Fast algorithm for transversely inhomogeneous optical fibres using power method and fast fourier transform

A scalar-field integral equation is employed to find the propagation characteristics of guided modes of an inhomogeneous optical fibre of arbitrary transverse shape. Two facts make the proposed method quite efficient. First, by employing the scalar-field integral equation, the propagation problem is reduced to a standard eigenvalue problem, where the lower-order modes correspond to the larger eigenvalues. Hence, the eigenproblem can be manipulated efficiently by variants of the power method. Further, the major computation in the associated power method can be arranged into the form of a convolution, which in turn can be performed using the fast Fourier transform (FFT).