Phase-matching control of high-order harmonic generation in a two-color laser field

The phase-matching condition of high-order harmonic generation driven by intense few-cycle pulses could be controlled by adding second-harmonic pulses to change the ionization fraction of the gaseous medium. The harmonic generation efficiency could be improved by moving the phase-matching point with an all-optical control of the ionization fraction or a proper change of the confocal parameter. A specific order of harmonics could be easily controlled to reach phase matching at a fixed higher gas pressure by adding second-harmonic pulses with a suitable intensity. Such an all-optical phase-matching control was demonstrated to be dependent upon the temporal delay between the fundamental-wave and second harmonic pulses.

Generation of an extreme ultraviolet supercontinuum in a two-color laser field

We theoretically investigate the high-order harmonic generation in a helium atom with a two-color optical field synthesized by an intense 6 fs pulse at 800 nm and a relatively weak 21.3 fs pulse at 400 nm. When the frequency-doubled pulse is properly time shifted with respect to the fundamental pulse, an ultrabroad extreme ultraviolet supercontinuum spectrum with a 148 eV spectral width can be generated which directly creates an isolated 65 as pulse even without phase compensation. We explain this extraordinary phenomenon by analyzing maximum electron kinetic energies at different return times.

Three-dimensional superconformal field theory, Chern-Simons theory, and their correspondence

In this thesis, we discuss 3d-3d correspondence between Chern-Simons theory and three-dimensional N = 2 superconformal field theory. In the 3d-3d correspondence proposed by Dimofte-Gaiotto-Gukov information of abelian flat connection in Chern-Simons theory was not captured. However, considering M-theory configuration giving the 3d-3d correspondence and also other several developments, the abelian flat connection should be taken into account in 3d-3d correspondence. With help of the homological knot invariants, we construct 3d N = 2 theories on knot complement in 3-sphere for several simple knots. Previous theories obtained by Dimofte-Gaiotto-Gukov can be obtained by Higgsing of the full theories. We also discuss the importance of all flat connections in the 3d-3d correspondence by considering boundary conditions in 3d N = 2 theories and 3-manifold.