<title>Rational harmonic mode-locking fiber laser</title>

Optical pulse sources with repetition rate approaching terahertz are very important for many photonics applications including ultra-high speed optical communication and generation of sub-mm waves. Both active and passive mode locked fiber lasers are the appropriate choice for this purpose because of the availability of erbium doped fiber amplifier. In general, the mode locking occurs with a repetition rate of nf₀, where n is an integer and f₀ is the longitudinal mode frequency spacing. This is called harmonic mode locking. In the case of rational harmonic mode locking, the repetition rate is (np plus 1) f₀ where p is also another integer. For the case of active mode locking, this is obtained when the modulation frequency to the amplitude or phase modulator used for mode locking is given by (n plus 1/p) f₀. For the case of passive mode-locking, the rational harmonic mode-locking occurs when the saturable absorber in a ring laser is offset by a fraction p/L: from the center where L is the length of the cavity. We have developed a theory of the rational mode locked fiber laser. The results of the theory are compared with experimental results obtained from a 1.5 (mu) fiber laser actively mode-locked with a LiNbO₃ electro-optic phase modulator.