Second-harmonic generation by a Gaussian beam on a fourth-order optical nonlinearity in the interior of an isotropic and gyrotropic medium

A theoretical investigation is made of second- harmonic generation in the interior of an isotropic and gyrotropic medium on a fourth-order optical nonlinearity. It is shown that a correct description of this experimentally detected effect requires taking into account the spatially finite nature of the fundamental-frequency wave, giving rise to a small longitudinal (directed along the beam axis) component of the electric field. Quadrature formulas are derived for the transverse distribution of the second harmonic field and for the total power of the harmonic. A detailed study is made of the special cases of tight focusing of the pump (fundamental-frequency) wave at the centre of a long medium and of exact phase matching. In these cases the quadrature expressions can be reduced to an analytic form. A study is reported of the characteristic features of the transverse profile of the second-harmonic intensity and of the dependence of the harmonic power on the state of polarisation of the pump wave.