 35 dB, and a spurious free dynamic range (SFDR) of 107.4 dB·Hz 2/3 with a FWHM of 260 MHz are achieved by cascading OC and UC ring resonators on the same photonic chip. Furthermore, scalable multi-bands MPBPF with optimized RF gain can be realized by simply activating more ring resonators. A dual-passbands MPBPF based on three cascaded ring resonators with tunable central frequencies and frequency spacing has been demonstrated. The proposed chip-based MPBPF paves the way toward the real-world applications of low loss, high signal-to-noise ratio, and large dynamic range integrated RF photonic systems.