Study On Gauge Dependency Problem Of Strong Field Ionzation Of Atom And Molecule

Recently, owing to the rapid advancement of laser technology, nonlinearphenomena associated with ionization of atoms and molecules in intense laser fieldshave aroused considerable experimental and theoretical interest. Strong fieldionization processes of atoms and molecules are the foundation of many importantprocesses of interaction between the electromagnetic fields and material. To describethese processes, the most important and widely used theory is the strong fieldapproximation(SFA) given by Keldysh-Faisal-Reiss(KFR). However, the SFA isdivided into the length gauge(LG) and the velocity gauge(VG) theories due to theHamiltonian form of the laser-atom interaction are different. Since an electromagneticinteraction is gauge invariant, one would expect that calculations which use differentgauges should produce the same results. While in the last several decades the SFA inthe velocity gauge and the length gauge differ and apparently constitute two distinctmodels. The discrepancy between the KFR theories in the two gauges has caused anextensive controversy about which gauge is more appropriate for the SFA. In thispaper, we focus on the gauge dependence problem of KFR theories, and theionization rate formulas for atoms and molecules in the linearly polarized laser fieldare derived.The atomic KFR theories are the foundation of the molecular strong fieldapproximation (MO-SFA). A detailed derivation for the ionization rate of diatomicmolecules in an intense laser field using the length gauge is presented. Then weextend the derivation to the ionization rate of diatomic molecules in the velocitygauge and derive a general ionization rate formula for the system of diatomicmolecules. More concise expression of the photoionization rate in the tunnel region isobtained for the first time. Comparisons are made among the different versions ofMO-SFA. The numerical study shows that the photoionization rates of the molecularsystems in velocity gauge and length gauge indicate similar or even more pronouncedgauge dependency and the ionization rate in the velocity gauge is underestimated by a few orders compared with that in the length gauge.Next, we derive a simple ionization rate formula for the ground state of ahydrogen atom in the velocity gauge in the tunneling regime. Comparisons are madeamong the different versions of KFR theories. The numerical study shows that if thequasi-classical (WKB) Coulomb correction in the final state of the ionized electron isincluded, the photoionization rates are enhanced compared with those in the absenceof the Coulomb correction and the discrepancy between the two gauges is reduced.Moreover, Reiss theory with the WKB Coulomb correction gives the correct result inthe tunneling regime. The simple formulas derived in this thesis may provide moreinsight into the ionization mechanism for atoms and molecules subjected to a strong,linearly polarized laser pulse.At last, some conclusions and outlooks of the future work are given in the end ofthis thesis.