An optical fiber is disclosed which comprises (a) a central core section (4) of constant thickness which terminates in an outwardly gradually expanded end section (3), and (b) a cladding layer (5) enveloping the core. Both the core and the cladding layer are of constant compositions throughout the fiber's length and width. Additionally, the difference between the refractive indices of the core and the cladding layer remains constant throughout the length of the fiber. Where the core gradually increases in width in the outwardly expanded end section of the fiber, the V number normalized frequency increases in like manner. In such optical fiber, propagation of a predetermined mode or modes is maintained throughout the entire length of the fiber, so long as the expansion of the end section occurs gradually over the order of many wavelengths.