IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 54, NO. 2, APRIL 2005 767 Building a Frequency-Stabilized Mode-Locked Femtosecond Laser for Optical Frequency Metrology Hyeyoung Ahn, Ren-Huei Shu, Robert S. Windeler, and Jin-Long Peng Abstract—We have built a frequency-stabilized mode-locked (ML) femtosecond (fs) Ti:Sapphire laser designed to serve national frequency metrology in Taiwan. We find that the self-referencing technique can be realized by single-beam f-2f as well as two-beam f-2f interferometers with the proper choice of photonic crystal fibers. The stabilized repetition frequency and offset frequency of the laser is found to have a one standard deviation of fluctuation of 0.3 and 1.3 mHz, respectively in a 1-s gate time. The frequency comb created by the ML fs laser is used to measure the frequencies of stabilized single-frequency lasers. Index Terms—Frequency measurement, frequency stability, mode-locked lasers, ultrafast optics. I. INTRODUCTION M ODE-LOCKED (ML) femtosecond (fs) lasers have been shown to be a powerful tool for optical frequency metrology [1]. In the time domain, an ML laser consists of periodic optical pulses. In the frequency domain, such pulses are coherently superpositioned to form a broadband optical frequency comb. Each comb line has a frequency of integer multiples of the repetition frequency plus an offset frequency, i.e., , where is the ordinal comb number, is the repetition frequency of the pulse train, and is the offset frequency [2]. A self-referencing (f-2f) technique is usually used to detect the offset frequency, which is based on comparing low-frequency comb lines to high-frequency comb lines with approximately twice the frequency. This technique requires an optical spectrum that spans more than one optical octave, which can be simply obtained in a photonic crystal fiber (PCF fiber) [3]. Usually, a Mach–Zender type of interferometer is used to measure the difference between the fundamental and second harmonic and a fine temporal/spatial alignment of two beams is critical to observe the offset beat signal. The temporal overlap between f and 2f can be achieved by translating a right-angle prism in the delay line. However, we find that with a careful choice of the PCF fibers, the f-2f technique can be realized in a single-arm interferometer. Here, we describe a frequency-stabilization of a fs Ti:Sapphire laser based on such a single-beam f-2f technique. The stabilities of the offset beat frequencies are studied in both the single-beam f-2f (SBF2F) and the two-beam f-2f (TBF2F) interferometers. Manuscript received July 1, 2004; revised October 15, 2004. This work was supported by the Bureau of Standards, Metrology, and Inspection, Taiwan. H. Ahn, R.-H. Shu, and J.-L. Peng are with the Center for Measurement Stan- dards, 30042 Hsinchu, Taiwan (e-mail: jlpeng@itri.org.tw). R. S. Windeler is with Optical Fiber Solutions, OFS Laboratories, Murray Hill, NJ 07974 USA (e-mail: rsw@ofsoptics.com). Digital Object Identifier 10.1109/TIM.2004.843115 Fig. 1. Spectrum of the supercontinuum generated from the PCF1 photonic crystal fiber. The spectrum of the input pulse is also shown as the dashed line. The absolute optical frequency measurements of an I -stabi- lized frequency-doubled 532-nm Nd:YAG laser, an I -stabilized 633-nm HeNe laser, and a Cs-stabilized 852-nm diode laser were demonstrated with this frequency-stabilized optical comb. II. THE FS LASER AND SUPERCONTINUUM GENERATION A commercial ring cavity Ti:Sapphire fs laser with a pulsewidth of 50 fs has been used for the optical comb generation. The fs laser has a repetition frequency of 1 GHz and an average power of more than 750 mW at 5-W pump power. The laser oscillator is placed in a metal box to prevent environmental perturbations. The box is then mounted on a 5-cm-thick aluminum block and a chiller provides cooling water at 19 C to control the temperature of the fs laser crystal, the aluminum block, and the base-plate of the pump laser for better thermal stability. Two photonic crystal fibers, PCF1 and PCF2, were tested to generate a supercontinuum with an octave span. The PCF1 fiber has a core diameter of 1.7 m with the zero dispersion at about 767 nm [3], while the PCF2 fiber has a core diameter of 1.8 m with the zero dispersion at about 710 nm. The fibers used for the supercontinuum generation are about 50-cm long. A micro- scope objective with a magnification of 60x was used to couple the laser beam into the PCF fiber. The typical output power was more than 200 mW after the fibers. Fig. 1 shows the optical spec- trum before and after the PCF1 fiber. The expanded spectrum generated by the PCF2 fiber is similar, but shifted toward shorter wavelengths. III. STABILIZING THE REPETITION FREQUENCY The repetition frequency of the fs laser is phase-locked to a 1-GHz reference signal by controlling a piezoelectric transducer mounted on a cavity mirror. The 1-GHz signal is synthesized by 0018-9456/$20.00 © 2005 IEEE