## 2 Dispersive Fourier Transformation Technique
### Implementation of DFT
#### 2.2.2 Dispersive Devices  
Another essential requirement for implementing DFT is a dispersive device with sufficient and uniform chromatic dispersion to allow linear DFT process without distortion. The simplest and most commonly used dispersive element in DFT is standard single-mode fibers (SMF) [33,36,63]. SMF has a smooth dispersion curve for a broad optical bandwidth of more than 200 nm in the telecommunications band. The GVD coefficient is about 17 ps/nm/km at 1550 nm. To provide sufficient dispersion, a very long fiber is usually required, which makes the system bulky with high loss, and suffer from the higher-order dispersion and polarization mode dispersion [64]. Dispersion compensation fibers (DCF) offer a much larger chromatic dispersion (-120 ps/nm/km at 1550 nm) and have become a promising solution for DFT [45,65] thanks to its high dispersion-to-loss ratio. To further overcome propagation losses, distributed Raman amplification has been implemented simultaneously within the DCF, a process called amplified DFT [31]. Significant optical gain would enhance the sensitivity and resolution of DFT in high-throughput measurements [45]. However, one major difficulty is that no efficient DCFs are available outside the telecommunications band around 1550 nm.  
The use of a linearly chirped fiber Bragg grating (LCFBG) provides a compact solution for implementing DFT [13,34]. A fiber Bragg grating (FBG) is basically a section of optical fiber where the refractive index of the fiber core is periodically modulated, normally via UV illumination [66]. Mode coupling between counter-propagation modes in the fiber core, which is induced by perturbation of refractive index, results in wavelength-dependent reflection. Thanks to the flexible spectral characteristics [67], all-fiber geometry, low insertion loss, compact size, and low cost, FBGs have been widely employed in microwave photonics applications [13,68,69]. In an LCFBG, different spectral components of an optical signal are reflected from different position of the grating due to the chirped grating period, making it a compact and broadband dispersive element with a large GVD. In addition,nonlinear optical effects are also reduced due to the short interaction length of the LCFBG. However, the main problem of the LCFBG for DFT is the group delay ripples (GDRs). The GDR is a result of the interference between the broadband reflection due to the edge of the grating and the distributed nature of the grating reflection [70] and may cause unwanted fast temporal modulations in the stretched pulses [71]. The GDR of an LCFBG can be significantly reduced by applying apodization during the fabrication process. However, an apodized LCFBG still exhibits pseudoperiodic GDRs due to the errors in grating period and the index modulation deviations resulting from imperfections in the fabrication process [72].  
An alternative dispersive device exploits both spatial (angular) dispersion in a diffraction grating and the large modal dispersion [73] in a multimode waveguide. Such a chromo-modal dispersion (CMD) device has been successfully employed to achieve DFT for real-time absorption spectroscopy [74]. The CMD device offers large GVD in a huge spectral bandwidth where the multimode waveguide is transparent. Moreover, both amount and sign of the GVD can be easily tuned by changing the alignment conditions. However, since its group delay response has a nonlinear relation with respect to the optical wavelength, careful calibration and correction are required for linear DFT.