This paper proposes new optical fibers with angularly nonuniform index distributions featured by one circular pit in the core, two circular pits in the core, and noncoaxial W-type distribution. The field problems are analyzed by the improved point-matching method. Waveguide parameters of single circular-pit fibers, double circular-pit fibers, and noncoaxial W-type fibers that provide the largest modal birefringence are investigated. It is found that (1) the maximum modal birefringence Bmax for single circular-pit fibers and noncoaxial W-type fibers is much larger than those for double circular pit fibers, (2) noncoaxial W-type fibers exhibit larger modal birefringence than single circular-pit fibers in the range Δn < 1.8% (Δn is relative index difference), and (3) the value Bmax of 1.7 × 10−4 has been attained for Δn = 0.42%. These results are quite reliable because (1) the relative error of the modal birefringence computed by our method is less than 10−4, and (2) this new method never produces ghost solutions.