Numerical modeling, design, and time-frequency metrology applications of low-noise optical frequency combs

Optical frequency combs are very versatile tools, which revolutionized many areas, and enabled novel applications, especially in time-frequency metrology. In this thesis, I tried to convey a complete picture of the road that goes from conception through design to applications of optical frequency combs. To this end, implementation details of a free, publicly-available numerical pulse propagation simulation software, which can be used for, but not limited to, simulating and designing complete femtosecond laser and amplifier systems, supercontinuum generation, and Raman lasers, is presented. An algorithmic design methodology, which was used for designing all of the femtosecond lasers and fiber amplifiers presented in this thesis, is introduced, which might pave the way to discovery of new laser pulse evolution regimes. Several optical frequency combs were developed and utilized in time-frequency metrology applications. A fully-stabilized, robust, and transportable low-noise Yb-fiber optical frequency comb was developed and used for absolute frequency measurements of iodine-stabilized Nd:YAG and two-mode stabilized HeNe lasers. Studies were conducted on generating RF-MW signals with ultra-low phase noise by utilizing optical frequency combs. High-harmonic mode-locking and repetition-rate multiplication methods were used to generate ultra-low phase noise RF-MW signals with frequencies ranging from 78.125 MHz to 10 GHz. A femtosecond fiber laser that can be automatically mode-locked was also developed during these studies. Finally, an atomic frequency standard based on a passively mode-locked femtosecond laser was developed, for the first time to the best of my knowledge. Resulting Rb atomic frequency standard was demonstrated to perform at a similar level to the commercial Rb atomic frequency standards, with much better phase noise at high frequency offsets.