# Ultrafast and Wideband Microwave Photonic Frequency-Hopping Systems: A Review
## 2 Microwave Photonic Frequency-Hopping Systems
### Frequency-Hopping through Period-One Nonlinear Dynamcis in Semiconductor Lasers  
When a slave semiconductor laser experiences optical pumping from a master laser, various nonlinear dynamics can be excited, such as chaotic dynamics, injection locking dynamics, and periodic oscillations [21; 22; 40; 41]. Depending on the detuning frequency, injection power ratio, as well as the controlling of polarization relationship between the slave and master lasers, different nonlinear dynamics and characteristics could be induced. Among all the nonlinear dynamics in semiconductor lasers, period-one (P1) dynamics is a good candidate to achieve frequency-hopping due to its unique spectral phenomenon as well as fast hopping speed of up to nanoseconds range. The schematic diagram of period-one dynamics-based frequency-hopping system [29] is shown in Figure 5a. A master laser that is emitting continuous wave at \(f_{m}\) is attenuated and then intensity modulated by a hopping code sequence \(S(t)\). The modulated master laser light is launched to a free running slave laser at \(f_{s}\) via an optical circulator. The lasing frequency difference between the master and slave lasers is \(f_{s}\). Through injection locking, the master laser pulls the slave laser oscillating frequency towards the master laser frequency \(f_{m}\) by locking its phase, forcing the slave laser to last at \(f_{m}\). At the same time, the gain region of the slave laser is red-shifted (i.e., shifting\(f_{s}\) to \(f_{s}\)') due to the refractive index change inside the cavity resulted from an increase in carrier density through master laser light injection. Therefore, the two effects compete--injection-induced gain region shifting to red while phase locking from master laser shift the lasing to blue, leading to period-one nonlinear dynamics, i.e., the slave laser loses at both \(f_{m}\) and \(f_{s}\)'. As illustrated in Figure 5b, a RF signal with frequency \(f_{o}\) results after photodetection, which is governed by the frequency difference between the two lasing frequencies of the slave laser (\(f_{o}=f_{m}-f_{s}\)'). The observed asymmetric double-sideband spectrum is due to Hopf bifurcation. The resultant lasing frequency \(f_{s}\)' due to refractive index change is determined by the strength of the injection light. Therefore, frequency of the resultant RF signal can be adjusted through the control of the injection light power. Figure 4: Measured hopping code sequence (green), waveform of the generated frequency-hopping microwave signal (blue), and the calculated instantaneous frequency of the frequency-hopping signal (red). (**a**) Frequency-hopping between 17.1 GHz and 15.75 GHz; (**b**) Frequency-hopping between 9.58 GHz and 8.65 GHz (with the courtesy of Dr [PERSON]). Figure 5: (**a**) Schematic diagram of the period-one (P1) nonlinear dynamic-based frequency-hopping signal-generation scheme. (**b**) Operation principle of P1 dynamics in an optically injected semiconductor laser. ML: master laser, Att: optical attenuator; IM: intensity modulator, S(t): hopping code sequence; PC: polarization controller, CIR: optical circulator; SL: slave laser, PD: photodetector (with the courtesy of Dr [PERSON]). Figure 6a-c show the temporal measurement of the generated RF signal under different injection conditions, while the corresponding hopping code sequence \(S(t)\) is shown in the insets. The injection strength is defined as \(\xi\), which is proportional to the injected power. Therefore, for a fixed detuning frequency \(f_{i}=f_{s}-f_{m}\), the generated RF signal frequency \(f_{o}\) would increase linearly with the injection amplitude. Therefore, by controlling the optical injection power using a hopping code sequence, frequency-hopping signal can be generated. Figure 6d-f shows the measured instantaneous frequency of the generated RF signal. By setting the hopping code sequence to a two-level square wave, frequency-hopping signal with frequencies at 13.1 and 17.6 GHz is resultant.