## Abstract

A tunable bandpass microwave photonic filter can be achieved by using a notch ring resonator with optical phase modulation. However, the filter’s out of band rejection ratio and shape factor are limited due to the ring resonator’s residual phase, which can seriously degrade the filter’s performance. By using dual optical carriers and setting their wavelengths oppositely detuned from two resonant frequencies of a notch ring resonator, the residual phase induced by the ring resonator at radio frequencies falling outside the region of the notch stopband is reduced, thus the out-of-band rejection ratio and shape factor of the microwave photonic filter are greatly improved. The proposed microwave photonic filter was both verified theoretically and experimentally. Compared with single optical carrier method, the out-of-band rejection ratio of the filter can be enhanced from 17.7dB to 31.5dB, and the filter’s shape factor is improved from 3.05 to 1.78. Besides, the filter’s frequency and bandwidth can be tuned by varying the wavelengths of the two optical carriers and the ring resonator’s coupling coefficients. Finally, a tunable bandpass microwave photonic filter with frequency tuning range of 2~14GHz, 3dB bandwidth tuning range of 0.673~2.798GHz is demonstrated.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

The microwave photonic filter is one of the most important devices for microwave signal processing, and can filter the wideband microwave signal in the optical frequency domain. Compared with traditional microwave filters, microwave photonic filters (MPFs) have the advantages of larger frequency tuning range, bandwidth reconfiguration and electromagnetic immunity [1–4]. Therefore, MPFs are widely used in microwave photonic signal processing systems. Until now, many microwave photonic filters based on discrete fiber components have been proposed, such as Fabry-Perot filter [5,6], fiber Bragg grating [7,8] etc. However, these microwave photonic filters have shortcomings of big footprint and slow tuning rate. Recently, the integrated microwave photonic filters have aroused people’s attention due to their compact sizes. So far, notch MPF [9–11] and bandpass MPF [12–21] have been reported by adopting integrated optical filters including Mach-Zehnder interferometer, micro ring resonator, micro disk resonator and so on.

The reconfigurable bandpass MPF can be implemented by using intensity modulation or phase modulation methods. For intensity modulation method, a bandpass MPF can be obtained with an optical bandpass filter [12,13], while for phase modulation method, a bandpass MPF can be achieved with an optical notch filter that converts phase modulation to intensity modulation. Compared with intensity modulation, phase modulation method has a simple structure and good stability because no bias control is needed. Therefore, the bandpass MPFs based on silicon micro-ring resonator (MRR) notch filter and phase modulation have been extensively studied [15–18]. However, since the MRR induces residual phase outside the region of the notch stopband, the microwave signal cannot be completely cancelled outside the passband. As a consequence, the out-of-band rejection ratio and the shape factor of the bandpass MPF are poor due to the residue phase induced by the MRR. For example, the out-of-band rejection ratios of the MPF are less than 10dB in [16] and 12dB in [17], which hinder their applications. Recently, some methods have been proposed to solve the residual phase issue. In [18], the shape factor and the sideband rejection ratio are improved by employing a phase compensator after the MRR. However, the approach has limitation because the phase compensator is costly and difficult to realize integration. A single bandpass MPF using a dual parallel Mach–Zehnder modulator (DPMZM) instead of a PM to compensate the unwanted phase is reported [19]. Nevertheless, the out-of-band rejection ratio is not obviously improved and still less than 20dB, moreover the link is more complicated due to the requirement of three bias voltages. Also a MPF with a shape factor of 1.78 based on a cascaded pair of MRRs is proposed [20], but the bandwidth reconfigurability is limited and the out-of-band rejection ratio of about 20dB is still not good enough. Recently, by using a semiconductor optical amplifier (FP-SOA) with phase modulation and dual optical carriers, F. Jiang et al. reported a excellent bandpass MPF with ultrahigh stopband attenuation and skirt selectivity based on the microwave cancellation effect [6]. But the linear amplification requirement of the SOA limited the input optical carriers’ power and the bandwidth reconfigurability of the MPF is not studied, which is very important for the MPF. And H. Jiang et al. first proposed an algorithm-driven reconfigurable bandpass MPF based on phase modulation of single laser and phase tailoring of cascade MRRs [21]. However, the precise spectra aligning and tuning of four cascade MRRs are relatively complex.

In this paper, a tunable bandpass MPF based on a silicon nitride (Si_{3}N_{4}) MRR and phase modulation with dual optical carriers is proposed to alleviate the residue phase which limits the out-of-band rejection ratio. By setting the two optical carriers’ frequencies on the high and low frequency sides of two resonances of the MRR, the effect introduced by the unwanted residue phase of the MRR is alleviated. So the out-of-band rejection ratio of the MPF is greatly improved. And the filter's frequency can be tuned by simultaneously changing the frequency difference between the two optical carriers and their adjacent notch frequencies (Δ*f*_{1} and Δ*f*_{2}). In addition, the bandwidth of designed bandpass MPF can be easily tuned by varying the spacing with Δ*f*_{1} and Δ*f*_{2}, or the self-coupling coefficient of the tunable MRR. The characteristics of the proposed tunable bandpass MPF were analyzed theoretically and experimentally verified. The experimental results show that the out-of-band rejection ratio can be enhanced from 17.7 to 31.5dB and the filter’s shape factor can be improved from 3.05 to 1.78 comparing with the single optical carrier method. Besides, a frequency tuning range of 2~14GHz and variable 3dB bandwidth of 0.673~2.798GHz were achieved for the proposed tunable bandpass MPF.

## 2. Principle

As known, the conventional bandpass MPF can be achieved by using phase modulation method which includes a tunable laser diode (TLD), a phase modulator (PM), a micro-ring resonator (MRR), and a photodetector (PD) as shown in Fig. 1. The continuous optical carrier enters the PM which is modulated by the radio frequency (RF) signal. And the upper and lower sidebands with π phase shift and equal magnitude are generated. Then the modulated optical signal is injected into a MRR notch filter, where the phase to intensity conversion occurs after photodetection and a bandpass filter response can be obtained.

Under small signal conditions, the optical field after PM can be described as:

_{C}, ω

_{C}, and φ

_{C}are the amplitude, angular frequency and initial phase of the optical carrier, respectively. And m = πV

_{RF}/V

_{π}is the phase modulation index, where V

_{π}is the half-wave voltage of the modulator. V

_{RF}and ω

*is the magnitude and angular frequency of the RF signal. J*

_{f}_{0}(m) and J

_{1}(m) are the zero and first order Bessel functions of first kind.

The RF response of the MPF can be obtained through beating between the optical carrier and the sidebands respectively. Assuming T(ω) and φ_{MRR}(ω) are the transmittance and phase of the MRR at angular frequency ω, the beating photocurrent detected by the PD can be written as:

*i*

_{0, −1}and

*i*

_{0, + 1}are the photocurrents obtained by beating between the optical carrier and the −1

^{st}and + 1

^{st}order sidebands, respectively. And α and η represent the link loss and the responsibility of the PD. φ

_{0, −1}and φ

_{0, + 1}are the phases of

*i*

_{0, −1}and

*i*

_{0, + 1}, which are induced by the phase of the MRR and can be written as:

_{out}is the matched load impedance. For instance, when the optical carrier has 10GHz frequency offset with one notch frequency of an over coupled MRR (Free spectra region = 37.7GHz, Extinction ratio = 20.7dB), the simulated RF response of the bandpass MPF is shown in Fig. 2(a). It is obvious that RF response is not symmetrical and the out-of-band rejection ratio is much larger in the low frequency side comparing with the high frequency side. And the out-of-band rejection ratio is less than 18dB, which leads to the poor performance of the bandpass MPF. This means the two beat RF signals are not well cancelled on the high frequency side due to the residual phase induced by the MRR.

In order to clarify the mechanism of the residual phase effect of the MRR, the magnitudes and phases of photocurrent *i*_{0, −1} and *i*_{0, + 1} are analyzed. It can be seen from Eq. (2) that the RF response is related to the transmittance and phase of the MRR, which are shown in Fig. 2(c). Here the free spectra region (FSR) of the MRR is chosen as 37.7GHz and a total phase shift of 2π is introduced in a FSR, in which a π phase shift occurs at the resonances. Figures 2(b) and 2(d) show variations of the amplitude and phase of photocurrent induced by the MRR with RF frequency. And three regions (including low frequency band, passband, high frequency band) are divided in order to explain the asymmetrical RF response of the MPF. As we can see, the phase can be neglected in the passband of the MPF because the + 1st order optical sideband is markedly filtered out and an RF passband is formed by the beating frequency of the −1st order optical sideband and optical carrier, which is usually defined as the phase to intensity conversion. However, for the low frequency band and the high frequency band, the T(ω_{C} + ω* _{f}*) and T(ω

_{C}-ω

*) are almost same and there is always an intrinsic π phase shift between the + 1st and −1st order optical sidebands induced by the phase modulation. So in these two regions, the out-of-band RF rejection caused by the RF cancelation should be determined by the residual phase shift induced by the MRR. In other words, the out-of-band rejection ratio of the MPF should get larger if the phase difference between φ*

_{f}_{0, −1}and φ

_{0, + 1}is getting closer to 2kπ (k is an integer). As seen from Fig. 2(d), it is obvious that φ

_{0, + 1}-φ

_{0, −1}≈0 in the low frequency band since the two optical sidebands are both on the low frequency side of resonance at 193.426THz, where the phase difference between φ

_{0, −1}and φ

_{0, + 1}is relatively small. Therefore, two RF signals induced by the beating of the + 1

^{st}and −1

^{st}order optical sidebands and the optical carrier can be well cancelled and relatively good out-of-band RF rejection ratio can be obtained as shown in Fig. 2(a). However, the phase difference between φ

_{0, −1}and φ

_{0, + 1}is relative larger and φ

_{0, + 1}-φ

_{0, −1}is deviated from 2π in the high frequency band, which breaks the RF cancellation condition and deteriorates the out-of-band rejection ratio of the MPF. In a word, the deviation of the phase difference φ

_{0, + 1}-φ

_{0, −1}from 2π is caused by the residual phase induced by the asymmetry location of the optical carrier relative to the MRR resonance. And it prevents the full cancellation of the two sidebands, which seriously degrades the out-of-band rejection ratio.

In order to improve the performance of the MPF, dual optical carriers are introduced with phase modulation to compensate the unwanted residual phase induced by the MRR. The schematic diagram of the proposed MPF is shown in Fig. 3(a). Two optical carriers with different frequencies *f*_{C1} and *f*_{C2} launched by two TLDs enter the PM through a wavelength division multiplexer (WDM). The PM is modulated by RF signal generated by the vector network analyzer (VNA). The laser frequencies are set as shown in Fig. 3(b), where the optical carriers are set on the low and high frequency sides of two non-adjacent resonances of the MRR. So the beating signal between the two optical carriers cannot be detected due to the limited bandwidth of the PD. The frequency difference between the optical carriers and the nearest resonances are denoted by Δ*f*_{1} and Δ*f*_{2}. Also Δ*f* = Δ*f*_{2}-Δ*f*_{1} is defined to analyze the bandwidth of the MPF.

Under small signal modulation, the optical field using dual optical carriers after the PM can be written as:

_{C1}, E

_{C2}, ω

_{C1}, ω

_{C2}, φ

_{C1}and φ

_{C2}are the amplitudes, the angular frequencies, the initial phases of two optical carriers, respectively. Assuming that the link losses and optical powers of two optical carriers are same, the beating photocurrents between optical carriers and the optical sidebands after the MRR detected by the PD are as follows,

_{1, + 1}and φ

_{1, −1}, φ

_{2, + 1}and φ

_{2, −1}are the phases induced by the MRR and can be given by:

Figures 4(a) and (b) show the normalized amplitudes and phase responses of photocurrents induced by the MRR with varying RF frequency relative to the two optical carriers. As can be seen from Figs. 4(a) and 4(b), T(ω_{C1}-ω* _{f}*) and T(ω

_{C2}+ ω

*), φ*

_{f}_{1, −1}and φ

_{2, + 1}are approximately equal, respectively. Therefore,

*i*

_{1, −1}, and

*i*

_{2, + 1}can be well cancelled out each other owing to the intrinsic π phase shift between the −1st and + 1st order optical sidebands. Besides, it is noteworthy that φ

_{1, + 1}and φ

_{2, −1}are also approximately equal outside the passband region due to the symmetry of two optical carriers relative to the MRR’s resonances. Therefore,

*i*

_{1, + 1}and

*i*

_{2, −1}can be well cancelled outside the passband region, which is different from the single optical carrier case. In addition, the bandwidth of the obtained MPF can be tuned by varying Δ

*f*. As an example, a flat-top bandpass MPF filter can be obtained when Δ

*f*= 1GHz as shown in Fig. 4(c), where the RF response of the MPF with single optical carrier is introduced for comparison. As can be seen, a 31dB enhancement of the out-of-band RF rejection ratio is achieved in the high frequency band. Besides, the out-of-band RF rejection ratio in the low frequency band is also enhanced. Moreover, based on the out-of-band RF rejection ratio enhancement, the MPF’s shape factor defined as the ratio of 10dB bandwidth to 3dB bandwidth is decreased from 3.431 to 1.898, which is very important for the applications.

The MPF’s frequency is related to Δ*f*_{1} and Δ*f*_{2}, and it can be written as

*f*

_{center}can be tuned within half of free spectrum region (FSR) of the MRR by changing the frequencies of two optical carriers. And the 3dB bandwidth of the MPF can also be tuned by varying $\Delta f$ as long as no obvious dip occurs in the RF response. Besides, the tuning range of the MPF’s bandwidth can be even enlarged by varying the self-coupling coefficient t of the MMR according to the full width of half maximum (FWHM) written as [22],where a is the single round trip amplitude transmission in the ring resonator.

## 3. Experimental results and discussion

In order to validate the proposed MPF, we make an experimental setup as shown in Fig. 3. Two optical carriers from tunable laser array(IDphotonics, CoBrite_{MX}) were combined in a wavelength division multiplexer (WDM) and injected into the PM(Eospace, PM-0S5-20-PFA-PFA)with half-wave voltage and insertion loss of 4.6V@1GHz and 2.0dB, respectively. The powers of the two optical carriers are respectively set as 15.00dBm and 15.76dBm in order to ensure the same optical power entering the WDM. The two optical carriers were then phase modulated by the RF driving signal from VNA (Agilent, N5242A) and the RF power is 5dBm. Then the modulated optical carriers were input into a tunable Si_{3}N_{4} waveguide ring resonator, which is fabricated by the TriPleX waveguide technology [23]. After the Si_{3}N_{4} waveguide MRR, the filtered optical signals were beaten on a fast PD (Finisar, XPDV2120RA) with bandwidth and responsivity of 50GHz and 0.65A/W, respectively. Then the converted RF current was input to the VNA to get the RF response of the proposed MPF.

The schematic of the tunable MRR is shown in Fig. 5(a). The perimeter of the ring is about 4650μm and the group index of the Si_{3}N_{4} waveguide mode is about 1.71, which leads to a FSR about 0.3nm. And by using the thermo-optic effect, the resonance wavelength and extinction ratio of the MRR can be tuned by the heater2 and heater1, respectively. The lengths of the heater1 and heater2 are 1000μm and 1800μm, respectively. First, the optical transmission and the phase spectra of the MRR as shown in Fig. 5 were measured by the Agilent lightwave measurement system (8164A) and optical vector network analyzer (OVNA) method [24]. The measured FSR and optical extinction ratio (ER) are 0.302nm and 19.5dB, respectively. The frequencies of two optical carriers are set on the high and low frequency sides of two non-adjacent resonances of the MRR, respectively. As seen from Fig. 5(c), the measured phase response with a π phase shift at the resonance is according with the simulation results shown in Fig. 2(c) well.

When Δ*f*_{1} and Δ*f*_{2} are set as 10.000GHz and 10.800GHz, a bandpass MPF with frequency *f*_{center} = 10.360 GHz is obtained as shown in Fig. 6, and the 3dB bandwidth of the passband is 1.178 GHz. By shutting off one laser in Fig. 3(a), the RF response of the MPF using single optical carrier was also measured and shown in Fig. 6 for comparison. Comparing with single optical carrier method, a notable out-of-band RF rejection ratio enhancement from 17.7dB to 31.5dB is achieved with dual optical carriers. And the shape factor of the MPF is improved from 3.05 to 1.78.

Then the filter’s frequency of the proposed MPF was tuned by changing the wavelengths of two optical carriers with a fixed Δλ = 8pm (Δλ = |Δλ_{1}-Δλ_{2}| is defined as the difference between ∆λ_{1} and ∆λ_{2}), and the measured RF responses are shown in Fig. 7. A frequency tuning range of 2~14GHz was obtained, which is mainly determined by the FSR of the Si_{3}N_{4} waveguide MRR we used. By using waveguide MRR with larger FSR, the frequency tuning range can be easily increased.

As analyzed above, the bandwidth of the MPF can also be varied by changing ∆λ. The self-coupling coefficient t can be tuned by changing the voltage applied the heater1. And the value of a and t of the MRR can be obtained through fitting the measured transmittance spectra of the MRR with Eq. (11), where L and Φ are the perimeter and the initial phase of the MRR, respectively. And λ, Loss, n_{eff}(λ) are wavelength, fiber-to-chip coupling loss and waveguide mode effective index, respectively. Figures 8(a)-8(c) show the variations of the 3dB bandwidth with ∆λ when the MRR is under coupling (t = 0.9715, a = 0.9574), near critical coupling (t = 0.9429, a = 0.9500) and over coupling (t = 0.9123, a = 0.9500), respectively. It can be found that the 3dB bandwidth of the MRR gradually increase as ∆λ changes from 4pm at a fixed t. The maximum ∆λ that ensures no obvious ripple inside the passband increases from under coupling to over coupling. Figure 8(d) shows that the trend of 3dB bandwidth with ∆λ at different self-coupling coefficients. The 3dB bandwidth of MPF increases with the decrease of t since the FWHM of the MRR is enlarged, and it can be tuned from 0.673~2.798GHz when t varies from 0.9123 to 0.9715.

## 4. Conclusion

A tunable bandpass MPF based on the MRR and phase modulation with dual optical carriers is proposed and experimentally demonstrated in order to alleviate the residue phase of the MRR, which limits the out-of-band rejection ratio of conventional MPF based on phase modulation with single optical carrier. And comparing with single optical carrier method, the out-of-band rejection ratio and the shape factor of the proposed MPF can be improved from 17.7dB to 31.5dB and 3.05 to 1.78, respectively. Moreover, a filter frequency tuning range of 2~14GHz and the 3-dB bandwidth reconfigurability of 0.673~2.798GHz were achieved.

## Funding

Natural Science Foundation of Jiangsu Province (BK 20161429) and the National Natural Science Foundation of China (61601118).

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