Light is capable of directly manipulating and probing molecular dynamics at its most fundamental level. One versatile
approach to influencing such dynamics exploits temporally shaped femtosecond laser pulses. Oftentimes the control
mechanisms necessary to induce a desired reaction cannot be determined theoretically a priori. However under certain
circumstances these mechanisms can be extracted experimentally through trial and error. This can be implemented
systematically by using an evolutionary learning algorithm (LA) with closed loop feedback. Most frequently, pulse
shaping algorithms operate within either the time or frequency domain, however seldom both. This may influence the
physical insight gained due to dependence on the search basis, as well as influence the speed the algorithm takes to
converge. As an alternative to the Fourier domain basis, we make use of a combined time-frequency representation
known as the von Neumann basis where we observe temporal and spectral effects at the same time.
We report on the numerical and experimental results obtained using the Fourier, as well as the von Neumann basis to
maximize the second harmonic generation (SHG) output in a non-linear crystal. We show that the von Neumann
representation converges faster than the Fourier domain when compared to searches in the Fourier domain. We also
show a reduced parameter space is required for the Fourier domain to converge efficiently, but not for von Neumann
domain. Finally we show the highest SHG signal is not only a consequence of the shortest pulse, but that the pulse
central frequency also plays a key role.
Taken together these results suggest that the von Neumann basis can be used as a viable alternative to the Fourier domain
with improved convergence time and potentially deeper physical insight.
Simulating coherent control with femtosecond pulses on a polyatomic molecule with anharmonic splitting was
demonstrated. The simulation mimicked pulse shaping of a Spatial Light Modulator (SLM) and the interaction was
described with the Von Neumann equation. A transform limited pulse with a fluence of 600 J/m2 produced 18% of the
population in an arbitrarily chosen upper vibrational state, n =2. Phase only and amplitude only shaped pulse produced
optimum values of 60% and 40% respectively, of the population in the vibrational state, n=2, after interaction with the
ultra short pulse. The combination of phase and amplitude shaping produced the best results, 80% of the population was
in the targeted vibrational state, n=2, after interaction. These simulations were carried out with all the population initially
in the ground vibrational level. It was found that even at room temperatures (300 Kelvin) that the population in the
selected level is comparable with the case where all population is initially in the ground vibrational state. With a 10%
noise added to the amplitude and phase masks, selective excitation of the targeted vibrational state is still possible.
Infra-red laser beam shaping has the inherent difficulty that simple ray tracing methods often yield anomalous results, due primarily to the propagation effects at longer wavelengths. Techniques based on diffraction theory have been developed to overcome this, with associated parameters to determine when one approach is needed versus another. In this paper, infra-red (IR) beam shaping by diffractive methods is investigated and compared to refractive methods. Theoretical results on the beam shapers are calculated through a combination of analytical and numerical techniques, and using both ideal and non-ideal inputs. We show that the diffractive optical element (DOE) is remarkably resilient to input errors of wavelength and beam quality, while the refractive shaper is found to be difficult to model. Optical elements based on the two approaches were designed, and then fabricated from ZnSe. A comparison between the fabricated elements and the designed elements is presented, and some of the findings on practical problems in having such elements fabricated are highlighted.