High-Order Harmonic Generation Of A United-Atom Model

It is well known that the interaction of the intense laser pulsewith atoms, molecules, solids and clusters can lead to HHG of thelaser frequency. In the presence of linearly polarized laser fields, acommon characteristic of HHG power spectra has been confirmedby a variety of experiments: it generally shows a marked drop inintensity for the first few harmonics, and then levels off forming aplateau region in which the harmonic intensity remainsapproximately constant up to a rather sharp cutoff. The plateaustructures of HHG power spectra make HHG possible sources ofradiation in x-ray and XUV regions as well as a promising means ofgenerating laser pulses of attosecond scale. Due to these potentialapplications, it has become a focus of study and attention in recentyears. In order to realize these prospects the unremitting pursuit inHHG studies is to simultaneously increase conversion efficienciesand reach shorter wavelengths. That is to say, it is necessary tobring the HHG in control to satisfy one's needs.The mechanism of HHG should be investigated in order tocontrol it. Recently, the semi-classical "three-step" model wasaccepted widely in the understanding of the harmonic generation:the electron is first ionized due to tunneling through the potentialbarrier formed by the laser field and the ionic field or due toabsorbing one or several photons, and then oscillates in the laserfield. When the laser field reverses direction, part of ionizedelectrons come back to the vicinity of their parent ions and transitback to the bound states. At the same time, the system emits highenergy photons. The photon energy is the sum of the kinetic energythat electrons acquire from the light field and the ionizationpotential of the electrons in the atom. According to the classicalcalculation, when the ionized electron comes back to the parent ion,its maximal kinetic energy is 3.2U p, so that the maximal photonenergy is Ec utoff = I p + 3.2Up. Here I p is the ionization potential andU pis the ponderomotive energy.From the cutoff law, we notice that for a single atom model,taking the atom or ion with larger ionization potential as target isthe one of most direct way in extending the harmonic plateau. Infact, the maximal cutoff position was currently achieved from theinteraction of intense laser pulse with He atom with the largestionization potential among all atoms. Using highly charged ions,which have much higher ionization potentials, has been proposed tofurther extend cutoff position. Unfortunately, the small ionizationyield leads to a poor harmonic efficiency. Another direct way is toincrease ponderomotive energy. To realize the aim, it is necessary toraise the intensity of the laser pulse when laser wavelength is keptconstant. However, an atom will be depleted completely when thelaser intensity rises up to a certain threshold amount, so that thecorresponding harmonic emission process also terminates. Toovercome current difficulty, one turns to short pulse lasers, whichprovides the advantage that the depletion of atom is avoided whenrelatively stronger lasers are employed. Experimentally, theenergetic photons of 500ev can be generated using the laser pulseswith duration of 5-7fs, which is close to one optical cycle.Therefore, the HHG plateau can no longer be extended through thefurther shortening the pulse duration. The above analysis shows thatthe existing methods are limited in extending the width of theplateau. To obtain more energetic photons, new approaches must besuggested.In this thesis, we got a high efficiency of HHG with a cutoff ofI p + 8Up the emission efficiencies of the harmonics near the cutoffare especially enhanced to 10-9 by proposing a scheme speciallydesigned.Firstly, a united-atom system with an optimized inter-nuclearseparation was denoted to extend the HHG spectrum. We know thatthere are plenty of electrons which have kinetic energy exceed 3.2U pfrom the analysis of the dynamic behavior of a P-T potential modelatom employing the semi-classical "three-step model" theory. Thehighest kinetic will be 8U p after a half cycle of acceleration if theelectrons were ionized around the zero-zone of the low-frequencypulse. The electron can't convert into high-energy photon owing toits positions being far away from parent-ion, thus it have no chanceto recombine with the parent-ion. It's supposed that a high emissionefficiency of HHG with a cutoff of I p + 8Up was achieved if theelectron was providing with another recombination object, and theinter-nuclear separation of the united-atom system was optimized asπ r0( r0 is the quiver radius) which is the distance that the electronfar away from the parent-ion when it has the highest energy.Secondly, we have discussed the major factors that influence theemission efficiency of the HHG, including the abundance of theelectron with high energy which can recombine with the parent-ionand the population of the bound state. The higher emissionefficiency we will get the higher abundance and the higherpopulation of bound state population is. Therefore, as far as theharmonic order efficiency enhancement is concerned, it is necessaryto raise the abundance to an appropriate extent if we had got anenough population of the bound state. However, the abundance ofthe system which can achieve a 8U p kinetic energy is very lowbecause the ionization course was happened around the zero-zone ofthe low-frequency pulse. In order to conquer this difficulty, acombined lasers scheme was adopted as below: some few-circlelasers with high frequency and amplitude were added to the zerozone of low-frequency laser. Under this scheme, the ionizationcourse will concentratedly take place during the time thehigh-frequency laser exists (that is also the zero zone of thelow-frequency pulse) and the abundance is high enough. Henceforth,the ionized electron will be accelerated by the low-frequency laserfield for half its cycle and the utmost kinetic energy is just8U p.Hence, we have got abundance high-energy electrons and as aconsequence the efficiency of harmonics is enhanced. According tothe scheme mentioned above, we have got a high efficiency ofharmonics whose cut-off position is I p + 8Up, the efficiency isbeyond 10-9.Finally, we gave a reasonable explanation of the HHG spectrum wehave got in this thesis and have a thorough understanding of themechanism of the spectrum. There are two brilliance characters inthe spectrum we got: firstly, the cut-off position we got exceeds theposition designed;secondly, the efficiency of harmonics with loworder is also considerably. We obtained an academic explanationabout the structure of the spectrum, through the analysis thedynamic behavior of the atom employing the "three-step model"theory, and the wavepack evolution of the ionized electron.The designed cut-off position is the result we drew consideringonly the acceleration of the low-frequency laser field neglecting theacceleration caused by the high-frequency laser field, however thisacceleration is significant and thus it caused the result that thecut-off position we got exceed I p + 8Up designed in this thesis. Thewavepack of the ionized electron has a "primary peak" and a"secondary peak" according to the magnitude of their areas owing tothe complex structure with a positive and a negative orientationelement at the beginning of born. The wavepack born in the rightwell will pass the left well droved by the low-frequency laser field.We draw a conclusion that the HHG with high order was generatedwhen the "primary peak" passes the left well;the HHG with loworder was generated when the "secondary peak" passes the left well.The efficiency of recombination is very significant owing to the lowvelocity it travels despite the little magnitude of the "secondarypeak's area", and this leads to the high efficiency of harmonics.