## 3 Microwave Photonics Applications of DFT
### DFT for Microwave Arbitrary Waveform Generation
#### 3.2.2 All-Fiber DFT-Based Microwave AWG  
Various configurations for all-fiber spectral shaping have been proposed for photonic generation of microwave arbitrary waveforms. For example, ultra-wide band (UWB) pulse generation based on spectral shaping using two uniform FBGs with one in transmission and the other in reflection, and DFT in a length of dispersive fiber has been recently demonstrated [36]. The optical fiber does not only serve as the dispersive element to accomplish the DFT-enabled wavelength-to-time mapping, but also as the optical link to distribute the UWB pulse to a remote site. UWB pulses have found wide applications in short-range high-data-rate wireless communications [101].  
Chirped microwave pulses, due to their large time-bandwidth product (TBWP), have been widely used in modern radar systems to significantly improve the range resolution. Based on the DFT  
Figure 5: Schematic diagram to show microwave arbitrary waveform generation based on spectral shaping and DFT. PD: photodetector.  
technique, a few methods have been reported to generate chirped microwave waveforms [102]. The main effort in DFT-based approach is to design an optical spectral shaper with its magnitude response having a chirped oscillating response with a varying free-spectral range (FSR). One design of such an optical spectral shaper is based on superimposing two chirped fiber Bragg gratings with different chirp rates into a same fiber with a small longitudinal offset [103]. As illustrated in Figure 6, a distributed Fabry-Perot cavity is formed in the fiber core region due to the broadband reflections between the two LCFBGs. Since the cavity length \(L(\lambda)\) is linearly dependent on the resonance wavelength, its spectral response has a linearly increasing or decreasing FSR inversely proportional to the cavity length. When an ultrashort optical pulse is shaped by this specially designed filter and dispersed by a dispersive fiber, a linearly chirped microwave waveform can be generated thanks to the DFT process. The central frequency and chirp rate of the microwave waveform are determined by the chirp rates and longitudinal offset of the two superimposed chirped FBGs. Since no discrete interferometric structures are involved, the system is more compact with better resistance to environmental changes.  
The main difficulty associated with the method in [103] is that the spectral response of the optical spectral shaper cannot be easily tuned once the two superimposed chirped FBGs have are fabricated. For many applications, however, tunable chirped rate and center frequency of the generated microwave waveform are required. In addition, two LCFBGs with different chirp rates are required, making the fabrication process complicated. To solve the problems, we proposed a new spectral shaper design which offers tunable spectral response based on a Sagnac-loop mirror structure incorporating only a single LCFBG [104]. Similar to [103], a distributed Fabry-Perot interference is produced between the counter-propagating reflections from the opposite sides of the same highly-reflective LCFBG. The cavity length is wavelength-dependent due to the use of LCFBG. Compared to [103], since only one single LCFBG is required, both fabrication challenge and system complexity are reduced. Moreover, by tuning the time-delay within the fiber loop, both the central frequency and the sign of chirp of the generated chirped microwave waveforms can be easily tuned. To enable the tuning of the chirp rate of  
Figure 6: An optical spectral shaper consisting of two superimposed chirped fiber Bragg gratings with different chirp rates and a small longitudinal offset. The spectral shaper has a chirped spectral response thus can be used to generate chirped microwave waveforms based on DFT technique. CFBG: chirped fiber Bragg grating.  
the microwave waveform, the chirp rate of FBG should be tunable, which can be achieved by optically pumping the LCFBG written in an active fiber [105].