## 1 Introduction
However, the signal's maximum frequency was restricted by the operating bandwidth of the directly modulated semiconductor laser, which was usually lower than the bandwidth of external modulator. In Ref. [16], a dual-loop OEO with a large tunable frequency range of 60 GHz, which was constructed by utilizing stimulated Brillouin scattering (SBS), was proposed. However, the SMSR was only 35 dB. The performance of the oscillation signal was mainly restricted by the stability of its frequency and power. In Ref. [17], a coupled dual-loop SBS-based OEO was investigated to improve the stability of the system. The obtained 15 GHz signal had a phase noise of only \(-\)95 dBc/Hz at 10 kHz frequency offset, while the performance of the near end phase noise (<1 kHz) was poor. In Ref. [18], a new type of OEO (known as a parity-time symmetric OEO) was proposed to suppress the side modes. The OEO could generate a 4.07 GHz single-mode microwave signal, with phase noise of \(-\)108 dBc/Hz at 10 kHz frequency offset when there is no filter in the OEO loop. In Ref. [19], an OEO with higher frequency up to W-band was implemented. In this scheme, the side modes could be suppressed by introducing electrical injection locking technique. On the other hand, an integrated OEO based on micro-disk resonator, which was fabricated on silicon-based photonic platform, was proposed [20]. The research made a huge contribution to the development of integrated frequency tunable OEO. Furthermore, with the recent progress in multiband microwave systems (such as multifunctional modern radar and next-generation (such as 5G) wireless and mobile radio communication [21]), the demand for tunable dual-frequency OEOs has been increasing. In Ref. [22], a dual-frequency OEO was employed on the basis of a PS-FBG, so as to realize the conversion similarly to [12]. In this scheme, the frequencies of two generated signals could be defined by the differential in frequency between the two light sources and the frequency of a notch in the PS-FBG. By tuning the wavelengths of different light sources, the central frequencies of the two generated signals could be independently adjusted. However, the quality of the oscillation signal was influenced by the fluctuation of the notch frequency in the grating reflection spectrum of the PS-FBG. In Ref. [23], a dual-frequency OEO based on the dual-parallel Mach-Zehnder modulator (DPMZM) and CFBG was proposed. The DPMZM was utilized to implement carrier phase-shifted double sideband (CPS-DSB) modulation so that the frequency-doubled microwave signal could be obtained. The CFBG was utilized to ensure that another signal oscillated at base frequency by adjusting the phase between the sideband signals and the optical carrier signal. Finally, the two oscillation signals with frequencies of 10 and 20 GHz were generated. Although the system was simple to construct, bias drifts deteriorated the stability of the proposed dual-frequency DPMZM-based OEO. In this article, we proposed a tunable dual-frequency OEO based on an OISL for microwave signal generation with low phase noise and wide tunability. By introducing the subharmonic microwave signal applied to a PM in the proposed system, the linewidth and SMSR could be optimized. The optical signal after optical injection was modulated via a dual-output Mach-Zehnder modulator (DOMZM) to achieve complementary intensity modulation. Then, the output of the two optical paths from the DOMZM was connected with different fiber lengths in the loop, respectively. Hence, the side mode and the phase noise could be rejected by the Vernier effect. After the optical signals beating in the balanced photodetector (BPD), the microwave signal was fed back to the DOMZM to construct the OEO loop. The experimental results on the OEO showed that the high-quality microwave signals (with the tunable frequency up to 18 GHz) could be obtained. The phase noise was lower than \(-81\) dBc/Hz at 1 kHz frequency offset when the frequency of the generated signal was 15 GHz.