Abstract
One current and evolving use of fibre gratings is for chirped grating dispersion compensation[1]. Another is in the formation of effective λ/4 lasing cavities for DFB fibre lasers by imposing a slow local perturbation on the grating parameters[2], In both cases the essential analytical problem is the same: How to treat the behaviour of light in spatially heterogeneous Bragg gratings? In this paper an approach is developed based on the Hamiltonian optics elegantly summarised by a number of authors, including notably Arnaud in his 1976 book Beam and Fibre Optics[3]. The Hamiltonian approach can be applied where the dispersion relation in the homogeneous structure is known, and where, in the heterogeneous real structure, parameters like average index vary slowly in space. It is essentially an analytical method for stepping through a non-uniform structure, matching phase velocities normal to the gradient of the heterogeneity at each step, and propagating along the local group velocity to the next point.
© 1995 Optical Society of America
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