An analytical study of second harmonic generation due to interaction an intense, p-polarized laser beam propagating obliquely in homogeneous underdense plasma, in the mildly relativistic regime, has been presented. The efficiency of the second harmonic radiation as well as its detuning length has been obtained and their variation with the angle of incidence is analyzed. It is shown that, for a given plasma electron density, the second harmonic efficiency increases with the angle of incidence while the detuning length decreases. The second harmonic amplitude vanishes at normal incidence of the laser beam.

An analytical study of the generation of even and odd harmonics by the propagation of two color circularly polarized laser beams through homogeneous, underdense plasma has been presented. The two laser beams are considered to be either co-rotating (co-polarized) or counter-rotating (counter-polarized). Considering the mildly relativistic regime of laser plasma interaction, a perturbative technique is used to evaluate the amplitude of various harmonic frequencies. It is shown that the even and odd harmonics of the fundamental laser frequency arise due to counter- as well as co-polarized laser fields. The generated harmonics are seen to be circularly polarized.

When an intense laser pulse interacts with homogeneous plasma in the presence of a transverse, spatially distributed static electric field, a transverse current density oscillating at a frequency twice that of the laser pulse is set up. This leads to the generation of second-harmonic radiation. The periodicity of the applied static electric field allows the second-harmonic radiation to be phase-matched. It is shown that under phase-matched conditions, the efficiency of the second-harmonic radiation in the presence of the spatially distributed static electric field is significantly enhanced as compared to that obtained for a uniform static electric field.

An analytical theory is developed for studying the phenomenon of generation of harmonics by the propagation of an obliquely incident, circularly polarized laser beam in homogeneous, underdense plasma. The amplitudes of second and third harmonic radiation as well as detuning distance have been obtained and their variation with the angle of incidence is analyzed. The amplitude of harmonic radiation increases with the angle of incidence while the detuning distance decreases, for a given plasma electron density. It is observed that the generated second and third harmonic radiation is linearly and elliptically polarized, respectively. The harmonic radiation vanishes at normal incidence of the circularly polarized laser beam.

A theoretical model is developed for studying the generation of third-harmonic radiation by the interaction of obliquely incident, two-color p-polarized laser beams with spatially varying plasma density. The ratio of the fundamental frequencies of the two laser beams are considered to be an arbitrary integer. The amplitude of harmonic radiation obtained by oblique incidence of two-color laser fields propagating in homogeneous plasma is enhanced in comparison with that obtained by normal incidence of two-color laser beams. The periodicity of the plasma density allows the harmonic radiation to be phase-matched, leading to further increase in the amplitude of phase-matched harmonic radiation by an order of magnitude. The amplitude of the generated harmonic radiation increases with the increase in angle of incidence.