Pulsed laser field errors: theoretical and experimental analysis of a phase error figure of merit

Abstract

506 / CLEO'99 / FRIDAY MORNING 150 IO0 50 0 50 1M 150 time (15) CFA6 Fig. 2. Target intensity and phase (solid lines), intensity and phase retrieved from the genetic algorithm (dashed lines), and the intensity and phase from the composite algorithm (dotted lines) in the SHG FROG case. The genetic algorithm returned an error of 0.00175, and the composite algorithm returned an error of 0.00256.that generate the same FROG trace. This ambiguity has been shown to cause difficulties in the retrieval ofpulses with flat temporal phases using the standard iterative algorithm. Genetic algorithms, however, are less susceptible to being trapped by degenerate solutions, due to the parallel nature of their search. The results of the reconstruction of a theoretical pulse measured with SHG FROG are shown in Fig. 2. An asymmetric pulse with flat temporal phase was chosen (solid lines), and 3% additive and multiplicative noise was added to the FROG trace. The pulse was then reconstructed from the FROG trace using the genetic algorithm, and a composite iterative algorithm, available commercially. Whereas the composite algorithm (dotted lines) stagnates on a chirped symmetric pulse, the genetic algorithm was able to successfully retrieve the pulse.In conclusion, we have demonstrated phase reconstruction from FROG using a genetic algorithm. Even though only the most basic evolutionary operators were used, the genetic algorithm returned lower FROG errors on certain types of experimental and theoretical pulses then the standard composite iterative algorithm.Several pulse distortion analysis methods have been recently used to quantify pulse errors. These include: truncated Taylor series representations, spectral group delay optimization, peak intensity measurements, pulse FWHM, and time-intensity moments.' The application of these measures for pulse distortions is by no means uniform with the exception of the Taylor series representation, whose relevance is limited for many pulses today.2 The unsettled question, therefore, is which analysis method is best suited to quantify current optical pulse errors.We explore an analysis of pulse errors using intensity weighted spectral phase deviations between the spectral phase, + = k r and a desired reference phase, +?, Comparisons between this definition of and many other measures ofpulse characteristics have revealed that +em accurately represents pulse distortion for complicated phase errors where traditional methods fail. For example, using etalons or multilayered, chirped mirrors with a pulse can result in an oscillating spectral phase distortion. With this type of distortion, even closely related traditional figures-of-merit for a pulse can vary greatly. Increasing this type of distortion can, for example, change the pulse FWHM by only 6% while the integrated half-energy width of the pulse changes by an order of magnitude. +em, however, gives a faithful and general rendering of the oscdlating pulse distortion by increasing in linear proportion to the average of the pulse FWHM, RMS width, 50...