## 2 Operation Principle  
A schematic diagram of the tunable dual-passband MPF is shown in Figure 1. The MPF link consists of a laser source, a dual-output Mach-Zehnder modulator (DOMZM), two polarization controllers (PCs), two optical circulators (CIRs), two DFB semiconductor lasers and a balanced photodetector (BPD). The performance of the MPF is evaluated using a vector network analyzer (VNA). As shown in Figure 1, a tunable laser source (TLS) is used as a master laser (ML), two DFB lasers are used as slave lasers (SLs) and the DOMZM is set at quadrature bias point in the proposed structure. The microwave signals modulate optical signal in the DOMZM and the high order sidebands (\(\geq\)2) can be ignored where only \(\pm\)1 st sidebands are considered under small signal modulation conditions. So, the microwave signals are applied to the light wave from the ML with the frequency \(f_{m}\). Two modulated optical signals with equal intensities are obtained via complementary intensity modulations at the output of DOMZM, and two modulated optical signals are then individually injected into the SLs DFB1 and DFB2 through CIRs to realize optical injection. The PCs in the link are used to adjust the polarization between the ML and SLs to maximize the injection efficiency. Finally, the optical signals from the SLs are coupled into the BPD. The principle of the dual-passband MPF is shown in Figure 2, where \(f_{0},f_{1},f_{2},f_{3}\) and \(f_{4}\) are the frequencies of the microwave signals to be processed. The free-running frequencies of DFB1 and DFB2 are \(f_{s1}\) and \(f_{s2}\). However, \(f_{s1}\) is different from \(f_{s2}\) in our structure. As shown in Figure 2a, when the optical carrier is modulated by microwave signals, \(-\)1 st sidebands of the modulated optical signals are generated with the frequencies of \(f_{m}-f_{0},f_{m}-f_{1},f_{m}-f_{2},f_{m}-f_{3}\) and \(f_{m}-f_{4}\). When the modulated optical signals are sent to the slave laser, the cavity mode of the slave DFB laser is red-shifted due to the change in carrier concentration based on the effect of the optical injection [13], and an optical gain spectrum centered at the red-shifted cavity mode with frequency \(f_{cav}\) will be produced. When the sidebands of modulated optical signals fall into the range of the gain spectrum, the optical signals will be selected and amplified. After beating in the BPD, signals of interest are selected and an MPF can be realized at the output of the BPD. The center frequency of the passband can be set by adjusting the detuning frequency and the injected ratio individually or together. In the proposed approach, the frequencies of the optical gain spectrum of two DFB lasers are \(f_{cav1}\) and \(f_{cav2}\), respectively. The modulated signals with small sideband amplitudes falling into the range of the optical gain spectrum are amplified depending on the detuning frequency. The amplitude of the other sideband signals remains unchanged. Finally, two microwave signals with different frequencies are generated at the output of the BPD by beating the amplified optical component with the optical carrier, and other microwave signals are suppressed, realizing the dual-passband microwave photonic filtering. Figure 1: Schematic diagram of the tunable dual-passband microwave photonic filter (MPF). ML: master laser; SL: slave laser; DOMZM: dual-output Mach–Zehnder modulator; CIR: optical circulator; PC: polarization controller BPD: balanced photodetector; VNA: vector network analyzer; OSA: optical spectrum analyzer. Assuming that optical carrier is modulated in DOMZM by microwave signals with different frequencies, one of the microwave signals can be expressed as:  
\[V(t)=V_{DC}+V_{0}\cos(2\pi f_{0}t) \tag{1}\]  
where \(V_{DC}\) is the bias voltage applied to the DOMZM, \(V_{0}\) is the amplitude of the microwave signal and \(f_{0}\) is the frequency of the microwave signal. The DOMZM is set at quadrature bias point by using a modulator bias controller.