Abstract

The field in optical fibers, whether they are longitudinally uniform or not, may be expanded over a complete set of modes. Whereas for uniform fibers the field evolution simply depends on beating given by modal phase differences, in the nonuniform case it can be described by a coupled-mode formalism.¹ The choice of the set over which the expansion is made and the number of modes to be considered in a numerical simulation are both important. Two cases are examined: an abruptly tapered fiber² and a nonlinear index fiber.³ In the case of an abruptly tapered fiber the nonuniformity comes from the fiber radius variation, and the set of normal modes is naturally chosen to be the local modes.¹ In the nonlinear case the field is expanded over the linear modes, i.e., the modes of the guide when the Kerr nonlinearity coefficient n₂ is zero or the injected power is low. For typically tapered fibers,² a reasonably uniform convergence of the results is usually observed when the number of the guided modes involved is increased to between 3 and 6, the required number depending on the magnitude of the nonuniformity. However, the validity of such a convergence in terms of only low-order modes may be questioned. To verify these results, we developed a modified beam-propagating method (BPM) program to simulate the field evolution in cylindrically symmetric guides.⁴ Figure 1 gives a sample simulation for a finite-cladding tapered fiber. Figure 2 shows in this case the comparison of the power in each mode given in (i) the coupled-mode simulation (with sufficient modes for convergence) by the expansion coefficients and (ii) the BPM simulation by the overlap of the total field with the modal fields. The good agreement suggests that radiation is negligible and that only a small number of guided modes is adequate for a coupled-mode formulation to describe the field well. The nonlinear case comparison is also examined to check the convergence criterion validity.

© 1990 Optical Society of America