0030-400X/03/9501- $24.00 © 2003 MAIK “Nauka/Interperiodica” 0154 Optics and Spectroscopy, Vol. 95, No. 1, 2003, pp. 154–157. Translated from Optika i Spektroskopiya, Vol. 95, No. 1, 2003, pp. 163–167. Original Russian Text Copyright © 2003 by Sapaev. INTRODUCTION At present, techniques of generation and ampliﬁca- tion of phase-modulated (so-called chirp-modulated) laser pulses with intensities as high as ~10 18 – 10 20 W/cm 2 are well developed [1]. Interest in such radiation sources is associated, in particular, with prob- lems of creation of superdense high-temperature laser plasma [2]. Laser sources for efﬁcient plasma excita- tion should have a short wavelength and a high pulse contrast. These factors stimulate interest in highly efﬁ- cient second harmonic generation (SHG) of intense laser radiation. SHG is also of interest since it allows one to obtain intense coherent radiation in spectral regions of highest media transparency. Among main factors limiting the efﬁciency of SHG in nonlinear crystals in the presence of comparatively strong ﬁelds of pumping radiation are self-action effects, which lead to a change in the phase and ampli- tude distribution of interacting bounded wave packets and beams [3–5]. Causing nonlinear phase mismatch during the frequency conversion process, these effects disturb the optimum conditions of phase matching between interacting nonlinear waves. This process leads to the reverse transfer of the energy of the second harmonic to the fundamental radiation. In this case, the SHG efﬁciency can be increased if the phase shifts caused by the nonlinear and linear phase mismatch are mutually compensated. However, in the case of waves in modulated space and time, i.e., in a real energy-trans- fer process, such compensation can only be partial. This is related to the fact that phase shifts caused by self-action effects depend on the radiation intensity and are different in different points of bounded wave pack- ets and beams, while the linear phase mismatch depends neither on the temporal nor on the spatial coor- dinates. Thus, the complete compensation of the phase shifts caused by the cubic nonlinearity and the phase mismatch is impossible. Nevertheless, the most efﬁ- cient SHG can be achieved by changing the proﬁle of the pumping beam. Decreasing in the inhomogeneity of the spatial distribution of the intensity of the laser beam leads to a more complete mutual compensation of the phase shifts caused by the self-action and the linear phase mismatch. Hence, to determine the highest efﬁciency of fre- quency conversion, it is necessary to study SHG in detail under real conditions. Numerical analysis of SHG in the presence of self-action of intense laser radi- ation is a difﬁcult task because one needs to take into account simultaneously both the temporal and the spa- tial modulation of the interacting waves. At the same time, theoretically, as was mentioned above, one should consider the waves modulated in space and time in order to study the inﬂuence of the self-action on the efﬁciency of frequency doubling. To solve this prob- lem, we suggest below an approximate method for the theoretical analysis of SHG under conditions of self- action, speciﬁcally, the approximation of a strong inter- action between nonlinear waves in a new (generalized) form [6]. Thus, in this paper, we analyze the effect of self- action on the efﬁciency of SHG for various spatial dis- tributions of the amplitude of intense fundamental laser radiation. It will be shown the spatial shapes of beams and the phase mismatch of the interacting waves can play that an important part in the frequency conversion of intense laser radiation. LASERS AND THEIR APPLICATIONS Optimum Conditions for the Generation of the Second Harmonic of Intense Laser Radiation U. K. Sapaev Akadempribor Research and Development Association, Academy of Sciences of Uzbekistan, Tashkent, 700125 Uzbekistan e-mail: sapaev@mail.tps.uz Received October 28, 2002 Abstract—A generalized approximation of strong interactions of waves is suggested for the theoretical analy- sis of second-harmonic generation under conditions of self-action. On the basis of the method suggested, approximate solutions for the efﬁciency of second-harmonic generation are obtained with regard to the inﬂu- ence of higher nonlinearities, depletion of pumping radiation, and linear phase mismatch. The effects of the phase mismatch and the spatial distribution of the amplitude of the fundamental harmonic on the efﬁciency of second harmonic generation by intense laser radiation is analyzed. The results obtained with the approximate method developed are shown to be in good agreement with known experimental data and numerical calcula- tions. Optimum conditions for second harmonic generation are determined in a wide range of laser radiation intensity and at different spatial distributions of the fundamental harmonic amplitude. © 2003 MAIK “Nauka/Interperiodica”.