Fields in a bent single-mode fibre

Gaussian functions are commonly used to approximate the fundamental mode field in a straight fibre. If used as a basis for perturbation theory in a bent fibre, then the perturbation terms can be summed to all orders to give a new expression for the field and propagation constant in a bent fibre. These expressions are not the usual first-order corrections to the unperturbed quantities, and not restricted by the magnitude of the perturbation. The expression for field shift is compared to experimentel results.