# Stable and Low-Spurs Optoelectronic Oscillators: A Review
## 3 Improvement of Optoelectronic Oscillators
### Spurious Suppression  
In order to produce a microwave signal with superior phase noise performance, an OEO is supposed to equip high Q-value oscillating cavity and achieve long delay time, which is proportional to the length of the fiber. When fiber length and oscillation frequency are \(L\) and \(f\) respectively, Q-value of oscillating cavity can be represented as  
\[Q=2\pi f\tau=2\pi f\frac{nL}{c} \tag{1}\]  
where \(\tau\) and \(n\) are respectively the delay time and the effective refractive index of fiber, and \(c\) represents the speed of light. It can be summarized from Equation (1), that the longer the fiber the greater the delay time and the Q-value. However, the mode spacing of OEO \(\Delta f\) is inversely proportional to the length of fiber, which can be expressed as  
\[\Delta f=\frac{1}{\tau}=\frac{c}{nL}. \tag{2}\]  
For example, the mode spacing of an OEO is about 50 kHz when the length of fiber is 4 km, and the Q-value of band-pass filter in the OEO loop is accordingly required to be as high as 100,000 so as to obtain 10-GHz single mode oscillation. Nevertheless, Q value of available microwave band-pass filter will decrease along with the operating frequency, and it is difficult to achieve microwave band-pass filtering with a bandwidth of the order of 10 kHz and then reject the unwanted oscillation modes [29; 30; 31]. Several methods have been proposed to settle this problem, such as dual-loop OEOs [32], coupled optoelectronic oscillators (COEOs) [33], injection-locking technique [34], and high-Q microwave photonic filter [35]. The dual-loop OEOs are implemented based on two fiber loops with different lengths in parallel as shown in Figure 2. These fiber loops have their own phase match conditions and mode spacing. Because of the gain-competition between these series of modes, only the frequency components that meet the phase matching requirements of both loops can stably oscillate. In order to achieve the oscillating mode match and realize the Vernier effect, the precise control of the loop lengths is necessary. As a result, the mode spacing of multi-loop OEO is expanded, alleviating the high demand for the Q-value of filter, and the spurs of OEOs can be effectively suppressed. In [36], [PERSON] et al. reported a dual-loop OEO scheme employing a pair of polarization-beam splitter and combiner, and the spurious suppression ratio was improved to about 60 dB. However, the overall Q-value of the dual-loop OEO is between the long-loop OEO and the short-loop OEO. Compared to the single-loop OEO with a long fiber, the Q value of dual-loop OEO decreases and the phase noise correspondingly increases. To overcome the diminution of phase-noise performance, [PERSON] et al. found that the spurious modes of dual-loop OEO can be reduced while maintaining the phase noise performance by properly controlling the gains of the OEO, as shown in Figure 3, after investigating the open-loop characteristics. Through the precise open-loop gain control, they demonstrated the suppression of spurious modes by more than 21 dB [37]. To further shorten the fiber length, [PERSON] designed a compact architecture named compact optoelectronic oscillator (COEO) [33], which is another solution to suppress spurs as shown in Figure 4. The COEO includes an active mode-locked laser loop and an optoelectronic feedback loop. To enhance the Q value and decrease the phase noise of the oscillator, several hundred meters of fiber are employed in the active mode-locked laser loop. Since COEO employs shorter fiber to store energy, the oscillation mode spacing is correspondingly enlarged and the spurs can be suppressed effectively via conventional microwave band-pass filter. In order to further suppress the spurs of COEO, our research group proposed that an optical pulse power feedforward scheme can effectively suppress such side-modes of COEO as shown in Figure 5[38], through which the mode-locked optical pulse is reversely intensity-modulated by itself, resulting in fast power limiting.