Second-harmonic generation in the interior of an isotropic medium with quadratic nonlinearity by a focused inhomogeneously polarized pump beam

This paper presents a theoretical study of second-harmonic generation (SHG) by a focused pump beam in the interior of an isotropic medium, experimentally observed earlier. It shows that the spatial dispersion of the quadratic optical response of the substance can be responsible for this nonlinear process even when a macroscopic inversion center is present in the medium. It is established that this effect, which is impossible in the plane-wave approximation, also does not occur when a Gaussian pump beam with uniform distribution of the polarization state of the wave field over the cross section is used, but that the presence in the pump beam of higher transverse modes with polarization different from the fundamental mode can cause an SHG signal to appear. The conditions for a wave to appear at the doubled frequency are found, analytical dependences for its electric field and total power on the propagation coordinate, the degree of focusing, and the other parameters of the problem are obtained, and the requirements on the optimum experimental geometry are formulated. The dependence of the signal-beam power on the wavevector detuning is studied, and it is shown that interference effects can cause the wave at the second harmonic to disappear when a normal dispersion law is obeyed in the region between the fundamental and doubled frequencies. Zh. éksp. Teor. Fiz. 113, 1261–1276 (April 1998)