Doctor of Philosophy / Department of Physics / Brian R. Washburn / Optical frequency combs produced by mode-locked fiber lasers are useful tools for high precision frequency metrology and molecular spectroscopy in a robust and portable format. We have specifically investigated erbium doped fiber mode-locked lasers that use single-walled carbon nanotubes as a saturable absorber. We have, for the first time, developed and phase- stabilized a carbon nanotube fiber laser (CNFL) frequency comb. The carbon nanotube saturable absorber, which was fabricated using an optically driven deposition method, permits a high repetition frequency (>150 MHz) since an optical nonlinearity of fibers is not used for mode-locking. The CNFL comb combined with a parabolic pulse erbium doped fiber amplifier (EDFA) has shown a compact, robust, and cost-effective supercontinuum source. The amplified pulse from the parabolic pulse EDFA was compressed with a hollow-core photonic bandgap fiber, which produced a wave-breaking-free pulse with an all-fiber set-up. The stabilized comb has demonstrated a fractional instability of 1.2 ×10[superscript]-11 at 1 sec averaging time, the reference-limited instability. We have performed optical frequency metrology with the CNFL comb and have measured an optical frequency, P(13) which is a molecular overtone transition of C2H2. The measured frequency has shown a good agreement with the known value within an uncertainty of 10 kHz. In order to extend the application of the CNFL comb such as multi-heterodyne dual comb spectroscopy, we have investigated the noise of the CNFL comb and particularly, the broad carrier envelope offset frequency (f[subscript]0) linewidth of the CNFL comb. The primary noise source is shown to be white amplitude noise on the oscillator pump laser combined with the sensitivity of the mode-locked laser to pump power fluctuations. The control bandwidth of f[subscipt]0 was limited by the response dynamics of the CNFL comb. The significant reduction of comb noise has been observed by implementing a phase-lead compensation to extend control bandwidth of the comb and by reducing the pump relative intensity noise simultaneously. Therefore the f[subscipt]0 linewidth has been narrower from 850 kHz to 220 kHz. The integrated phase noise for the f[subscipt]0 lock is 1.6 radians from 100 Hz to 102 kHz.