generated concentrating near the third harmonic of the original pulse.According to the numerical calculations of the system of Eq. (15), when phase synchronicity does not occur over the whole pulse spectrum, an extraordinary wave optical videopulse arises in the crystal, and in its spectrum the sum and difference frequency regions are clearly defined. Two maxima of the frequency spectrum are centered at 2 ⅐ 0 and 3 ⅐ 0 . The widths of the maxima are determined by the phase matching condition for different spectral components of the pump pulse. The maximum in the difference frequencies region is at zero frequency. A constant component of the field is also noticeable on the time profile of extraordinary polarized pulse, the broad spectrum of which is determined by the duration of the pump pulse.
CONCLUSIONIn this paper we derived a system of nonlinear wave equations (Eq. (15)) that describes the propagation of a femtosecond laser pulse of a few optical oscillations in a negative uniaxial crystal in the direction normal to the optical axis, taking into account both second-and third-order nonlinearity. In particular, we looked at the case where phase synchronicity did not apply for the whole pulse spectrum.In the linear part of the medium polarization, we expanded the nonlinear equations around a small parameter equal to the ratio of the medium response time to the average oscillation period of a femtosecond pulse. This expansion was used for the description of a uniaxial crystal's linear response to laser radiation of a few optical oscillations in the near infrared spectrum range. In the nonlinear part of the polarization of a 3-m group uniaxial crystal, which is responsible for second-and third-order nonlinearity, we confined ourselves to the quasi-static approximation for the near infrared spectral range and for small thickness of nonlinear crystal.From the numerical simulation of Eq. (15) we found that including third-order nonlinearity effects yields spectral components of an extraordinary polarization concentrated in the third harmonic of the original pulse.Lastly, we obtain the radiation-conversion ratio ␥ ϳ (S z ()/ S x0 ()) 2 as a function of both femtosecond pulse duration and intensity, and on crystal length at frequencies near the second harmonic of the original pulse 2 ⅐ 0 .
ACKNOWLEDGMENTS