# Fiber Bragg Grating-Based Optical Signal Processing: Review and Survey
## 3 Survey of Signal Processing Units based on FBGs
### Optical Pulse-Shapers  
Optical pulse shapers are devices that synthesize the user-defined shape of the complex-valued time-domain envelope of an optical wave. Pulse shapers play a fundamental role in computation and communication systems [80]. The more direct approach of using FBGs as a pulse-shaping processor consists of employing the first-order Born approximation [81; 82; 83; 84; 85]. As significant examples of this design approach, we can mention the implementation of flat-top [81; 82], saw-tooth (triangular) [83], parabolic [84] and antisymmetric Hermite-Gauss [85] pulse shapers. These kinds of pulse-shaping processors permit the synthesis of a wide variety of important ultra-fast optical signal processing operations. Among them, we can mention the following: flat-top waveforms can be employed as all-optical control signals in nonlinear switching procedures; parabolic pulses can be used as pump signals in all-optical non-linear implementations of time-lens processes or pulse retiming; triangular waveforms can be used to implement tunable delay lines, time-domain add-and-drop multiplexers, wavelength converters, or doubling of optical signals; sinc-shape are used in optical time division multiplexing (OTDM) systems with Nyquist pulse shaping; and the generation of high-order modulation codes are necessary for optical code-division multiple access (OCDMA) and optical-label-switching communications. Based on grating analysis algorithms, applications of ultrashort pulse propagation in FBG were proposed for DWDM and OCDMA [86]. Different approaches have been proposed in the literature. For example, arrays of uniform FBGs have been utilized for generation of bipolar codes. In addition, schemes relying on superstructured FBGs, or step-chirped FBGs were also presented, representing more compact solutions [87; 88; 89; 90]. Based on grating synthesis algorithms, a flat-top pulse-shaper based on uniform FBG operating in transmission was proposed with an operation bandwidth in the order of tens of GHz (but with a very complex refractive index profile with high peaks and several precisely distributed phase shifts) [92]. Later, rectangular, parabolic and triangular pulse shapers based on phase-modulated FBGs in transmission have been proposed using grating synthesis  
Figure 10: PHT implemented in an FBG in transmission: Comparison between the specified reflectivity (**a**) and group delay (**b**) (in dashed black line) and the experimentally implemented structure (in solid red). Comparison between the experimentally obtained output component of the fabricated integer (**c**) and fractional (**d**) PHTs (solid blue line) and the ideal output (dashed pink line) for an input Gaussian pulse with 0.88 ps-FWHM. algorithms and numerical optimization [93]. More in particular, a method is employed that is based on finding a suitable period profile \(\Lambda(z)\) that attains the target transmissive spectral response from the FBG, while the apodization profile remains constant. This technique implies a simpler grating writing process, as the coupling strength remains constant along most of the device length. However, the complexity is transferred to the fabrication of the phase mask, which now needs to have a user-defined, relatively complex shape. The aforementioned implementations for FBG-based all-optical pulse shapers present a limited operation bandwidth (i.e., of hundreds of GHz, as explained in Section 2.4). The implementation of optical pulse shapers using FBG operating in transmission, following the design approach presented in Section 2.4.1, raised particular interest for increasing the operation bandwidth. In general, any pulse shaping functionality can be implemented using this configuration provided that its transfer function is minimum-phase. By using this configuration, a 5 THz bandwidth flat-top pulse shaper has been experimentally demonstrated [94].