The HE<sub>11</sub> fields of weakly guiding fibers with graded refractive-index profiles are nearly identical to the fields of a step-index fiber with dimensionless frequency V¯ and radius ρ¯, where V¯ and ρ¯ are found by an elementary variational method. The results are remarkably accurate, with errors of a fraction of a percent at most, so that a simple, closed-form expression for the HE<sub>11</sub> fields of graded fibers is now available. The step-fiber approximation is more widely applicable than the Gaussian field approximation which is inadequate for small <i>V</i> and for describing the evanescent field. However, the variational procedure also complements the Gaussian field approximation by providing analytical expressions for the spot size and propagation constant in several profiles of interest.
© 1980 Optical Society of AmericaPDF Article