Study of High Harmonic Generation Beyond dipole Approximation
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The thesis entitled, DStudy of high harmonic generation beyond dipole approxi- mationD is divided into six chapters. The details of different chapters are as follows, Chapter 1, gives a brief introduction regarding the pedagogical background as well as literature survey of High Harmonic Generation (HHG) and in addition a general state-of-art of the existing literature on various aspects related to the above men- tioned topic is covered. HHG is a process in which usually noble gas atoms when excited by an intense laser field at frequency ! emit radiation of higher frequencies that are usually odd integer multiples of !. Driven by an infrared laser, high har- monic radiation can span from optical frequency upto extreme ultraviolet (XUV) frequency range. HHG is a coherent, directional, and short-pulsed source of XUV ra- diation, whose applications include the time-dependent XUV spectroscopy and XUV interferometry. In recent years it also has been exploited to study the orbital shape and molecular properties. HHG gives a deep insight about molecular structure since the recombination step produces coherent emission, and recombination probability depends strongly on initial state electronic wave function. In addition, the harmonic radiation is an excellent seed for a soft X-ray laser. The generated beam being co- herent, follow the similar properties of laser light. This chapter also describes the widely used three step process (Ionization, Propagation and Recombination) during HHG mechanism. In chapter 2 and 3, We have presented formulation and methology used in this thesis and a study of high harmonic generation with model system of the polyacety-of monomer units in the system which can be quantified by comparing intensity, of even harmonics to odd harmonics. The intensity difference between odd harmonics and even harmonics is strongly dependent on number of monomer unit of ethylene taken and the intensity of applied laser field e.g. in case of high intensity of laser field and higher number of monomer units of ethylene, even harmonics become more intense than odd harmonics. It is observed that even if electron oscillation is confined to a small region, non dipole term can not be ignored. Within DA, due to dynamical symmetry we must get only odd order harmonics. But we expect to get the both (even as well as odd order) kind of harmonics in the case of beyond dipole approximation depending upon the extent of breakdown of DA. The validity of the DA can be checked by observing the intensity of dipole forbidden even harmonics. In chapter 4,We have studied spectral entropy during the process of HHG. Entropy relates to the fluctuation of population in different states. The entropy (S) of the system is defined as, S = X |pi|log(|pi|). (1) where p0 is are the population of the electron in ith molecular orbitals. As in previous chapter we have considered the same model system of polyethylene irradiated with intense, linearly polarised laser field propagating along the system axis. There is no change in maximum spectral entropy in the case of within DA. But it is observed that maximum entropy of the system increases continuously when calculated in the case of beyond DA regime. With this study we have attempted to understand the mechanism of HHG from model system of polyethylene discussed in the previous chapter. In the case of within DA the ground state couples only with single excite.
Supervisor: Ashish K Gupta