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Tunable bandpass microwave photonic filter with largely reconfigurable bandwidth and steep shape factor based on cascaded silicon nitride micro-ring resonators

Wei Cheng, Dongdong Lin, Pengfei Wang, Shangqing Shi, Mengjia Lu, Jin Wang, Chen Guo, Yifei Chen, Zhao Cang, Zhuang Tian, Zien Liang, Guohua Hu, and Binfeng Yun

Open Access Open Access

Abstract

Bandpass microwave photonic filter (MPF) can be achieved based on the well-known phase to intensity conversion method by using phase modulation and single micro-ring resonator (MRR) notch filter. Since MRR could introduce residual phase in handling one optical sideband, the out-of-band radio frequency (RF) rejection ratio and the shape factor of the bandpass MPF are very limited. Here, by introducing another MRR to handle the other optical sideband, the residual phase can be greatly suppressed, thus the filter’s performance can be greatly improved. The proposed bandpass MPF was both verified theoretically and experimentally. Compared with the single MRR, the out-of-band RF rejection ratio and the shape factor were improved by 20 dB and 1.67, respectively. Furthermore, the bandpass MPF’s bandwidth is reconfigurable by adjusting the optical carrier’s frequency or the two MRRs’ amplitude coupling coefficients. The bandpass MPF’s center frequency is also tunable by changing the resonant wavelengths of two MRRs in the opposite direction simultaneously. Experimentally, bandwidth reconfiguration from 0.38 GHz to 15.74 GHz, the shape factor optimization from 2 to 1.23, and frequency tuning from 4 GHz to 21.5 GHz were achieved. We believe that the proposed bandpass MPF has great potential for microwave photonic signal processing.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Microwave photonic filter (MPF) is one of the most critical components in microwave photonic signal processing and microwave photonic communication systems [1–3]. The MPF has outstanding advantages of frequency tunability, bandwidth reconfigurability and electromagnetic immunity compared with the conventional microwave filter [4]. The integrated MPF can further reduce size, weight, link loss, power consumption and cost [5,6]. Nowadays, the integrated MPF has been demonstrated based on multiple platforms, such as silicon-on-insulator (SOI) [7–9], silicon nitride (Si3N4) [10–12], indium phosphide [13], and As2S3 [14]. Generally, high-performance integrated bandpass MPF has the following characteristics such as low insertion loss, high out-of-band radio frequency (RF) rejection ratio, large frequency tuning range, reconfigurable bandwidth, and good shape factor. Over the past few decades, great efforts have been made to achieve high-performance integrated bandpass MPF. Among them, optical single-sideband (OSSB) modulation and optical double-sidebands (ODSB) modulation are two main methods to achieve integrated bandpass MPF. For the OSSB modulation, the shape and performance indicators of the bandpass MPF nearly depend on the used optical filter, which exhibits a one-to-one mapping relationship. Therefore, it is particularly important to design high-performance optical filters, which brings great challenges.

For the ODSB obtained by phase modulation, two optical sidebands with anti-phase and identical amplitude can be obtained. The conventional and simple way for achieving bandpass MPF is introducing an optical notch filter based on single micro-ring resonator (MRR) to process one of two optical sidebands, thus achieving phase to intensity conversion by frequency beating in the photodetector (PD). However, the single MRR notch filter could introduce residual phase outside the passband, which may break the symmetrical Lorentz line shape, especially in the high frequency region, thus deteriorating the out-of-band RF rejection ratio and the shape factor of the bandpass MPF [15]. In order to reduce the negative impact of the residual phase, a cascaded pair of non-identical SOI MRRs with different free spectrum ranges (FSRs) and 3-dB bandwidths were used to process two optical sidebands separately, achieving the shape factor of 1.78 and the out-of-band RF rejection ratio of 20 dB [16]. Since the bandwidth of achieved bandpass MPF is the difference between two MRRs’ bandwidths, it is hard to align two frequencies of the MRRs in the experiment. Thus, the out-of-band RF rejection ratio is also limited and bandwidth reconfiguration is not implemented. By using single MRR with much narrower 3-dB bandwidth of 0.17 GHz working at the under coupling condition, the negative impact of the residual phase on the performance of the bandpass MPF can be reduced and a symmetric RF response was obtained [8], but the bandwidth tuning range is limited. Then, dual optical carriers were introduced into phase modulation with single Si3N4 MRR to reduce the residue phase which limits the out-of-band RF rejection ratio [17]. In this way, a tunable bandpass MPF with frequency tuning range of 2∼14 GHz and 3-dB bandwidth tuning range of 0.673∼2.798 GHz were demonstrated. However, the used dual optical carriers from different lasers are incoherent and need to be tuned individually, the instability of two lasers’ wavelength could increase the risk of the instability of the tunable bandpass MPF. Recently, four cascaded add-drop SOI MRRs with OSSB modulation have been proposed to achieve MPF’s frequency tuning from 5.2 to 35.8 GHz with out-of-band RF rejection ratio of 40 dB [18]. In this method, by increasing the amplitude coupling coefficient to enlarge the optical bandwidth of the every MRR or increasing the distance between the resonant frequencies of each two MRRs, the cascaded MRRs’ optical bandwidth can be enlarged, thus increasing MPF’s bandwidth with the OSSB modulation. However, for the over coupling status, cascaded MRRs’ optical extinction ratio (ER) decreases with the increase of the bandwidth, thus the out-of-band RF rejection ratio could decrease correspondingly. Therefore, it is hard to achieve high out-of-band RF rejection ratio and large reconfiguration bandwidth simultaneously. To maintain high out-of-band RF rejection ratio more than 40 dB, the bandwidth reconfiguration is limited to only 0.7 ∼ 2 GHz. What’s more, because twenty heaters need to be adjusted simultaneously, the proposed method is not easy to implement from the point of the experiment. In conclusion, it is still challenging to achieve high-performance bandpass MPF with high out-of-band RF rejection ratio, large frequency tuning range, broadly reconfigurable bandwidth, and steep shape factor.

In this paper, we introduce double cascaded Si3N4 MRRs to handle two optical sidebands separately generated by phase modulation, which reduces the unwanted effect of the residual phase and thus greatly improves the performance of the bandpass MPF. Compared with the single MRR, the out-of-band RF rejection ratio was enhanced by 20 dB and the shape factor was improved by 1.67. Furthermore, the bandpass MPF’s bandwidth is reconfigurable by adjusting optical carrier’s frequency or the two MRRs’ amplitude coupling coefficients. Besides, the bandpass MPF’s center frequency is tunable by changing the resonant wavelengths of two MRRs in the opposite direction simultaneously. In the experiment, bandwidth reconfiguration from 0.38 GHz to 15.74 GHz was achieved, the shape factor optimization from 2 to 1.23 was got, and frequency tuning from 4 GHz to 21.5 GHz was obtained. We believe that the proposed bandpass MPF would be a promising candidate for microwave photonic signal processing and microwave photonic communication systems.

2. Principle and simulation

The working principle of the bandpass MPF based on phase modulation with single MRR is shown in Fig. 1(a). The optical carrier with fixed frequency fc from the tunable semiconductor laser (TSL) passes through the polarization controller (PC1) and injects into the phase modulator (PM). Then, the optical carrier is modulated by the RF signal, generating ±1st order optical sidebands with π phase difference and identical amplitude. The obtained two optical sidebands inject into single MRR after the PC2, which is used to adjust the polarization state. The +1st order optical sideband is filtered by the single MRR and generates a dip here. After phase to intensity conversion by frequency beating in the PD, a bandpass MPF can be achieved.

 figure: Fig. 1.

Fig. 1. (a) The working principle of the bandpass MPF based on phase modulation with single MRR. (b) The schematic illustration of the tunable balanced Mach-Zehnder interferometer (MZI) coupled MRR. (c) The cross section of the Si3N4 optical waveguide with heater.

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Under the small signal modulation condition, higher-order optical sidebands can be ignored and the optical field after phase modulation can be expressed as:

$$\begin{aligned} E(t) &= {E_0}(t) + {E_{ + 1}}(t) + {E_{ - 1}}(t)\\ &= {E_C}{e^{j{\varphi _c}}}({J_0}(m){e^{j{\omega _c}t}} + {J_{ + 1}}(m){e^{j({\omega _c} + {\omega _f})t}} + {J_{ - 1}}(m){e^{j({\omega _c} - {\omega _f})t}}) \end{aligned}$$
where En is the nth order optical field and Jn is the nth order Bessel function of the first kind. EC, ωC, and φC are the amplitude, angular frequency and initial phase of the optical carrier, respectively. ωf is angular frequency of the RF signal. The phase modulation index is m = πVRF/Vπ, where Vπ is the half-wave voltage of the PM and VRF is the amplitude of the RF signal. After the single MRR processes the +1st order optical sideband, the optical field can be described as:
$$\begin{aligned} {E_0}(t) &= {E_C}{e^{j{\varphi _c}}}{J_0}(m){e^{j{\omega _c}t}}H({\omega _c})\\ {E_{ + 1}}(t) &= {E_C}{e^{j{\varphi _c}}}{J_{ + 1}}(m){e^{j({\omega _c} + {\omega _f})t}}H({\omega _c} + {\omega _f})\\ {E_{ - 1}}(t) &= {E_C}{e^{j{\varphi _c}}}{J_{ - 1}}(m){e^{j({\omega _c} - {\omega _f})t}}H({\omega _c} - {\omega _f}) \end{aligned}$$
where H(ω) denotes the transfer matrix of the filter. The filtered optical signal then injects into the PD and the obtained photocurrent i can be calculated as:
$$\begin{aligned} i(t) &= {i_{0, + 1}}(t) + {i_{0, - 1}}(t)\\ {i_{0, + 1}}(t) &= \beta \eta (E_0^\ast {E_{ + 1}} + {E_0}E_{ + 1}^\ast )\\ &= 2\beta \eta {P_c}{J_0}(m){J_1}(m)\sqrt {T({\omega _c})} \sqrt {T({\omega _c} + {\omega _f})} \cos ({\omega _f}t + {\varphi _{0, + 1}})\\ {i_{0, - 1}}(t) &= \beta \eta (E_0^\ast {E_{ - 1}} + {E_0}E_{ - 1}^\ast )\\ &= 2\beta \eta {P_c}{J_0}(m){J_1}(m)\sqrt {T({\omega _c})} \sqrt {T({\omega _c} - {\omega _f})} \cos ({\omega _f}t - {\varphi _{0, + 1}}) \end{aligned}$$
where i0, + 1 and i0, −1 are the photocurrents through frequency beating between the optical carrier and the +1st and −1st order optical sidebands, respectively. T(ω) and φMRR(ω) are the transmittance and phase of the MRR. Pc is the power of the optical carrier, β is the link loss, and η is the responsibility of the PD. φ0, −1 and φ0, + 1 are the phases of i0, −1 and i0, + 1, which are induced by the phase of the MRR, given by:
$$\begin{aligned} {\varphi _{0, + 1}} &= {\varphi _{MRR}}({\omega _c} + {\omega _f}) - {\varphi _{MRR}}({\omega _c})\\ {\varphi _{0, - 1}} &= {\varphi _{MRR}}({\omega _c}) - {\varphi _{MRR}}({\omega _c} - {\omega _f}) \end{aligned}$$

The obtained output RF power of the bandpass MPF can be expressed as:

$$\begin{aligned} {P_{out}} &= \frac{1}{2}{i_{eff}}{(t)^2}{R_{out}}\\ {i_{eff}}(t) &= \frac{{i(t)}}{{\sqrt 2 }} \end{aligned}$$
where Rout and ieff are the matched load impedance and the effective photocurrent. Finally, the RF gain can be calculated by Eq. (6), where PRF is the power of the input RF signal.
$$RF\textrm{ }gain = 10{\log _{10}}\frac{{{P_{out}}}}{{{P_{RF}}}}$$

To achieve bandwidth reconfiguration of the bandpass MPF, the coupling region of MRR is constructed by a tunable balanced MZI as shown in Fig. 1(b). The tunable MZI coupler is composed of two 50:50 directional couplers (DCs) connected with one optical waveguide and one phase shifter. Assuming the coupling region is lossless, the transfer matrix of the tunable MZI coupler can be described as:

$$\begin{array}{l} \textrm{ }\left( \begin{array}{l} {E_4}\\ {E_3} \end{array} \right) = {T_{MZI}}\left( \begin{array}{l} {E_2}\\ {E_1} \end{array} \right),\textrm{ }{T_{DC}} = \frac{1}{{\sqrt 2 }}\left( {\begin{array}{{cc}} 1&\textrm{i}\\ i&1 \end{array}} \right)\\ {T_{MZI}} = {T_{DC}}\left( {\begin{array}{{cc}} 1&0\\ 0&{{e^{i\varphi }}} \end{array}} \right){T_{DC}} = \frac{1}{2}\left( {\begin{array}{{cc}} { - {e^{i\varphi }} + 1}&{i{e^{i\varphi }} + i}\\ {i{e^{i\varphi }} + i}&{{e^{i\varphi }} - 1} \end{array}} \right) \end{array}$$
where TMZI is the transfer matrix of the MZI coupler, TDC is the transfer matrix of the 50:50 DC, φ is the phase shift added by the Heater2. The calculated amplitude coupling coefficient of the MZI coupler is represented by k = |cos(φ/2)|.

The proposed single MRR can be fabricated on the double strip Si3N4 platform and the cross section of the Si3N4 optical waveguide with heater is shown in Fig. 1(c). The geometric parameters of the Si3N4 optical waveguide are: W = 1.1 µm, α = 82°, H1 = 0.175 µm, Gap = 0.1 µm, H2 = 0.075 µm. The propagation loss of the fabricated double strip Si3N4 waveguide is about 0.37 dB/cm and the effective index neff around 1.55 µm wavelength is expressed in Eq. (10) calculated by finite difference time domain method. The transfer matrix of the MRR constructed with the tunable MZI coupler can be calculated as:

$${H_{MRR}} = \frac{{\frac{1}{2}({e^{i\varphi }} - 1) - a{e^{i(\varphi + {\theta _0} + {\varphi _1})}}}}{{1 - \frac{1}{2}a( - {e^{i\varphi }} + 1){e^{i({\theta _0} + {\varphi _1})}}}}$$
$${\theta _0} = \frac{{2\pi {n_{eff}}L}}{\lambda }$$
$${n_{eff}}(\lambda ) ={-} 0.15771\lambda [\mu m] + 1.77206$$
where HMRR is the transfer matrix of the MRR, a is the amplitude transmission coefficient, φ1 is the phase shift added by the Heater1, θ0 is the accumulative phase shift of the optical signal traveling around the MRR, L is the perimeter of the MRR.

For the bandpass MPF based on phase modulation with single MRR above, the MRR operating at the over coupling status can achieve a stronger passband with relatively higher RF gain compared with the under coupling status [19]. Because π phase shift can be introduced at the notch frequency in the upper sideband at the over coupling status, the constructive interference between mixing products of the optical carrier and two optical sidebands takes place in the passband, thus forming a strong RF signal. In contrast, for the under coupling MRR, zero phase shift is introduced at the notch frequency, the partial destructive interference between mixing signals takes place in the passband after photodetection. Compared with the under coupling status, the RF gain at the over coupling status can be optimized by 15 dB in the experiment [19]. Therefore, the MRR operating at the over coupling status is selected to achieve the conventional bandpass MPF. As shown in Fig. 2(c), the total phase shift 2π is introduced in one FSR (50 GHz) where π phase shift occurs at the resonance. The full width at half maximum (FWHM) is 2 GHz and the transmittance is 0.62 (ER is 2 dB). According to the experimental results below, the parameters are taken into Eqs. (1)–(10) to analyze the bandpass MPF based on phase modulation with single MRR (Experimental parameters: Pc = 13 dBm, PRF = 5 dBm, β = 0.1, link loss is 10 dB, VRF = 4.6 V, Rout = 50 Ω, m = 0.384, η = 0.65 A/W, L = 3351 µm). The optical carrier is placed 12.5 GHz away from one resonant frequency of the MRR. The simulated RF response of the bandpass MPF is shown in Fig. 2(a). The achieved 3-dB bandwidth of the bandpass MPF is consistent with the optical bandwidth of the MRR, which shows that this method has the characteristic of bandwidth mapping from optical to RF regions [7]. It also indicates that bandwidth reconfiguration of the bandpass MPF only comes from the adjustment of the optical bandwidth by changing the amplitude coupling coefficient of the MRR. On the other hand, it is clear that the out-of-band RF rejection ratio of the bandpass MPF is 12 dB, higher than that of the optical filter’ ER, which exhibits the advantage of the phase modulation compared with the OSSB modulation. However, limited by the introduced residual phase by the MRR, perfect destructive interference in the high frequency region is hard to achieve. From Eqs. (3)–(4), the transmittance and phase of the MRR can influence the amplitudes and phases of the photocurrent i0, −1 and i0, + 1, finally changing the total photocurrent i. Figure 2(b) and Fig. 2(d) show the variations of the amplitudes and phases of two photocurrents induced by the MRR in the RF region. At the resonant frequency in the passband, π phase shift is introduced by the over coupling MRR, combined with the intrinsic π phase difference between the ±1st optical sidebands after phase modulation, thus constructive interference between mixing products of optical carrier and two optical sidebands takes place and a strong passband is formed. For the low frequency region, the T(ωc+ωf) and T(ωc−ωf) are almost identical and φ0, + 1 - φ0, −1 ≈ 0 since these frequencies are close to the frequency of the optical carrier. Due to the intrinsic π phase difference between the ±1st optical sidebands after phase modulation, perfect destructive interference can be achieved in the low frequency region. For the high frequency region, φ0, + 1 - φ0, −1 is relatively far away from 2π, making it hard to achieve perfect destructive interference. Finally, the symmetric Lorentz line shape of the MRR response is broken, and the out-of-band RF rejection ratio along with shape factor deteriorates.

 figure: Fig. 2.

Fig. 2. (a) The simulated bandpass MPF based on phase modulation with single MRR; (b) The amplitudes of photocurrents i0, + 1 and i0, −1; (c) The transmission and phase spectra of single MRR; (d) The phases introduced by the single MRR for i0, + 1 and i0, −1.

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To reduce the unwanted effects caused by the residual phase, double MRRs with identical bandwidth are introduced to process the two optical sidebands generated by phase modulation, respectively. The working principle of the bandpass MPF based on phase modulation with double MRRs is shown in Fig. 3.

 figure: Fig. 3.

Fig. 3. The working principle of the bandpass MPF based on phase modulation with double MRRs.

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The optical carrier with fixed frequency from the TSL passes through the PC1 and injects into the PM. Then, the optical carrier is modulated by the RF signal, generating ±1st order optical sidebands with π phase difference and identical amplitude. The two optical sidebands inject into double MRRs after the PC2, where one MRR is used to processes the +1st order optical sideband to generate one dip and the other is used to processes the -1st order optical sideband to generate another dip. After phase to intensity conversion by frequency beating in the PD, the bandpass MPF can be achieved. The transfer matrix of the cascaded optical filter H(ω) is expressed as:

$$H(\omega ) = {H_{MRR1}}{H_{MRR2}}$$
where, HMRR1 and HMRR2 denote the transfer matrix of the two MRRs, respectively. Referring to the MPF obtained with single MRR and phase modulation, the two MRRs both operate at the over coupling status and have the same FWHM of 2 GHz and FSR of 50 GHz, as shown in Fig. 4(c). The same experimental parameters are taken into Eqs. (1)–(11) to analyze the improved bandpass MPF based on phase modulation with double MRRs. The optical carrier is placed between the resonant frequencies of the two MRRs, 13.48 GHz away from the first resonant frequency f1 and 11.75 GHz away from the second resonant frequency f2. The simulated bandpass MPF is shown in Fig. 4(a). The achieved 3-dB bandwidth of the bandpass MPF is 2.5 GHz, larger than the 2 GHz optical bandwidth of one MRR, which is caused by the unequal frequency difference |f2-fc| ≠ |f1-fc| as shown in Fig. 4(c). It is clear that the simulated out-of-band RF rejection ratio of the bandpass MPF is much higher than that in Fig. 2(a), showing a nearly perfect destructive interference both in the low frequency and high frequency regions. Figure 4(b) and Fig. 4(d) show the variations of the amplitudes and phases of the two photocurrents induced by the two MRRs in the RF region. In the passband, the introduced π phase shift of the two MRRs working at the over coupling status, combined with the intrinsic π phase difference between the ±1st optical sidebands after phase modulation, can make constructive interference between the mixing products of the optical carrier and two optical sidebands, then forming a strong passband. After setting the optical carrier’s frequency fc for the proposed bandpass MPF, by tuning the amplitude coupling coefficients and resonant frequencies of two MRRs and optical carrier’s frequency with resolution of 0.1 pm in sequence, the phase difference between the two MRRs can be adjusted to be π exactly. Besides, it is worth noting that in both the high and low frequency regions, φ0, + 1 - φ0, −1 is very close to zero, which is helpful to achieve perfect destructive interferences.

 figure: Fig. 4.

Fig. 4. (a) The simulated bandpass MPF based on phase modulation with double MRRs; (b) The amplitudes of photocurrents i0, + 1 and i0, −1; (c) The transmission and phase spectra of double MRRs; (d) The phases introduced by the double MRRs for i0, + 1 and i0, −1.

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Apart from the method that changing the amplitude coupling coefficients of the two MRRs to achieve bandwidth reconfiguration, changing the frequency of the optical carrier between the two MRRs’ resonant frequencies (f1 ∼ f2) can also achieve the fine bandwidth adjustment. When the frequency of the optical carrier changes by 1.1 GHz, the simulated 3-dB bandwidth of the bandpass MPF changes by 2.1 GHz (from 1.9 GHz to 4 GHz), as shown in Fig. 5(b). On the other hand, the center frequency tuning of the bandpass MPF can be realized by changing the resonant frequencies of the two MRRs in the opposite direction simultaneously with fixed optical carrier. As the resonant frequencies of the two MRRs get close to the optical carrier, the MPF’s center frequency decreases while increases when the resonant frequencies of the two MRRs move away from the optical carrier. By using this method, the MPF’s frequency can be tuned from 4 GHz to 21.5 GHz, as shown in Fig. 5(d).

 figure: Fig. 5.

Fig. 5. (a) Bandwidth reconfiguration of the bandpass MPF realized by changing the optical carrier’s frequency; (b) The simulated bandwidth reconfiguration; (c) The center frequency tuning of the bandpass MPF realized by changing two MRRs’ resonant frequencies in the opposite direction simultaneously with fixed optical carrier; (d) The simulated center frequency tuning.

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3. Experiment and discussion

The proposed cascaded and tunable MRRs were fabricated on the double strip Si3N4 platform (the TriPleX ADS technology of Lionix international corporation) [20,21]. The waveguide fabrication process of the double strip Si3N4 optical waveguide is given in Ref. [21]. Figure 6(a) shows the optical microscope image of the fabricated Si3N4 double MRRs based on the tunable balanced MZI coupler. The perimeter of the each MRR is L = 3351 µm. Four heaters (Heater1, Heater2, Heater3, Heater4) made of Cr/Au were used to tune the amplitude coupling coefficients and resonant frequencies of the two MRRs. Figure 6(b) shows the experimental setup of the transmission spectrum measurement based on tunable laser scanning method. By scanning the TSL (Santec, TSL-710) in wavelength range of 1562.4 nm ∼ 1563.2 nm with wavelength resolution of 0.1 pm and injecting the laser into the chip after a PC (Thorlabs FPC561), the optical transmission spectrum of the chip can be measured by an optical power meter (Santec, MPM-210). A multi-channel programmable current source (NI, PXIE-4322) was used to adjust the four driving currents of the four heaters respectively. The fiber-to-fiber insertion loss of the chip is 2.6 dB. The electrical powers applied to Heater1, Heater2, Heater3, Heater4 were set as 0 mW, 239.2 mW, 190.8 mW, 192.9 mW, respectively. The measured normalized transmission spectrum is shown in Fig. 6(c). FSRs and FWHMs of the double MRRs are FSR1 = FSR2 = 0.4 nm (50 GHz) and FWHM1 = FWHM2 = 2 GHz, respectively. The optical carrier’s wavelength was set as 1562.792 nm and the RF signal for phase modulation came from the electric vector network analyzer (VNA, Aglient N5242A). According to the working principle of the bandpass MPF based on phase modulation with double MRRs as shown in Fig. 3, the RF response was measured as shown in Fig. 6(d) (red solid line) and a strong bandpass MPF was obtained, whose center frequency, 3-dB bandwidth and out-of-band RF rejection ratio were 12.7 GHz, 2.5 GHz and 34 dB, respectively. Compared with the measured RF response of the bandpass MPF based on single MRR shown in Fig. 6(d) (blue solid line), the achieved out-of-band RF rejection ratio was enhanced by 20 dB and the shape factor was improved from 3.39 to 1.72 by introducing two cascaded MRRs (Shape factor is defined as the ratio of the 10-dB bandwidth to the 3-dB bandwidth). It indicates that the proposed method using two cascaded MRRs to tailor the amplitudes and phases of the two optical sidebands after phase modulation can effectively reduce the negative effect of the single MRR’s residual phase. It should be noted that no electrical or optical amplifiers were used in the bandpass MPF system. The relatively low RF gain about -30 dB could be increased by using electrical or optical amplifiers.

 figure: Fig. 6.

Fig. 6. (a) Optical microscope image of the fabricated Si3N4 double MRRs based on the tunable balanced MZI coupler; (b) Experimental setup of the transmission spectrum measurement based on tunable laser scanning method; (c) The measured transmission spectrum at 1562.4 nm ∼1563.2 nm with wavelength resolution of 0.1 pm; (d) The measured RF responses of the bandpass MPFs using single MRR and double MRRs based on phase modulation.

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Then, bandwidth reconfiguration of the bandpass MPF by changing the optical carrier’s frequency, and frequency tuning of the bandpass MPF by changing the resonant frequencies of the two MRRs in the opposite direction simultaneously with the fixed optical carrier were demonstrated. In the experiment, when the wavelength of the optical carrier changes by 0.008 nm (from 1562.79 nm to 1562.798 nm), the measured 3-dB bandwidth of the MPF changes by 2.38 GHz (from 1.89 GHz to 4.27 GHz), as shown in Fig. 7(a). Shape factors of the measured bandpass MPFs at different bandwidths are shown in Table 1. The shape factor can decrease from 1.96 to 1.48 when the 3-dB bandwidth increases from 1.89 GHz to 4.27 GHz. It is worth mentioning that high out-of-band RF rejection ratio (more than 32 dB) and flat-top passband (ripple is smaller than 1.2 dB) can be maintained in the process of bandwidth reconfiguration. Moreover, when the electrical powers applied to Heater1 and Heater3 increased from 1.5 mW to 386 mW, the resonant frequencies of the two MRRs moved away from the optical carrier simultaneously. And the center frequency of the RF signal can be changed from 4 GHz to 21.5 GHz, as shown in Fig. 7(b). The influence factor for the lower limiting value of the frequency is the optical 3-dB bandwidths of the two MRRs. For the bandpass MPF with center frequency of 4 GHz, the resonant frequencies of two MRRs are located about 4 GHz on each side of optical carrier. As shown in Fig. 6(c), the total resonant bandwidth of each MRR is larger than 4 GHz. Therefore, when using one MRR to tailor the -1st order optical sideband, part of its resonance will overlap with the +1st order optical sideband and then introduce unwanted phase shift. So does the other MRR. In this case, it is hard to achieve complete destructive interference outside the passband of the proposed bandpass MPF. Therefore, the RF rejection ratio of the bandpass MPF with center frequency of 4 GHz is only about 20 dB. When the center frequency of the proposed bandpass MPF is lower than 4 GHz, the RF rejection ratio would be lower than 20 dB, which may not be used for microwave photonic systems. By decreasing the optical 3-dB bandwidths of the two MRRs, the introduced unwanted phase shift mentioned above can be effectively reduced, thus the lower limiting value of the bandpass MPF’s frequency can be further decreased. However, decreasing the optical 3-dB bandwidths of the two MRRs could also reduce the bandwidth tuning range of the proposed bandpass MPF. Therefore, there is a trade-off between the lowest frequency and bandwidth tuning range of the proposed bandpass MPF. The upper limit of the tuning range on center frequency by the proposed approach is half of the FSR of the MRR. In this paper, the FSR of the MRR is 50 GHz, thus the upper limit of the tuning range on center frequency is 25 GHz. By increasing the FSR of the MRR, the tuning range of center frequency can be increased.

 figure: Fig. 7.

Fig. 7. (a) The measured bandwidth reconfiguration of the bandpass MPF by changing the frequency of the optical carrier; (b) The measured frequency tuning of the bandpass MPF by changing the resonant frequencies of two MRRs in the opposite direction simultaneously with the fixed optical carrier.

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Tables Icon

Table 1. Shape factors of the measured bandpass MPFs at different bandwidths

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By changing the frequency of the optical carrier and the amplitude coupling coefficients of the two MRRs simultaneously, the bandwidth reconfigurability of the proposed bandpass MPF based on phase modulation with two cascaded MRRs can be further enhanced. In the experiment, by setting the electrical powers applied to Heater2 and Heater4 as 161.8 mW and 117.6 mW, the amplitude coupling coefficients of the two MRRs working at the over coupling condition were changed and an optical 3-dB bandwidth of 6 GHz was obtained. Similarly, different optical 3-dB bandwidths of 2 GHz (over coupling), 0.47 GHz (critical coupling) and 0.36 GHz (under coupling) were also obtained. Then, by changing the optical carrier’s frequency, the measured 3-dB bandwidths of the bandpass MPF ranging from 5.59 GHz to 15.74 GHz can be achieved when the optical 3-dB bandwidth is 6 GHz, as shown in Fig. 8(a). For the optical 3-dB bandwidths of 2 GHz, 0.47 GHz and 0.36 GHz, the measured 3-dB bandwidths of the bandpass MPFs ranging from 1.89 GHz to 4.27 GHz, from 0.44 GHz to 1.25 GHz, from 0.38 GHz to 0.98 GHz were obtained, respectively, as shown in Fig. 8(b-d). Therefore, a large bandwidth reconfiguration ranging from 0.38 GHz to 15.74 GHz was achieved by the proposed bandpass MPF. As can be seen in Fig. 8(b), the re-rising waveforms are generated in the low frequency region. The reason is that the resonances of two MRRs are very close and the induced residual phase will affect the RF response in the low frequency region. By increasing the FSR of the two MRRs or decreasing the optical 3-dB bandwidth of the two MRRs, the re-rising waveforms can be effectively suppressed. The stability of the laser used in the experiment is ± 125 MHz (For period of 1 hour, within ± 0.5 °C). The wavelength drifting of the laser affects the maximal bandwidth (15.74 GHz) of the MPF weakly, but it may affect the MPF’s minimal bandwidth (0.38 GHz). The bandwidth stability of the proposed MPF could be improved by using wavelength feedback control in the future. Because the resonant frequencies of the two MRRs have the relationship: |f2-fc| ≠ |f1-fc|, as shown in Fig. 4(c), the achieved RF passband by the proposed method can be seen as the combination of two RF responses, each of which is generated by phase modulation with one MRR. For the phase modulation with one MRR, over coupling status can achieve a stronger RF passband with relatively higher RF gain compared with the under coupling status [19]. After the combination of two RF responses, the obtained RF gain of the MPF with MRRs working at the over coupling status is higher than that of the under coupling status. According to Fig. 8, the relationship between shape factor and 3-dB bandwidth at different coupling status is shown in Fig. 9. It shows that the shape factor can decrease with the increase of the 3-dB bandwidth for all the coupling status and the best shape factor of 1.23 was obtained when the 3-dB bandwidth was 15.74 GHz.

 figure: Fig. 8.

Fig. 8. The measured bandwidth reconfigurations of (a) over coupling (optical 3-dB bandwidth of 6 GHz); (b) over coupling (optical 3-dB bandwidth of 2 GHz); (c) critical coupling (optical 3-dB bandwidth of 0.47 GHz); (d) under coupling (optical 3-dB bandwidth of 0.36 GHz) with the frequency tuning of the optical carrier.

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 figure: Fig. 9.

Fig. 9. The relationship between shape factor and 3-dB bandwidth at different coupling status.

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Finally, we compared our work with the previously reported results as summarized in Table 2. It can be seen that the bandwidth reconfiguration range is the largest and the shape factor of 1.23 is the best obtained in this work. Compared with utilizing two non-identical SOI MRRs with different FSRs to improve the performance of bandpass MPF [16], this work can achieve large bandwidth tuning by adjusting the optical carrier’s frequency along with two MRRs’ amplitude coupling coefficients. In addition, two identical MRRs with same 3-dB bandwidth were used here, which is helpful to achieve perfect destructive interference outside the passband, thus obviously improving the RF rejection ratio and the shape factor. The double cascaded Si3N4 MRRs have a relatively low waveguide propagation loss about 0.37 dB/cm, which can support bandpass MPF with narrow bandwidth and low insertion loss. The tunable balanced MZI coupler of MRR can support the amplitude coupling coefficients tuning of the two MRRs, helpful to achieve large reconfigurable RF bandwidth. Compared with high-order MRRs, the used two MRRs only have four heaters, which greatly reduces the difficulty in the experiment. Nearly, a notch MPF based on two cascaded SOI MZI-coupled MRRs has been demonstrated and an extremely high rejection ratio beyond 70 dB was achieved [24]. However, only bandstop filtering function is achieved, which is different from our proposed bandpass filter. Besides, the achieved 3-dB bandwidth ranging from 0.185 to 1.263 GHz is relatively smaller. For the proposed bandpass MPF based on phase modulation with double MRRs, its frequency tuning range can be further enlarged by increasing the FSR of the two MRRs, and the bandwidth reconfigurability can be further enhanced by using high-order MRRs. Besides, other material platforms have been used to achieve compact optoelectronic structures [25–27], which may be applied in microwave photonic area in the future.

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Table 2. The performance comparison of the previously reported results with this work

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4. Conclusion

In conclusion, two cascaded Si3N4 MRRs have been introduced to handle two optical sidebands separately generated by phase modulation, which effectively reduces the unwanted effect of the MRR’s residual phase and then greatly improves the bandpass MPF’s performances. In the experiment, compared with the single MRR, the out-of-band RF rejection ratio of the proposed bandpass MPF was enhanced by 20 dB, and the shape factor was improved by 1.67. The bandwidth reconfiguration from 0.38 GHz to 15.74 GHz was achieved, the shape factor improved from 2 to 1.23 was got, and frequency tuning from 4 GHz to 21.5 GHz was obtained. We believe that the proposed bandpass MPF has great potential for microwave photonic signal processing.

Funding

National Natural Science Foundation of China (62171118).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (9)
Fig. 1.
Fig. 1. (a) The working principle of the bandpass MPF based on phase modulation with single MRR. (b) The schematic illustration of the tunable balanced Mach-Zehnder interferometer (MZI) coupled MRR. (c) The cross section of the Si3N4 optical waveguide with heater.

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Fig. 2.
Fig. 2. (a) The simulated bandpass MPF based on phase modulation with single MRR; (b) The amplitudes of photocurrents i0, + 1 and i0, −1; (c) The transmission and phase spectra of single MRR; (d) The phases introduced by the single MRR for i0, + 1 and i0, −1.

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Fig. 3.
Fig. 3. The working principle of the bandpass MPF based on phase modulation with double MRRs.

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Fig. 4.
Fig. 4. (a) The simulated bandpass MPF based on phase modulation with double MRRs; (b) The amplitudes of photocurrents i0, + 1 and i0, −1; (c) The transmission and phase spectra of double MRRs; (d) The phases introduced by the double MRRs for i0, + 1 and i0, −1.

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Fig. 5.
Fig. 5. (a) Bandwidth reconfiguration of the bandpass MPF realized by changing the optical carrier’s frequency; (b) The simulated bandwidth reconfiguration; (c) The center frequency tuning of the bandpass MPF realized by changing two MRRs’ resonant frequencies in the opposite direction simultaneously with fixed optical carrier; (d) The simulated center frequency tuning.

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Fig. 6.
Fig. 6. (a) Optical microscope image of the fabricated Si3N4 double MRRs based on the tunable balanced MZI coupler; (b) Experimental setup of the transmission spectrum measurement based on tunable laser scanning method; (c) The measured transmission spectrum at 1562.4 nm ∼1563.2 nm with wavelength resolution of 0.1 pm; (d) The measured RF responses of the bandpass MPFs using single MRR and double MRRs based on phase modulation.

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Fig. 7.
Fig. 7. (a) The measured bandwidth reconfiguration of the bandpass MPF by changing the frequency of the optical carrier; (b) The measured frequency tuning of the bandpass MPF by changing the resonant frequencies of two MRRs in the opposite direction simultaneously with the fixed optical carrier.

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Fig. 8.
Fig. 8. The measured bandwidth reconfigurations of (a) over coupling (optical 3-dB bandwidth of 6 GHz); (b) over coupling (optical 3-dB bandwidth of 2 GHz); (c) critical coupling (optical 3-dB bandwidth of 0.47 GHz); (d) under coupling (optical 3-dB bandwidth of 0.36 GHz) with the frequency tuning of the optical carrier.

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Fig. 9.
Fig. 9. The relationship between shape factor and 3-dB bandwidth at different coupling status.

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Tables (2)

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Table 1. Shape factors of the measured bandpass MPFs at different bandwidths

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Tables Icon

Table 2. The performance comparison of the previously reported results with this work

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Equations (11)

Equations on this page are rendered with MathJax. Learn more.

E ( t ) = E 0 ( t ) + E + 1 ( t ) + E − 1 ( t ) = E C e j φ c ( J 0 ( m ) e j ω c t + J + 1 ( m ) e j ( ω c + ω f ) t + J − 1 ( m ) e j ( ω c − ω f ) t )
E 0 ( t ) = E C e j φ c J 0 ( m ) e j ω c t H ( ω c ) E + 1 ( t ) = E C e j φ c J + 1 ( m ) e j ( ω c + ω f ) t H ( ω c + ω f ) E − 1 ( t ) = E C e j φ c J − 1 ( m ) e j ( ω c − ω f ) t H ( ω c − ω f )
i ( t ) = i 0 , + 1 ( t ) + i 0 , − 1 ( t ) i 0 , + 1 ( t ) = β η ( E 0 ∗ E + 1 + E 0 E + 1 ∗ ) = 2 β η P c J 0 ( m ) J 1 ( m ) T ( ω c ) T ( ω c + ω f ) cos ⁡ ( ω f t + φ 0 , + 1 ) i 0 , − 1 ( t ) = β η ( E 0 ∗ E − 1 + E 0 E − 1 ∗ ) = 2 β η P c J 0 ( m ) J 1 ( m ) T ( ω c ) T ( ω c − ω f ) cos ⁡ ( ω f t − φ 0 , + 1 )
φ 0 , + 1 = φ M R R ( ω c + ω f ) − φ M R R ( ω c ) φ 0 , − 1 = φ M R R ( ω c ) − φ M R R ( ω c − ω f )
P o u t = 1 2 i e f f ( t ) 2 R o u t i e f f ( t ) = i ( t ) 2
R F   g a i n = 10 log 10 P o u t P R F
  ( E 4 E 3 ) = T M Z I ( E 2 E 1 ) ,   T D C = 1 2 ( 1 i i 1 ) T M Z I = T D C ( 1 0 0 e i φ ) T D C = 1 2 ( − e i φ + 1 i e i φ + i i e i φ + i e i φ − 1 )
H M R R = 1 2 ( e i φ − 1 ) − a e i ( φ + θ 0 + φ 1 ) 1 − 1 2 a ( − e i φ + 1 ) e i ( θ 0 + φ 1 )
θ 0 = 2 π n e f f L λ
n e f f ( λ ) = − 0.15771 λ [ μ m ] + 1.77206
H ( ω ) = H M R R 1 H M R R 2
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