General Method for Reducing Adaptive Laser Pulse-Shaping Experiments to a Single Control Variable

Abstract

Adaptive laser pulse shaping has proven to be expeditious for discovering laser pulse shapes capable of manipulating complex systems. However, if adaptive control is to be a valuable interrogative technique that informs physical and chemical research, methods that make it possible to infer mechanistic information from experimental results must be developed. Here, we demonstrate multivariate statistical analysis to extract a single control variable from results of a 137-parameter adaptive laser pulse-shaping optimization of multiphoton electronic excitation in a ruthenium(II) coordination complex in solution. We show that this single variable can be used to linearly manipulate the observed fitness, which is determined by the ratio of molecular emission to second harmonic generation of the laser pulse, over the range explored during the adaptive optimization. Further, manipulation of this variable reveals the latent control mechanism. For this system, that mechanism entails focusing the second harmonic power spectrum of the laser field in a spectral region where the probability of two-photon absorption by the molecule is also large. The statistical tools developed are general and will help elucidate control mechanisms in future adaptive pulse-shaping experiments.

Extracting Information from Adaptive Control Experiments

“…During each GA search, hundreds or thousands of different pulses shapes are evaluated. Systematic analysis of correlations between pulse characteristics and pulse performance for all of the pulses in the search set [72,73] has the potential to reduce the multidimensional genome space to a minimal set of control parameters. [38,52,[73][74][75][76] Intuitive parameter reduction is guided by a phenomenological hypothesis: if a parameter X is highly correlated with fitness, then parameter X is a control parameter.…”

“…[29] Recent work has concentrated on elucidation of the nature of fitness landscapes using two photon absorption and second harmonic generation as test cases. [27,29,[77][78][79] More formally, several strategies based on covariance analysis have been demonstrated recently to determine minimal sets of control parameters in complex reactive systems, including applications of principle component analysis (PCA) (dubbed Principle Control Analysis by White et al), [73] and partial least squares regression (PLS) analysis by Montgomery et al [72,75] Before discussing these multivariate techniques, we review single-parameter controls.…”

“…Two methods that have been successfully applied to coherent control problems are principle components analysis (PCA) [73] (used in what White et al dub Principle Control Analysis) and partial least squares regression (PLS) analysis. [72,75] The goal of both of these methods is to find a transformation from the original space to a natural control basis, by which we mean a subspace spanned by a minimum number of vectors needed to define the active control space. In general, a global linear transformation is not adequate to diagonalize the control space.…”

Multidimensional spectroscopy with a single broadband phase-shaped laser pulse

“…Coherent control is carried out using an adaptive (closed loop) pulse shaping scheme that employs genetic algorithm to optimize many control parameters [30][31][32][33][34][35] of the laser pulses [36]. Here we use a few control paramters.…”

Strong-field control landscapes of coherent electronic excitation

“…In this approach, artificial phase jumps are introduced by undersampling simple continuous phase functions. Another approach utilizes the set of pulse shapes obtained during an optimization procedure to extract relevant degrees of freedom by statistical analysis [26][27][28]. Pulse parameterization, i.e.…”