## 2 Operating Principle  
The schematic diagram of the dual-loop dual-frequency OEO is shown in Figure 1. The OEO loop is made up of two tunable laser sources, a 3-dB optical coupler (OC), a DOMZM, a PM, three PCs, an optical circulator (CIR), a pool of single-mode fiber (SMF), a variable optical delay line (VODL), a distributed-feedback semiconductor laser diode (DFB-LD) or an FP-LD, a BPD, an EBPF and an electrical amplifier (EA). The generated microwave signals of the proposed OEO can be tested using the electrical spectrum analyzer (ESA) and signal source analyzer (SSA), respectively. As shown in Figure 1, two laser sources were utilized as master lasers (MLs). An FP-LD without an optical isolator was used as a slave laser (SL). Two optical signals emitted from two MLs with the frequencies of \(f_{m1}\) and \(f_{m2}\) were combined by an OC. Then, the optical signals were modulated by the microwave signal with the frequency of \(f_{0}/N\) (\(N\) is an integer) via a PM to realize phase modulation. The frequency \(f_{0}/N\) was used to implement subharmonic microwave modulation, which could improve the frequency stability and spur the suppression ratio in the OEO loop [24; 25]. In addition, under subharmonic microwave modulation, the 3-dB bandwidth of the oscillated signal would be optimized. The modulated optical signals output from the PM were injected into the SL through a CIR to achieve optical injection. The PCs were utilized to modify the polarization state between the MLs and SL to obtain proper injection efficiency in the system. Under proper optical injection, the cavity mode of the SL was red-shifted. At the same time, the optical gain spectrum could be produced when one of the modulated \(N\)th-order sideband signals fell into the locking area of the SL. Thus, the sideband signal of interest could be selected and amplified. Meanwhile, through the influence of subharmonic microwave modulation, one of the \(N\)th-order modulation sidebands after modulation would locate nearby the red-shifted light and lock it to ameliorate the signal's quality. Then, the optical signals from the SL were sent to the DOMZM through the CIR again. The DOMZM was set at the quadrature bias point in the OEO loop to realize complementary intensity modulation. The two optical outputs of the DOMZM passed through a spool of SMF and the VODL individually. The VODL was used to adjust the phase of the optical signals, so that balanced differential detection could be accomplished to improve the quality of the generated microwave signal. Afterwards, the two paths of the optical signals were coupled into the BPD. After beating in the BPD, the signals were processed by the EA and EBPF. Then, two microwave signals with different frequencies would be brought out. Finally, by using the electrical divider, the microwave signals were divided into two parts: one was returned to the DOMZM's RF port to achieve a closed loop, and the other was measured via the ESA and SSA. The operating principle of the OISL is shown in Figure 2. We assumed that the system was under single optical injection. The detuning frequency could be expressed as \(\Delta f=f_{m}-f_{s}\), which was the differential in wavelength between the ML and the free-running SL. Before the CIR, a PC could be utilized to modify the polarization state of the injected signal so that the SL could work at the P1 oscillation state under proper optical injection. Meanwhile, the cavity mode of the SL red-shifted to the frequency \(f_{avv}\) through the changing effect in carrier concentration under P1 oscillation [26]. In this way, a new frequency \(f_{avv}\) was produced because of the disappearance of the frequency \(f_{s}\) when the SL entered the P1 state.