High-order Harmonic Emission And Isolated Attosecond Pulse Generation From Heliuim Ion In Intense Laser Fields

When matter such as atoms or molecules is subject to a high-intense laser pulse, the electronic response is highly nonlinear. As a result of this, a coherent wave whose frequency is an integral multiple of that of the incident laser field is radiated, which is known as high-order harmonic generation (HHG). Since the HHG covers the spectral range from the infrared to xuv and even to soft x-rays regions, it is fast becoming a candidate for breaking through femtosecond limit and realizing attosecond pulse generation. Currently, the HHG is the most promising way to generate attosecond (as) pulses in experiment. Almost all harmonic spectra experimently and theoretically show a common characteristic: the harmonic intensities decrease rapidly for the few low orders, then the intensities keep almost constant for many orders to form a broad plateau, and finally the intensity drops sharply at the highest harmonic orders, which is named the cutoff. The physical picture of the HHG process can be well understood by the semiclassical three-step model and the fully quantum theory. According to the three-step model, the electron first tunnels through the effective barrier formed by the atomic potential and the laser field, then it oscillates almost freely in the laser field and gains additional kinetic energy, and finally when the laser field reverses its direction, it may recombine with the parent ion and emit a harmonic photon with energy up to I_p+3.17U_p, where I_p is the atomic ionization potential and U_p is the ponderomotive energy. The above process is repeated every half an optical cycle of the driving laser field, which leads to the generaton of an attosecond pulse train with a periodicity of half an optical cycle. However, the generation of a single attosecond pulse can play a very important role in practical application, because it enables the researches of the ultrafast sciences to enter into a drastically new regime, where it is possible for people to trace the movement of the electrons and observe the electronic relaxation processes inside atoms and molecules, etc. Hence, how to produce an isolated attosecond pulse has attracted a lot of attention. The classical and quantum theory have shown that there are two dominant quantum paths to each harmonic emission, one path with earlier ionization time but later emission time is called the long path and the other path with later ionization time but earlier emission time is called the short path. In the classical picture of the HHG, for the harmonics in the plateau, since each harmonic originates from two different electronic paths with different emission times in each half optical cycle of the fundamental laser, the plateau harmonics are not emitted at the same time, thereby, the superposition of several harmonics results in an irregular as pulse train (APT) including the two bursts in every half optical cycle. For the harmonics in the cutoff region, since the emission times of the long and short paths are almost the same, the cutoff harmonics are emitted in phase, therefore, the superposition of severalharmonics results in the generation of an isolated as pulse in every one optical cycle. Though an isolated and clean as pulse can be created by filtering several continuous harmonics in the cutoff, it is very difficult to obtain an isolated as pulse with a duration shorter than 100 as due to the limitation of the continuous spectrum width. In order to obtain a single as pulse with much shorter pulse duration, the bandwidth of much broader supercontinuous harmonics is acquired strongly. Recently, a lot of schemes have been theoretically proposed to broaden the bandwidth and reduce the pulse duration. For the single-atom response, the control of quantum path is an efficient method to generate an isolated as pulse. Its main idea is by means of waveform control of laser pulse to further control the quantum paths of the electrons, thus the continuous harmonics are mainly attributed to the contribution of one dominating electron path. Once a single quantum path is selected, in terms of the harmonic synthesis technique, an isolated as pulse is producted by superposing some properly selected harmonics in the supercontinuum.In this thesis, based on the single-active electron approximation, we numerically solve the 1D time-dependent Schr?dinger equation (TDSE) for interacting the intense laser with He⁺ ion with the help of the two-order splitting-operator fast-Fourier transform technique. By the numerical approach, we investigate the high-order harmonic emission and an isolated as pulse generation from He⁺ ion in the combined laser field and put forward three kinds of methods of not only enhancing the harmonics conversion efficiency and generating an ultrabroad extreme ultraviolet (xuv) supercontinuum, but also obtaining an isolated as pulse with short pulse duration. We also analyse the results and give some reasonable explanation. The main work of this thesis is composed of three parts:In the first part, we theoretically investigate that the high-order harmonic generation when a helium ion is subject to a two-color laser field. It is shown that when the initial state is prepared as a coherent superposition of the ground and the first excited states, not only the conversion efficiency of the harmonics is enhanced significantly and an ultrabroad xuv supercontinuum is generated, but also the cutoff energy is extended effectively. In our simulation, we find that the contribution from the long path can be suppressed, wherease the contribution from the short path can be enhanced. Then by superposing some properly selected harmonic orders, an intense isolated 47 as pulse is generated successfully. Compared with the case of the ground state in a one-color field, the intensity of this isolated as pulse is 5 orders of magnitude higher. It is noteworthy that the two-color scheme presents several unique characteristics. First, when the relative phaseφbetween two laser pulses changes from 0 to 0.45Ï€, we can still obtain an isolated sub-50 as pulse by superposing proper continuous harmonics. Second, the duration of the 2400 nm laser pulse in this scheme has little effect on our simulation results (e.g., from 10 to 64 fs). Third, the population of the first excited state is not stringent; a little more or less population than 0.5 will not result in obvious changes of the HHG and as pulses generation. The fascinating characteristics above make one more easily manipulate our scheme in practical experimental implementations. What is more important, this scheme overcomes a limitation of generating a broad frequence bandwidth and can produce an ultrabroad xuv supercontinuum, which is in favour of the generation of a short and intense isolated as pulse.In the second part, we theoretically present an efficient method to generate an isolated short as pulse in the combination of a synthesized two-color field and an xuv as pulse. We also show that the selection of a specific quantum path can be realized by using an xuv pulse with different central energy at a proper time. Concretely, by adding a 0.5-fs, 62.3-nm xuv pulse to the synthesized two-color field atω₀Ï„_delay=-0.9Ï€, the harmonic intensity is effectively enhanced and an ultrabroad xuv supercontinuum can be formed compared with the two-color case. In addition, the short path is selected to effectively contribute to the HHG, then an isolated 40 as pulse is generated directly by filtering out harmonics from 265th to 325th. Furthermore, by adding a 0.5-fs, 29.6-nm xuv pulse to the synthesized two-color field atω₀Ï„_delay=-1.22Ï€, both the enhancement of the HHG and the generattion of a broadband continuous harmonic spectrum can be observed, and the long path is selected, then an isolated 39 as pulse is obtained straightforwardly by superposing harmonics from 265th to 325th. Specifically, in our two schemes, the enhancement of the harmonics in the supercontinuum region is much more efficient. Since the xuv pulse holds the high photon energy and the extremely short pulse duration, the production time and property of the electron wave packet (EWP) can be operated. As a result, the ionization yields of the electrons with a specific quantum path can be increased, i.e., one of two quantum paths (long and short) is selected to effectively contribute to the HHG. It should be emphasized that, in our schemes, increasing the duration of the 1200 nm laser pulse up to 64 fs or keeping the wavelength of the subharmonic laser pulse in the region of 1160-1240 nm, we find that the results have little change. In our numerical simulation, we select the laser parameters achievable in the current laboratory. Therefore, the schemes presented here are feasible for an experimental demonstration in the near future. The importance we think is that our schemes can overcome the limitation of the low efficiency in the HHG emission and produce an ultrabroad xuv supercontinuum spectrum, which benefits to the generation of an intense short as pulse.In the third part, we theoretically present an efficient method to generate an intense isolated as pulse. When a 0.9 fs, 29.6 nm xuv pulse is added to a 12.5 fs, 2000 nm mid-IR laser pulse at a different time delay, not only the enhancement of the HHG and the formation of an ultrabroad supercontinuum are observed, but also the selection of a single quantum path is achieved and an isolated sub-100 as pulse is obtained. By superposing the different harmonic ranges in continuum region, isolated sub-100 as pulses with extremely short and tunable central wavelengths can be generated, which may play an important role in controlling and studying the core-level dynamics inside atoms. In our schemes, the 2000 nm laser pulse can effectively extend the harmonic cutoff and generate energetic harmonics photons due to theλ2 scaling of Up; on the other hand, the conversion efficiency of the HHG is low, specially for the continuous harmonics in the cutoff region, this is owing to the increase of the spreading of the wave packets. However, the 29.6 nm xuv pulse holds the high photon energy and the extremely short pulse duration, it can promote electronic transition from the ground state to the second excited state for a He⁺ system, thus the second excited state has a large electron population. Combining the advantages of both the long wavelength laser pulse and the xuv pulse, the ionization yields of the electrons corresponding to a single quantum path which contribute to the continuous harmonics can be significantly increased, then the efficiency of the continuous harmonics is higher. As a result, an intense isolated as pulse can be produced. Considering the practical application of this scheme, we take the laser parameters achievable in the current laboratory, which makes it feasible for one to carry out our scheme in practical experimental implementations.