Study On The Optical Comb Filter And Its Applications In Optical Communications And Microwave Signal Processing

Due to their cyclical amplitude filtering or phase filtering characteristics, the comb filters have attracted great interest in optical communications and microwave signal processing. For instance, the sampled fiber Bragg grating- (SFBG), the Mach-Zehnder interferometer- and high birefringence fiber (HBF)-based comb filters can find applications in the wavelength division multiplexer/demultiplexer, the multi-channel dispersion compensator, the high-speed pulse generator, the microwave filter, the instantaneous microwave frequency measurement, and so on. At the same time, along with the emergence of novel technologies and requirements, the research and the application about the optical comb filters are facing new challenges and opportunities. Against such a profound background, in this dissertation the investigation on the SFBG- and the HBF-based comb filters has been performed. Firstly, the peak wavelengths of reflection channels and the channel density techniques are theoretically investigated for the SFBG-based comb filters. Secondly, instantaneous microwave frequency measurement approaches using HBF-based comb filters are proposed and demonstrated. Finally, based on the equivalent comb filtering effect, a simple approach is designed to generate pulse trains with a tunable repetition rate.During the theoretical investigation and analysis on the filtering characteristics of SFBGs, three analysis tools have been used, i.e., the Fourier series method, the Fourier transform method, and the transfer matrix method. With the Fourier series method and the Fourier transform method, results and conclusions which describe the peak wavelengths or the channel spacing are derived. The transfer matrix method is then adopted to verify the derived results or conclusions. As for the HBF-based comb filter and the equivalent comb filtering effect, the application investigation focuses on the proposal of novel approaches or architectures. Related experiments have been performed to confirm the effectiveness and the advantages of proposed approaches. According to the analysis tools and the design ideas aforementioned, the main research work and results are listed in the following.An in-depth analysis about the distribution of peak wavelengths of SFBGs has been conducted. The uniform or apodized SFBG is decomposed into a number of ghost gratings using Fourier series method. All peak wavelengths of SFBG are obtained as the peak wavelength of each ghost grating is calculated. The peak wavelengths of SFBG are associated with the duty cycle, the sampling period, and the phase-matching condition. While in the SFBG having large chirp effect, the chirp effect is transformed into discrete phase shifts to implement the Fourier transform, with the wavelength drift induced by Talbot effect being derived. The sums of this wavelength drift and the peak wavelengths of uniform SFBG are the peak wavelengths of SFBG having large chirp.The periodic chirp structure is firstly proposed to get narrow channel spacing in the spectrum of SFBG. The periodic chirp structure consists of a number of identical chirp structures (or superstructures). The channel density can be realized by the spectral Talbot effect, as long as both the phase condition for Talbot effect and the equivalence of integer multiple of 2πin the phase plane are satisfied. Moreover, the periodic chirp structure can be further extended, with the phase condition being extended from parabolic to the high-order and the design degree being extended from one-dimensional to three-dimensional.The sampling approaches can find applications in designing the ultra-narrow, flat-top filter and the one-dimension photonic crystal-based filter. The combination of the equivalent phase shift (EPS) technique in SFBG and the multiple phase shift technique in fiber grating is able to open an ultranarrow (several tens of pico-meter) and flat transmission peak in the -1^st reflection band of SFBG. Namely, ultra-narrow and flat-top filters have been achieved. In the one-dimension photonic crystal, the inversion in the alternate arrange of low- and high- refractive index layers is defined as the equivalentπphase shift. A number of phase transmit points are then obtained using optimal algorithms. Therefore, the binary sampling function can be used to implement comb filters based on one-dimension photonic crystal.Instantaneous microwave frequency measurement approaches with a tunable measurement range or a wideband measurement range, are designed by the use of a length of dispersive fiber or a polarization modulator (PolM). Due to the dispersion slope of the dispersive fiber, two different microwave power fading functions caused by dispersion effect are detected, with the microwave frequency being calculated from the ratio of two functions. Since different fading functions can be achieved by adjusting the wavelength spacing, a tunable measurement range has been achieved. With the joint function of a PolM and a polarizer, a phase-modulated lightwave and an intensity-modulated lightwave, with an identical modulation index, are simultaneously generated. Two complementary microwave power fading functions resulted from dispersion effect are detected from the two modulated lightwaves. By estimating the microwave frequency from the ratio of the two complementary functions, a large measurement range is realized.Two frequency measurement approaches in the way of optical power detection are proposed by using HBF-based comb filters. Under the condition of the carrier-suppressed, small-signal modulation, two lightwaves are modulated by an unknown microwave signal to generate±1^st optical sidebands. The two carriers of the two lightwaves are located at a peak and a valley of the Sagnac loop's comb response, to perform two complementary comb filtering functions. The frequency to be measured is estimated by detecting the optical powers at two lightwaves. Moreover, a more stable measurement approach is implemented by using a single lightwave and a complementary comb filter pair. In a similar way, the carrier-suppressed, small-signal modulation is employed. The carrier of the modulated lighwave is simultaneously set at the peak of one transmission comb and the valley of the other complementary transmission comb. The microwave frequency is then estimated by monitoring the optical powers from the two outputs of the filter pair. In the latter approach, the setup is greatly simplified and the influence of the optical power fluctuations on the frequency measurement is eliminated completely.A simple approach is proposed and implemented to generate high-speed pulse trains having a tunable repetition rate. The odd- and the even-order sidebands are separated along the two polarization states by the use of a PolM and a polarization beam splitter, leading to an equivalent comb filtering effect. The comb spacing of the equivalent comb filtering effect varies automatically with the microwave frequency, without additional tuning mechanism. With the equivalent comb filtering effect, return-to-zero (RZ) and carrier-suppressed return-to-zero (CS-RZ) pulse trains having a repetition rate twice of the microwave frequency are generated, leading to the adjustment of the repetition rate greatly simplified.