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We present results of novel broadband long-period gratings (LPGs) that were fabricated axially symmetric in single-mode fiber with a carbon-dioxide laser. The discrete layer-peeling (DLP) technique and a genetic algorithm (GA) were used to design the LPGs. Numerical simulations were used to indicate the performance and absolute error of reconstructing a complex spectral profile for a particular synthesis technique. We found that the DLP technique has the highest performance and executes in the least amount of time. However, a GA could not efficiently synthesize an LPG, but produced a refractive index change profile that can be implemented using a common LPG fabrication system. It is shown that the experimental results obtained with the GA are superior to that obtained with the DLP technique.