Multiphoton Processes Of Atomic Hydrogen In Intense Laser Field

In this thesis, an advanced pseudospectral method is used to solve time-dependentSchrSdinger equation, which treats with the atomic hydrogen in intense laser field:With this method, the ground wavefunction of atomic hydrogen, which is calculatedby the pseudospectral method, is treated as the initial wavefunction. Then, takethe time-dependent SchrSdinger equation as an equation about the first derivation ofwavefunction for the time. It can induce higher order derivations of wavefunction.According to the Taylor expansion, the wavefunction at later time can be obtainedfrom the wavefunction at former time, and then get the wavefunction at any time.Choose the whole evolving time based on the actual cases. The high order harmonicgeneration are proportional to the Fourier transform of the average values of accel-eration, velocity or coordinate at every time. Project the wavefunction on all thecontinuous states with laser field absent, we can get the summation as the ionizationprobability. If we take the projection as the function of energy, we can get the spectralof above-threshold ionization.Because of the use of Causs-Legendre integral, high accuracy can be obtainedby using a few of grid points. A matrix multiple on the wave vector directly, to getwavefunction of the next time, which doesn't need to calculate the matrix elements orthe expansion coefficients at every step, comparing to the other methods. It decreasesthe calculating time greatly. For simplicity, we just regard the linear polarized laser.Choose the spherical coordinates, and make the axisθ=0 parallel to the polarizationorientation of the laser. Then, the system has the rotational symmetry about coor-dinateψ, so the variableψcan be separated, and analytic presentation ofψcan beobtained. The system reduced to two-dimensionγandθ, which should be dispersednumerically. In pseudospectral method, use Legend polynomials to derive the basesf_i(r), whose number equals to the number of grid points, and occupy the unique prop-erty: on the grid points, f_i(r_j)=δ_ij, then, the wavefunction itself can be taken as theexpansion coefficients. Operating the harmiltonian on the expanded wavefunction, itderives a system of linear equations formally, of which the variables are just the valueof the wavefunction on the grid points, we can't get values of the wavefunction noton the grid points just by solving the system of linear equations, but if the pointsare dense enough, the wavefunction can be described finely. And what's more, onlysufficient grid points can provide sufficient bases(the number of bases equal to thenumber of grid points), which make the values of wavefunction on the grids accurate enough.The obtained spectra of high order harmonic generation, spectra of above thresh-old ionization and the ionization probability as a function of time, are all accordantwith the results from other methods, experiments and the theoretical analysis. In thisthesis, the influence of magnetic field to the high order harmonic generation is alsoconsidered. Generally, with the increase of the magnetic field, the intensity and thecutoff are increasing, which comes from the second order of the magnetic term, andthe higher orders of harmonics are infected more violently.