Emission Of High-Order Harmonics And Generation Of Isolated Attosecond Pulses Under The Interation Of Model Atoms With Laser Pulses

Coherent harmonic radiations will be produced in the interaction of intense laser fields with atoms, molecules, clusters, and solids. The frequency of the harmonics generated is integer multiples of that of the driving field. The emitted power spectrum of the harmonic radiations shows itself a structure of rapid falling first, then a plateau, and a cutoff at last. Appearance of the plateau indicates the possibility of up-transforming the infrared radiations to XUV radiations, even soft-X rays realized in the one step. One calls this process the generation of high-order harmonics (HHG). Nowadays, HHG studies are intensively advancing towards the generation of trains of attosecond pulses and an isolated attosecond pulse. The study of producing isolated attosecond pulses by means of the HHG has become a focus of attention of most researchers in recent years due to the progress in laser technologies and the prospect of the important applications to superfast science. It is just our goal pursued in this thesis.It is based on the classic trajectory theory (the three-step model) that the harmonic emission of atoms in intense laser fields is determined by the following three-step processes: (1) the electrons in an atom are ejected by incident driving laser fields. (2) the ejected electron moves in the fields, and obtains a definite kinetic energy when it comes back to the parent ion. (3) the ejected electron will recombine with the parent ion with a definite probability, and in the same time, a photon of the relevant energy is emitted. According to the semiclassical argument describing the motion of electrons in the laser field, on the one hand (in the pure classical aspect), the electrons of a definite energy when they return to the parent ion but ejected at different phases of the driving field correspond to different trajectories in which the one that experiences longer recursion time is called the long trajectory, and the other that experiences shorter recursion time is called the short trajectory; on the other hand (in the quantum aspect), this argument defines two kinds of wavepackets, the long trajectory- and the short trajectory- wavepackets, by considering respectively all together the long trajectory electrons or the short trajectory electrons, in this way, some quantum effects such as the wavepacket spreading can be reflected in the theoretical description. In this argument, the characteristics of the harmonic emission including the harmonic intensity, the cutoff frequency, and the emission time, etc., are all determined by those electron trajectories. For instance, when the incident laser is a linearly polarized long pulse of a single central frequency, the detail of the harmonic spectrum shows itself a structure like a comb in shape, because the time when a trajectory of a definite energy comes to the parent core is repeated according to the period of the laser field in the large portion of the temporal domain except in the smaller time intervals on the leading-, and the falling- edges of the pulse. Consequently, the resulting harmonic radiations filtered through in a chosen frequency section become a train of pulses in the temporal domain. However, in the rapid development of modern laser techniques, the driving pulses as short as a few femtoseconds have been already prepared in many laboratories in the world. The breaking down of the abovementioned periodicity under the action of those supershort pulses gives rise to remarkable changes in the multiformity, for example, a supercontinuum or/and multiple plateaus appear in harmonic spectra. Therefore, if one can control those electron trajectories, then he can manipulate the emission process of the HHG, further he can steer the generation of the attosecond pulses.In this thesis, we have numerically solved the time-dependent Schr?dinger equations of the helium atom models in intense and short laser pulse fields under the Born-Oppenheimer and electric dipole approximations by using the splitting operator technique. The power spectra of the emitted harmonics have been obtained by performing a Fourier transform from the expectation value of the dipole acceleration. Under the guidance of the semiclassical trajectory argument, we renovated the theoretical simulation of the HHG process of the model helium atom in various supershort driving pulses, and have found out two ways for producing a strong and clean (without satellite pulses by the pulse generated) isolated attosecond pulse. These two ways are novel in the senses either it is never used before, or some certain aspects are greatly improved in it though it had been previously used. In the following we introduce them, respectively.The first phase of our work in this thesis is the generation of a clean isolated 80 attosecond pulse in the spectral region of 93-155 electron volts by using two orthogonally polarized laser pulses irradiating jointly on a two-dimensional model helium atom. In this study, a weak assistant driving pulse is added on the suitable position of the strong main driving pulse. The linear polarization directions of these two pulses are perpendicular to each other. The central wavelength of the main pulse is 400 nm, and its full width at half magnitude (FWHM) is 2.66 femtoseconds; while the central wavelength of the assistant pulse is 800 nm, and its FWHM is 10.6 femtoseconds. The target is a two-dimensional model helium atom in the single active electron approximation. Adjusting the peak amplitude of the main field makes the atom have considerable ionization under its action; and adjusting the peak amplitude of the assistant field makes it biggest, provided the atom has no substantial ionization under alone action of this field. After the atomic ionization, the foundational dynamic behavior of the ejected electron is determined by the electric field of the main pulse, while the role of the assistant pulse is limited only to steer the electrons belonging to various trajectories in order to control their possibility of returning to the parent ion in the direction perpendicular to the main dynamical axis. The result shows that this is not only a very simple, but also very effective means for manipulation of the harmonic emission. The key point of this method lies in the fact that the electron recombination, and hence the harmonic emission processes occur with a definite probability only when the electron re-arrives simultaneously in the core in the two orthogonal axes. Therefore, if we can control the phase difference between these two electric fields of the pulses, then we shall choose some certain limited electron trajectories which can return to the parent ion after experiencing some certain recursion time, and in the same time, we can make the other large portions of the electron wavepackets go far out of the parent ion and exclude the possibility for them to participate in the harmonic emission process. In this way we have achieved the effective suppressing to all other wavepackets except a short-trajectory wavepacket remained, and realized the harmonic emission purely from the electron recombination of a single short-trajectory wavepacket. Furthermore, filtering through a suitable frequency band on the rear portion of the plateau in the HHG spectrum, we obtained a clean isolated pulse with the FWHM of 80 attoseconds in the spectral region of 93-155 electron volts.In the second phase of our work, the first of our goals is to greatly raise the efficiency of the HHG process to finally obtain a strong isolated attosecond pulse. In order to achieve this purpose, we prepared antecedently the initial state of the target atom on a superposition state composed of an excited state and the ground state populated equally (Experimentally, such a superposition state can be produced through resonant excitation.), before the intense field working pulse comes. Thus in this superposition state scheme, when the driving pulse of a appropriate peak amplitude comes, on the one hand, the initial population on the ground state can be basically kept up, and on the other hand, the excited state can be ionized with an extremely large rate, so that both the ionization and the recombination processes can take unusually high efficiencies. The second of our goals is shaping the leading edge of the Gaussian driving pulse by using a shaping pulse (An amplitude-reduced pulse of the main pulse is good), in order to exclude the possibility of production of the long-trajectory electron wavepackets and return for them to the parent ion, so that the design of pure short-trajectory electron recombination can be realized, which gives at last rise to the generation of a strong and clean isolated attosecond pulse. The third point of originality is the discovery of the Rabi-like oscillations between the time-dependent populations of the ground state and the continuum in the electron recombination process. Originally, the Rabi oscillations appear theoretically between the time-dependent populations of two bound states in a model two-level atom. However, in the long term, we persist in believing that such a kind of oscillations should also occur between the time-dependent populations of the ground state and the continuum in the electron recombination process after the atom has been sufficiently ionized, if the populations on the other bound states (except the population on the ground state) are all trivial in the whole temporal domain and hence cannot be taken into account. Of course, the continuum is an infinite set of states with definite energies, i.e., a wavepacket composed of various energy states, instead of a level. However, in the electric field of the laser pulse, the actual recombination processes occur consecutively in the interference between the ground state and a moving differential state of the continuum wavepacket. Consequently, such Rabi-like oscillations will definitely occur. There is certainly a difference between the original Rabi oscillations and the Rabi-like oscillations here: the original Rabi oscillations are simple harmonic, because the event occurs between two fixed levels; while the Rabi-like oscillations here are chirped, because the events occur consecutively between a fixed level and a changing differential state with a different energy in the moving wavepacket. The reason why the people (including ourselves) has not observed previously this phenomenon lies in the fact that its clear emergence depends strongly upon the following two necessary conditions: one is that the actual ionization and the recombination processes must simultaneously be of unusually high efficiencies, and the other is that the numerical computations for various populations, especially for the computation of the ionization product, must be of high accuracies. In this work we have for the first time observed those Rabi-like oscillations, because we had simultaneously satisfied the aforementioned demands.The road that lies before us is just long. We understand deeply that the work which has been done by us is only a beginning on this road. Both our computing capability and the relevant theoretical models are needed to be improved as soon as possible for covering more novel ideas and resorts.