With the development of photonic integrated circuit technology, integrated optical filters have become a hot research topic.1^–7 Silicon-based microring resonators (MRRs) are ideal units for realizing large-scale integrated optical circuits due to their compact size, flexible function configuration, and excellent filtering performance.8^–11 In addition, both bandpass and bandstop filtering shapes can be obtained at the drop and through ports of the MRR, respectively. As is known, in an optical filter, a high rejection ratio is desired to significantly improve the signal-to-noise ratio and eliminate interferences completely. Therefore, much effort has been paid to improve the filter rejection.

As is known, optical interferometry has been previously used to enhance the rejection ratio of MRRs.7^,12 To improve the rejection ratio of the MRR at its through port, which is a bandstop filter, the approach of employing two cascaded tunable Mach–Zehnder interferometers (MZIs) is proposed.13 By adjusting microheaters to equalize the amplitudes and obtain a precise $\pi$ phase difference between the two sidebands in the two arms of the MZI, destructive interference is realized. Hence, the rejection ratio of the obtained MRR at its through port is increased to exceed 60 dB. To realize a high rejection ratio and reconfigurable optical bandstop filter, three-waveguide-coupled Sagnac loop reflectors are proposed.14 The bus waveguides situated between the Sagnac loop reflectors introduce an additional feedback path for coherent optical interference. By adjusting the coherent mode interference within the device, the rejection ratio of the filter is significantly enhanced. However, the device complexity is significantly increased and cannot be fabricated in the foundry. However, compared with the MRR-based bandstop filter, it is more challenging to achieve a high rejection MRR at its drop port, which is a bandpass filter. This is because the interferences in a much larger spectral range must be eliminated. To enhance the rejection ratio of MRR at its through port, it was proposed to use a pair of cascaded MRRs combined with optical phase modulation. By employing amplitude cancellation in the stopband, the rejection ratio is increased.15 However, the proposed approach is only applied to a microwave photonic filter and cannot increase the rejection of the MRR-based optical filter. In addition, the rejection ratio of this filter is only 20 dB. To realize a flat-top, high-rejection-ratio optical bandpass filter, an integrated photonic chip consisting of a 10th-order MRR and a photodetector (PD) is proposed.16 By controlling the resonant wavelength of each MRR, the 10th-order MRR achieves a flat-top optical filter at its drop port, and the rejection ratio is higher than 30 dB. However, it is difficult to design and control the operation state of each MRR, and the complexity of the system is increased significantly. To improve the rejection ratio of MRR-based bandpass filters, high-order optical bandpass filters based on multi-MRRs have been proposed, such as using coupled resonator optical waveguides (CROWs)17^–19 or cascaded MRRs.20 However, the rejection improvement is related to the number of employed MRRs. To achieve a high rejection ratio, multiple MRRs are used. Therefore, both the insertion loss and system complexity are significantly increased. How to improve the rejection ratio of the MRR-based bandpass filter is still a challenge.

In this paper, we propose to use an all-pass filter (APF) to enhance the rejection ratio of an MRR-based optical bandpass filter. With the assistance of APF, constructive interference occurs in the passband, and destructive interference occurs in the stopband of the optical bandpass filter simultaneously. Therefore, the rejection ratio of the optical bandpass filter can be significantly promoted. In the experiment, the rejection ratio of the MRR-based optical bandpass filter is increased from 24.1 to 47.7 dB compared with that of a single MRR. Meanwhile, due to the constructive interference in the center of the passband, the bandwidth of the bandpass filter is reduced from 2.62 to 1.14 GHz. The quality factor ($Q$) of the MRR is improved from $7.4\times {10}^4$ to $1.7\times {10}^5$. In addition, the center frequency of this bandpass filter can be continuously tuned from 6.26 to 46.25 GHz. Therefore, the proposed approach can effectively improve the performance of the MRR, thus enhancing the performance of optical systems.

Figure 1 shows the principle of the ultrahigh rejection MRR. Figure 1(a) illustrates the schematic structure of the MRR. The APF has a constant amplitude response and a phase change of $2\pi$ in a free spectral range (FSR),21 as shown in Fig. 1(b). The amplitude and phase responses from the “input port” to the “drop port” of the MRR (${\mathrm{MRR}}_{\text{Drop}}$) are shown as the blue solid curve and the red dashed curve in Fig. 1(b), respectively.22 We can see that the frequency response of ${\mathrm{MRR}}_{\text{Drop}}$ is a bandpass filter with a phase change of $\pi$ in an FSR. Therefore, the frequency response of the cascaded APF and ${\mathrm{MRR}}_{\text{Drop}}$ is a bandpass filter ($\mathrm{APF}\times {\mathrm{MRR}}_{\text{Drop}}$) with a phase change of $3\pi$ in an FSR. Then, the frequency response of the cascaded APF and the MRR-based bandpass filter is superimposed with the frequency response of the MRR-based bandpass filter, as shown in Fig. 1(c). It should be noted that the two frequency responses have the same amplitude frequency response but different phase frequency responses. The phase difference between the two frequency responses is 0 at the center of the passband and tends to be $\pi$ as the frequency deviates away from the passband center. Therefore, constructive interference occurs in the passband and destructive interference occurs in the stopband. As a result, the rejection ratio of the optical bandpass filter (${\mathrm{MRR}}_{\text{Final}}$) can be improved and the bandwidth is reduced, as shown in Fig. 1(c).

The schematic diagram of the proposed ultrahigh rejection bandpass filter assisted by APF is shown in Fig. 2. We can see that the proposed device mainly consists of an MZI, an APF, a parallel straight waveguide, and an MRR. The optical signal is coupled into the photonic chip through a grating coupler (${\mathrm{GC}}_1$), and the optical field is donated by $E_1$, as shown in Fig. 2. Then, the input optical field $E_1$ is divided into two parts by ${\mathrm{MZI}}_1$, whose amplitude splitting ratio can be adjusted by controlling the electrical heating power applied to the microheater ${\mathrm{H}}_1$. The optical field of the upper part is denoted by $E_2$. Then, the upper part passes through the APF, which consists of ${\mathrm{MZI}}_2$, ${\mathrm{MZI}}_3$, and ${\mathrm{MRR}}_1$. The optical amplitude splitting ratio of ${\mathrm{MZI}}_2$ can be adjusted by controlling the electrical heating power applied to the microheater ${\mathrm{H}}_2$. In ${\mathrm{MZI}}_3$, the optical field in the upper arm is coupled with ${\mathrm{MRR}}_1$, and the microheaters ${\mathrm{H}}_4$ and ${\mathrm{H}}_5$ are used to adjust the resonant wavelength of ${\mathrm{MRR}}_1$ and the coupling coefficient between ${\mathrm{MRR}}_1$ and the upper arm of ${\mathrm{MZI}}_3$, respectively. On the lower arm of ${\mathrm{MZI}}_3$, the microheater ${\mathrm{H}}_3$ is used to adjust the phase difference between the two arms of ${\mathrm{MZI}}_3$. Notably, all the MZIs in the proposed device have a balanced structure. The optical field output from the APF is denoted by $E_3$. Meanwhile, the optical field at the lower output port of ${\mathrm{MZI}}_1$ is denoted by $E_4$.

Based on the transmission matrix, the transfer function of the APF is given by $$H_{\mathrm{APF}}=\frac{\sqrt{2}}{4}(1+j{e}^{j{\phi }_2})\frac{[(t_0+x{e}^{j{\phi }_3})-\alpha (1+t_{0}x{e}^{j{\phi }_3})e^{-{\varphi }_1}]}{1-\alpha t_0{e}^{-{\varphi }_1}},$$(1)where ${\phi }_1$, ${\phi }_2$, and ${\phi }_3$ are the phase differences between the upper and lower arms of ${\mathrm{MZI}}_1$, ${\mathrm{MZI}}_2$, and ${\mathrm{MZI}}_3$, respectively. $t_0$ is the self-coupling coefficient between the upper arm of ${\mathrm{MZI}}_3$ and ${\mathrm{MRR}}_1$, $\alpha$ is the round-trip amplitude transmission of ${\mathrm{MRR}}_1$, and ${\varphi }_1$ is the round-trip phase shift of the ${\mathrm{MRR}}_1$. The optical amplitude splitting ratio $x$ of the upper arm to the lower arm of ${\mathrm{MZI}}_3$ is related to ${\phi }_2$, where $x$ satisfies $x=(j+e^{j{\phi }_2})/(1+e^{j{\phi }_2})$. According to the all-pass condition,21 the transmission $T$ of the APF can be expressed as $$T=H_{\mathrm{APF}}\times H_{\mathrm{APF}}^{*}=\frac{(1+\cos {\phi }_2){\alpha }^2(1-t_0^2{)}^2}{2(1-{\alpha }^2{t}_0^2{)}^2}.$$(2)

From Eq. (2), we can find that the amplitude frequency response is constant, and thus an APF is obtained. Meanwhile, the lower output of ${\mathrm{MZI}}_1$ passes through a straight waveguide. The output signal of APF is divided into two parts by ${\mathrm{MMI}}_6$. One part is output from the chip through ${\mathrm{GC}}_2$ for facilitating the experiment, and the other part is combined with one part of the optical signal from the lower output arm of ${\mathrm{MZI}}_1$ by ${\mathrm{MMI}}_7$. The other part of the optical signal from the lower output arm of ${\mathrm{MZI}}_1$, which is coupled out of the chip by ${\mathrm{GC}}_5$, is also used to facilitate the experiment. The output optical field through ${\mathrm{MMI}}_7$ is donated by $E_5$, and then coupled with ${\mathrm{MMR}}_2$. The optical field at the “drop” port of ${\mathrm{MRR}}_2$ is donated by $E_6$, which is coupled out of a chip by ${\mathrm{GC}}_3$. Notably, the transmission and the phase shift from the “In” port to the “Drop” port of ${\mathrm{MRR}}_2$ can be expressed as20$$H_{\text{Drop}}=\frac{-k_1{k}_2{\alpha }^{\frac{1}{2}}{e}^{-j\frac{{\varphi }_2}{2}}}{1-\alpha t_1{t}_2{e}^{-j{\varphi }_2}},$$(3)where $t_1$ and $t_2$ are the self-coupling coefficients of the upper and lower coupling regions of ${\mathrm{MRR}}_2$, respectively, and $k_1$ and $k_2$ are the cross-coupling coefficients of the upper and lower coupling regions of ${\mathrm{MRR}}_2$, respectively. Neglecting the coupling loss, we can obtain $t_1^2+k_1^2=1$, $t_2^2+k_2^2=1$. $\alpha$ is the round-trip amplitude transmission of ${\mathrm{MRR}}_2$ and ${\varphi }_2$ is the round-trip phase shift of the ${\mathrm{MRR}}_2$. Neglecting the losses caused by ${\mathrm{MMI}}_5$, ${\mathrm{MMI}}_6$, ${\mathrm{MMI}}_7$, and ${\mathrm{MMI}}_8$, the transfer function of the proposed ultrahigh rejection bandpass filter can be expressed as $$H_{\mathrm{BPF}}=\frac{1}{\sqrt{2(1+y^2)}}(1+y{H}_{\mathrm{APF}})H_{\text{Drop}}=\frac{1}{\sqrt{2(1+y^2)}}(H_{\text{drop}}+y{H}_{\mathrm{APF}}{H}_{\text{drop}}).$$(4)

The optical amplitude splitting ratio of the upper arm to the lower arm of ${\mathrm{MZI}}_1$ is assumed to be $y:1$, where $y$ satisfies $y=(j+e^{j{\phi }_1})/(1+e^{j{\phi }_1})$. According to Eq. (4), we can see that the frequency response of the proposed structure can indeed be regarded as the superposition of the frequency response of the ${\mathrm{MRR}}_2$-based bandpass filter ($H_{\text{Drop}}$), and the frequency response of cascading the APF with the ${\mathrm{MRR}}_2$-based bandpass filter ($H_{\text{Drop}}\times H_{\mathrm{APF}}$). As is known, the frequency response $H_{\text{Drop}}$ exhibits a Lorentzian bandpass shape with a phase variation of $\pi$ in an FSR. The frequency response $H_{\text{Drop}}\times H_{\mathrm{APF}}$ has the same shape as that of $H_{\text{Drop}}$ but with a phase variation of $3\pi$. We can align the resonant wavelengths of ${\mathrm{MRR}}_1$ and ${\mathrm{MRR}}_2$ by adjusting electrical powers applied to the microheater ${\mathrm{H}}_4$ on ${\mathrm{MRR}}_1$ and ${\mathrm{H}}_7$ on ${\mathrm{MRR}}_2$, respectively. Therefore, after superposition, the phase difference between the two frequency responses is 0 in the center of the passband and tends to be $\pi$ as deviating from the center of the passband. When the deviation is FSR/2, the phase difference is $\pi$. Hence, constructive interference occurs in the passband and destructive interference occurs in the stopband of the bandpass filter. Consequently, a high rejection bandpass filter can be realized.

To validate our theory, we carry out simulations on the proposed device. In simulation, the three self-coupling coefficients of ${\mathrm{MRR}}_1$ and ${\mathrm{MRR}}_2$ are assumed to be $t_{0 }=0.98$, $t_{1 }=0.98$, and $t_{2 }=0.98$, respectively. Both circumferences of the two MRRs are set as $251.2\mu \mathrm{m}$. In addition, the silicon waveguide propagation loss is assumed to be $1.5\mathrm{dB}/\mathrm{cm}$. The simulated results are shown in Fig. 3. Figure 3(a) shows the simulated amplitude (black solid curve) and phase (yellow dashed curve) responses of the APF, which is indicated by the red dashed rectangle in Fig. 2. Notably, the APF can be realized at arbitrary self-coupling coefficient value of $t_0$ as long as the zero and pole satisfy Eq. (4).23 It can be observed that the phase response of the APF has a phase variation of $2\pi$ in an FSR. The comparisons of the phase and amplitude responses of $H_{\text{Drop}}$ (blue dashed curve) and $H_{\text{Drop}}\times H_{\mathrm{APF}}$ (green solid curve) are shown in Figs. 3(b) and 3(c), respectively. It can be observed that the rejection ratio and the phase variation in an FSR of ${\mathrm{MRR}}_2$-based bandpass filter are 33.8 dB and $\pi$, respectively. Notably, the amplitude responses of $H_{\text{Drop}}$ and $H_{\text{Drop}}\times H_{\mathrm{APF}}$ have exactly the same shape except for the insertion loss, which is caused by the insertion loss of the APF, as shown in Fig. 3(b). However, it is important to ensure that the insertion losses of the two bandpass filters are equal to each other, which can maximize the benefits of the optical interference. Therefore, to offset the insertion loss, we can adjust the power-splitting ratio of ${\mathrm{MZI}}_1$ by changing the electrical power applied to $H_1$, as shown in Fig. 1. Meanwhile, the phase difference between $H_{\text{Drop}}$ and $H_{\text{Drop}}\times H_{\mathrm{APF}}$ is 0 at the passband center and tends to be π as the frequency deviates from the center of the passband. When the deviation from the passband center is FSR/2, the phase difference is $\pi$. As a result, after superimposing the frequency response of $H_{\text{Drop}}$ and $H_{\text{Drop}}\times H_{\mathrm{APF}}$, constructive interference occurs in the passband, and destructive interference occurs in the stopband simultaneously. Figure 3(d) shows the simulated results of our proposed ultrahigh rejection MRR. The simulated results show that the rejection ratio of ${\mathrm{MRR}}_2$ is significantly improved with the assistance of the APF. When the wavelength deviates the resonance center of the ${\mathrm{MRR}}_2$ by 0.5 nm, the rejection ratio can be improved from 28.9 to 64.0 dB. Meanwhile, thanks to constructive interference at the passband, the bandwidth is reduced from 2.36 to 1.11 GHz simultaneously.

The chip is fabricated by Chongqing United Micro-Electronics Center (CUMEC), as shown in Fig. 2. According to Fig. 2, the proposed device is fabricated based on a silicon-on-insulator (SOI) wafer, which has a top layer thickness of 220 nm and a buried oxide (BOX) layer thickness of $2\mu \mathrm{m}$. The waveguide width and etching depth are 500 and 150 nm, respectively. Figure 4 shows the micrograph of the fabricated device. The coupling gaps between the directional couplers in ${\mathrm{MZI}}_1$, ${\mathrm{MZ}1}_2$, and ${\mathrm{MZI}}_3$ are all 200 nm. The titanium nitride (TiN) material deposited on the waveguide is used as the microheater. In addition, the microheaters deposited on the MZIs, optical straight waveguides, and MRRs are used to adjust the optical splitting ratio, the optical phase, and the resonant wavelengths of the MRRs, respectively. Both circumferences of the two MRRs are set as $251.2\mu \mathrm{m}$. In addition, there are 16 pads fabricated on the chip for applying electrical power to the microheaters. The size of the whole device is $2.35\mathrm{mm}\times 0.95\mathrm{mm}$.

Due to the limited resolution of the optical spectrum analyzer, we perform the microwave photonic approach to measure the frequency responses of the proposed device precisely, as shown in Fig. 5. Another advantage of the microwave photonic measurement is that the phase response of the device can be obtained. As shown in Fig. 5, the continuous wave (CW) light at 1550 nm emitted from the tunable laser source (TLS, NKT Basik E15) is split into two parts by an optical coupler (${\mathrm{OC}}_1$). One part of the CW light is phase-modulated by the microwave signal emitted by a vector network analyzer (VNA, Anritsu MS4647B) via a phase modulator (PM, Covega Mach-40). Since the PM is polarization-dependent, a polarization controller (${\mathrm{PC}}_1$) is used to align the state of polarization (SOP) of the CW light with the polarization axis of the PM to ensure maximal modulation efficiency. Then the $+1\mathrm{st}$-order sideband of the phase-modulated signal is suppressed by an optical bandpass filter (OBPF) to obtain a single sideband (SSB) signal. An erbium-doped fiber amplifier (EDFA) is used to boost the optical power. Notably, the fabricated device is polarization-dependent because of the difference in vertical and horizontal dimensions. Therefore, to maximize the coupling efficiency, ${\mathrm{PC}}_2$ is used to adjust the SSB signal to TE mode. After adjusting the SOP by ${\mathrm{PC}}_2$, the SSB signal is coupled into the chip for sweeping the device under test (DUT). After processing, the optical signal is output out of the chip and combined with the optical carrier via ${\mathrm{OC}}_2$. To achieve a polarization-independent chip, the thick silicon wafer can be used.24^,25${\mathrm{PC}}_3$ is used to adjust the SOP of the optical carrier to be aligned with the SOP of the optical signal after DUT. A variable optical attenuator (VOA) regulates the optical power injected into a PD by adjusting the power of the optical carrier. Finally, the PD converts the optical signal back to the electrical signal and returns it to the VNA for measurement.

To measure the frequency response of the APF, we attenuate the optical carrier injected into ${\mathrm{OC}}_2$ in Fig. 5 completely. Then, the splitting ratio of ${\mathrm{MZI}}_1$ is adjusted by changing the electrical power applied to the microheater ${\mathrm{H}}_1$ so that all the input CW light passes through the upper output of ${\mathrm{MZI}}_1$, as shown in Fig. 1. Then, the amplitude and the phase differences between the upper and lower outputs of ${\mathrm{MZI}}_2$ are adjusted by changing the electrical power applied to ${\mathrm{H}}_2$ and ${\mathrm{H}}_3$. The electrical powers applied to ${\mathrm{H}}_1$, ${\mathrm{H}}_2$, and ${\mathrm{H}}_3$ are 38.0, 44.0, and 9.0 mW, respectively; the measured amplitude and phase responses of APF via ${\mathrm{GC}}_2$ are shown as the black solid curve and the red dashed curve in Fig. 6(a), respectively. It can be observed that the amplitude variation of the optical APF is within 1.5 dB, and the phase variation from 5 to 40 GHz is $1.95\pi$, respectively. Notably, the amplitude variation of the APF is mainly caused by the FP effect, which originates from the backreflection of ${\mathrm{GC}}_1$ and ${\mathrm{GC}}_3$.

To measure the amplitude response of ${\mathrm{MRR}}_2$ from ${\mathrm{GC}}_3$ without APF assistance, we adjusted the splitting ratio of ${\mathrm{MZI}}_1$ to make all the optical signal transmitted along the lower output waveguide of ${\mathrm{MZI}}_1$. When the electrical power applied to ${\mathrm{H}}_1$ is 10.7 mW, the measured amplitude response of ${\mathrm{MRR}}_2$-based bandpass filter via ${\mathrm{GC}}_3$ is shown as the black curve in Fig. 6(b). It can be observed that the measured rejection ratio of the bandpass filter is only 24.1 dB, and the bandwidth of the bandpass filter is 2.61 GHz. To obtain a bandpass filter with an ultrahigh rejection ratio, the electrical power applied to the microheaters of the APF remains unchanged. Then, the electrical powers of the microheaters ${\mathrm{H}}_4$ and ${\mathrm{H}}_7$ applied to ${\mathrm{MRR}}_1$ and ${\mathrm{MRR}}_2$ are adjusted to align the resonant wavelengths of ${\mathrm{MRR}}_1$ and ${\mathrm{MRR}}_2$. Finally, the electrical powers of the microheaters ${\mathrm{H}}_1$ and ${\mathrm{H}}_6$ are adjusted to change the splitting ratio and the phase difference between the APF and the lower output straight waveguide of ${\mathrm{MZI}}_1$. The powers applied to microheaters ${\mathrm{H}}_1$, ${\mathrm{H}}_2$, ${\mathrm{H}}_3$, ${\mathrm{H}}_4$, ${\mathrm{H}}_6$, and ${\mathrm{H}}_7$ are 38.0, 44.0, 6.0, 21.6, 59.3, and 15.2 mW, respectively; the measured amplitude-frequency response of the ultrahigh rejection optical bandpass filter via ${\mathrm{GC}}_3$ is shown as the red solid curve in Fig. 6(b). We can observe that the measured rejection ratio of the bandpass filter is increased to as high as 47.7 dB with the assistance of the APF. Hence, the rejection ratio is improved by 23.6 dB compared with that of ${\mathrm{MRR}}_2$. The insertion loss of the fabricated device is $\sim 10\mathrm{dB}$. It is mainly caused by the insertion loss introduced by the MMIs designed to assist the experiment and the insertion loss of the APF. In addition, we can see a notch around 35 GHz. This is because the upper arm and lower arm optical field propagation paths of ${\mathrm{MZI}}_1$ are not precisely equal to each other. In addition, the measured bandwidth of the proposed structure is simultaneously reduced from 2.61 to 1.14 GHz with the assistance of the APF. The Q of the MRR is improved from $7.4\times {10}^4$ to $1.7\times {10}^5$. Because the phase difference between $H_{\text{Drop}}$ and $H_{\text{Drop}}\times {\mathrm{H}}_{\mathrm{APF}}$ is 0 in the passband center, constructive interference occurs at the center of the passband. When the phase difference in the passband between $H_{\text{Drop}}$ and $H_{\text{Drop}}\times H_{\mathrm{APF}}$ is not 0 because of frequency deviation, the amplitude enhancement due to optical interference is not so high. Therefore, the bandwidth of the optical bandpass filter is reduced. Furthermore, the bandpass filter with the ultrahigh rejection ratio can also be tuned by adjusting the resonant wavelengths of ${\mathrm{MRR}}_1$ and ${\mathrm{MRR}}_2$ simultaneously. This can be achieved by adjusting the electrical powers applied to ${\mathrm{H}}_4$ and ${\mathrm{H}}_7$, as shown in Fig. 6(c). Notably, the rejection ratio of the proposed device exceeds 40 dB during the tuning process. In our design, we sacrifice insertion loss and chip size to obtain a higher rejection ratio bandpass filter. Besides, a larger self-coupling coefficient of ${\mathrm{MRR}}_1$ allows for a smaller bandwidth of the device. However, the insertion loss of the APF will be increased, and thus the insertion loss of the device will be increased. Therefore, trade-off considerations should be made among rejection ratio, bandwidth, integration, and insertion loss.

A comparison between previously reported integrated optical bandpass filters and this work is shown in Table 1. Our proposed ultrahigh rejection MRR assisted by APF exhibits a high rejection ratio. With the assistance of an APF, the rejection ratio is increased from 24.1 to 47.7 dB compared with that of a single MRR. In addition, the bandwidth of our proposed device is reduced by more than one-half of the bandwidth of the single MRR. Simultaneously, a large frequency tuning range is obtained while maintaining a narrow full width at half-maximum (FWHM) bandwidth. Further, the coupling region of ${\mathrm{MRR}}_2$ can be designed with an adjustable coupling coefficient to reconfigure the bandwidth of the filter.

We have proposed and demonstrated an ultrahigh rejection MRR with the assistance of an APF. Due to the APF, we can obtain constructive interference in the passband and destructive interference in the stopband simultaneously. Therefore, the rejection ratio of the MRR is significantly increased. In the experiment, the rejection ratio of the optical bandpass filter is increased to as high as 47.7 dB, which is improved by 23.6 dB compared with that of the single MRR. In addition, the bandwidth of the MRR is also reduced from 2.61 to 1.14 GHz. With the assistance of the APF, the $Q$ of the MRR is improved from $7.4\times {10}^4$ to $1.7\times {10}^5$. Meanwhile, the center frequency of ultrahigh rejection MRR can be continuously tuned from 6.26 to 46.25 GHz. The ultrahigh rejection ratio MRR proposed in this paper is implemented based on SOI. It is compatible with large-scale integrated photonic circuits. The proposed approach can potentially be applied to an important part of signal processing in large-scale integrated photonic circuits and provide different filtering functions to meet different requirements.

We perform a microwave photonic link, as shown in Fig. 5, to measure the frequency response of ${\mathrm{MRR}}_2$ by VNA. As both the bandwidths of PD and PM are 40 GHz, the measuring range of the VNA is also limited to 40 GHz, which corresponds to a wavelength range of 0.32 at 1550 nm. Hence, the measuring range of the microwave photonic approach is much less than the FSR of ${\mathrm{MRR}}_2$, which is as large as approximately 300.0 GHz. To demonstrate the rejection ratio enhancement of ${\mathrm{MRR}}_2$ with the assistance of APF, the measured frequency response of the ${\mathrm{MRR}}_2$ by VNA must be spliced.29 At first, the wavelength of the TLS is adjusted to 1549.66 nm, and the OBPF is adjusted to eliminate the $+1\mathrm{st}$-order sideband of the phase-modulated light. Then, the transmission of MRR2 from 1549.50 to 1549.82 nm can be measured by the VNA, which corresponds to the frequency response from $-50$ to $-10\mathrm{GHz}$ in Fig. 6(b). The next step is to adjust the wavelength of the TLS to 1549.98 nm; the OBPF is also adjusted correspondingly to eliminate the $+1\mathrm{st}$-order sideband of the phase-modulated light. Then, the transmission of ${\mathrm{MRR}}_2$ from 1549.82 to 1550.14 nm can be measured by the VNA, which corresponds to the frequency response from $-10$ to 30 GHz in Fig. 6(b). In a similar way, the frequency response of ${\mathrm{MRR}}_2$ from 30 to 50 GHz in Fig. 6(b) can be measured by the VNA. Finally, the frequency response from $-50$ to 50 GHz of the ${\mathrm{MRR}}_2$ as shown in Fig. 6(b) can be obtained by splicing the three measured transmission spectra by VNA.

Ming Chen received his master’s degree from the Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology (HUST), Wuhan, China, in 2024. His research interest is microwave signal processing.

Yifan Liu received his PhD from the Wuhan National Laboratory for Optoelectronics, HUST, Wuhan, China, in 2023. His research interest is microwave signal processing.

Kaixiang Cao received his master’s degree from the Wuhan National Laboratory for Optoelectronics, HUST, Wuhan, China, in 2024. His research interest is microwave signal processing.

Yuan Yu (Member, IEEE) received his PhD in optoelectronic information engineering from the School of Optical and Electronic Information, HUST, Wuhan, China, in 2013. He is currently an associate professor at the Wuhan National Laboratory for Optoelectronics and the Institute of Optoelectronics Science and Engineering, HUST. His research interests include microwave photonics and silicon-based integrated devices.

Fangzheng Zhang (Senior Member, IEEE) received his BS degree from the HUST, Wuhan, China, in 2008, and his PhD from the Beijing University of Posts and Telecommunications, Beijing, China, in 2013. He is currently a professor at the College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China. His main research interests include microwave photonics, radar imaging, and machine learning.

Xinliang Zhang (Senior Member, IEEE) received his PhD in physical electronics from the HUST, Wuhan, China, in 2001. He is currently a professor at the Wuhan National Laboratory for Optoelectronics and the Institute of Optoelectronics Science and Engineering, HUST. His main research interests include information optoelectronic devices and integration.