Robust single frequency index-patterned laser design using a Fourier design method

We use a Fourier-transform based method to investigate the magnitude and robustness of mode selectivity in as-cleaved discrete-mode semiconductor lasers, where a small number of refractive index perturbations are introduced into a Fabry-P\'{e}rot laser cavity. Three exemplar index perturbation patterns are considered. Our results demonstrate the capability to significantly improve modal selectivity by choosing a perturbation distribution function that avoids placing perturbations near to the cavity centre. Our analysis also highlights the ability to select functions that can increase the yield despite facet phase errors introduced during device fabrication.