### Abstract:

The nonlinear optical response of graphene has been studied by the newly developed technique which is an alternative to rotating wave approximation (RWA). This is referred to as asymptotic RWA (ARWA). is a single layer of graphite material possessing a degree of freedom known as pseudospin. It is a bridge between condensed matter and relativistic electrodynamics, since the low energy spectrum of graphene near some particular points called Dirac points is linear in momentum. The interaction between the charge carrier and the periodic potential of graphene leads to quasiparticles which obey the Dirac relativistic equation. At the Dirac points, the conduction band just touches the valance band due to which it is also called zero band gap semiconductor. These peculiar properties of graphene are the motivation behind our work and are studied using optical means, specifically through nonlinear optical response. As the title of the thesis itself suggests, this work is the study of the well-known coherent optical phenomenon in nonlinear optics viz. Rabi oscillation - a periodic exchange of energy between a two level system in case of atoms and two band system in case of semiconductors and the applied optical field. It is the oscillation in the population and polarization of carries (with a given wave-vector in case of a band) with a frequency !R determined by the intensity of the externally applied optical field. This frequency !R is typically much smaller than the optical frequency ! itself. This phenomenon is well described in various textbooks on quantum optics. The same phenomenon manifests itself in semiconductors, which have bands instead of energy levels. It is therefore appropriate to investigate the same effects in graphene where the bands are linear instead of parabolic and the system is two dimensional instead of three and there is pseudospin character. The phenomenon of Rabi oscillations in graphene has been studied by Mishchenko among others, near the particle-hole resonance using the well known rotating wave approximation (RWA).