| The structure-property relationship of third-order nonlinearity plays a very important role in the field of nonlinear optics. One method of determining third-order nonlinearity is applying Fourier transform analysis to experimentally obtained nonlinear optical responses. An effective method of approximating the Fourier transform is the fast Fourier transform (FFT). The FFT has been one of the central topics in computational Mathematics. In the past decades, most attention was paid to the computational speed of the FFT. This work focuses on the accuracy of the FFT.;In this thesis new algorithms, called here Romberg FFTs, are developed to increase the accuracy. These methods combine the FFT and Romberg integration to take the advantage of both speed and precision. The superiority of Romberg FFTs over the usual FFT is illustrated by their implementations for a known Fourier transform. Although accuracy is increased by Romberg FFTs, the complexity is not increased. Romberg FFTs are then applied to determine third-order nonlinearity. |
