Susanne Fechner’s research while affiliated with University of Wuerzburg and other places

Recently we introduced the von Neumann representation as a joint time-frequency description for femtosecond laser pulses and suggested its use as a basis for pulse shaping experiments. Here we use the von Neumann basis to represent multidimensional molecular control landscapes, providing insight into the molecular dynamics. We present three kinds of time-frequency phase space scanning procedures based on the von Neumann formalism: variation of intensity, time-frequency phase space position, and/or the relative phase of single subpulses. The shaped pulses produced are characterized via Fourier-transform spectral interferometry. Quantum control is demonstrated on the laser dye IR140 elucidating a time-frequency pump-dump mechanism.

We recently introduced the von Neumann picture, a joint time–frequency representation, for describing ultrashort laser pulses. The method exploits a discrete phase-space lattice of nonorthogonal Gaussians to represent the pulses; an arbitrary pulse shape can be represented on this lattice in a one-to-one manner. Although the representation was originally defined for signals with an infinite continuous spectrum, it can be adapted to signals with discrete and finite spectrum with great computational savings, provided that discretization and truncation effects are handled with care. In this paper, we present three methods that avoid loss of accuracy due to these effects. The approach has immediate application to the representation and manipulation of femtosecond laser pulses produced by a liquid-crystal mask with a discrete and finite number of pixels.

We present an experimental concept for the generation and characterization of polarization-shaped femtosecond laser pulses in the ultraviolet. Polarization-shaped laser pulses are frequency-doubled in an interferometrically stable setup comprising two perpendicularly oriented nonlinear crystals. Dual-channel spectral interferometry is employed to fully characterize the electric field of the polarization-shaped ultraviolet pulses. The method is experimentally demonstrated for a central wavelength of 400 nm. Advantages and prospective applications, as well as limitations and possible alternatives, are discussed.

The characterization and interpretation of ultrashort laser pulses is most intuitive in the joint time–frequency domain, where structures like multiple pulses become immediately apparent. For practical reasons, ultrafast femtosecond laser pulse shaping, however, is commonly carried out in the frequency domain. Here we implement pulse shaping of optical fields defined in the von Neumann representation, which is a joint time–frequency distribution with complex-valued Gaussian basis functions. We discuss the feasibility as well as the principal limitations of this technique, show illustrative examples, and propose possible applications in coherent control.

Die in der vorliegenden Arbeit eingeführte von Neumann-Darstellung beschreibt jeden Laserpuls auf eineindeutige Weise als Summe von an verschiedenen Punkten des Zeit-Frequenz-Phasenraumes zentrierten, bandbreitebegrenzten Gaußimpulsen. Diese Laserpulse bilden sozusagen die „elementaren“ Bausteine, aus denen jeder beliebige Lichtimpuls konstruiert werden kann. Die von Neumann-Darstellung vereint eine Reihe von Eigenschaften, die sie für eine Anwendung auf dem Gebiet der Quantenkontrolle besonders geeignet erscheinen lässt. So ist sie eine bijektive Abbildung zwischen den Freiheitsgraden des verwendeten Impulsformers und der Phasenraumdarstellung der resultierenden, geformten Laserpulse. Jeder denkbaren Wahl von Impulsformerparametern entspricht genau eine von Neumann-Darstellung und umgekehrt. Trotzdem ermöglicht sie, ebenso wie die Husimi- oder die Wigner-Darstellung, eine intuitive Interpretation der dargestellten Lichtimpulse, da deren zeitliche und spektrale Struktur sofort zu erkennen ist. The von Neumann-representation introduced in this thesis describes each laser pulse in a one-to-one manner as a sum of bandwidth-limited, Gaussian laser pulses centered around different points in phase space. These pulses can be regarded as elementary building blocks from which every single laser pulse can be constructed. The von Neumann-representation combines different useful properties for applications in quantum control. First, it is a one-to-one map between the degrees of freedom of the pulse shaper and the phase-space representation of the corresponding shaped laser pulse. In other words: Every possible choice of pulse shaper parameters corresponds to exactly one von Neumann-representation and vice versa. Moreover, since temporal and spectral structures become immediately seizable, the von Neumann-representation, as well as the Husimi- or the Wigner-representations, allows for an intuitive interpretation of the represented laser pulse.

We experimentally demonstrate the generation and characterization of polarization-shaped femtosecond laser pulses in the ultraviolet at a central wavelength of 400 nm . Near-infrared laser pulses are first polarization shaped and then frequency doubled in an interferometrically stable setup that employs two perpendicularly oriented nonlinear crystals. A new pulse shaper design involving volume phase holographic gratings reduces losses and hence leads to an increase in pulse energy.

In recent years, the use of joint time-frequency representations to characterize and interpret shaped femtosecond laser pulses has proven to be very useful. However, the number of points in a joint time-frequency representation is daunting as compared with those in either the frequency or time representation. In this article we introduce the use of the von Neumann representation, in which a femtosecond pulse is represented on a discrete lattice of evenly spaced time-frequency points using a non-orthogonal Gaussian basis. We show that the information content in the von Neumann representation using a lattice of N points in time and √N points in frequency is exactly the same as in a frequency (or time) array of N points. Explicit formulas are given for the forward and reverse transformation between an N-point frequency signal and the von Neumann representation. We provide numerical examples of the forward and reverse transformation between the two representations for a variety of different pulse shapes; in all cases the original pulse is reconstructed with excellent precision. The von Neumann representation has the interpretational advantages of the Husimi representation but requires a bare minimum number of points and is stably and conveniently inverted; moreover, it avoids the periodic boundary conditions of the Fourier representation.

We experimentally demonstrate a method to generate shaped femtosecond laser pulses in the ultraviolet at a central wavelength of 267nm, the third harmonic of conventional titanium-sapphire femtosecond laser systems. Employing a 128-pixel liquid-crystal spatial light modulator, we impose variable spectral phase modulations upon the near-infrared laser pulses. By this, complex laser pulses can be shaped whose overall spectrum is still conserved. Our experiments show that it is possible to easily transfer these pulses into the ultraviolet at 267nm via sum-frequency mixing in nonlinear crystals and to predictably generate multistructured ultraviolet femtosecond laser pulses. We analyze the temporal and spectral composition of these pulses after frequency conversion into the ultraviolet using difference-frequency cross-correlation and XFROG (cross-correlation frequency-resolved optical gating) techniques with an unmodulated fundamental laser pulse. The method can be employed to facilitate adaptive quantum control experiments in the ultraviolet wavelength regime, where the major absorption bands of many organic molecular systems are located.

We employ a 128-pixel liquid-crystal spatial light modulator to generate variable pulse sequences from a titanium-sapphire femtosecond laser amplifier system centered at 800 nm. By applying phase modulations based on triangular-shaped spectral phase patterns, pulse sequences can be generated whose overall spectrum is still conserved but whose subpulses differ in their spectral composition. We further use nonlinear crystals to analyze the shape of these pulses after frequency conversion. Our experiments show that it is possible to transfer these pulse sequences into the ultraviolet at central wavelengths of 400 nm and 267 nm without losing the ability to spectrally distinguish between the femtosecond subpulses. This is affirmed by measurements using cross-correlation and XFROG (cross-correlation frequency resolved optical gating) techniques with an unmodulated laser pulse. Simulations of the experiments are performed for comparison. We also discuss promising applications in spectroscopy or information encoding.