Modeling generation and characterization of attosecond pulses

Abstract

Generation of high-order harmonics has emerged as a powerful technique for the generation of broadband coherent radiation in the EUV regime. This has lead to the development of table-top EUV sources that can produce attosecond pulses. These pulses can serve as a probe to resolve atomic attosecond dynamics and image atomic orbitals and molecular motion. Due to high spatial and temporal coherence, high-order harmonic radiation can also be used to seed free electron lasers, which allow the generation of high-intensity X-ray radiation that can be used for imaging biomolecules. Since the first observation of high-order harmonics, effort has been made to accurately model both the generation and the characterization of attosecond pulses. Work on the modeling of high harmonic generation can be divided into two parts: (a) description of the interaction between the JR pulse and atoms that leads to emission of attosecond pulses (the single atom response) and (b) modeling of the propagation of attosecond pulses by accounting for macroscopic phase matching effects. In this work, we will focus on the single atom response which can be calculated either by numerically solving the time dependent Schrodinger equation (TDSE) or through the semi-classical three step model (TSM). In Chapter 2, the theory of light-atom interaction will be reviewed with the focus on the calculation of the dipole trasition matrix element (DTME) in the strong field formalism. It will be shown that the choice of the basis states - Volkov states and Coulomb Volkov states - to describe electrons in the continuum is crucial to the accuracy of DTME calculation. In Chapter 3, the TSM will be derived from the Schrodinger equation by using the saddle point approximation. Through this derivation, the quantum mechanical laser-atom interaction is reduced to a semi-classical model comprising of ionization, propagation and recombination . The numerical scheme for solving the TDSE will be discussed. It will then be used to demonstrate the generation of isolated attosecond pulses from non-sinusoidal sub-cycle pulses. The results of ADK and non-adiabatic ionization models will be compared with that from numerical TDSE, and then used to calculate the harmonic spectra in the tunneling and multi-photon ionization regimes. The recombination step of the TSM, which plays a crucial role in determining the qualitative shape of the high-order harmonic spectrum, will be investigated in Chapter 4. A commonly observed feature of Argon's high-order harmonic spectrum is the presence of a minimum at around 50 eV called the Cooper minimum. The minimum in the high-order harmonic spectrum has been attributed to the minimum in the recombination amplitude. The recombination amplitude will be calculated - in the strong field formalism - using length and acceleration form for two choices of continuum electron wavefunction description (Volkov and Coulomb-Volkov). Attosecond pulse characterization techniques, which are an extension of the subpicosecond pulse characterization technique like FROG and SPIDER, rely on the photoionization process to transfer the amplitude and phase information of the attosecond pulse to the photoelectron spectrum. For accurate pulse characterization, it is crucial to model the photoionization process accurately. Since photoionization and recombination are reverse processes, the improvements in the calculation of the recombination amplitude in Chapter 4, can be used to improve the model function of the pulse retrieval algorithm. It will be shown that the proposed improvements are crucial for accurate characterization of low energy EUV pulses.