Design of microstructured fibers with fixed chromatic dispersion properties

Summary form only given: In contrast to analysis techniques of microstructured fibres, which have already started being tackled efficiently, the available design methods are still incipient. In general, real inverse design procedures involve an optimization algorithm to carry out the minimization of a certain merit function. In this contribution we present a differential algorithm to design photonic crystal fibres (PCFs). Specifically, we focus our attention on controlling their chromatic dispersion behaviour. It is based on an original analytical formulation to compute the gradient of the propagation constant, beta, defined in the multidimensional design-parameter space, combined with an appropriate gradient-based optimization algorithm. First, we use our 2D Fourier iterative modal method to compute the propagation constant of the guided modes at different wavelengths and their corresponding transverse magnetic field for the reference values of the previously selected design parameters of the fibre. This is a really fast and accurate approach as it does not need the explicit representation of the operator that involves the dynamic of the system. Thus, it is possible to work with more coefficients in the series expansions maintaining a very reasonable computing time. Next, we derive an analytical expression for the calculation of the gradient of beta, which is defined in the multidimensional design-parameter space of the fibre. In a second stage, we take advantage of gradient-based algorithms, which are certainly the first choice in multidimensional optimization, to carry out the minimization process of a suitable merit function involving the magnitude whose behaviour we want to shape. Typical design parameters are the hole size for each ring, the hole shape, the lattice pitch, the refractive index of materials, etc. The information provided by the derivatives of such a function at a given point in the multidimensional parameter space is used to decide in which direction it is more convenient to move forward to find, after a few iterations, the final configuration that matches the design goal. Finally, we use some of the possibilities provided by the available optimization methods (for example, multi-objective minimization, constrained optimization, etc.) to model microstructured fibres with fixed chromatic dispersion behaviour within a specific wavelength interval. In particular, we will show some illustrative numerical simulations concerning bandwidth compensating PCFs, which are enforced to maintain a certain modal-area value