The present invention provides an optical fiber of a high nonlinear characteristic which has low dispersion values in a wide wavelength region in the vicinity of a wavelength of 1550 nm. An excellent optical signal processing apparatus is realized by using this optical fiber, such as an optical wavelength converter and a pulse compressor. The optical fiber has characteristics; a dispersion slope at the wavelength of 1550 nm of -0.01 to 0.01 ps/nm.sup.2/km, an absolute value of dispersion at the wavelength of 1550 nm of 10 ps/nm/km or less, and a nonlinear constant at the wavelength of 1550 nm of 30.times.10.sup.-10/W or more. A polarization retaining maintaining members are uniquely applied.