Exploring, tailoring, and traversing the solution landscape of a phase-shaped CARS process

Pulse shaping techniques are used to improve the selectivity of broadband CARS experiments, and to reject the overwhelming background. Knowledge about the fitness landscape and the capability of tailoring it is crucial for both fundamental insight and performing an efficient optimization of phase shapes. We use an evolutionary algorithm to find the optimal spectral phase of the broadband pump and probe beams in a background-suppressed shaped CARS process. We then investigate the shapes, symmetries, and topologies of the landscape contour lines around the optimal solution and also around the point corresponding to zero phase. We demonstrate the significance of the employed phase bases in achieving convex contour lines, suppressed local optima, and high optimization fitness with a few (and even a single) optimization parameter

Coherent control of vibrational transitions: Discriminating molecules in mixtures

Identifying complex molecules often entails detection of multiple vibrational resonances, especially in the case of mixtures. Phase shaping of broadband pump and probe pulses allows for the coherent superposition of several resonances, such that specific molecules can be detected directly and with high selectivity. Our particular implementation of coherent anti-Stokes Raman scattering (CARS) spectroscopy and imaging employs broadband pump and probe fields in combination with a narrowband Stokes field. We describe our approach for combining spectral phase shaping and closed-loop optimization strategies to perform chemically-selective microscopy. To predict the optimal excitation profile we employ evolutionary algorithms that use the vibrational phase responses of five distinct molecules with overlapping resonances and investigate the effect of phase instability on the optimization. We have recently shown that modified polynomials and orthogonal rational functions can give rise to improved contours for CARS fitness landscapes. Now, by considering the landscapes associated with different basis sets, we introduce two figures of merit to quantitatively rank basis functions in terms of their ‘‘appropriateness’’ for modeling nonlinear phase-shaped processes