# Ultrafast and Wideband Microwave Photonic Frequency-Hopping Systems: A Review
## 2 Microwave Photonic Frequency-Hopping Systems
### MWP RF Switch for Frequency-Hopping Signal Generation
#### 2.4.1 Pockels Effect Based Fast Tunable MWP Switch for Frequency-Hopping Signal Generation  
Pockels effect in LiNbO\({}_{3}\) modulators is well known for its fast response time in the order of tens of picosecond. By incorporating a LiNbO\({}_{3}\) phase modulator in a loop mirror filter, an ultrafast RF switch can be achieved, as shown in Figure 8a [26; 48]. First, a single sideband modulated optical signal is generated at the dual-drive Mach-Zehnder modulator (DD-MZM), which is then launched into a phase modulator incorporated loop mirror filter (PM-LMF) for optical spectral filtering. If the RF spectral component in the single sideband optical signal is being blocked by the PM-LMF, the RF signal cannot be reconstructed at the photodetector and results in a notch in the frequency response at that particular frequency. The PM-LMF consists of a piece of polarization-maintaining fiber (PMF), a polarization controller (PC), a phase modulator (PM), and an OC. First, the input light is spilt into two branches at the OC, then the two light beams counter propagate in the LMF and interferer when they arrive at the OC again. Depending on the phase difference experienced by the two light beams, a periodic transmission function is resulted and can be expressed as,  
\[T(\lambda)=\frac{1}{2}[1-\cos(\varphi(\lambda))] \tag{3}\]  
where \(\varphi(\lambda)\) denotes the phase difference between the light travelling clockwise and anti-clockwise. Due to the total phase difference induced by both the PMF and a short tunable birefringence medium (e.g., PM), periodic optical comb response is resulted. When the transverse electric axis of the PM is aligned with the fast axis of the PMF, the corresponding comb spacing can be described as,  
\[\Delta\lambda=\frac{\lambda^{2}}{B_{PMF}L_{PMF}+B_{PM}L_{PM}} \tag{4}\]  
where \(B_{PMF}\), \(L_{PMF}\), \(B_{PM}\), and \(L_{PM}\) are the birefringence and length of the PMF and PM, respectively. Birefringence of the PM is proportional to the electric field around the LiNbO\({}_{3}\) crystal waveguide. Therefore, the comb spacing can be shifted by controlling the applied DC voltage to the PM. Considering a small optical spectral region, a shift in the optical comb is observed, resulting in a shift in the transmission notch of the comb filter, as shown in Figure 8b. Since there is a direct corresponding between the transmission notch in the optical comb filter and the transmission notch in the RF filter, the RF transmission notch can also be tuned by controlling the DC voltage applied to the PM, as shown in Figure 8c.  
To generate a frequency-hopping signal, two RF signals at \(f_{1}\) and \(f_{2}\) are modulated onto the optical carrier as a single sideband signal. A hopping code sequence with two voltage levels at \(V_{1}\) and \(V_{2}\) is used to control the birefringence of the PM, i.e., the RF transmission notch. When the RF notch is aligned with \(f_{1}\), then only \(f_{2}\) can be found at the output while \(f_{1}\) is being blocked, or vice versa. Therefore, when the control signal is switched between \(V_{1}\) and \(V_{2}\), a frequency-hopping signal between \(f_{1}\) and \(f_{2}\) can be generated. As shown in Figure 8d, two-level frequency-hopping signal between 6 GHz and 12 GHz with 170 ps hopping speed is achieved by setting the applied voltage of bit \"1\" at 2.8 V and that of bit \"0\" at 0 V. Due to the fast response time of Pockels effect, hopping speed of tens of GHz can be achieved which is governed by the modulation bandwidth of PM. Although the hopping speed is fast, there is a requirement of the frequency separation between the hopping frequencies due to the periodicity and bandwidth of the MWP filter.