Interaction of lasers with noble gases for the high-order harmonics generation

Resumen

In the mid-1980s, for the first time, the appearance of high order harmonics was observed through the interaction of a noble gas with a laser. Since then, its importance in physics has not stopped growing. High-order harmonics open a window to X-ray lasers. Currently there are several sources of X-rays that produce a high number of photons, such as synchrotrons and acceleration of free electrons. However, although desktop lasers have a smaller flow of photons, they offer a higher quality X-ray source. The importance of this source is manifold. The grouping of different harmonics has made it possible to get the shortest electromagnetic pulses in history. This opens the possibility of studying the movements of an electron in an atom, as well as the speeds of certain chemical reactions. Another line, is the study of dichroism in molecules through the use of circularly polarized X-ray lasers. The research carried out in this thesis is oriented towards the desktop lasers with the aim of improving their efficiency in the generation of harmonics. With this purpose, two codes were developed: one of them allows to know the interaction of the laser with a gas jet. The other is a code that studies the interaction of a laser with an atom. Both codes will be related, since the first one will use the second one for the necessary atomic calculations when the laser interacts with the gas. Thus, in this thesis it is presented: • An introductory chapter that tells the historical development of the generation of harmonics of high order. It contains a summary of the most relevant contributions in this field. • Theoretical development. It introduces the mathematical and physical fundamentals that serve as the basis for the calculation of harmonics, as well as the approximations applied: dipolar approximation, single atom electron approximation, direct bound-free transitions, strong field approximation, non-relativistic approximation. By means of the theory of the time evolution operator we arrive at the Lewenstein equation, which is a quantum equation that allows to obtain: the amplitude of a transition of an electron in an intense field and the dipole moment; which is the key in the study of high order harmonics. Using the above approximations, an analytical solution of the equation is possible. A fundamental part of this model is the calculation of the analytical expression of the dipolar transition matrix. This chapter shows how to derive this function from the various mathematical expressions for the wavefunction. The mathematical form of the Gordon-Volkov wave functions that describe the movement of a free electron in an electromagnetic field, are crucial for the analytical calculation of the transition matrix, since it allows to obtain a solution by means of the Fourier transform. The resolution of the integral of the dipole moment by means of the technique of the stationary phase, gives rise to the appearance of the quantum trajectories; which allow to treat all type of problem of interaction between a laser with an atom by means of a limited number of classic trajectories of the electron. This technique is very powerful, since it allows to know which are the mechanisms for the production of harmonics and to be able to modify them. • By mixing two gases with different ionization energy such as helium and neon, and using the technique of quantum paths, we analyze what must be the ratio of this mixture to modify the intensity of a harmonic. This study has needed to develop a new dipolar transition matrix, since the one used in the literature generates an erroneous phase for the dipole. The results obtained have been compared with experimental data to where possible. For regions of the spectrum where no experimental data were available, it has been compared with results obtained with a TDSE solver. As a result, an article has been published in a leading scientific journal. • The study of dichroism is done by X-ray lasers with circular polarization. To this end, a new dipole transition matrix for neon has been developed, including magnetic quantum numbers. This study has provided some surprising results, for a laser with orthogonal polarization ω 2ω, the two electrons with quantum numbers m = ±1 produce even and odd harmonics, but due to destructive interference some are annihilated. With this model has been studied how it affects the shape of the envelope of the electric field to the ellipticity of harmonics, showing that only fields with a non-constant envelope are capable of producing circular harmonics. • Finally, the interaction of the laser with a gas is tackled. This chapter establishes the theoretical foundations for the propagation of an electromagnetic field in a gaseous medium. A mathematical expression has been developed for the calculation of susceptibility in the case of high intensity lasers. Computational simulations show how the propagation of the laser in a gas is modified when it is ionized. Also as it depends the emission of the harmonics modifying some parameters like, the pressure of the gas, the intensity of the laser, the position of the focus. The comparison with experimental results offers a good degree of agreement.