# Ultrafast and Wideband Microwave Photonic Frequency-Hopping Systems: A Review
## 2 Microwave Photonic Frequency-Hopping Systems
### Real-Time Nonlinear Optical Mixing for Frequency-Hopping Signal Generation  
In the above MWP-based frequency-hopping signal-generation schemes, frequency-hopping signal is strongly depending on the center frequencies of the MWP passbands. In this approach, a more flexible allocation of the hopping frequency can be achieved using nonlinear optical mixing for the generation of frequency-hopping signal. Optical nonlinear four wave mixing (FWM) is well known for its transparency to amplitude, phase and frequency [57; 58; 59], and has been used for a wide range of signal processing applications, including wavelength conversion, multicasting, parametric amplification, and laser spectroscopy. In this section, the use of FWM for generating frequency-hopping signal with instantaneous hopping speed (Figure 12) will be discussed [23]. The key of the system is to  
Figure 11: **(a)** Measured frequency response of the single passband microwave photonic filter based on an integrated optical spectral shaper. **(b)** Temporal waveform of the generated frequency-hopping signal, inset: zoom-in view of the two hopping frequencies (with the courtesy of Dr [PERSON]).  
Figure 10: **(a)** Structure diagram of the optical spectral shaper. **(b)** The overall layout of the device. **(c)** Cross-section view of the waveguide (with the courtesy of Dr [PERSON]).  
modulate RF signals on different polarization of the input light--such that only the polarization aligned with that of the hopping code sequence is switched out by FWM. In this approach, a PM is used for polarization modulation by aligning the input optical carrier at 45\({}^{\circ}\) with respect to the PM waveguide axes. Therefore, the polarization of the pump light will change with specified hopping code sequence applied onto the PM. In degenerate FWM, FWM efficiency is the strongest if the polarization of the two signals are the same, while no FWM occurs if the polarization of the two signals is orthogonal. Thus, the hopping code sequence modulated pump light will only interact with the either \(f_{1}\) or \(f_{2}\) modulated light that has the same polarization.  
In the scheme, the optical carrier at \(\lambda_{m}\) carries the RF signals \(f_{1}\) and \(f_{2}\) at two orthogonal polarizations, while the hopping code sequence for frequency-hopping control is modulated on \(\lambda_{c}\), with \(x\) polarization to represent bit 1 and \(y\)-polarization to represent bit 0. Therefore, only\(f_{1}\) is switching out when the hopping code sequence is at bit 1, while only \(f_{2}\) is switched out when the hopping code sequence is at bit 0, as shown in Figure 13a,b. The experiment also shows that switching speed for two-level frequency-hopping signals can be up to tens of picoseconds (\(<\)50 ps) resulting from the instantaneous response of nonlinear optical mixing and is currently limited by the rise and fall time of the hopping code sequence, as shown in Figure 13f.  
Figure 12: Experimental setup and operation principle of real-time RF switching for frequency hopping system using optical four wave mixing. CW: continuous wavelength laser source; EOM: electro optical modulator; EDFA: Erbium-doped fiber amplifier; HNLF: highly nonlinear fiber; OTF: optical tunable filter; PD: photodetector. (**a**) hopping code sequence; (**b**) and (**c**) modulated RF signals on the same wavelength but different polarization;(**d**) FWM results after HNLF; (**e**) resultant frequency-hopping signals.  
Figure 13: **(a)** and **(b)** Temporal waveforms of only 5 GHz or 8 GHz RF signals when a hopping code sequence of “1011010010” is used in the FWM RF switch; (**c**) Generated frequency-hopping signal between 5 GHz and 8 GHz from FWM RF switch controlled by a “1011010010” code sequence, inset: zoom-in waveform of the orange shaded area; (**d**) and (**e**) FWM outputs at \(x\)- and \(y\)-polarization when no RF signals are used; (**f**) Response time measurement for (i) Rising and (ii) Falling edge.