Since their discovery in 1978 by Hill et al. and the development of the transverse holographic technique for their fabrication by Meltz et al. in 1989, fiber Bragg gratings (FBG) have become an important device for applications in optical communications, optical signal processing and fiber-optical sensors. A superstructured fiber Bragg grating (SFBG), also called a sampled fiber Bragg grating, is a special FBG that consists of a several small FBGs placed in close proximity to one another. SFBGs have attracted much attention in recent years with the discovery of techniques allowing the creation of equivalent chirp or equivalent phase shifts. The biggest advantage of an SFBG with equivalent chirp or equivalent phase shifts is the possibility to design and fabricate gratings with greatly varying phase and amplitude responses by adjusting the spatial profile of the superstructure. The realization of SFBGs with equivalent chirp or equivalent phase shifts requires only sub-millimeter precision. This is a relief from the sub-micron precision required by traditional approaches. In this thesis, the mathematical modeling of FBGs and SFBGs is reviewed. The use of SFBGs for various applications in photonic microwave signal processing is considered. Four main topics are presented in this thesis. The first topic is the use of SFBG as a photonic true-time delay (TTD) beamformer for phased array antennas (PAAs). The second topic addresses non-linearities in the group delay response of an SFBG with equivalent chirp in its sampling period. An SFBG with an equivalent chirp using only a linear chirp coefficient may yield a group delay response that deviates from the linear response required by a TTD beamformer. In the thesis, a technique to improve the linearity of the group delay response is proposed and an adaptive algorithm to find the optimal linear and non-linear chirp coefficients to produce the best linear group delay response is described. Since no closed-form solution exists to represent the amplitude and phase responses of an SFBG, we rely on a Fourier transform analogy under a weak grating approximation as a starting point in the design of an SFBG. Simulations are then used to refine the response of the SFBG. The algorithm proposed provides an optimal set of chirp coefficients that minimizes the error in the group delay response. Four gratings are fabricated using the optimized chirp coefficients and their application in a TTD PAA system is discussed. The third topic discusses the use of an SFBG with equivalent phase shifts in its sampling period as a means to realize optical single sideband (SSB) modulation. SSB modulation eliminates the power penalty caused by chromatic dispersion experienced by an optical signal traveling through a long length of optical fiber. By introducing two π phase shifts through equivalent sampling to the SFBG, two ultra-narrow transmission bands are created in the grating stop band of the +/- 1st spectral orders. In the proposed system, a double-sideband plus carrier (DSB+C) modulated optical signal is sent to the input of an optical SSB filter based on the equivalent phase-shift SFBG in order to select the optical carrier and a single sideband, effectively blocking one sideband from propagating. Finally, the fourth topic focuses on the implementation of a photonic microwave bandpass filter based on an SFBG with equivalent chirp. Photonic microwave filters are used to process microwave signals in the optical domain. By using a technique called phase-modulation to intensity-modulation (PM-IM) conversion, a two-tap delay line filter is created with one negative tap. A single SFBG with a chirp in its sampling period is used as a means to achieve the PM-IM conversion for the two taps. Two phase modulated optical carriers are used to generate the two taps, each entering a different port of the SFBG and thus experiencing an opposite dispersion value. The two optical signals are then recombined before being sent to a photodetector (PD) where the filtered microwave signal is recovered.

Since their discovery in 1978 by Hill et al. and the development of the transverse holographic technique for their fabrication by Meltz et al. in 1989, fiber Bragg gratings (FBG) have become an important device for applications in optical communications, optical signal processing and fiber-optical sensors. A superstructured fiber Bragg grating (SFBG), also called a sampled fiber Bragg grating, is a special FBG that consists of a several small FBGs placed in close proximity to one another. SFBGs have attracted much attention in recent years with the discovery of techniques allowing the creation of equivalent chirp or equivalent phase shifts. The biggest advantage of an SFBG with equivalent chirp or equivalent phase shifts is the possibility to design and fabricate gratings with greatly varying phase and amplitude responses by adjusting the spatial profile of the superstructure. The realization of SFBGs with equivalent chirp or equivalent phase shifts requires only sub-millimeter precision. This is a relief from the sub-micron precision required by traditional approaches. In this thesis, the mathematical modeling of FBGs and SFBGs is reviewed. The use of SFBGs for various applications in photonic microwave signal processing is considered. Four main topics are presented in this thesis. The first topic is the use of SFBG as a photonic true-time delay (TTD) beamformer for phased array antennas (PAAs). The second topic addresses non-linearities in the group delay response of an SFBG with equivalent chirp in its sampling period. An SFBG with an equivalent chirp using only a linear chirp coefficient may yield a group delay response that deviates from the linear response required by a TTD beamformer. In the thesis, a technique to improve the linearity of the group delay response is proposed and an adaptive algorithm to find the optimal linear and non-linear chirp coefficients to produce the best linear group delay response is described. Since no closed-form solution exists to represent the amplitude and phase responses of an SFBG, we rely on a Fourier transform analogy under a weak grating approximation as a starting point in the design of an SFBG. Simulations are then used to refine the response of the SFBG. The algorithm proposed provides an optimal set of chirp coefficients that minimizes the error in the group delay response. Four gratings are fabricated using the optimized chirp coefficients and their application in a TTD PAA system is discussed. The third topic discusses the use of an SFBG with equivalent phase shifts in its sampling period as a means to realize optical single sideband (SSB) modulation. SSB modulation eliminates the power penalty caused by chromatic dispersion experienced by an optical signal traveling through a long length of optical fiber. By introducing two π phase shifts through equivalent sampling to the SFBG, two ultra-narrow transmission bands are created in the grating stop band of the +/- 1st spectral orders. In the proposed system, a double-sideband plus carrier (DSB+C) modulated optical signal is sent to the input of an optical SSB filter based on the equivalent phase-shift SFBG in order to select the optical carrier and a single sideband, effectively blocking one sideband from propagating. Finally, the fourth topic focuses on the implementation of a photonic microwave bandpass filter based on an SFBG with equivalent chirp. Photonic microwave filters are used to process microwave signals in the optical domain. By using a technique called phase-modulation to intensity-modulation (PM-IM) conversion, a two-tap delay line filter is created with one negative tap. A single SFBG with a chirp in its sampling period is used as a means to achieve the PM-IM conversion for the two taps. Two phase modulated optical carriers are used to generate the two taps, each entering a different port of the SFBG and thus experiencing an opposite dispersion value. The two optical signals are then recombined before being sent to a photodetector (PD) where the filtered microwave signal is recovered.