Final Report Summary - HHG-NANOTOMOGRAPHY (High-Harmonic tomography and characterization of Nano-structures)
Main objective of our project is to develop foundation for usage of attosecond pulses and high harmonics in studies of molecules, nanostructures and nanomaterials. During preliminary studies it turned out that the critical step in achieving this goal is to fully characterise spatial properties of the generated high harmonics. There were no tool available hitherto which were up to this task.
To achieve this goal I invented and experimentally demonstrated new approach for frequency-resolved high harmonic wavefront characterisation [1] (Following tradition in the area, we called it SWORD-Spectral Wavefront Optical Reconstruction by Diffraction).
We used SWORD to study spatial properties of high harmonic generation (HHG). Our measurements reveal that the short-trajectory harmonics have an essentially Gaussian spatial profile and that the root-mean-square deviations from a parabolic wavefront are only 0. 2 radians. They also reveal that different harmonics have a significantly different wavefront curvature upon emerging from the generating region [2]. Since we measured both amplitude and phase of each harmonic, we are able to propagate the fields and determine their spatial properties anywhere along the direction of propagation. Specifically we determine their waist position (position of the flat phase) and size-the virtual origin of the coherent beams. We find that this virtual origin of each harmonic is at significantly different position. Particularly important, the distance between the waist positions of some harmonics can be larger than their respective Rayleigh ranges. Since the harmonics are generated in the gas jet, this observation means that they are produced with different radii-of-curvature, depending on the harmonic order.
The dependence of wavefront structure on harmonic order means that it is impossible to focus the attosecond pulse into one diffraction limited spot by achromatic optics (by using mirrors for example). It also means that, if the harmonics are focused to measure their temporal structure, the duration of the pulse will depend on where the measurement is made.
Our approach of frequency resolved wavefront characterisation opens the door for complete spatial-temporal reconstruction of attosecond pulses. Given the measured spectral wavefront, and spectral wavefront amplitude at any plane along the beam propagation, it is enough to have temporal information at any single point across the beam to determine the temporal structure everywhere in space and time. If we know the position of the generating medium with sufficient accuracy, this includes the position at the generating medium itself.
The wave front amplitude and phase in the generating medium contains an imprint of the underlying single atom or molecule response. We have shown that we can use the frequency resolved wavefronts to measure previously experimentally inaccessible and not yet fully understood fundamental quantities in HHG process, such as tunneling phase.
No matter what the pulse temporal structure should prove to be, we have determined that there will be significantly different temporal profile at the center and at the edges of a beam and the temporal profile must change as the beam passes through the respective foci of the harmonics. Therefore, any spatially extended measurement with attosecond pulses will be affected and any measurement of the pulse itself is also affected. The result of any experiment will be effectively averaged over the different temporal profiles at different positions in the interaction region of the focal volume.
Finally, attosecond science has been restricted to spatially averaged measurements to image orbitals, tracing molecular dynamics, identify and time resolve tunneling wave packets and to follow Auger decay. Spectrally resolved wavefronts and the complete spatio-temporal characterisation of attosecond pulses that they facilitate will allow us much greater experimental precision in all of these experiments.
In addition, during the project I suggested a way and experimentally demonstrated, for the first time, generation of the high-harmonics with oriented molecules using all optical orientation approach. The HHG with oriented molecules is characterised by generation of even-order high harmonics that arise from the broken symmetry induced by the orientation dynamics. The even-order harmonic radiation that we measure appears on a zero background, enabling us to accurately follow the temporal evolution of the wave packet. Using this approach we found that the mechanism of molecular orientation in optical w+ 2w scheme is preferential ionisation [3] and not hyperpolarisability as was previously believed.
We have shown, that high harmonic generation is an effective way to study oriented molecules [4]. Asymmetric molecules look different when viewed from one side or the other. This difference influences the electronic structure of the valence electrons, thereby giving stereo sensitivity to chemistry and biology. We have shown that attosecond and re-collision science provides a detailed and sensitive probe of electronic asymmetry. On each 1/2 cycle of an intense light pulse, laser induced tunneling extracts an electron wave packet from the molecule. When the electron wave packet recombines, alternately from one side of the molecule or the other, its amplitude and phase asymmetry determines the even and odd harmonics radiation that it generates. We determined the phase asymmetry of the attosecond XUV pulses emitted when an electron recollides from opposite sides of the CO molecule, and the phase asymmetry of the recollision electron just before recombination. This opens a route for applying orbital tomography to polar molecules.
To summarise, during the project we developed the foundations for usage of HHG in nanotomography. However, at least as important, during the project we discovered the remarkable properties of high harmonic wavefronts that will have an impact across the entire field of attosecond science and lightwave engineering. We studied these properties and came up with the major conclusions.
In addition, we achieved the long standing goal in experimental attosecond science-first demonstration of HHG with oriented polar molecules. Along with experimental progress, we developed the theoretical foundation of attosecond spectroscopy of polar molecules and found a real mechanism of molecular orientation
To achieve this goal I invented and experimentally demonstrated new approach for frequency-resolved high harmonic wavefront characterisation [1] (Following tradition in the area, we called it SWORD-Spectral Wavefront Optical Reconstruction by Diffraction).
We used SWORD to study spatial properties of high harmonic generation (HHG). Our measurements reveal that the short-trajectory harmonics have an essentially Gaussian spatial profile and that the root-mean-square deviations from a parabolic wavefront are only 0. 2 radians. They also reveal that different harmonics have a significantly different wavefront curvature upon emerging from the generating region [2]. Since we measured both amplitude and phase of each harmonic, we are able to propagate the fields and determine their spatial properties anywhere along the direction of propagation. Specifically we determine their waist position (position of the flat phase) and size-the virtual origin of the coherent beams. We find that this virtual origin of each harmonic is at significantly different position. Particularly important, the distance between the waist positions of some harmonics can be larger than their respective Rayleigh ranges. Since the harmonics are generated in the gas jet, this observation means that they are produced with different radii-of-curvature, depending on the harmonic order.
The dependence of wavefront structure on harmonic order means that it is impossible to focus the attosecond pulse into one diffraction limited spot by achromatic optics (by using mirrors for example). It also means that, if the harmonics are focused to measure their temporal structure, the duration of the pulse will depend on where the measurement is made.
Our approach of frequency resolved wavefront characterisation opens the door for complete spatial-temporal reconstruction of attosecond pulses. Given the measured spectral wavefront, and spectral wavefront amplitude at any plane along the beam propagation, it is enough to have temporal information at any single point across the beam to determine the temporal structure everywhere in space and time. If we know the position of the generating medium with sufficient accuracy, this includes the position at the generating medium itself.
The wave front amplitude and phase in the generating medium contains an imprint of the underlying single atom or molecule response. We have shown that we can use the frequency resolved wavefronts to measure previously experimentally inaccessible and not yet fully understood fundamental quantities in HHG process, such as tunneling phase.
No matter what the pulse temporal structure should prove to be, we have determined that there will be significantly different temporal profile at the center and at the edges of a beam and the temporal profile must change as the beam passes through the respective foci of the harmonics. Therefore, any spatially extended measurement with attosecond pulses will be affected and any measurement of the pulse itself is also affected. The result of any experiment will be effectively averaged over the different temporal profiles at different positions in the interaction region of the focal volume.
Finally, attosecond science has been restricted to spatially averaged measurements to image orbitals, tracing molecular dynamics, identify and time resolve tunneling wave packets and to follow Auger decay. Spectrally resolved wavefronts and the complete spatio-temporal characterisation of attosecond pulses that they facilitate will allow us much greater experimental precision in all of these experiments.
In addition, during the project I suggested a way and experimentally demonstrated, for the first time, generation of the high-harmonics with oriented molecules using all optical orientation approach. The HHG with oriented molecules is characterised by generation of even-order high harmonics that arise from the broken symmetry induced by the orientation dynamics. The even-order harmonic radiation that we measure appears on a zero background, enabling us to accurately follow the temporal evolution of the wave packet. Using this approach we found that the mechanism of molecular orientation in optical w+ 2w scheme is preferential ionisation [3] and not hyperpolarisability as was previously believed.
We have shown, that high harmonic generation is an effective way to study oriented molecules [4]. Asymmetric molecules look different when viewed from one side or the other. This difference influences the electronic structure of the valence electrons, thereby giving stereo sensitivity to chemistry and biology. We have shown that attosecond and re-collision science provides a detailed and sensitive probe of electronic asymmetry. On each 1/2 cycle of an intense light pulse, laser induced tunneling extracts an electron wave packet from the molecule. When the electron wave packet recombines, alternately from one side of the molecule or the other, its amplitude and phase asymmetry determines the even and odd harmonics radiation that it generates. We determined the phase asymmetry of the attosecond XUV pulses emitted when an electron recollides from opposite sides of the CO molecule, and the phase asymmetry of the recollision electron just before recombination. This opens a route for applying orbital tomography to polar molecules.
To summarise, during the project we developed the foundations for usage of HHG in nanotomography. However, at least as important, during the project we discovered the remarkable properties of high harmonic wavefronts that will have an impact across the entire field of attosecond science and lightwave engineering. We studied these properties and came up with the major conclusions.
In addition, we achieved the long standing goal in experimental attosecond science-first demonstration of HHG with oriented polar molecules. Along with experimental progress, we developed the theoretical foundation of attosecond spectroscopy of polar molecules and found a real mechanism of molecular orientation