Third-order harmonic generation in P‎propagation of cylindrical ‎waves ‎in‎‎ ‎‎‎inhomogeneous nonlinear ‎media

Propagation of electromagnetic waves in the nonlinear homogeneous and nonhomogeneous cylindrical media to generate of third order harmonics is investigated by using numerical solving of the coupled wave equations.ýý
Calculation show, that the characteristic length of the interaction in homogenous media is very shorter than one in inhomogeneous media. ýý The reason for this behavior is that for inhomogeneous media ý$ ýDelta ýký $ý is very small and the output wave can get out of phase with its driving polarization at very big length of the interaction (ý$ ýrý $ý). Therefore, as ý$ ýDelta ýký $ý increases the length of the interaction and the maximum intensity of the generated wave ýdecrease.ýý Numerical calculations show that ýin homogeneous nonlinear optical ýmedia phase matching ýconditioný is not satisfied, and the generated ýwave ýamplitudeý is smaller than ýýýinhomogeneous nonlinear optical ýmedia. The effect of ýthird ýorderý nonlinear optical ýsusceptibilityý ýon the generated wave ýamplitudeý ýin inhomogeneous ýmedia has been ýinvestigated.ý