Light propagation in graded-index optical fibers

Abstract

An accurate numerical method is described for solving the Helmholtz equation for a general class of optical fibers. The method yields detailed information about the spatial and angular properties of the propagating beam as well as the modal propagation constants for the fiber. The method is applied to a practical graded-index fiber under the assumptions of both coherent and incoherent illumination. A spectral analysis of the calculated field shows that leaky modes are lost and steady-state propagating conditions are established over a propagation distance of a fraction of a meter.

Multiplexed Optical Fiber Sensors for Coal Fired Advanced Fossil Energy Systems

“…Thus the refocusing can only held for a certain distance before reaching an unfocused equilibrium state, which, together with the decay of the leaky modes, sets up a steady-state propagation within centimeters [15].…”

The One-Way Wave Equation: A Full-Waveform Tool for Modeling Seismic Body Wave Phenomena

“…A different approach to the parabolic approximation involves an operator technique proposed by [55], which was used to approximate the Helmholtz equation for wide-angle light propagation in optical fibers. This approach involves splitting (or factoring) the wave equation into two parts, followed by an approximation of the 'operator-root'.…”

“…These approximations were implemented within the acoustic split-step computer algorithm of [25] so that the accuracies of all three operator-root approximations could be compared. Their results indicated that the wider angle parabolic equation of [55] was least sensitive to the choice of reference phase and least effected by phase errors.…”

“…Unfortunately these restrictions are frequently violated in seismological applications. The operator technique proposed by [55] is an improvement upon the reference phase approach because it does not involve a localization of the wave equation operator. However, this operator approach makes the explicit assumption of weak heterogeneity to obtain a 'simple' expression for the operator-root in terms of a perturbation series.…”

“…However, this operator approach makes the explicit assumption of weak heterogeneity to obtain a 'simple' expression for the operator-root in terms of a perturbation series. A significant step forward was realized by [26] who applied a similar operatorsplitting approach to that of [55], but sought a more detailed and widely applicable expression for the operator-root. This permits a generalization of the one-way wave equation technique and introduces a new class of propagation algorithms.…”