Systematic Control of Nonlinear Optical Processes Using Optimally Shaped Femtosecond Pulses

This article reviews experimental efforts to control multiphoton transitions using shaped femtosecond laser pulses, and it lays out the systematic study being followed by us for elucidating the effect of phase on nonlinear optical laser-molecule interactions. Starting with a brief review of nonlinear optics and how nonlinear optical processes depend on the electric field inducing them, a number of conclusions can be drawn directly from analytical solutions of the equations. From a Taylor expansion of the phase in the frequency domain, we learn that nonlinear optical processes are affected only by the second- and higher-order terms. This simple result has significant implications on how pulse-shaping experiments are to be designed. If the phase is allowed to vary arbitrarily as a continuous function, then an infinite redundancy that arises from the addition of a linear phase function across the spectrum with arbitrary offset and slope could prevent us from carrying out a closed-loop optimization experiment. The early results illustrate how the outcome of a nonlinear optical transition depends on the cooperative action of all frequencies in the bandwidth of a laser pulse. Maximum constructive or destructive interference can be achieved by programming the phase using only two phase values, 0 and pi. This assertion has been confirmed experimentally, where binary phase shaping (BPS) was shown to outperform other alternative functions, sometimes by at least on order of magnitude, in controlling multiphoton processes. Here we discuss the solution of a number of nonlinear problems that range from narrowing the second harmonic spectrum of a laser pulse to optimizing the competition between two- and three-photon transitions. This Review explores some present and future applications of pulse shaping and coherent control.

Optimized isotope-selective ionization of 23Na39K and 23Na41K by applying evolutionary strategies

We study specific properties of different isotopes by applying optimal control. Selective optimization for 23Na39K and 23Na41K isotopes is reported at two different central wavelengths by employing evolutionary strategies on shaped femtosecond laser pulses. The optimized ionization processes exhibit high enhancements of one isotope compared to the other and reversed. We analyze the pulse spectra for extracting information about the optimally chosen ionization paths and observe vibrational transitions to differing electronic states for the different isotope selections. To get a deeper insight we compare simultaneous phase and amplitude modulation with pure amplitude modulation and as well pure phase modulation. Our approach reveals how the optimization algorithm precisely addresses the vibrational wave functions by coherent interaction with the corresponding pulse components.