## 3 Microwave Photonics Applications of DFT
### DFT for Microwave Arbitrary Waveform Generation
#### 3.2.4 \"Two-in-One\" Design  
In the most of DFT-based microwave arbitrary waveform generation systems, the optical spectral filter for spectrum shaping and the dispersive device for frequency-to-time mapping are two separate devices. The system is thus complicated, costly and with high insertion loss. Therefore, it is desirable to find a multifunctional fiber-optics device, whose magnitude response and the group delay response can be individually controlled, to achieve both spectral shaping and frequency-to-time mapping processes for photonic microwave arbitrary waveform generation. The use of a LCFBG may provide a  
Figure 7: (**a**) A nonlinearly chirped fiber Bragg grating (NL-CFBG) produced using strain-gradient beam tuning. (**b**) Simulated group delay characteristics of the produced NL-CFBG at different beam displacements.  
promising solution. First, the reflection magnitude response of the FBG can be almost arbitrarily controlled by properly designing the refractive index modulation profile. In addition, the inherent linear group delay response of the LCFBG can perfectly perform the dispersion-induced linear frequency-to-time mapping. In [107], photonic microwave arbitrary waveform generation based on the \"two-in-one\" design using a single LCFBG to perform both the functions is demonstrated, featuring greatly simplified system structure. The LCFBG with desired reflection response is synthesized using a simplified designing approach based on an accurate mapping of the grating reflection response to the refractive index modulation in a strongly chirped FBG [107]. Since amplitude-only index modulation function is required, the designed LCFBG can be easily fabricated with the current FBG fabrication technology.  
In fact, a LCFBG can provide not only linear but also discrete (jumped) group delay. Most recently, we have developed a spatially-discrete chirped fiber Bragg grating (SD-CFBG) with jumped group delay response for microwave arbitrary waveform generation [39]. Discrete time shifts, which are caused by the group delay jumps, can be introduced to the mapped temporal waveform. Therefore, an additional flexibility is created for microwave arbitrary waveform generation. The SD-CFBG has a multichannel reflection response and a discrete group delay response with user-defined delay jumps between channels, as shown in Figure 8. The SD-CFBG functions to perform simultaneously spectral slicing, frequency-to-time mapping, and temporal shifting of the input optical pulse, leading to the generation of an optical pulse burst. The amplitude and time delay of each daughter pulse can be individually tailored by controlling the structure of the SD-CFBG. With the help of bandwidth-limited photodetector, a smooth microwave waveform is generated from the optical pulse burst. By properly designing the SD-CFBG, microwave waveforms with large time-bandwidth-product, such as frequency-chirped [107] and phase-coded [108] waveforms have been generated.  
Figure 8: Illustration of the structure and fabrication of a spatially discrete chirped fiber Bragg grating (SD-CFBG) for simultaneous spectral slicing, frequency-to-time mapping and temporal shifting of the input optical pulse, leading to the generation of an optical pulse burst.