An optical fiber for transmitting light, said optical fiber having an axial direction and a cross section perpendicular to said axial direction, said optical fiber comprising: (1) a first core region comprising a first core material having a refractive index N.sub.co,1; (2) a microstructured first cladding region surrounding the first core region, said first cladding region comprising a first cladding material and a plurality of spaced apart first cladding features or elements that are elongated in the fiber axial direction and disposed in the first cladding material, said first cladding material having a refractive index N.sub.cl,1 and each said first cladding feature or element having a refractive index being lower than N.sub.cl,1, whereby a resultant geometrical index Nge,cl, 1? of the first cladding region is lowered compared to N.sub.cl,1; (3) a second core region surrounding said first cladding region, said second core region comprising a second core material having a refractive index N.sub.co,2, and (4) a second cladding region surrounding the second core region, said second cladding region comprising a second cladding material having a refractive index N.sub.cl,2, wherein the first core material, the first cladding material and the first cladding features, the second core material, and the second cladding material are selected and arranged so that N.sub.co,1>N.sub.ge,cl,1, N.sub.co,2>N.sub.ge,cl,1, and N.sub.co,2>N.sub.cl,2.